Since triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1), the scale factor used is: D. 1/3.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Scale factor = -1/-3
Scale factor = 1/3.
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Answer: D = 1/3
Step-by-step explanation: Took the test and got it right :>
Find the equation of the line shown
Answer:
using the equation of the straight line we solve
Write an exponential decay function to model each situation. Then estimate the value of x for the given value of f(x)
initial value: 100
decay factor: .95
f(x)=60
Answer:
f(x) = 100(0.95^x)x ≈ 9.959 for f(x) = 60Step-by-step explanation:
You want the value of x that makes f(x) = 60, when f(x) is the exponential function with an initial value of 100 and a decay factor of 0.95.
Exponential functionThe form of an exponential function is ...
f(x) = (initial value) · (decay factor)^x
ApplicationFor the given initial value and decay factor, the function is ...
f(x) = 100 (0.95^x)
Solving for x, we find ...
f(x)/100 = 0.95^x
log(f(x)/100) = x·log(0.95)
x = log(f(x)/100)/log(0.95)
For f(x) = 60, the value of x is about ...
x = log(60/100)/log(0.95) ≈ 9.959
The value of x is about 9.959.
determine the probability that the first child of clara and charles will be a boy with both albinism and hemophilia.
The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.
The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%. Albinism and hemophilia are both recessive genetic conditions, meaning that both parents must have the recessive gene in order for a child to be born with either condition. Since neither Clara nor Charles have either condition, the probability that their first child will be a boy with both albinism and hemophilia is 0%.
The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.
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the sum of a five-term arithmetic sequence is 100. if all terms are positive integers, what is the smallest possible value for a term?
The smallest possible value for a term in the five-term arithmetic sequence is 1.The sum of a five-term arithmetic sequence is given as 100 and all terms are positive integers. Let's call the first term "a" and the common difference "d".
The five terms can be represented as a, a + d, a + 2d, a + 3d, and a + 4d. The sum of these five terms is 100, which can be represented as:
a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 100
Simplifying the expression, we get:
5a + 10d = 100
Dividing both sides by 5, we get:
a + 2d = 20
Since all terms are positive integers, it follows that "a" and "d" must also be positive integers. The smallest possible value for "a" is 1, and the smallest possible value for "d" is 1. Substituting these values into the expression for "a + 2d" yields:
1 + 2 * 1 = 3
Thus, the smallest possible value for a term in the five-term arithmetic sequence is 1.
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write a recursive rule for the sequence: 100,3,97,-94,191
The recursive rule for the sequence is T(n) = T(n - 2) - T(n - 1)
How to determine the recursive rule for the sequence?From the question, we have the following parameters that can be used in our computation:
100, 3 , 97 ,-94 , 191
The above definitions imply that we simply subtract the current from the previous term to get the next term
Using the above as a guide,
So, we have the following representation
T(n) = T(n - 2) - T(n - 1)
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find each sum by graphing on the complex plane. (-4-4i)+(4+2i)
Answer:
To find the sum of two complex numbers on the complex plane, we can simply add their real and imaginary parts separately. The real part of a complex number is the x-coordinate on the complex plane, while the imaginary part is the y-coordinate.
In this case, the two complex numbers are (-4-4i) and (4+2i). To find their sum, we add their real and imaginary parts separately:
Real part: -4 + 4 = 0
Imaginary part: -4 + 2 = -2
So, the sum of (-4-4i) and (4+2i) is 0 - 2i, which can be represented as a point on the complex plane with x-coordinate 0 and y-coordinate -2.
Step-by-step explanation:
Mr. Ford wants to better understand the value of used cars over time. He reviewed some
used-car ads and recorded the relationship between age and price in a table. Finally, he
calculated a line of best fit.
Used cars
Age in years (x) 3 6 4
2
6
Price (y) $15,000 $8,000 $12,000 $5,000 $19,000 $10,000
The equation for the line of best fit is y = -2,200x + 22,000.
Based on the equation, what estimates can you make about the used cars Mr. Ford reviewed?
Select all that apply.
They are worth roughly $2,200 less now than when they were new:
They likely had an average price around $22,000 when new.
They typically lose $2,200 of value per year.
At 5 years old, they had an average value of around $11,000.
