The cross-sectional area is (h × w ) + ((1 ÷ 2) × 0.9 × w²) and the dimensions of the window which minimize the perimeter is (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A.
height of rectangle = h
height of the triangle = t
T = 0.9
width of the rectangle = w
The formula of Cross-sectional area is,
A = h × w + (1 ÷ 2)T × w
A = (h × w ) + ((1 ÷ 2) × 0.9 × w²)
Perimeter,
P = w + (2 × h) + 2√(T² + (w ÷ 2)²)
P = w + (2 × h) + 2√((0.9)² + (1 ÷ 2)²)
P = 2h + 2√((0.9)² + (1 ÷ 2)² + 1) × w
Therefore, [tex]C_{0}[/tex] = 0.9 ÷ 2, [tex]C_{1}[/tex] = 2, [tex]C_{2}[/tex] = 2√((0.9)² + (1 ÷ 2)² + 1)
minP=[tex]c_1[/tex]h+[tex]c_2[/tex]w
A = (h × w) + [tex]c_{0}[/tex]w²
substituting h = (A - [tex]c_{0}[/tex]w²) ÷ hw in P,
P = [tex]c_1[/tex]w + ([tex]c_1[/tex](A - [tex]c_{0}[/tex]w²) ÷ w)
Differentiating both sides,
(dP ÷ dw) = -2[tex]c_{0}[/tex][tex]c_{1}[/tex] + [tex]c_{2}[/tex] - ([tex]c_{2}[/tex](A - [tex]c_{0}[/tex]w²) ÷ w²) = 0
[tex]w_{0}[/tex] = (√[tex]c_{1}[/tex]A ÷ (√[tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex])) = 0.962445√A
and consequently,
[tex]h_{0}[/tex] = (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A
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an envelope contains eight bills: ones, fives, tens, and twenties. two bills are drawn at random without replacement. what is the probability that their sum is $ or more?
Using the concepts of probability, we got 0.5 is the probability of drawing the sum $20 or more when two bills are drawn randomly without replacement.
We have an envelope contains 8 bills;
Two of $1 bills, Two of $5 bills, Two of $10 bills, Two of $20 bills.
When two bills are drawn randomly without replacement, we have to find the probability that their sum is $20 or more.
Total outcomes = 2 x 2 x 2 x 2 = 16
Total possible outcomes, more than 20;
(1, 20), (20, 1), (5, 20), (20, 5), (10, 10), (20, 10), (10, 20), (20, 20) = 8 cases
That is,
The total possible outcomes is 8.
Now,
The probability of bill to be $20 or more = Possible outcome / Total outcome
Probability = 8/16 = 1/2=0.5
Hence, When two bills are drawn randomly without replacement, the probability that their sum is $20 or more is 0.5.
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(Complete question)
an envelope contains eight bills: 2 ones, 2 fives, 2 tens, and 2 twenties. two bills are drawn at random without replacement. what is the probability that their sum is $20 or more?
Tim and Jessica plan to rent a camper van for a vacation. The van costs $183 per day.
The rental includes 120 miles for free and then charges $0.39 per mile.
The total price Tim and Jessica paid to rent the camper van is $598.74. Write an
equation that models the cost of the van rental in terms of miles traveled, m.
Create an equation
The equation that represents the cost of the van rental is $598.74 = 136.20 + $0.39m .
What is the equation that represents the cost?The equation that would model the cost of the van rental is a linear equation. A linear equation is an equation that has one variable that is raised to the power of one.
