Sarah and Asher began saving money the same day. Sarah's savings can be modeled by f(x) =12x+6
and Asher's savings plan can be modeled by g(x) =9x+30
where x
is the amount of money they had saved after x
weeks. After how many weeks will Sarah and Asher have saved the same amount of money?

Answer:

a) Height of the ledge is 1.6 m.

b) roots of the equation are: [tex]\bf d = 2[/tex] ,  [tex]\bf d = -1[/tex]

c) Maximum height reached = 1.8 m.

Step-by-step explanation:

a) The height of the ledge is the same as the height at which Jake is when he hasn't moved any horizontal distance from the ledge yet, that is, when d = 0:

[tex]h = -0.8(0)^2 + 0.8(0) + 1.6[/tex]

⇒ [tex]\bf h = 1.6 \space\ m[/tex]

∴ Height of the ledge is 1.6 m.

b) The x-intercepts occur where y = 0, that is when h = 0:

[tex]-0.8d^2 + 0.8d + 1.6 = 0[/tex]

Divide both sides of the equation by -0.8:

[tex]d^2 - d -2 = 0[/tex]

Factorizing:

⇒ [tex]d^2 -2d + d - 2 = 0[/tex]

⇒ [tex]d(d-2) +1 (d-2) = 0[/tex]

⇒ [tex](d-2)(d+1) = 0[/tex]

⇒ [tex]d - 2 = 0[/tex]    or    [tex]d + 1 = 0[/tex]

∴ roots are :  [tex]\bf d = 2[/tex]   ,   [tex]\bf d = -1[/tex]

c) To find the maximum value of a quadratic equation in the form

y = ax² + bx + c , use the formula:

max = c - (b² / 4a).

Using the formula for [tex]h = -0.8x^2 + 0.8x + 1.6[/tex] :

max h =  [tex]1.6 - ( \frac{0.8^2}{4(-0.8)} )[/tex]

       = 1.8

∴ Maximum height reached = 1.8 m.

Answer:

  a) 1.6 m

  b) -1, 2 meters

  c) 1.8 m

Step-by-step explanation:

Apparently, technology tools are allowed when solving this problem. They readily show you the x- and y-intercepts and the vertex of the graph.

The height of the ledge is the value of h when d=0. It is the constant in the given equation, and the y-intercept of the graph.

The height of the ledge is 1.6 meters.

The x-intercepts are the values of d that make h equal to zero. The graph shows them to be ...

 d = -1

  d = 2 . . . . meters

The maximum height is the "h" coordinate of the vertex (d, h).

The maximum height is 1.8 meters.

__

Additional comment

"x" is the generic independent variable. The horizontal axis of a graph is often called the "x-axis" and places where the graph crosses that axis are called "x-intercepts" even when the independent variable is named something else. Here, the independent variable is "d", not "x".

Similarly, "y" is the generic dependent variable, and the vertical axis of a graph is often called the "y-axis" even when the dependent variable is something else. This is why we refer to h when d=0 as the "y-intercept". It is the point where the graph crosses the vertical axis.

The equation of the graph in which the vertex (4,2) and a=-2 is

y=-2[tex](x-4)^{2}[/tex]+2.

Given that the point of the vertex is (4,2) and a=-2.

Equation is like a relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. It may be a linear equation,quadratic equation, cubic equation or many more depending on the power of variable in the equation.

We know that point of vertex look like (h,k) in the equation and equation look like as under:

y=a[tex](x-h)^{2} +k[/tex].-----------1

So in order to find the equation we have to just put h=4 and k=2 and a=2 in equation 1.

y=-2[tex](x-4)^{2} +2[/tex]

Hence the equation of the graph in which the vertex (4,2) and a=-2 is

y=-2[tex](x-4)^{2}[/tex]+2.

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Transformation which can be used for mapping of one triangle to another are;

What does mapping mean in geometry?

