The Linear equation used is x -y = 1; to find the age of Isabelle's age.
What is Linear Equation?
An equation is said to be linear if the maximum power of the variable is consistent Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present. A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.
Let the age of Ben be x;
Let the age of Amara be y;
According to the question:
It is given that:
Ben is one year younger than Amara. That means we have to form a linear equation such that Amara is one year older than Ben.
So,
We have assumed the Age of Ben is x;
we have assumed the Age of Amara is y;
So, According to the question,
Framing the linear equation,
x -1 =y;
⇒x -y = 1;
Hence, We can find the age of Isabelle using the linear equation: x -y = 1;
where x is ben's age;
where y is Amara's age.
Therefore, The Linear equation used is x -y = 1; to find the age of Isabelle's age.
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A quadratic function subtracted from a cubic function is a cubic function? True or False
Add example problem:
When quadratic function is subtracted from cubic function, the resultant equation is cubic.
So, It is true.
What is function?Function is defined as, In any equation of two variable, we make change in one accompanied by second.
For example, [tex]F(x)=2x+1[/tex] when we make changes in x , different values of y will obtain.
what are Quadratic and Cubic function?Quadratic function in which maximum power of variable is two. Similarly, the function which has maximum power on variable is three is called cubic function.
To solve the given problem, let suppose we have,
Quadratic function:[tex]f(x)=x^{2} +x+1[/tex]
Cubic function: [tex]g(x)= x^{3}+x^{2} +x+1[/tex]
According to question,
Subtract quadratic function from cubic function,we get
[tex]g(x)-f(x)=( x^{3}+x^{2}+x+1)-(x^{2} +x+1 )[/tex]
⇒ [tex]h(x)=x^{3} +1[/tex]
It is a cubic function.
Thus, given statement is True.
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can y’all help me please
The slope of the line x = 3 is undefined
How to describe the slope of the line
The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.
Mathematically, the slope is the change in y divided by the change in x. That is:
Slope = y2-y1 / x2-x1
Let's pick any two convenient points on the line:
(3, 9) and (3, -9) = > x1 = 3, y1 = -9 and x2 = 3, y2 = 9
Slope = 9-(-9) / 3-3 = 18/0
The denominator here is 0, if you evaluate this using a calculator you will a maths error. So we say the slope is undefined
Notice that: There is no change in x i.e. x1 = x2
Therefore, the slope of x = 3 is undefined because x = 3 is a vertical line
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You have been gotten a job offer and the company wants you to start out at 45,000 and will give you 5% raise every year write an equation you could use to determine how much you could be making after x number of years
Answer:
$51,750
Step-by-step explanation: We are going to make x = 3 and we will use the i=prt equation meaning
Step 1: (45,000)(0.05)(3)= 6750
Step 2: 45,000+ 6750= 51,750
Solution: $ 51,750
A helicopter drops a bucket of water onto a forest fire from 38 meters above the blaze. How long does it take the water to fall and reach the flames?
The required time that would it takes to reach the flames is 2.78 sec.
Given that,
A helicopter drops a bucket of water onto a forest fire from 38 meters above the blaze how long it takes the water to fall and reach the flames is to be determined.
Here,
According to the question,
The initial velocity of the water is u = 0, and s = 38
Speed gain by the water is due to the acceleration due to gravity g = 9.8.
The time for water to reach to the ground is given by the second equation of motion.
s = u²t + 1/2gt²
Substitute the values in the above equation,
38 = 1/2(9.8)t²
(9.8)t² = 76
t = √(76/9.8)
t = 2.78 sec.
Thus, the required time that would it takes to reach the flames is 2.78 sec.
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4. Angle X in the triangle below is a right angle.
W
15
X
T
h
-25-
2
20
R
9²4625
9+ 25²..
= 20²
400
-625-625
19² √225
15
(a) What is the measure of angle W?
450
(b) What is the height, h, of the triangle?
15.
/2 pts)
a ) The required measure of x = 90°
b ) The height of the right angled triangle = = [tex]\sqrt{244}[/tex]
Given is a triangle with measure 15, 20 and 25
a ) Since a perpendicular is dropped from above
the two angles of x are equal because the angle is bisected by an angle bisector
So to check whether the angle x is a right angled or not
we can use the pythagoras theorem and check if the LHS = RHS or not
LHS = 15² + 20² = 225 + 400 = 625
and RHS = 25² = 625
Since LHS = RHS thus the angle is 90 degrees
b ) The height of the right triangle ;
by using the Pythagoras theorem again
12.5² + h² = 20² { side 25 is bisected = 12.5 }
h² = 400 - 156.25
h = [tex]\sqrt{244}[/tex]
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What is the relationship between Figure A and Figure B?