The general form of linear equations is: y = a + bx
Where:
a = intercept
b = slope
The form of the equation that models the cost is:
Total cost = cost of renting the van + [cost per mile x (m - 120 miles)
$598.74 = $183 + [$0.39 x (m - 120)
$598.74 = $183 + $0.39m - 46.80
$598.74 = 136.20 + $0.39m
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Find the value of x. Then find the measure of each labeled angle
(3x+6)
(4x-12)
answer:
x = 18, 60.
step-by-step explanation:
evaulating (3x+6) = (4x-12) and solving for x gives us x = 18. you didn't include the angle, so i can't give you that. but
(3x+6) = 60
(4x-12) = 60
if those were your angles, you would have an equilalateral triangle (all sides/angles even) and your missing angle would also be 60.
an srs of 29 students at uh gave an average height of 5.5 feet and a standard deviation of .3 feet. construct a 90% confidence interval for the mean height of students at uh. a) [4.250, 6.950] b) [5.405, 5.595] c) [4.990, 6.010] d) [4.000, 7.300] e) [5.482, 5.518] f) none of the above
NEED HELP ASAP!!!!!!!!!!!!!!
The number of solutions each polynomial has is 1, 5 and 3
What is a polynomial?In mathematics, a polynomial is an equation made up of coefficients and indeterminates, sometimes referred to as variables. Only addition, subtraction, multiplication, and powers of positive-integer variables may be used to solve it. An example of a polynomial with one undetermined x is x2 4x + 7.
Polynomials are often employed in both mathematics and science. In fundamental chemistry and physics, economics, and social science, for example, they are used to define polynomial functions. They are also employed in calculus and numerical analysis to approximate other functions. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a broad variety of topics. polynomials' usage in complex maths.
The number of solutions of a polynomial is equal to the highest degree of the polynomial.
So,
1) y = -6x -9
Has 1 solution as highest degree = 1
2) y = 2x⁵-x⁴ +2x³-6x²+2x+4
Has 5 solutions as highest degree = 5
3) y = -4x³-10x² +7x+5
Has 3 solutions as highest degree = 3
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Which equation is equivalent to y = 3x-6?
0 3x-2y = 6
000
2x+3y = -6
=
O 3x-2y = 12
2x-3y = 18
The equivalent equation for the expression y = 3x-6 is none.
Equivalent equation:
If the two equations are said to be equivalent when they have the same solution set. Then it is called as Equivalent equation.
Given,
Here we have the expression y = 3x-6
Now, we need to find the equivalent equation.
In order to find the equivalent equation, we have to take some sample values for x,
The sample value of x as 1, 2, 3
Now, we have to apply these values on the given expression first,
Then we get,
x = 1 => y = 3(1) - 6 = -3
x = 2 => y = 3(2) - 6 = 0
x = 3 => y = 3(3) -6 = 9
Now, we have to apply these to the given equation and which has the same value of the given expression,
x = 1 => 3(1) - 2y = 6 = -2y = 6 - 3 => y = -3/2
x = 2 => 3(2) - 2y = 6 = -2y = 6 - 6 => y = 0
x = 3 => 3(3) - 2y = 6 = -2y = 6 - 9 => y = 3/2
This is not equal one.
Move on to the second one,
x = 1 => 2(1) + 3y = -6 => 3y = -6 - 2 => y = -8/3
x = 2 => 2(2) + 3y = -6 = 3y = -6 - 4 => y = -10/3
x = 3 => 2(3) + 3y = -6 = 3y = -6 - 6 => y = -4
This is not a equivalent one.
Move on to the third expression,
x = 1 => 3(1) - 2y = 12 = -2y = 12 - 3 => y = -9/2
x = 2 => 3(2) - 2y = 12 = -2y = 12 - 6 => y = -3
x = 3 => 3(3) - 2y = 12 = -2y = 12 - 9 => y = -3/2
This is not a equivalent one.
Finally we have to use the last one, then we get,
x = 1 => 2(1) - 3y = 18 => -3y = 18 - 2 => y = -16/3
x = 2 => 2(2) - 3y = 18 => -3y = 18 - 4 => y = -14/3
x = 3 => 2(3) - 3y = 18 => -3y = 18 - 6 => y = -4
Therefore, none of them are the equivalent one.
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Write the equation of the line in fully simplified slope-intercept form.
ANSWER ASAP
WILL GIVE BRAINLIEST
The equation of the line in fully simplified slope - intercept form is 5x + 4y = 12 .