You can estimate that the used cars Mr. Ford reviewed were worth roughly $2,200 less now than when they were new, had an average price of around $22,000 when new, and typically lose $2,200 of value per year. (option 1, 2, 3)
To calculate this, you can substitute the x-values from the table into the equation and solve for y. For example, when x is 3,
y = -2,200(3) + 22,000 = $15,000which is the price of the car when it was 3 years old. This same formula can be used to calculate the price of the car at other age values and shows that the car loses an average of $2,200 of value per year. At 5 years old, the equation would be
y = -2,200(5) + 22,000 = $11,000which is the average value of the used car at that age.
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Complete Question:
Mr. Ford wants to better understand the value of used cars over time. He reviewed some used-car ads and recorded the relationship between age and price in a table. Finally, he calculated a line of best fit. Used cars Age in years (x) 3 6 4 2 6
Price (y) $15,000 $8,000 $12,000 $5,000 $19,000 $10,000
The equation for the line of best fit is y = -2,200x + 22,000.
Based on the equation, what estimates can you make about the used cars Mr. Ford reviewed?
Select all that apply.
They are worth roughly $2,200 less now than when they were new:They likely had an average price of around $22,000 when new.They typically lose $2,200 of value per year.At 5 years old, they had an average value of around $11,000.a right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters. what is the surface area in square centimeters if the height is 2 centimeters?
The surface area of the right triangular prism with legs of 5 centimeters and 12 centimeters, a hypotenuse of 13 centimeters, and a height of 2 centimeters is 108 square centimeters.
Surface area refers to the total area of the surface of a three-dimensional object. When it comes to a right triangular prism, the surface area includes the area of all six faces.
Let's call the height of the triangular prism "h" and label the legs of the triangle "a" and "b". Using these values, we can find the area of the base of the triangular prism. The area of a right triangle is equal to 1/2 times the product of the legs, so the area of the base is
=> (1/2) * a * b = (1/2) * 5 * 12 = 30 square centimeters.
Next, we need to find the surface area of each of the three lateral faces. Each of these faces is a rectangle, so we can find the area by multiplying the height of the prism by the length of one of the sides of the triangle base.
The length of one side of the triangle base is equal to the hypotenuse, which is 13 centimeters. So, the surface area of each of the three lateral faces is
=> h * 13 = 2 * 13 = 26 square centimeters.
Finally, we can find the total surface area by adding the surface area of the base and the surface area of the three lateral faces.
The surface area of the base is 30 square centimeters, and the surface area of each lateral face is 26 square centimeters, so the total surface area is
=> 30 + 3 * 26 = 30 + 78 = 108 square centimeters.
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TRIG STUFF EASY WILL GIVE BRAINLIEST IF ALL ARE CORRECT
Answer:
x = 46.2 (nearest tenth)KN = 34.5 (nearest tenth)KL = 41.1 (nearest tenth)x = 15.7 (nearest tenth)Step-by-step explanation:
To find the missing side lengths in the given right triangles, use trigonometric ratios.
[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
From inspection of the first triangle ABC, we have been given the angle, the side opposite the angle and the side adjacent the angle.
θ = 18°O = 15A = xTherefore, to calculate the length of the adjacent side, x, substitute the values into the tangent ratio:
[tex]\implies \tan 18^{\circ}=\dfrac{15}{x}[/tex]
[tex]\implies x\tan 18^{\circ}=15[/tex]
[tex]\implies x=\dfrac{15}{\tan 18^{\circ}}[/tex]
[tex]\implies x=46.165253...[/tex]
[tex]\implies x=46.2\;\;\sf(nearest\;tenth)[/tex]
----------------------------------------------------------------------------------------
Triangle LMN is a right triangle. Interior angles of a triangle sum to 180°.
Therefore, as m∠M = 50° and m∠MLN = 90°, then m∠MNL = 40°.
As KN is perpendicular to NM and m∠MNL = 40° then m∠KNL = 50°.
As KL is parallel to NM, then m∠K = 90°. Therefore, m∠KLN = 40°.
(Refer to the attached diagram).
For right triangle LMN, we have been given the angle (∠M) and the side adjacent to the angle (LM). To find an expression for the length of the side opposite the angle (LN), use the tangent ratio:
[tex]\implies \tan 50^{\circ}=\dfrac{LN}{45}[/tex]
[tex]\implies LN=45\tan 50^{\circ}[/tex]
LN is the hypotenuse of right triangle KLN.
If we use ∠KNL as θ, then side KN is adjacent to the angle.