We need to map one triangle to another ;

Hence, for mapping of one triangle to another,

The transformation which can be used from the given options are;

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Answer:

B. translation only

E. rotation then dilation

Step-by-step explanation:

B. translation only

E. rotation then dilation

The correct option for the inequality is

Week 4 = Week 5. Option B. This is further explained below.

Generally,  the relationship between two expressions that do not have the same value is denoted by a sign such as, which means "not equal to," >, which means "greater than," or, which means "less than."

In conclusion, When converted to decimal form, Week 5's score comes out to -1.8, which is the same as Week 4's score.

Week 4 = Week 5

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Answer:

The Answer Is B

Step-by-step explanation:

Week 4 = Week 5

Answer: 84

Step-by-step explanation:

When substituting this question into an algebraic equation you can write it as:

21=.25x

(x clearly represents the number you are trying to find)

When you divide both sides by .25 to isolate x you get x=84

Answer:

14 3/8 ft^2

Step-by-step explanation:

Area = length * width

=   2 7/8 * 5

=  23/8 * 5

= 115/8

= 14 3/8 ft^2.

Answer:

Step-by-step explanation:

sinA(1+sin^2A) = cos^2A

sinA(2 -cos^2A) = cos^2A

Squaring both sides,

sin^2A(4-4cos^2A +cos^4A) = cos^4A

(1-cos^2A)(4-4cos^2A +cos^4A) = cos^4A

4-4cos^2A +cos^4A-4cos^2A+4cos^4A-cos^6A = cos^4A

4 -cos^6A +4cos^4A -8cos^2A = 0

cos^6A - 4 cos^4A + 8cos^2A = 4

hence proveproven

Answer:

Step-by-step explanation:

sinA+sin

3

A=cos

2

A

⇒sinA[1+sin

2

A]=cos

2

A

⇒sinA[1+1−cos

2

A]=cos

2

A

squaring on both sides.

⇒sin

2

A[4+cos

4

A−4cos

2

A]=cos

4

A

⇒(1−cos

2

A)[4+cos

4

A−9cos

2

A]=cos

4

A

⇒4+cos

4

A−4cos

2

A−64cot

2

A−cos

6

A+9cos

4

A=cos

4

A

⇒

cos

6

A−4cos

4

A+8cos

2

A=4

​

Hence Prove

Formula  [tex]\text { area }=1 / 2 \times \text { base } \times \text { height }=1 / 2 \times 2 \pi r \times r=\pi r^{2}[/tex]  for the circumference of a circle.

Archimedes stated in his Proposition that the area of a circle is equal to the area of a triangle with a base equal to the circumference and a height equal to the radius: (1/2)(r · 2πr) = πr2. Archimedes arrived at his approximation of the circumference of the circle by increasing the number of sides of the hexagon. Archimedes claimed that the area of any circle is equal to the area of a right triangle, where the radius of the circle is represented by one side and the circumference by the other.

Archimedes demonstrated using a similar method that the area of a circle of diameter D is equal to the area of a right-angled triangle with one side equal to the radius and the other to the circumference of the circle on the right angle.

Formula for the circumference of a circle:

A circle's area is equal to pi times the radius squared (A = r2). Discover how to apply this formula to determine a circle's area given its diameter.

The circumference is diameter x pi, or 2 x radius x pi.

[tex]\text { area }=1 / 2 \times \text { base } \times \text { height }=1 / 2 \times 2 \pi r \times r=\pi r^{2}[/tex].

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Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

You need to add the amount Shawna & Ryan ate together, then subtract it from 1 to find the amount of pizza that was left for Dominic to eat.

[tex]\frac{1}{3}[/tex] + [tex]\frac{1}{2}[/tex] = ?

Make all the denominators the same to add fractions.