-Figure A was translated left 2 units and up 4 units
-Figure A was reflected over the y-axis
-Figure A was translated right 4 units and up 2 units
-Figure A was dilated by a scale factor of 2
Answer:
Figure A was translated right 4 units and up 2 units
Suppose that f(x)= −4x^2+5.
(A) Find the slope of the line tangent to f(x) at x= 1.
(B) Find the instantaneous rate of change of f(x) at x= 1.
(C) Find the equation of the line tangent to f(x) at x= 1. y=
The slope of the line tangent to f(x) at x = 1 is -8
The instantaneous rate of change of f(x) at x = 1 is -8
The equation of line tangent to f(x) at x = 1 is y = -8x + 9
What is a tangent to a curve?The tangent line to a curve at a given point is the line which intersects the curve at the point and has the same instantaneous slope as the curve at the point.
so the slope of a line at that point is the slope of the curve at that point.
f(x) = -4[tex]x^{2}[/tex] + 5
To find the slope, we differentiate f(x) with respect to x
dy/dx = d/dx( -4[tex]x^{2}[/tex]) + d/dx(5)
= -8x + 0
dy/dx = -8x
The slope = -8x
at x = 1,
the slope becomes, -8(1) = -8
The instantaneous rate of change of f(x) at x = 1 is the same as the slope of the line tangent to f(x) = -8
The slope of the line is -8
to find the equation of the tangent line, we need to find the coordinates of the point the line touches the curve.
one of the coordinates x = 1, to find y, we substitute x into f(x)
f(x) = -4[tex](1)^{2}[/tex] + 5
f(x) = 1
so the point is (1, 1)
so equation of straight line
[tex]\frac{y - y_{1} }{x - x_{1} }[/tex] = m
y - 1/x - 1 = -8
by cross multiplying
y - 1 = -8(x - 1)
y - 1 = -8x +8
y = -8x + 9
In conclusion,
The slope o the line tangent to f(x) at x = 1 is -8
The instantaneous rate off change of f(x) at x = 1 is -8
The equation of line tangent to f(x) at x = 1 is y = -8x + 9
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How to solve 3-2/5x-12/5=10-2x/5
Identities and properties of logarithms
[tex](2a^7b^5\cdot 3ab^8)^2\implies \left( 2^2 a^{(7)(2)} b^{(5)(2)} \cdot 3^2 a^2 b^{(8)(2)}\right)\implies 4a^{14}b^{10}\cdot 9a^2b^{16} \\\\\\ (4)(9)a^{14}a^2b^{10} b^{16}\implies 36a^{14+2}b^{10+16}\implies 36a^{16}b^{26}[/tex]
As part of a major renovation at the beginning of the year, Bonham’s Bakery sold shelving units (store fixtures) that were 13 years old for $2,300 cash. The original cost of the shelves was $7,000 and they had been depreciated on a straight-line basis over an estimated useful life of 15 years with an estimated residual value of $1,300.
Record the sale of the shelving units.
Cash 2300
Accumulated Depreciation 4940
Gain one of fixtures 240
Store fixtures 7000
From the question, we have
Bonham’s Bakery sold shelving units (store fixtures) that were 13 years old for $2,300 cash.
Accumulated Depreciation = (7000-1300)/15*13
=4940
Gain one of fixtures = 240
Store fixtures = 7000
Multiplication:
Mathematicians multiply the numbers in order to calculate the sum of two or more. A fundamental mathematical operation, it is applied frequently in daily life. In order to combine groups of similar sizes, we use multiplication. An illustration of the fundamental concept of repeated addition of the same number is multiplication. The product of two or more numbers refers to the result of the multiplication, and the factors are the amounts that are being multiplied. It is easier to add the same number repeatedly after it has been multiplied.
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Find the probability.
Um A has balls numbered 1 through 8. Urn B has balls numbered 1 through 5. What is the
probability that a 4 is drawn from A followed by a 2 from B?
The probability that a 4 is drawn from from Urn A followed by a 2 from Urn B is 1/40 .
In the question ,
it is given that
the number of balls in Urn A is 8
which are {1,2,3,4,5,6,7,8}
the probability of getting a 4 from Urn A is (P₁) = 1/8
the number of balls in Urn B is 5 .
which are {1,2,3,4,5}
the probability of getting 2 from Urn B is (P₂) = 1/5
So ,the required probability is = P₁ × P₂
On substituting the values of P₁ and P₂ ,
we get
= 1/8 × 1/5
= 1/40
Therefore , the required probability is 1/40 .