In the question ,
a graph of the line is given , we need to find the equation of the given line in the simplified slope - intercept form .
to find the equation , we need minimum two points ,
So , from the given graph ,
we can find that
when x [tex]=[/tex] 0 , the value of y [tex]=[/tex] 3 ,
the first point is (0 [tex],[/tex] 3) .
when x [tex]=[/tex] 4 , the value of y [tex]=[/tex] -2 ,
the second point is (4 [tex],[/tex] -2) .
the slope can be calculated by
slope = (-2-3)/(4-0)
= -5/4
So , the equation of the line passing through point (4,-2) with slope -5/4 , in the slope intercept form is
(y -(-2)) = (-5/4)(x-4)
y + 2 = (-5/4)x + 5
y = (-5/4)x + 5 - 2
y = (-5/4)x + 3
Simplifying further , we get
4y = -5x + 12
5x + 4y = 12
Therefore , The equation line in fully simplified slope - intercept form is 5x + 4y = 12 .
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A regular polygon has 16 sides. If one of its angles measures (5h − 29)°, what is the value of h?
Answer:10.3
Step-by-step explanation:
16(5h-29)=360
80h-464=360
80h-464+464=360+464
80h/80=824/80
h=10.3
A red-throated loon is a type of diving bird that dives for its food. One particular loon dives for 8 seconds to a depth of 12 feet under the surface of the water. A. Assume the loon dives at a constant rate. Write an equation that can be used to represent the elevation, y, of the loon after x seconds into the dive. B. If the loon is at a depth of 22 feet under the surface of the water, how long was it diving for? Show your work.
The equation representing the elevation of the loon and the time of the dive is 3x-2y = 0, and the Loon has been diving for 14.67 seconds.
The red throated loon dived down to a distance of 12 feet under the water in 8 seconds.
We can assume that the loon is diving at a constant rate.
The relation between the elevation wise of the loan after 1 second into the dive can be represented by the linear equation which has the slope,
Slope = 12/8
Slope = 3/2
Now as we have the slope of the equation we can write the equation by using the point slope form, with the point, (8,12)
(y - 12)/(x - 8) = 3/2
2y - 24 = 3x - 24
3x - 2y = 0
This is the equation that represent the elevation y of the loan after x seconds.
When the elevation of The Loon is 22 feet,
We can put y = 22,
3x = 2(22)
x = 14.67 seconds.
So, the loon has been diving for 14.67 seconds.
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its easy but i dont want to do it because im to lazy
The equation of the given line written in the slope-intercept form is: y = 21x + 10.25.
What is a slope?
The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.
Note that the general slope equation is:
y = mx + b
Where
m is the slope of the line and
b is the y-intercept.
In this specific instance, m is the change in the price of the ticket
b is the additional fee value that needs to be included for each ticket
Hence, the cost of the ticket (y) is given as:
y = (change rate of x) + added fee to every order
Where rate of change = 21; and
The fee added to each order is 10.25
Given the above, the general equation becomes:
y = 21x + 10.25
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Carly works 6 hours each day for 4 days a week
she earns £360 each week
How much does Carly earn each hour
Answer:
the answer is £15
Step-by-step explanation:
Carly works 6 hours for four days 6x4= 24
so she worked for 24 hours we know that she makes £360 per week.
so we divide 360 by 24 which gives us the total of
£15 per hour
Write the point-slope form of the equation of the line that passes through the origin and has a slope of 2. a. using variables, write out the formula for the point-slope form of the equation. b. identify the values for m, x1, and y1. c. fill these values into the point-slope form of the equation from part (a), and simplify as needed. use the box provided to submit all of your calculations and final answers.
The point slope form of the equation is = P2 = (11, 2)
What is point slope?The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables. Depending on the facts at hand, there are different ways to find a line's equation. Several techniques include:Form of point slopeForm of a slope-interceptTwo-point form for interceptingacc to our question-
Since m = and P1 = (2, -1) then x1 = 2 and y1 = -1. 1y – y1 = m (x – x1)y – (-1) = (x – 2)y + 1 = (x – 2)3 (y + 1) = 1(x – 2)3y + 3 = x – 25 = x – 3y or x – 3y = 5(This the standard formula of the line)Step 2: Calculate P2.Select any valueyou with for x or y and substitute it into the equation found instep 1. For this example y will equal 2.x – 3y = 5x – 3(2) = 5x – 6 = 6x = 11learn more about slope click here:
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If tan(A+B) = -4 and tan B=5/3, find tan A.
