If the relationship between his hours of work (x) and the amount of money in his bank account (y) is represented by equation "y = 10x + 50" , then the money did he have in his bank account before he started working is $50 .
The equation y = 10x + 50 shows the relationship between Hamal's hours of work (x) and the amount of money in his bank account (y).
When x = 0, the equation becomes y = 10(0) + 50, which simplifies to y = 50. So when Hamal has not worked any hours, he has $50 in his bank account.
In other words, the y-intercept of the equation is 50, which represent the amount of money Hamal had in his bank account before he started working.
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Help please help please
Answer:
x = 60.4
Step-by-step explanation:
First, let's remember the three different trigonometric functions: sine, cosine, and tangent. In this case, we would use cosine because the adjacent side to the angle and hypothenuse are used/given.
[tex]cos(22) = \frac{56}{x}[/tex]
We need to set up a proportion because there is not much else you could do here.
[tex]\frac{cos(22)}{1} =\frac{56}{x}[/tex]
Then, cross-multiply.
[tex]cos(22) * x = 56[/tex]
Finally, divide both sides by cos(22). You'll probably need your calculator and make sure it's in degrees mode and not radians!
[tex]\frac{cos(22) * x}{cos(22)} = \frac{56}{cos(22)}[/tex]
[tex]x = 60.4[/tex]
Rounded to the nearest tenth, x = 60.4.
Your friend
finds the sum. Is your friend correct?
Explain your reasoning.
-3.7 + (-0.25) = | 3.7 | + | 0.25 | = 3.7 + 0.25 = 3.95
Answer:
Yes, the friend is correct in finding the sum of -3.7 + (-0.25) = 3.95.
To find the sum, the friend first takes the absolute value of each number (ignoring the negative sign) to find that the absolute value of -3.7 is 3.7 and the absolute value of -0.25 is 0.25.
Then, the friend adds the absolute values of the numbers (3.7 + 0.25) to get 3.95 which is the final answer.
The order of operation is correct and the arithmetic is also correct, so the final result is the correct sum of the two given numbers.
Can someone please help me
The length of the segment PS is 100 units.
What is Pythagorean Theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
From the given image we can see that the segments PT, PQ, and TQ form a right- angled triangle PQT.
Applying Pythagorean theorem to this triangle we have:
PQ^2 + TQ^2 = PT^2
(45)^2 + (TQ)^2 = (53)^2
2025 + (TQ)^2 = 2809
(TQ)^2 = 2809 - 2025
(TQ)^2 = 784
TQ = 28
Similarly, segments PR, PS, and SR form a right-angled triangle PRS, where TQ = SR = 28 and PR = 96.
Applying Pythagorean theorem to this triangle we have:
PR^2 + SR^2 = PS^2
(96)^2 + (28)^2 = (PS)^2
(PS)^2 = 9216 + 784
(PS)^2 = 10000
PS = 100
Hence, the length of the segment PS is 100 units.
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3
The teacher estimated that she would have 68 students this school year. She actually had 74.
What is the percent error?
A 2. 08%
B
6%
8. 11%
D 191. 89%
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
The answer is C
Hope this helped!
Verify the trig identity
The verification of the given trig identity is shown in below.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²
Now, We can simplify as;
⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²
LHS;
⇒ (1 - sin x) / (1 + sin x)
⇒ (1 - sin x) (1 - sin x) / (1 + sin x) (1 - sin x)
⇒ (1 - sin x)² / (1 - sin²x)
⇒ (1 - sin x)² / cos²x
⇒ ( (1 - sin x )/ cos x )²
RHS;
⇒ (sec x - tan x)²
⇒ ( 1/cos x - sin x / cos x)²
⇒ ( (1 - sin x) / cos x )²
Hence, We get;
⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²
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Write the equation of the line with slope = 4/6 and passing through the point (1, -1)
Answer:
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).
Given that the slope of the line is m = 4/6, we can substitute it into the equation.
We know that the line passes through the point (1, -1), so we can use that point to find the value of b.
Plugging in the point (1, -1) into the equation, we get:
-1 = (4/6)(1) + b
Solving for b, we get:
b = -1 - (4/6) = -1 - 2/3 = -5/3
So the equation of the line is:
y = (4/6)x - (5/3)
which can be rewritten as
y = (2/3)x - (5/3)
this line is the equation of the line you are looking for.