Therefore, to find the KN use the cosine ratio:
[tex]\implies \cos 50^{\circ}=\dfrac{KN}{LN}[/tex]
[tex]\implies \cos 50^{\circ}=\dfrac{KN}{45\tan 50^{\circ}}[/tex]
[tex]\implies KN=45\tan 50^{\circ}\cos 50^{\circ}[/tex]
[tex]\implies KN=34.471999...[/tex]
[tex]\implies KN=34.5\;\; \sf (nearest\;tenth)[/tex]
As KL is the side opposite ∠KNL, to find KL use the sine ratio:
[tex]\implies \sin 50^{\circ}=\dfrac{KL}{LN}[/tex]
[tex]\implies \sin50^{\circ}=\dfrac{KL}{45\tan 50^{\circ}}[/tex]
[tex]\implies KL=45\tan 50^{\circ}\sin50^{\circ}[/tex]
[tex]\implies KL=41.0821297...[/tex]
[tex]\implies KL=41.1\;\;\sf (nearest\;tenth)[/tex]
----------------------------------------------------------------------------------------
From inspection of the second triangle ABC, we have been given the angle, the side adjacent the angle and the hypotenuse.
θ = 70°A = xH = 46Therefore, to calculate the length of the adjacent side, x, substitute the values into the cosine ratio:
[tex]\implies \cos 70^{\circ}=\dfrac{x}{46}[/tex]
[tex]\implies x=46\cos 70^{\circ}[/tex]
[tex]\implies x=15.732926...[/tex]
[tex]\implies x=15.7\;\;\sf(nearest\;tenth)[/tex]
Need help trying to get at least a 80
Answer:
B
Step-by-step explanation:
cause the premeter is way around the area
Answer:
B. V = pi*r^2*H/6
Step-by-step explanation:
The formula for the volume of a cone is V=pi*r^2*h/3, where h is the height of the cone, and r is the radius of the base. In this case, the hieght of the cone is equal to half the height of the cylinder, so it's h=H/2
If we substitute, we get
V = pi * r^2 * h / 3 = pi * r^2 * (H / 2) / 3 = pi * r^2 * H / 6
The parking lot at the local ice cream store has 4 cylindrical posts in front of the store. These post need to be painted bright yellow. The diameter of each post is 1 foot and each post is 3 feet high.
Use 3. 14 for pi.
Approximately how many square feet must be painted if all 4 posts are painted?
If all 4 posts are painted, 44 square feet must be painted.
We know that the formula for the surface area of the cylinder is:
A = 2πrh + 2πr²
Here, the dimensions of the each cylindrical post:
the diameter d = 1 foot and the height is 3 feet high.
So, the radius r = 0.5 ft and height h = 3 ft
Let us assume that the surface area of one post be A₁
Using above formula of surface area of cylinder,
A₁ = 2πr(h + r)
A₁ = 2 × π × 0.5 × (3 + 0.5)
A₁ = 2 × 3.14 × 0.5 × (3.5)
A₁ = 10.99
A₁ ≈ 11 sq.ft.
So, the total surface area of 4 cylindrical posts would be,
A = 4 × A₁
A = 4 × 11
A = 44 sq.ft.
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Given two vertices and the centroid of a triangle , how many possible locations are there for the third vertex?
Answer:i don't realy now so 5 point 3
[tex]\sqrt[4]{\frac{-15}{16} }[/tex]
Need help doing this please. I think it might be simple, just kinda unsure how to do it.
The solution to the expression ⁴√(-15/16) is (-15/16)^1/4
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
⁴√(-15/16)
The above expression means that we calculate the 4th root of -15/16
-15 and 16 do not have perfect fourth roots
This means that the expression can only be rewritten as
(-15/16)^1/4
It cannot be evaluated
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Every year, 4% of people drop out of their course at
SmartyPants University. 3,168 people made it to the end of this
year. How many people started this year?
On Monday, 5 painters took 7 hours and 36 minutes to paint an office.
On Tuesday, 8 painters are painting another office the same size.
a) Assuming the painters work at the same rate, how long will it take 8 painters to paint the office?
Give your answer in hours and minutes.
The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.
How to calculate working time for a certain number of workers?On Monday, 5 painters took 7 hours and 36 minutes to paint an office.On Tuesday, 8 painters are painting another office with the same size.If the they work at the same rate, find the time needed for the 8 painters to finish their job!