The value of tan A = 1
What are trigonometric ratios?Trigonometric ratios are the ratios of sides of a right-angle triangle. The six trigonometric ratios of a right angle triangle are Sin, Cos, Tan, Cosec, sec and cot.
The trigonometric ratios relate the sides of the triangle with the angles of the triangle.
tan(A+B) = -4, tan B = 5/3
But tan(A + B) = [tex]\frac{tan A + tanB}{1-tanAtanB}[/tex]
Substituting the values of tan(A +B) tan B
-4 = [tex]\frac{tan A + 5/3}{1 - 5/3tanA}[/tex]
multiply numerator and denominator by 3, you have
-4 = [tex]\frac{3tanA + 5}{3 -5tanA}[/tex]
-4(3-5tanA) = 3tanA +5
-12 +20tanA = 3tanA +5
collect like terms
20tanA - 3tanA = 5 +12
17tanA = 17
tan A = 17/17
tanA = 1
In conclusion, the value of tanA = 1
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-9 (9x -6) = 3 (4x+6)
Answer:
[tex]-9 (9x -6) = 3 (4x+6) \\ - 9 \times 9x + 9 \times 6 = 3 \times 4x + 3 \times 6 \\ - 81x + 54 = 12x + 18 \\ -81x - 12x = - 54 + 18 \\ - 93x = - 36 \\ x = \frac{36}{93} \\ x = \frac{18}{46.5} \\ x = 0.3870967742[/tex]
Aaliyah was given a gift card for a coffee shop. Each morning, Aaliyah uses the card to
buy one cup of coffee. The original amount of money on the gift card was $30 and
each
сир of coffee costs $2. Make a table of values and then write an equation for A,
in terms of x, representing the amount money remaining on the card after buying a
cups of coffee.
The equation in terms of x, which represents the amount of money left on the gift card of Aaliyah upon buying a cup of coffee is; A = 30 - 2x dollars.
Define the term equation?A single mathematical phrase is referred to as a term. It could be a single number (negatively or positively), a single variable (a letter), or a combination of variables multiplied but still never added or eliminated. Variables with such a number ahead of them are used in some words. A coefficient is the number that appears ahead of a phrase.The original value of the gift card was $30.
Coffee costs $2 per cup.
Let 'x' be the number of cup of coffee purchased by Aaliyah.
Total cost be 'A' be paid by her.
Thus, the equation in terms of x, which represents the amount of money left on the gift card upon buying a cup of coffee is;
A = 30 - 2x dollars.
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1. Vanessa works as an event planner during the summer. She makes $50 for every birthday
party she plans and $100 for every wedding she plans. Her goal every summer is to make
$1000 to put towards college. Write an equation that represents the number of parties (x) and
the number of weddings (y) that Vanessa could plan during the summer in order to meet her
$1000 goal:
The required equation for the given condition is 50x + 100y = 1000.
What is an algebraic expression?
An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division, and exponentiation by an exponent that is a rational number).
Given, the charge for every birthday party =$50
number of birthday parties = x
So, the total charge for birthday parties = 50x
the charge for every wedding = $100
the number of weddings = y
So, the total charge for the wedding = 100y
Then,
Total amount achieve = $1000
or, 50x + 100y = 1000
Hence, the required equation is 50x + 100y = 1000.
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10. Each term in a sequence is generated by
multiplying the previous term by 3 and then
adding 2. If the first term is -3, what will the 6th
term be?
a. -487
b. -165
C. -57
d. 57
e. 165
2
The 6th term is -487 i.e, option(a)
What is a Sequence ?
A sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms). The number of ordered elements (possibly infinite) is called the length of the sequence.
There are 4 types of sequence, arithmetic sequences, geometric sequences, quadratic sequences and special sequences.