Answer:
Y--1=m(x-1) this is the rule of the equation of straight line
100 points Factor completely and then place the factors in the proper location on the grid. 4 y2 + 25 y + 6
The factored expression to the expression is (4y + 1)(y + 6)
How to determine the factor to the equationFrom the question, we have the following parameters that can be used in our computation:
4 y2 + 25 y + 6
Express properly
So, we have the following representation
4y² + 25 y + 6
Expand the expression
This gives
4y² + 24y + y + 6
Next, we factor the expression
4y(y + 6) + 1(y + 6)
Factor out y + 6
(4y + 1)(y + 6)
Hence, the solution is (4y + 1)(y + 6)
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Roger received $200 for his birthday. He wants to use the money to buy new clothes for work. He can buy pants
for $30 and shirts for $20. He wants at least 6 new items. Determine the shirt and pants combination Roger
can buy.
From the inequalities 30x + 20y ≤ 200 and x + y ≥ 6, Roger can buy 3 pants and 3 shirts.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Inequalities is used for the non equal comparison of these numbers and variables.
Let x represent the number of pants that Roger buys and y represent the number of shirts he buys.
He can buy pants for $30 and shirts for $20. Roger received $200 for his birthday, therefore:
30x + 20y ≤ 200 (1)
Also:
He wants at least 6 new items. hence:
x + y ≥ 6 (2)
From both equations, the solution to these equalities is (3, 3)
Roger can buy 3 pants and 3 shirts.
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Your water hose leaking at a rate of 0.25 cups per hour. How many gallons did your hose leak in a full 24 hour day ?
well, let's first find out how many cups was that in 24 hours anyhow.
so in 1hr the hose leaks 0.25 cups, so in 24 hrs that'd be (24)(0.25) = 6 cups.
Since a gallon has 16 cups, that'd be 6/16 gallons or 3/8 = 0.375 of a gallon.
2. compute the following summary statisticsa) the mean for the low income group is: b) the median for the low income group is: c) the standard deviation for the low income group is: d) the mean for the high income group is: e) the median for the high income group is: f) the standard deviation for the high income group is:
The mean for the low income group is the average of all the values in the group.
It is calculated by adding up all the values and then dividing by the total number of values. In the low income group, the mean is calculated by adding up all the incomes, and then dividing by the total number of people.
The median for the low income group is the middle value when all the values are arranged in order. To calculate the median, first arrange the incomes in order from lowest to highest, and then find the middle value.
The standard deviation for the low income group is a measure of how spread out the values are. It is calculated by taking the square root of the variance, which is calculated by taking the average of the squared difference between each value and the mean, and then dividing by the number of values.
The mean for the high income group is the average of all the values in the group. It is calculated by adding up all the values and then dividing by the total number of values. In the high income group, the mean is calculated by adding up all the incomes, and then dividing by the total number of people.
The median for the high income group is the middle value when all the values are arranged in order. To calculate the median, first arrange the incomes in order from lowest to highest, and then find the middle value.
The standard deviation for the high income group is a measure of how spread out the values are. It is calculated by taking the square root of the variance, which is calculated by taking the average of the squared difference between each value and the mean, and then dividing by the number of values.
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For the following right traingle, find the side length x. Round your answer to the nearest hundredth
7.21
Step-by-step explanation:The Pythagoras theorem allows us to solve for unknown sides of right triangles.
Right Triangles
Right triangles are triangles that have one 90-degree angle (aka a right angle). The side directly across from the right angle is called the hypotenuse. The hypotenuse is always the longest side of a triangle. The other 2 sides of a right triangle are called the legs of the triangle.
Pythagorean Theorem
The Pythagorean theorem states that a² + b² = c², where a and b are the legs of the triangle and c is the hypotenuse. To find the missing side we can plug in the values we know and solve for b.
12² + b² = 14²Then, subtract 12² from both sides.
14² - 12² = b²52 = b²Finally, take the square root of both sides. When you square root a number, the resulting value is plus or minus, but since we are finding a distance, we will only take the positive answer.
7.21 ≈ bstate which theorem you can use to show that the quadrilateral is a parallelogram
Answer:
opposite angles are equal and parallel
Larry says all numbers that have a 2 in the one ones place are composite numbers. Explain if Larry is correct or incorrrect.
The information shows that Larry is incorrect as a composite number is a positive integer that has at least one positive divisor.
What're are composite numbers?It should be noted that composite numbers are those numbers that have more than two factors. Composite numbers have factors other than 1 and itself
Larry is incorrect. A composite number is a positive integer that has at least one positive divisor other than one and itself. For example, 4 is composite because it can be divided by 2 (and 1). However, a number's ones place simply refers to the digit in the units place and has no bearing on whether a number is prime or composite.
For example, the number 22 is composite because it is divisible by 2 and 11, but the number 12 is composite because it is divisible by 2,3,4 and 6.