Let's say
w = number of workerst = time durationWe convert the unit of time in hours.
t₁ = 7 h 36 min
t₁ = (7 + 36/60) h
t₁ = (7 + 0.6) h
t₁ = 7.6 hours
If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,
w₁/w₂ = t₁/t₂
5/8 = 7.6/t₂
t₂ = 8/5 × 7.6
t₂ = 12.16 hours
In hours and minutes,
t₂ = 12 h + (0.16 × 60) min
t₂ = 12 h 9.6 min
Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.
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Look at the digram.
If AB BC and AB = 18 inches, AE = 5 inches, and CE = 6 inches, what is the length of AD?
A. 1.5 inches
B. 2.5 inches
C. 6.5 inches
D. 7.5 inches
Length of AD is, 2.5 inches
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
Values are,
AB = 18 inches,
AE = 5 inches,
CE = 6 inches,
Let the length of ED = x
Now, By the figure,
⇒ ΔABD ≈ ΔECD
Hence, By definition of proportional we get;
⇒ AB / AD = EC / ED
⇒ AB / (AE + ED) = EC / ED
⇒ 18 / (5 + x) = 6 / x
⇒ 3x = 5 + x
⇒ 3x - x =5
⇒ 2x = 5
⇒ x = 2.5 inches
Thus, Length of AD is, 2.5 inches
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Geometric number between 7 and 28.
Answer: 16
Step-by-step explanation:
The geometric number between 7 and 28 is 16. Geometric numbers are the numbers you get by multiplying by a factor. If we multiply by 2 for this common geometric sequence, we get 16:
1 * 2 = 2, 2 * 2 = 4, 4 * 2 = 8, 8 * 2 = 16,16 * 2 = 32, etc.
7 < 16 < 28
Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup.
How many grams of 25% sugar syrup did Samantha use?
Pls help :D Thxs
Samantha used 120 grams of 25% sugar syrup.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup.
Let Samantha used y grams of 25% sugar syrup.
Then, she used (120 - y) grams of 10% sugar syrup.
We know that the final concentration of sugar syrup is 15%, which means that 15% of the total 120 grams of the syrup is sugar.
This can be expressed as:
0.15 x (y + (120 - y)) = 0.15 x 120
Expanding and simplifying the equation, we get:
0.15y + 0.15 x 120 - 0.15y = 18
0.15 x 120 = 18
Solving for y, we get:
y = 120 x 18 / (0.15 x 120)
= 120 x 18 / 18
= 120.
Hence, Samantha used 120 grams of 25% sugar syrup.
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Answer:
work hard you can get it
Step-by-step explanation:
lol
Given: KLMN is a trapezoid, KL=MN,
m∠1=m∠2,
LM:KN = 8/9, PKLMN=132
Find The length of midsegment
KLMN is a trapezoid where KL=MN and m∠1=m∠2 . It is also given that LM:KN = 8/9 and PKLMN=132.The midsegment is 34 units long.
The trapezoidal shape KLMN, where KL = MN.
m∠1=m∠2
Moreover, LM/KN = 8/9
Additionally, KLMN's perimeter is 132 units.
The midsegment's size (KM).
We can see that in the above case, KM is a transversal in relation to the parallel lines LM and KN. which implies,
∠KML=∠MKN
∠1=∠2
Two base angles are clearly equal. So, KLM and KMN are isosceles triangles.
Using the side ratios of two triangles as an example,
= KL: LM: MN: KN
= 8 : 8 : 8 : 9
The ratio units add out to 8 + 8 + 8 + 9 = 33. Consequently, each ratio's value is,
=[tex]\frac{perimeter}{33} \\\\\frac{132}{33} \\\\=4[/tex]
The segment LM's length is thus,
LM=8×4=32
Additionally, section KN's length is
KN=9×4=36
Taking the average of LM and KN as, one can then determine the length of the midsegment KM.
[tex]KM=\frac{LM+KN}{2} \\\\\\KM=\frac{32+36}{2}[/tex]
KE=34
As a result, the midsegment is 34 units long.
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I need help with this question ASP
The greater surface area with similar volume will be of the side, 6ft, 2ft and 2ft.
What is cube?
The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.
In the given box it is given sides are 2, 3 and 4 ft.
So the volume of the rectangular prism is V = 2*3*4 = 24 ft².
So the greater surface area in the given description is 6ft, 2ft and 2ft.
Where the surface area will be 12ft ²
Hence The greater surface area with similar volume will be of the side, 6ft, 2ft and 2ft.
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****
Identify the transformations that have been applied to the parent function
y=-1/(x-3)²-5.
Select all that apply.