The given question is incomplete , the complete question is
Find the probability.
Urn A has balls numbered 1 through 8. Urn B has balls numbered 1 through 5. What is the probability that a 4 is drawn from A followed by a 2 from B?
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Boxes of Valentine’s Day chocolate truffles come in a variety of sizes. The dimensions of the box you decided to purchase are 15 inches by 12 inches by 1.5 inches. If each truffle in this box has a volume of 2 cubic inches, how many truffles are included in the box?
The no. of truffles than can be included in the box is 135.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.
Given, The dimensions of the box you decided to purchase are 15 inches by 12 inches by 1.5 inches.
∴ The volume of the box is,
= (15×12×1.5) inches³.
= 270 inches³.
Given each truffle has a volume of 2 iches³.
∴ No. of truffles than can be included in the box is,
= (270/2).
= 135.
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Question
In 8 years, Estelle's bank account earned $1,270
simple interest at 2.5%. How much had she
deposited in the account?
Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.
According to the question,
We have the following information:
In 8 years, Estelle's bank account earned $1,270 simple interest at 2.5%.
Now, let's take the principal amount to be $x.
We know that the following formula is used to find simple interest:
Simple interest = (principal*rate*time)/100
(x*2.5*8)/100 = 1270
Using the cross multiplication method:
20x = 127000
x = 127000/20
x = $6350
Hence, Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.
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Please help!
Find the amount of money( future value) in an account where 8,800 is deposited ( present value) at an interest rate 6.5% per year compounded continuously and the money is left in the account for 7 years.
The final amount is $ ?
Round your answer to 2 decimal places.
By using the formula for amount of money in a compound interest, it can be calculated that
Amount received after 7 years is $13675.08
What is a compound interest?
If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, then the interest earned is called compound interest.
If p is the principal, r is the rate and n is the time in years, then
amount = [tex]p(1+\frac{r}{100})^n[/tex]
Difference between amount and principal gives the compound interest.
Principal = $8800
Rate = 6.5 %
Time = 7 years
Amount received = [tex]8800(1 + \frac{6.5}{100})^7[/tex]
$13675.08
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Solve for (A) current ratio, (B) acid test (quick), (C) average day's collection (D) asset turnover, and (E) profit margin on sales. Round to nearest hundredth or hundredth percent as needed. Current Assets $ 21,000 Accounts Receivable 4,200 Current Liabilities 16,000 Inventory 3,500 Net Sales 41,000 Total Assets 32,000 Net Income 6,000
a. The current ratio is 1.3125
b. The acid test is 1.09375.
c. The average day collection is 37 days.
d. The asset turnover is 1.28.
e. The profit margin on sales is 14.63%.
How to calculate the current ratio?a. The current ratio will be:
= Current asset / Current liability
= 21000 / 16000
= 1.3125
b. Acid test quick ratio will be:
= (Current asset - Inventory) / Current liability
= (21000 - 3500) / 16000
= 1.09375
c. Average day collection will be:
= Account receivable / (Net sales / 360)
= 4200 / (41000 / 36)
= 4200 / 114
= 37 days.
d. Asset turnover will be:
= Net sales / Total asset
= 41000 / 28000
= 1.28
e. Profit margin will be:
= Net income / Net sales
= 6000 / 41000
= 14.63%
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Find all x ∈ R that are solutions to this equation:
0 = ( 1- X- X^2-...) (2- X- X^2-...)
The solution of the geometric equation is x = 1/2 or x = 1
What is an equation?An equation is a mathematical expression that shows the relationship between variables.
What is a geometic series?A geometric series is the sum of a geometric sequence.
How to find the solution to the equation?Since the equation 0 = ( 1 - X - X²-...) (2 - X - X²-...). To solve this, let the series x + x² + ... = p
So, 0 = ( 1 - X - X²-...) (2 - X - X²-...).
0 = (1 - [X + X²+...) (2 - [X + X²+...).
Substitute x + x² + ... = p. So,
0 = (1 - [X + X²+...) (2 - [X + X²+...).
0 = (1 - p)(2 - p).
So, (1 - p) = 0 or (2 - p) = 0
p = 1 or p = 2
Since x + x² + ... = p, the left side of the equation is the sum to infinity of a geometric series.