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I believe A and C are part of the answer but I am unsure of the rest
Please find attached the image of the enlargement of the shape X by a scale factor of -1 created using MS Word, which is a drawing equivalent to option B. The correct option is therefore;
B.
What is an enlargement transformation?An enlargement transformation is one in which the pri-image object size is scaled about a center of enlargement, using a scale factor, with the sign of the scale factor indicating the direction of the enlargement, which for a +ve sign is on the same side, and for a -ve sign is on the other side of the center of enlargement.
An enlargement by a scale factor of -1, can be obtained by producing the image on the alternate side of the center of enlargement, which with a scale factor of -1, is the same size as the size of the image.
Therefore, the dilation by a scale factor of -1, with the center at the origin, produces an image which is equivalent to a reflection of the original object (pre-image), across the y-axis followed by a reflection across the y-axis.
The image of the object following the dilation will therefore be the mirror image of the mirror image of the object reflected across the y-axis, which takes the shape of a vertically flipped, left flipped F, which is option B
Please find attached a drawing of the shape of the image of the enlargement of shape X by a scale factor of -1, created with MS Word
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Justin punts a football. The height of the football
could be described by the model:
--1672 +64 + 1
'h describes the height of the ball in feet and the
time in seconds after the ball was kicked.
At what time in seconds is the ball at its highest
point after being kicked?
If the height of the football could be described by the model: f(x) = -16x² + 64x , then the time at which the ball at its highest point after being kicked is t = 2 seconds .
In order to find time at which ball is at its highest point,
we have to find the time at which the derivative of height function is = 0.
the height function is ⇒ f(x) = -16x² + 64x ;
So , the derivative of the height function will be :
⇒ f'(x) = -32x + 64 ;
equating the derivative of height function to 0 , and solving for x ,
we get ;
⇒ -32x + 64 = 0
⇒ -32x = -64
⇒ x = 2
Therefore , the time at which the ball is at its highest point is 2 seconds .
The given question is incomplete , the complete question is
Justin punts a football. The height of the football could be described by the model: f(x) = -16x² + 64x. h describes the height of the ball in feet and the time in seconds after the ball was kicked.
At what time in seconds is the ball at its highest point after being kicked ?
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If 3+x<5 and 8+x>5,What range of values of x satisfies both inequalities?
The range of values of x which satisifies both of the inequalities is:
(-3, 2)
What range of values of x satisfies both inequalities?Here we have two inequalities:
3 + x < 5
8 + x > 5
And we want to see which range of values of x satisfie both of these inequalities.
If we isolate x on both inequalities, we will get:
3 + x < 5
x < 5 - 3
x < 2
And the other one is:
8 + x > 5
x > 5 - 8
x > -3
Then we havethe compound inequality:
x < 2
x > -3
Then the range of values that satisfies both inequalities is (-3, 2)
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(a) A ball rotates 2π rad in 4.0 s. What is its angular velocity?
(b) A bicycle tire moving at ω = 3.5 rad/s accelerates at a constant rate to 4.2 rad/s in 3.0 s. What is its angular acceleration?
a. The angular velocity of the ball is 1.57rad/sec
b. The angular acceleration of the bicycle is 0.23 rad/sec²
What is angular acceleration and angular velocity?angular is the rate of change of angular distance . it is measured in rad/sec. it is represented by w. Angular acceleration is the rate of change in angular velocity with time.
angular velocity = change in angle/ time
w = 2π/t
w = 2× 3.14/4
w = 6.28/4
w = 1.57 rad/sec
angular acceleration =( final angular velocity - initial angular velocity )/time
= (4.2 - 3.5)/3
= 0.7/3
= 0.23 rad/s²
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area of the segment?
Answer:
A ≈ 34.91 m²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{40}{360}[/tex] ( r is the radius )
= π × 10² × [tex]\frac{1}{9}[/tex]
= [tex]\frac{100\pi }{9}[/tex]
≈ 34.91 m² ( to 2 decimal places )
Answer:
34.88m²
(round 35m²)
Step-by-step explanation:
a round angle, that of the circle, is 360°, here we have a portion of 40°, we divide 360° by 40° and we have the percentage with respect to the circle
360° : 40° = 9
we now know that the wedge is 1/9 of the circlefind the area of the whole circle having the radius (10m)Area of Circle Formulas · Area = π × r2, where 'r' is the radius
Area = π × r2
Area = π × 10²
Area = π × 100
Area = 3.14 × 100
Area = 314 m²
now we divide by 9 and we have the area of the wedge314 : 9 = 34.88m² (round 35m²)
Ella's family took a road trip to Niagara Falls. Ella slept through the last 14% of the trip. If Ella fell asleep after they had travelled 602 miles, what was the total length of the trip?