Given, the 1st term = -3
According to question, we get the term by multiplying the previous term by 3 and then adding 2.
Now, calculate the other terms.
so, the 2nd term will be
-3 * 3 + 2 = -7
3rd term
-7 * 3 + 2 = -19
4th term
-19 * 3 + 2 = - 55
5th term
-55 * 3 + 2 = -163
6th term
-163 * 3 + 2 = -487
Hence, the 6th term is -487 i.e, option(a)
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Just 2 questions.
Explaining the Converse of the Pythagorean Theorem
Task 1
Part A
The Pythagorean Theorem states that for any given right triangle, a2 + b2 = c2. Using the Pythagorean Theorem, what should be the relationship between the areas of the three squares?
Task 2
Part E What does this show about the relationship between the two triangles?
The Pythagorean Theorem indicates the following relationship between the squares and triangles.
Part A
The relationship between the areas of the squares is that the area of the large square is the sum of the areas of the other two squares.Part E
The point that the length c on one triangle is equal to the length n on the other triangle and that the other two sides of both triangles are congruent, the two triangles are congruent by SSS congruency rule.What is the Pythagorean Theorem?Pythagoras theorem can be stated as follows; The square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.
Part A
The possible squares in the question are the three squares arranged on the three sides of the triangle, and having a side length which is the same as the length of the side of the triangle to which the square is attached
The relationship between the three squares of side length a, b, and c according to Pythagorean theorem is; a² + b² = c²
Therefore, the area of the largest square that is located on the hypotenuse side of the triangle is equal to the sum of the areas of the other two squares.
Part E
The length of the sides of the triangles, obtained from a similar question on the site are; a, b, and c and a, b, and n
It was shown that c² = n²
Therefore;
c = n
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when the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. what is the original number?
The original number from the given decimal number is 0.02.
Define the term reciprocal of the number?A multiplicative inverse of such a number is referred to as the reciprocal. In other words, 1 divided by a number is the definition of the reciprocal. Any given number multiplied by its reciprocal would always yield the value 1. By swapping the values of a numerator and denominator, one can find exact reciprocal of a fraction.For the given question;
Moving a decimal point 4 places towards the right corresponds to multiplying the given integer by 10,000 if it is x.
This results in:
10000x = 4.(1/x)
Simplifying.
x² = 4/10000
x > 0.
Taking square root of the number.
x = 2/100
x = 0.02
Thus, the original number from the given decimal number is 0.02.
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a recent survey showed that 9393 full-time employees out of a sample of 400400 did not use all of their vacation days last year. however, 118118 of those studied expressed a desire for more vacation time. based on this sample, if a full-time employee is chosen at random, what is the probability that he or she is content with the vacation allowance? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability that he or she will be happy with the travel reimbursement will be 0.705.
The number of people who requested more vacation time indicates that they are plainly dissatisfied.
400 employees are satisfied with the vacation allowance. - The number of workers that requested greater vacation time.
Employees who are satisfied with their vacation pay are represented by the numbers 400 - 118 = 282.
The likelihood that he or she will be happy with the vacation allowance =
Employees that are happy with their vacation pay / Total number of employees
= 282 / 400 = 0.705.
Therefore, the likelihood that he or she will be happy with the vacation allowance = 70.5%
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7. Eugene earns $2,700 monthly. He is going to be receiving a 3.5% raise. With this new raise, he
Inelieves he will earn more than $2,800 a month. Is Eugene correct in his thinking? Why or why
rot? Justify your reasoning.
Answer: No
Step-by-step explanation: to find out how much more money Eugene will be making we need to isolate the increased value provided by the raise and then add it to his already existing earnings. We do this by multiplying $2700 by 3.5%.
We would write this as 2700 x .035
This is because 100% can be converted to 1, for example if Eugene got a 100% raise we would multiply 2700 by 1 (which changes nothing) then add 2700 and 2700 together.