What is the sum to infinity of a geometric series?The sum to infinity of the geometric series is given by
S = a/(1 - r) where
a = first term and r = common ratioFor the given series,
a = x and r = xSo, S = a/(1 - r)
= x/(1 - x)
Since S = p, we have that
x/(1 - x) = 1 or x/(1 - x) = 2
So, x = 1 - x or x = 2 - x
x + x = 1 or x + x = 2
2x = 1 or 2x = 2
x = 1/2 or x = 2/2
x = 1/2 or x = 1
So, the solution is x = 1/2 or x = 1
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Please i need help urgently thanks
Answer:
Step-by-step explanation:
rate of change
[tex]=\frac{f(b)-f(a)}{b-a} \\=\frac{f(9)-f(1)}{9-1} \\=\frac{28-20}{8} \\=\frac{8}{8} \\=1[/tex]
Elena collects data to investigate the relationship between the number of bananas she buys at the store, , and the total cost of the bananas, . Which value for the correlation coefficient is most likely to match a line of best fit of the form for this situation?
The correlation coefficient that is most likely to match a line of best fit of the form y = mx + b for this situation is of:
0.9.
What is a correlation coefficient?The correlation coefficient is an index that measures correlation between two variables, assuming numeric values between -1 and 1.
If the correlation coefficient is positive, the relation is positive, that is, they are direct proportional. If the correlation coefficient is negative, they are inverse proportional.
If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the two variables is classified as strong.
In the context of this problem, the variables are listed as follows:
Number of bananas bought.Total price of the bananas.The total price increases with the number of bananas bought, and there is a strong positive relationship between these two variables, hence the coefficient should be greater than 0.6 and the correct option is:
0.9.
Missing InformationThe problem is given by the image shown at the end of the answer.
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I need this for today !!!
Answer:
1. reflection
2.translation
3.rotation
4.translation
5.translation
6.reflection
7.rotation
8.reflection
Hope this helps
have a good day
God bless you!
Write the equation of the line with a slope of 3/2that contains the point ( — 4, − 2).
The equation of line with a slope of 3/2 which passes through point (-4,-2) is y = (3/2)x + 4.
What is the equation of line with the given point and slope?
The equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point (-4, -2 )
x = -4y = -2Slope m = 3/2First, we determine the y-intercept 'b'.
Plug the point and slope slope into the equation of line formula and solve for b.
y = mx + b
-2 = (3/2)(-4) + b
-2 = (3)(-2) + b
-2 = -6 + b
b = -2 + 6
b = 4
Now, plug the slope and y-intercept into y = mx + b to determine the equation of the line.
y = mx + b
y = (3/2)x + 4
Therefore, the equation of the line is y = (3/2)x + 4.
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What are the factors of 4x2 - 4x - 15?
Select TWO correct answers.
2x-5
4x + 5
2x + 3
2x-3
x-3
2x + 5
2x+3 x-3 those are correct
Solve for x
150µ=0.694(x+7.2K)*10^-9
[tex]x=2.16*10^{11}u-7.2k[/tex].
Side note: This answer could be more precise if made usage of more significant figures. For practicality reasons, in this solution we reduced the amount of significant figures to use.
Step-by-step explanation:1. Write the expression.[tex]150u=0.694(x+7.2K)*10^-9[/tex]
2. Solve the parenthesis using the distributive property of multiplication.[tex]150u=[(0.694*x)+(0.694*7.2K)]*10^-9\\\\150u=[0.694x+4.9968k]*10^-9\\ \\150u=10^-9*0.694x+10^-9*4.9968k[/tex]
3. Subtract "10^-9*0.694x" from both sides of the equation.[tex]150u-10^-9*0.694x=10^-9*0.694x-10^-9*0.694x+10^-9*4.9968k\\ \\150u-10^-9*0.694x=10^-9*4.9968k[/tex]
4. Subtract "150µ" from both sides of the equation.[tex]-150u+150u-10^-9*0.694x=10^-9*4.9968k-150u\\ \\-10^-9*0.694x=10^-9*4.9968k-150u[/tex]
5. Divide both sides by "-10^-9*0.694".
[tex]\frac{-10^-9*0.694x}{-10^-9*0.694} =\frac{10^-9*4.9968k-150u}{-10^-9*0.694} \\ \\\frac{-10^-9*0.694x}{-10^-9*0.694} =\frac{10^-9*4.9968k}{-10^-9*0.694}-\frac{150u}{-10^-9*0.694} \\ \\x=-7.2k-(-2.16*10^{11} u)\\ \\x=-7.2k+2.16*10^{11}u\\ \\x=2.16*10^{11}u-7.2k[/tex]
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a coin is tossed 5 times. find the probability that none are tails
Answer:
[tex]( \frac{1}{2} )^5 = \frac{1}{32}[/tex]
Step-by-step explanation:
The probability of "not a tail" is 1/2. The five tosses are independent, so the probability of "not a tail" 5 times in succession is
[tex]\left(\frac{1}{2}\right) \cdot \left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right)[/tex]
Dog food comes in two different sized bags. The 4 lb bag sells for $19.49 while the 30 lb bag sells for $73.99. Which is cheaper per pound and by how much?