The total distance of the trip Ella's family took is 700 miles.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Ella slept through the last 14% of the trip.
So, Before Ella fell to asleep they covered (100 - 14)% = 86% of the trip.
Let The total distance be 'x'.
Therefore, 602 miles is 86% of 'x' which can be numerically expressed as,
(86/100)×x = 602.
0.86x = 602.
x = 602/0.86.
x = 700 miles.
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Using y = 6 - 2x, plot the ordered pairs from the table. Then graph the function represented by the ordered pairs and tell whether the function is linear or nonlinear. Part 1 out of 3 Complete the table. Input, x Output, y Check -1 3 Next
Answer:
.................................................................................
Step-by-step explanation:
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ok
-13, -17, -21, -25 write an equation for the nth term of the arithmetic sequence then find a10
The tenth term of the given arithmetic sequence is; -49
What is the nth term of an arithmetic sequence?The formula for the nth term of an arithmetic sequence is;
aₙ = a + (n - 1)d
where;
a is first term
d is common difference
From the given sequence, we see that;
a = -13
d = -17 - (-13)
d = -17 + 13
d = -4
Thus, the tenth term of the arithmetic sequence is;
a₁₀ = -13 + (10 - 1)-4
a₁₀ = -13 -36
a₁₀ = -49
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please help me with my homework!
Answer:
The machine makes 45 bottles per minute.
Step-by-step explanation:
We can first find the slope through this equation: [tex]\frac{y2-y1}{x2-x1}[/tex]
Since we are given two points, (2,90) and (7,315), we can plug those two points into the formula given above:
[tex]\frac{315-90}{7-2}[/tex]
= 45
Therefore, m = 45.
Now, we can pick one of the two points given--in this case, I'll use (2,90)--to find the equation of the line: [tex]y-y1 = m(x-x1)[/tex]
For (2,90), y1 will be 90, and x1 will be 2. Let's also plug in m:
y - (90) = 45(x - 2)
We can solve for y now to find what y=mx+b is:
y = 45(x-2) + 90
y = 45x
Since the problem asks how many bottles the machine can make per minute, we can plug x = 1: 45(1) = 45
The machine makes 45 bottles per minute.
(PLEASE HELP) At a local print shop, 15 copies can be made for $6. At this rate, how much would it cost to make 35 copies???
Answer:
14 dollars
Step-by-step explanation:
They vary in direct proportion
Thus; If 15 copies = 6dollars
35 copies = (35 × 6) ÷ 15
= 210 ÷ 15
= 14
It would cost 18$
Every fifteen copies you have to pay 6$, and since 35 is 3 times 15, it would also be 3 times the price, or 6 * 3$ which equals 18$
Quadrilateral EFGH is a rectangle. If m∠FEG=57° , find m∠GEH .
The measure of the angle m∠GEH = 33° for the given Quadrilateral EFGH which is a rectangle.
Define the term compliment angles?When two angles sum up to 90 degrees, they are complementary (a Right Angle).Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees & 60 degrees, for instance, are complimentary angles.They don't even have to be close to one another for the total to be 90 degrees.Examples:
The complimentary angles of 40° and 50°.The complementary angles of 60° and 30° are.The corresponding angles of 5° and 85° are.For this stated question:
In the rectangle EFGH.
m∠FEG=57°
Then,
m∠FEG + m∠GEH = 90 (complimentary angles)
57° + m∠GEH = 90
m∠GEH = 90 - 57
m∠GEH = 33°
Thus, the measure of the angle m∠GEH = 33° for the given Quadrilateral EFGH which is a rectangle.
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Jenny went for a drive in her new car. She drove for 198.4 miles at a speed of 62 miles per hour. For how many hours did she drive?
The number of hours that Jenny drove in her new car is 3.2 hours
How to calculate the number of hours that Jenny drove in her car?
The speed is 62 miles
The distance is 198.4 miles
The number of hours can be calculated as follows
speed= distance/time
62= 198.4/x
cross multiply both sides
62x= 198.4
x= 198.4/62
x= 3.2
Hence the number of hours that Jenny drove is 3.2 hours
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Think about what you know about breaking apart numbers with addition. Fill in each box. Use words, numbers. and picture. Show as many ideas as you can.
The breaking of number using addition is discussed above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the breaking apart of numbers with addition.
We can breaking apart the numbers with addition as follows. Assume the number to be 50. We can break the number 50 as follows -
50 = 25 + 25
50 = 15 + 10 + 15 + 10
50 = 10 + 10 + 10 + 10 + 10
50 = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5
Therefore, the breaking of number using addition is discussed above.