Oshift 3 to the left
stretch
reflection over the x-axis
Oshift 5 up
Oshift 3 to the right
Oshift 5 down
O compression
Answer:
Step-by-step explanation:
The transformations that have been applied to the parent function y = 1/x^2 are:
shift 3 units to the right
shift 5 units down
reflection over the x-axis
So the correct options are:
shift 3 to the right
shift 5 down
reflection over the x-axis
32c as a percentage of R3. 80
Answer:
40%
Step-by-step explanation:
32 out of 80 as a percentage it is 40%
(6 + 12.5a) − (8 + 2.9a)
0.96a + (−14)
9.6a + (−2)
15.4a + (−2)
15.4a + (−14) PLS HELP
Answer:
9.6a + (-2)
Step-by-step explanation:
(6 + 12.5a) - (8 + 2.9a) Distribute the negative sign
6 + 12.5a - 8 - 2.9a Combine like terms
12.5a - 2.9a +6 - 8
9.6a + (-2)
the population of all standardized exam scores has a mean of 500 and a standard deviation of 100. twenty-five students in a professor's class take the exam, and their average score is 525. what is the z statistic that is associated with the class's average?
The z statistic that is associated with the class's average is 1.25.
In the given question the population of all standardized ex scores has a mean of 500 and a standard deviation of 100 . Twenty-five students in a professor's class take the ex , and their average score is 525.
We have to find z statistic that is associated with the class's average.
n = 25
μ = 500
σ = 100
[tex]\bar X[/tex] = 525
Then ,
z statistic = [tex]\frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt n} }[/tex]
putting the value in the formula:
z statistic = (525-500)/(100/\sqrt 25)
z statistic = (25)/(100/5)
z statistic = (25)/(20)
z statistic = 1.25
Therefore,
The z statistic that is associated with the class's average is 1.25.
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A student was trying to write an exponential function to represent a fish population in a local stream decreasing at a rate of 3% per year. The original population was 48,000. The student made an error when writing their exponential function. Find and explain the error in the student’s work below.
y=48,000(1.03)^x
The error made by the student in the exponential function, y = 48,000(1.03)^x is that the function represented an exponential growth rather than an exponential decay.
What is an exponential function?An exponential function is written in the form y = abˣ.
In the exponential function, the exponent, x is a variable.
Annual decreasing rate of the fish population = 3% or 0.03
Original population = 48,000
Let the number of years = x
Exponential function: 48,000 (1 - 0.03)^x
= 48,000(0.97)^x
Thus, to represent an exponential decay, the exponential function should have been written as y = 48,000(0.97)^x.
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PLEASE PLEASE HELP!!!
Solve √3x + 4 - 2 = 3
a. x = -1
b. x = 7
c. x ≈ 9.7
d. no solution
H
Ex5: Solve for x.(1pt)
D
50°
8.x + 2
F
Em
So, on solving the provided question, we can say that the equation, we have been provided with is x = 48
Equation: What is it?The equal sign (=), which denotes equality, is used to unite two statements in a mathematical equation. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, the equal sign separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14.
A mathematical formula explains the connection between the two sentences on either side of a letter. There is typically just one variable, which also acts as the symbol. As an illustration, 2x - 4 = 2.
the equation, we have been provided with is
x + 2 = 50
x = 50-2
x = 48
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Maeve currently has $130 and plans to earn more money each of the 8 weekends this summer. She wants at least $1,250 by the end of the summer. How much does she need to earn each weekend? Assume she earns the same amount each weekend. Solve her problem, and then graph the solution on a number line.
Answer: $140 each weekend
Step-by-step explanation:
$1250 - $130 = $1,120
$1,120 divided by 8 weekends = $140
If the graph of f(x) = 9* is shifted 2 units to the right, then what would be the equation of the new graph?
The equation of the new graph is f(x) = 9^(x - 2)
What would be the equation of the new graph?From the question, we have the following parameters that can be used in our computation:
f(x) = 9^x
Also, we have
shifted 2 units to the right,
This is represented as
(x, y) = (x - 2, y)
Substitute the known values in the above equation, so, we have the following representation
f(x) = 9^(x - 2)
Hence, the function is f(x) = 9^(x - 2)
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IT NOT EIGHT
Factor 56−16 using the GCF.
56−16=
Answer:
It should be 8...
Step-by-step explanation:
16 / 8 = 2 and there is no higher number 16 that can be divided by. 56 is dividable by 8 so it makes sense.
Also 56 isn't dividable by 16