Since Eugene is only getting a 3.5% raise we would write it as .035 instead of 1
Now that we have our equation we first need to simplify. In this case it means we remove the two zero's from 2700 to make it 27. To make sure the answer does not get messed up will make the other side of the equation larger by moving everything two decimal points (one for each removed zero) like this.
27 x 3.5
This is much easier to work with but I will still show the steps I am using to prevent confusion.
27 x .5 = 13.5
27 x 3 = 20 x 3 + 7 x 3
20 x 3 = 60
7 x 3 =21
60+21 =81
81+13.5=94.5
Since 2700 + 94.5 = 2794.5 Eugene will not make more than $2800 dollars a month after his raise.
under what circumstances would a score that is 10 points below the mean be considered to be an extreme value? select one: a. when the mean is much greater than 10 b. when the mean is much less than 10 c. when the standard deviation is much greater than 10 d. when the standard deviation is much less than 10
The correct option d. when the standard deviation is much less than 10.
Describe the term standard deviation?The term "standard deviation" (or "σ") applies to a measurement of the data's dispersion from the mean. A low standard deviation indicate that the data are grouped around the mean, although a large standard deviation indicates that the data are more dispersed.When a value is 10 points beyond the norm, it is said to be an extreme value or an outlier.
When a point deviates significantly from the mean in comparison to other points, it is referred to as an outlier. Z-scores can be used to establish this. Remember the z-score formula:
z = (x - μ) / σ
μ = mean σ = standard deviationx = point of interestThe outlier should have a very big magnitude z-score. We are aware that the score in this issue is 10 points just below mean, we can say:
A lesser value of would raise the magnitude of a z-score, increasing it to the maximum extent achievable.
Therefore, this point would be an outlier whether its standard deviation was drastically lower than 10.
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60+16=x-16+16 x=? This math book hates me
Answer: 76
Step-by-step explanation: simplify equation
60+16=x-16+16 (cancel out 16 and add 60+16)
76=x
60+16=x-16+16
76=x
x=76
37, 38, 39, and 40 show that the series is convergent. how many terms of the series do we need to add in order to find the sum to the indicated accuracy?
In order to find the sum to the indicated accuracy we need to add
5 terms as the series is said to be convergent.
Given Series is Σ(-1/3)^n / n where error is less than 0.0005
= Σ (-1)^n / n3^n
For this series, we will use ratio test
if [tex]\lim_{n \to \infty} |an + 1 / an |[/tex] = L < 1 then series in convergent,
Let an = (-1)^n / n3^n , an+1 = (-1)^n+1 / (n+1)3^n+1
[tex]\lim_{n \to \infty} |an + 1 / an |[/tex] = [tex]\lim_{n \to \infty} | ((-1)^n+1 / (n+1)3^n+1)(n3^n/(-1)^n) |[/tex]
By solving we get,
[tex]\lim_{n \to \infty} |an + 1 / an |[/tex] = 1/3 < 1
Then given series is convergent.
By alternating series estimation theorem we have,
|Rn|=|S-Sn| <= an+1
an+1 <= 0.0005
1 / (n+1)3^n+1 <= 0.0005
(n+1)3^n+1 >= 2000
2 * [tex]3^{2}[/tex] >[tex]\neq[/tex] 2000 (n=1)
4 * [tex]3^{4}[/tex] >[tex]\neq[/tex] 2000 (n=3)
6 * [tex]3^{6}[/tex] >= 200 (n=5)
So required terms is n=5
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Jayden has two jobs. One week his paycheck was the same for both jobs. As a server
he earned $9.64 per hour plus $82.35 in tips. Working at a jewelry store he earned
$14.86 per hour plus $17.10 in sales bonuses. Write an equation that can be used to
determine the number of hours, h, that Jayden worked the week his paycheck was the
same for both jobs.
Create an equation
The equation for Jayden's paycheck is,
$9.64h+ 82.35= $14.86h+ $17.10
How to construct an algebraic equation?