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find the area of region s . find the volume of the solid generated when region s is revolved about the horizontal line y
The volume of solid generated when region s is revolved about the horizontal line y is 93.04919.
We have to find the volume of the solid generated when region s is revolved about the horizontal line y.
As shaded region is revolved around y = -3.
Outer radius = f(x) + 3
Inner radius = g(x) + 3
Width = dx
Thus small volume "dv" formed when shaded region in above diagram is revolved around y = -3.
dv = π[tex](f(x) + 3)^3[/tex]dx - π[tex](g(x) + 3)^2[/tex]dx
dv = π([tex]f^2[/tex](x) + 6f(x) + 9)dx - π([tex]g^2[/tex](x) + 6g(x) + 9)dx
dv = π([tex]f^2[/tex](x) + 6f(x))dx - π([tex]g^2[/tex](x) + 6g(x))dx
Now integrating on both side:
[tex]\int dv=\pi\int^{3}_{0}9(1+x)\cos(\pi x/6) + 6\int^{3}_{0}f(x)dx-\pi\times 5.32021-6\times3.24125[/tex]
Using the provided result or a scientific calculator, the entire definite integral was discovered.
v = π × 25.54298 + 6 × 8.16083 - π × 5.32021 - 6 × 3.24125
v = 93.04919
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The complete question is given below:
One ounce of solution X contains only ingredients a and b in a ratio of 2:3. One ounce of solution Y contains only ingredients a and b in a ratio of 1:2. If solution Z is created by mixing solutions X and Y in a ratio of 3:11, then 2520 ounces of solution Z contains how many ounces of a?
Applying proportion, 2520 ounces of solution Z will contain 44040 ounces of ingredient a.
How to Use Proportion to Calculate The Ounces Needed of a Solution?To determine the number of ounces of ingredient a in 2520 ounces of solution Z, we need to first calculate the proportion of ingredient a in solutions X and Y, and then use that information to determine the proportion of ingredient a in solution Z.
Solution X contains 2 ounces of ingredient a and 3 ounces of ingredient b in one ounce of solution, so the proportion of ingredient a is 2/(2+3) = 2/5.
Solution Y contains 1 ounce of ingredient a and 2 ounces of ingredient b in one ounce of solution, so the proportion of ingredient a is 1/(1+2) = 1/3.
Solution Z is created by mixing solutions X and Y in a ratio of 3:11, so 3 ounces of solution X are mixed with 11 ounces of solution Y.
Thus, the proportion of ingredient a in solution Z = (32/5) + (111/3) = 6/5 + 11/3.
To find out the number of ounces of ingredient a in 2520 ounces of solution Z, we need to multiply the proportion of ingredient a with the number of ounces of solution Z
2520 * (6/5 + 11/3) = 2520 * (6/5 + 11/3) = 2520 * (252/15 + 11/3) = 2520 * (16+11/3) = 2520 * (16+11/3) = 2520 * (16+11/3) = 2520 * (16+37/3) = 2520 * (16+37/3) = 2520 * (53/3) = 252053/3 = 252017.66666 = 44040 ounces of ingredient a.
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determine if the sequence is geometric. if it is, find the common ratio.
-1, 1, 4, 8, ...
Due to the lack of a common ratio, the above sequence is not geometric.
What is geometeric sequence?
A series of integers with a common ratio is referred to as a geometric sequence. A geometric sequence has a next number that is a multiple of the one before it.
if the sequence is geometric.the common ratio of the number's
-1, 1, 4, 8, are
-1/1 = -1 ratios of the numbers in the sequence
4/1 = 4
8/4 = 2
There isn't a ratio that unites the numbers.
The lack of a common ratio leads us to the conclusion that the presented sequence is not geometric.
Due to the lack of a common ratio, the above sequence is not geometric.
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A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately
1290 deer in the population. Which function can be used to determine the number of deer, y, in this population
at the end of t years?
The function is y = 1500[tex](0.985)^t[/tex].
What is function?
A mathematical function , rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Here initial population is 1500 .
Rate of decrease = 1.5%
Number of years = 10
After 10 years , the end population = 1290.
Now using formula,
=> P = [tex]P_0[/tex][tex](1-\frac{r}{100})^n[/tex]
Here number of deer, y, in this population at the end of t years then
=> y = 1500[tex](1-\frac{1.5}{100})^t[/tex]
=> y = 1500[tex](1-0.015)^t[/tex]
=> y = 1500[tex](0.985)^t[/tex]
Hence the function is y = 1500[tex](0.985)^t[/tex].
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