[tex]\frac{1}{3}[/tex]  is [tex]\frac{2}{6}[/tex]

[tex]\frac{1}{2}[/tex]  is [tex]\frac{3}{6}[/tex]

[tex]\frac{2}{6}[/tex] +  [tex]\frac{3}{6}[/tex] = [tex]\frac{5}{6}[/tex]

1 -  [tex]\frac{5}{6}[/tex] = [tex]\frac{1}{6}[/tex]

4) [tex]A_{QRST} = A_{Q'R'S'T'} = 9[/tex].

5) The areas of the rectangles QRST and Q'R'S'T' are the same since the translation of the geometric loci conserved the Euclidean distance.

6) x = 1, w = 3, y = - 1/4, z = 1/3

Rigid transformations are transformations applied on geometric loci such that Euclidean distance is conserved. In this question we have applications of translations, a kind of rigid transformation.

Exercise 4

In this part we must determine the areas of rectangles QRST and Q'R'S'T':

Rectangle QRST

A = RS · QT

A = 3 · 3

A = 9

Rectangle Q'R'S'T'

Q'(x, y) = (2, - 3) + (- 3, - 3)

Q'(x, y) = (- 1, - 6)

R'(x, y) = (2, 4) + (- 3, - 3)

R'(x, y) = (- 1, 1)

S'(x, y) = (5, 4) + (- 3, - 3)

S'(x, y) = (2, 1)

T'(x, y) = (5, - 3) + (- 3, - 3)

T'(x, y) = (2, - 6)

A = R'S' · Q'T'

A = 3 · 3

A = 9

The rectangles QRST and Q'R'S'T' have both an area of 9 square units.

Exercise 5

The areas of the rectangles QRST and Q'R'S'T' are the same since the translation of the geometric loci conserved the Euclidean distance.

Exercise 6

In this case, we must solve the following equations:

PQ = A'(x, y) - A(x, y)

(4, 1) = (2 · x + 1, 4) - (- 1, w)

(4, 1) = (2 · x + 2, 4 - w)

(4, 1) = (2 · x, - w) + (2, 4)

(2, - 3) = (2 · x, - w)

(x, w) = (1, 3)

PQ = B'(x, y) - B(x, y)

(4, 1) = (3, 3 · z) - (8 · y - 1, 1)

(4, 1) = (2 - 8 · y, 3 · z)

(4, 1) = (- 8 · y, 3 · z) + (2, 0)

(2, 1) = (- 8 · y, 3 · z)

(y, z) = (- 1/4, 1/3)

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Answer:

64

Step-by-step explanation:

evaluate by substituting x = 16 and x = 0 into f(x)

f(16) = 4(16) - 8 = 64 - 8 = 56

f(0) = 4(0) - 8 = 0 - 8 = - 8

then

f(16) - f(0) = 56 - (- 8) = 56 + 8 = 64

Answer:

64

Step-by-step explanation:

f(x) = 4x - 8

First find f(16)

f(16) = 4(16) -8 =64-8=56

Then find f(0) = 4)0) -8 = -8

f(16) - f(0) = 56 - (-8) = 56+8 = 64

The missing information of the triangle is C = 63°, b ≈ 28.084 and c ≈ 25.084. (Correct choice: C)

In this question we have a triangle with a known side lengths and two known angle measures. First, we find the missing angle by Euclidean geometry:

C = 180° - 94° - 23°

C = 63°

Lastly, we determine the missing sides by law of sines:

[tex]b = 11 \times \frac{\sin 94^{\circ}}{\sin 23^{\circ}}[/tex]

b ≈ 28.084

[tex]c = 11 \times \frac{\sin 63^{\circ}}{\sin 23^{\circ}}[/tex]

c ≈ 25.084

The missing information of the triangle is C = 63°, b ≈ 28.084 and c ≈ 25.084. (Correct choice: C)

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The ratio of the lateral surface area of cone A to the lateral surface area of cylinder B is equal to [tex]r = \frac{1}{2}\cdot \frac{\sqrt{r^{2}+h^{2}}}{h}[/tex]. (Correct choice: False)

In accordance with space geometry, the lateral areas of the cone and cylinder are described by the following equations:

Cone

[tex]A_{l} = \pi \cdot r \cdot \sqrt{r^{2}+h^{2}}[/tex]     (1)

Cylinder

[tex]A_{l} = 2\pi\cdot r\cdot h[/tex]     (2)

If we divide (2) by (1), then we have the following ratio:

[tex]r = \frac{1}{2}\cdot \frac{\sqrt{r^{2}+h^{2}}}{h}[/tex]

The ratio of the lateral surface area of cone A to the lateral surface area of cylinder B is equal to [tex]r = \frac{1}{2}\cdot \frac{\sqrt{r^{2}+h^{2}}}{h}[/tex]. (Correct choice: False)

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Answer:

43.5 unit^2.

Step-by-step explanation:

Area of the triangle

= 1/2 * base * height

= 1/2 * AB * AC.

AB = √ [(6-1)^2 + (6-8)^2] = √29

AC = √ [(8 - (-7))^2 + (1 - (-5)^2] = √261

So the area = 1/2 * √29  * √261

                    = 43.5

Answer:

[tex]\frac{4}{15}[/tex]

Step-by-step explanation:

Given the following question:

[tex]\frac{1}{5} \div\frac{3}{4}[/tex]

To find the answer we will use KCF (Keep, Change, Flip) apply it to the following question and then complete by multiplying and reducing. If needed of course.

[tex]\frac{1}{5} \div\frac{3}{4}[/tex]
Apply KCF:
[tex]\frac{1}{5} \div\frac{3}{4}=\frac{1}{5} \times\frac{4}{3}[/tex]
[tex]\frac{1}{5} \times\frac{4}{3}[/tex]
Solve:
[tex]1\times4=4[/tex]
[tex]5\times3=15[/tex]
[tex]=\frac{4}{15}[/tex]
Answer is in simplest terms.

Which means your answer is the first option or "4/15."

Hope this helps.

Answer:

[tex]\text{Midpoint} = (1, \; 1)[/tex]

Step-by-step explanation:

[tex]M = (x_M, \; y_M)[/tex]

[tex]M = \left(\dfrac{x_1 + x_2}{2}, \; \dfrac{y_1 + y_2}{2}\right)[/tex]

[tex]M = \left(\dfrac{0 + 2}{2}, \; \dfrac{4 + -2}{2}\right)[/tex]

[tex]M = \left(\dfrac{2}{2}, \; \dfrac{2}{2}\right)[/tex]

[tex]M = (1, \; 1)[/tex]

Answer: (1, 1)

Step by Step Explanation:

The midpoint formula is (x + x/2 ,  y + y/2)

If you plug in the coordinates it looks like this

( 0 + 2/2  ,  4 + (-2)/2)

That turns into this:

(2/2  ,  2/2)                              

Which gives you the final answer of (1, 1)          

The z-score is -0.428

A z-score, also known as a standard score, provides information on how far a data point is from the mean. Technically speaking, however, it's a measurement of how many standard deviations a raw score is from or above the population mean.

You can plot a z-score on a normal distribution curve.

You must be aware of the mean and population standard deviation to use a z-score.

Z-scores allow results to be compared to a "normal" population.

According to the question,

x=500

μ=533

σ=77

z-score=(x-μ)/σ

On substituting the values,

z-score=(500-533)/77

           = -0.428

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Answer:

That is a variable.

Step-by-step explanation:

- opposed to a constant which is known and does not change.

In data analytics, a population refers to all possible data values in a certain dataset

Data analysis is a systematic computer-aided analysis of data or statistics. [1] It is used to discover, interpret, and convey meaningful patterns in the data. It also includes applying data patterns for effective decision-making.

It may be useful in areas where there is a lot of recorded information. The analysis relies on the simultaneous application of statistics, computer programming, and operations research to quantify performance.

Organizations can apply analytics to business data to describe, predict, and improve business performance. Areas within the analysis include descriptive analysis, diagnostic analysis, predictive analysis, prescriptive analysis, and cognitive analysis in particular. [2] Analysis can be applied in various fields such as marketing, management, finance, online systems, information security, and software services.