STEPS TO CONSTRUCT AN ALGEBRAIC EQUATION---
Identify the inquiry being made.Simple statements should be used to record pertinent information.Assign symbols to values that are still unknown.Calculate the mathematical relationships between the assertions.let the number of hours Jayden works be h hours.
so, Jayden has got the total from the jewelry store is,,$9.64h+ 82.35
Jayden has got the total from the sales bonuses is, $14.86h+ $17.10
so, the total paycheck from the jewelry store is,,$9.64h+ 82.35
and from the sales bonuses is $14.86h+ $17.10.
as they are equal, the equation is, $9.64h+ 82.35= $14.86h+ $17.10
Hence, the equation is,$9.64h+ 82.35= $14.86h+ $17.10
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Two friends, Sophia and Ruby, took summer jobs. the equation y=23.9x represents ruby's earnings in dollars and cents, y, for working x hours. Sophia earned 1098.20 in 38 hours.
sophia earns $___ per hour (less/more) than ruby.
By performing some simple mathematical operations, we know that Sophia earns $366 per hour.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations. Parentheses, Exponents, Multiplication, Division (from Left to Right), Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).So, to calculate how much Sophia earns in 1 hour:
Total earnings are 1098.20.Total working hours are 38.Now, calculate earnings per hour:
1098.20/38366.06Rounding off: $366
Therefore, by performing some simple mathematical operations, we know that Sophia earns $366 per hour.
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Complete question:
Two friends, Sophia and Ruby, took summer jobs. the equation y=23.9x represents ruby's earnings in dollars and cents, y, for working x hours. Sophia earned 1098.20 in 38 hours.
sophia earns $___ per hour
Taub is saving up to buy a new bicycle. She already has $70 and can save an additional $10 per week using money from her after school job. How much total money would Taub have after 7 weeks of saving? Also, write an expression that represents the amount of money Taub would have saved in w weeks.
Total savings after 7 weeks:
Total savings after w weeks:
Total savings after 7 weeks : $140
Total savings after w weeks : $(70 + 10w)
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a phrase : Taub is saving up to buy a new bicycle. She already has $70 and can save an additional $10 per week using money from her after school job.
Taub will have a total of -
70 + 7 x 10 = $140
The expression that represents the amount of money Taub would have saved in [w] weeks is -
y = 70 + 10w
Therefore -
Total savings after 7 weeks : $140
Total savings after w weeks : $(70 + 10w)
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help meeeeeeeeeeeeeee pleaseee
The recommended screen size for the television is 59.85 inches.
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, the expression for the size of the television is given as:
S = 0.228x² + 8.154x - 8.3
where x = 7 feet
S = 0.228x² + 8.154x - 8.3
S = 0.228(7)² + 8.154(7) - 8.3
S = 11.172 + 57.078 - 8.4
S = 59.85
The size is 59.85 inches.
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Justify each step of the solution by stating the property that was used to get to each step. (4 points - 1 point each correct answer)
Given: 2(10 - 13x) + 9x) = -34x + 60
Step 1: 20 + 26x + 9x = -34x + 60
Step 2: -17x = -34x + 40
Step 3: 17x = 40
Step 4: x = 40/17
Sample Answer
Step 1: _____ property
Step 2: ______ property
Step 3: ______ property
Step 4: ______ property
What is the solution to the following equation?
x² + 3x + 7 = 0
A. x= 3+-√25/2
B. x= -3+-√37/2
C. x= -3+-√²7/2
D. x= -3+-√-19/2
Answer: D
Step-by-step explanation:
Answer: Choice D
[tex]x = \frac{-3\pm\sqrt{-19}}{2}\\\\[/tex]
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Explanation:
Compare the given equation x² + 3x + 7 = 0 to ax² + bx + c = 0 to find that,
a = 1b = 3c = 7Those values are plugged into the quadratic formula to get the following:
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-3\pm\sqrt{(3)^2-4(1)(7)}}{2(1)}\\\\x = \frac{-3\pm\sqrt{-19}}{2}\\\\[/tex]
which points us to choice D being the final answer.
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Side note:
The discriminant [tex]d = b^2 - 4ac = (3)^2-4(1)(7) = -19[/tex] is negative, so there are no real solutions. Instead, the two solutions are non-real complex numbers.