Answer:
30 lb bag is cheaper by about $2.40
Step-by-step explanation:
to find per pound we divide
19.49/4= 4.8725
$4.87per pound
$73.99/30=2.46633
$2.47 per pound
30 lb bag is cheaper per pound
4.87-2.47=2.40
hopes this helps please mark brainliest
bill wrote all the numbers from 1 to 1000. how many digits did he write down?
Answer:
2890 digits--------------------------
One - digit numbers1 to 9 ⇒ 9 numbersTwo - digit numbers10 to 99 ⇒ 100 - 10 = 90Three - digit numbers100 to 999 ⇒ 1000 - 100 = 900Four - digit number 1000 ⇒ 1Number of digits1*9 + 2*90 + 3*900 + 1 = 2890Please Help
Find (f+g)(x)if f(x)=4x2-5x+8 and g(x)=2x2+x-2
Answer: (f+g)(x) = 6x²- 4x + 6
Step-by-step explanation:
We add f(x) and g(x) together, (4x²-5x+8) + (2x²+x-2)
Add like terms together, (4x²+2x²) + (-5x+x) +(8-2)
We are left with (f+g)(x) = 6x²- 4x + 6
Customer account "numbers" for a certain company consists of 4 letters followed by 3 single-digit numbers. How many different account numbers are possible if repetitions of letters and digits are allowed?
If the number of different account numbers are possible if repetitions of letters and digits are allowed is:45,697,600,000.
How to determine the total possibilities?Let assume you have 26 choices for each of the first 4 slots and 10 choices for each of the last 5 slots.
Hence,
Total possibilities = (26× 26× 26×26) × (10×10×10×10×10)
Total possibilities = 26^4 × 10^5
Total possibilities = 456976×100000
Total possibilities = 45,697,600,000
Therefore we can assume that the total possibilities is : 45,697,600,000.
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A firecracker is fired straight up into the air out of a window of a building. Its height, in feet, is given by
h - 16t² + 96t + 112, where t is the time, in seconds, the fircracker has been in the air.
At some point in its path it reaches a highest point.
Step-by-step explanation:
I assume our task is to find that point of time, when it reaches the highest point.
and the function is
h(t) = -16t² + 96t + 112
well, a maximum or minimum of a curve (function) is found as a zero solution of the first derivative of the function.
given the nature of the function, the extreme point has to be a maximum (the firecracker goes up and then down again).
h'(t) = -32t + 96
we are looking for the zero :
0 = -32t + 96
32t = 96
t = 3 seconds
so, after 3 seconds, the firecracker reaches its highest point, which is at
-16×3² + 96×3 + 112 = -16×9 + 96×3 + 112 =
= -144 + 288 + 112 = 256 ft
FYI - we know for x = 0 (the starting point) the height of the starting window was 112 ft.
Complete the statement about the model. The model shows that there are 4 pieces that are each (?) ft long.
The correct statement about the model, using proportions, is given as follows:
The model shows that there are 4 pieces that are each 0.75 ft long.
What is a proportion?A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in whichever context of the problem.
The application of proportions in this problem is to find the length of each piece, which is obtained as the division of the total length of the model by the number of pieces, hence:
Length of each piece = Total length/number of pieces.
The measures are given as follows:
Total length: 3 ft.Number of pieces: 4 pieces.Hence the length per piece is given by:
3 ft / 4 = 0.75 ft.
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Answer:
answer is 3/4!!! hope this helped
A plane car fly 300 miles in the same time as it takes a car to go 120 miles. If the car travels 90 mph
slower than the plane, find the speed of the plane.
Using r as your variable to represent the speed of the plane in miles per hour, write an equation
using the information above that can be solved to find the answer to this problem.
Equation:____?
The plane flies___?
The plane flies at a speed of 150mph
A plane can fly 300 miles in the same time as it takes a car to go 120 miles
Let the time taken be t
Let the speed of the plane be x
the car travels 90 mph slower than the plane,
Speed of the car is x - 90
Speed = distance / time
Time taken by plane = time taken by car
300/ x = 120/x - 90
300(x - 90) = 120x
300x - 27000 = 120x
300x - 120x = 27000
180x = 27000
x = 27000/180
x = 150
Therefore, the plane flies at a speed of 150mph
To learn more about speed and distance refer here
https://brainly.com/question/17146782
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