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Answer:

x-2

Step-by-step explanation:

The formula for area of rectangle is length x width
And we know that width is x-16
And we know that the area is [tex]x^{2} -18x +32[/tex]

So we know that when x-2 is multiplied with  x-16, it gives off [tex]x^{2} -18x +32[/tex]

The correct option is option () Connect the point with a line through the center of the circle.

According to the problem,

So, the correct option is option ()Connect the point with a line through the center of the circle.

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Answer:

The last answer is correct.

Step-by-step explanation:

The w stands for the number of words that she can have.  She has to have at least 150 words so the w has to be equal to 150 or greater.  The w also has to be less then or equal to 500

Answer:

y < x

y < 4

Step-by-step explanation:

Dotted line means < or >, and since the shaded region is below the lines y = 4 and y = x, the answer is A.

Answer:

f[g(4)] = 4

Step-by-step explanation:

Given table:

[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} x & -6 & -4 & 1 & 3 & 4\\\cline{1-6} f(x) & 4 & -1 & -6 & 1 & 3 \\\cline{1-6} g(x) & 1 & 4 & 3 & -4 & -6 \\\cline{1-6}\end{array}[/tex]

f[g(4)] is a composite function.

When calculating composite functions, always work from inside the brackets out.

Begin with g(4):  g(4) is the value of function g(x) when x = 4.

From inspection of the given table, g(4) = -6

Therefore, f[g(4)] = f(-6)

f(-6) is the value of function f(x) when x = -6.

From inspection of the given table, f(-6) = 4

Therefore, f[g(4)] = 4

As we can see

So

The equation of the parent square root function to represent the equation of the graphed function will be, y=√x-2

According to the statement

we have to show the square root function as a equation in the graphical representation.

So,

we know that the definition of a

Graph a diagram showing the relation between variable quantities, typically of two variables and it also show the relation between more than two variables.

Now, we know that the definition of Equation is a mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

And the equation obtained from the graph is a y=√x-2 by a some calculations in the graph.

So, The equation of the parent square root function to represent the equation of the graphed function will be, y=√x-2

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Answer:

2/3

Step-by-step explanation:

1/3 cup powdered sugar

2/6 cup brown sugar

Reduce 2/6 to 1/3.

1/3 + 1/3 = 2/3

By definite integrals and area formula of a rectangle, we find that the area of the region in the first quadrant is 147 / 4 square units.

Integrals can be used to determine the area of regions bounded by curves set on Cartesian plane. The upper limit of the integral of the question is initially found:

(2 / 3) · x = 7

x = 21 / 2

The area can be defined as an rectangle in the first quadrant minus the area below the linear equation:

[tex]A = \left(\frac{21}{2} \right) \cdot (7) - \frac{2}{3} \int\limits^{\frac{21}{2} }_{0} {x} \, dx[/tex]

[tex]A = \frac{147}{2} - \frac{1}{3} \cdot \left[\left(\frac{21}{2} \right)^{2}-0^{2}\right][/tex]

A = 147/4

By definite integrals and area formula of a rectangle, we find that the area of the region in the first quadrant is 147 / 4 square units.

The statement is poorly formatted and incomplete. Correct form is shown below:

A region in the first quadrant is bounded by the line y = (2/3) · x, the y-axis and the horizontal line y = 7. Determine the area of the region.

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Step-by-step explanation:

When evaluating piecewise function, make sure the x value satisfies the function we use.

since 5>3, we use the second equations

That function is a constant function, this means at any x>3, exclusive, we will have a y value of -1.

So

[tex]f(5) = - 1[/tex]

Answer:

80

Step-by-step explanation:

The sum of the interior angles of a triangle is 180.  Subtract out the 2 angles that you know.

180 - 70 - 30 = 80

Answer:

c

Step-by-step explanation:

im smart like that