Special air bags are used to protect scientific equipment when a rover lands on the surface of Mars. On Earth, the function approximates an object's downward speed in feet per second as the object hits the ground after bouncing x ft in height. The corresponding function for Mars is compressed vertically by a factor of about 2/3. Estimate to the nearest tenth how fast a rover will hit Mars' surface after a bounce of 15 ft in height.

Answer:

The solution to the inequality [tex]$2|v-7|-4 \geq 42$[/tex] in interval notation is given by [tex]$-16 \leq v \leq 30$[/tex].

Step-by-step explanation:

An absolute value inequality [tex]$2|v-7|-4 \geq 42$[/tex] is given.

It is required to solve the inequality and write the solution in interval form.

To write the solution, first solve the given absolute value inequality algebraically and then write it in interval notation.

Step 1 of 4

The given absolute value inequality is [tex]$2|v-7|-4 \geq 42$[/tex].

Add on both 4 sides,

[tex]$$\begin{aligned}&2|v-7|-4 \geq 42 \\&2|v-7|-4+4 \geq 42+4 \\&2|v-7| \geq 46\end{aligned}$$[/tex]

Step 2 of 4

Divide by 2 on both sides,

[tex]$$\begin{aligned}&\frac{2|v-7|}{2} \geq \frac{46}{2} \\&|v-7| \geq 23\end{aligned}$$[/tex]

The inequality can be written as [tex]$v-7 \leq 23$[/tex] and [tex]$v-7 \geq-23$[/tex]

Step 3 of 4

First solve the inequality, [tex]$v-7 \leq 23$[/tex].

Add 7 on both sides,

[tex]$$\begin{aligned}&v-7 \leq 23 \\&v-7+7 \leq 23+7 \\&v \leq 30\end{aligned}$$[/tex]

Step 4 of 4

Solve the inequality [tex]$v-7 \geq-23$[/tex].

Add 7 on both sides,

[tex]$$\begin{aligned}&v-7 \geq-23 \\&v-7+7 \geq-23+7 \\&v \geq-16\end{aligned}$$[/tex]

The solution of the inequality in interval notation is given by [tex]$-16 \leq v \leq 30$[/tex].

The computation shows that the thickness of the beam is 3.75 inches.

11. The thickness of the beam will be:

= 3/4 inch × 5

= 3.75 inches.

12. The length of the board will be:

= 7 5/8 × 5

= 38.125 inches.

13. The total height of the stairs will be:

= 8 3/16 × 13

= 106.4375 inches.

14. The height of the stack will be:

= 55 × 3/8in

= 20.625 inches.

15. The length of the board will be:

= 3/4 × 86 1/4

= 64.6875 inches.

16. The number of hours that it'll take to replace the trim will be:

= 37 1/2 × 1/4

= 9.375 hours.

17. The height of the will required will be:

= 22 × 5/12

= 9.167 feet

18. The inches removed from the wood will be:

= 1/16 × 7

= 0.4375 inches.

19. The shortest finish stock will be:

= 3/16 × 15

= 2.8125 feet.

20. The total amount of board wasted will be:

= 3/16 × 11

= 2.0625 inches.

21. The total rise in the staircase will be:

= 22 × 7 3/8

= 162.25 inches.

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Answer:

[tex]a.) y=\frac{1}{4} x+3[/tex]

Step-by-step explanation:

Any two points along the line are (4,4) and (0,3),

[tex]Gradient= \frac{4-3}{4-0}=\frac{1}{4}[/tex]

we know the y intercept is 3

Therefore equation of the line is : [tex]y=\frac{1}{4} x+3[/tex]

Answer: the height of the pyramid is 6 inch.

Step-by-step explanation:

V=50 inch³    a=5 inch     H=?

Formula of  volume square pyramid is:

                    [tex]\boxed {V=\frac{1}{3}*S_{base}*H },[/tex]        

where:   Sbase - pyramid base area;

              H -   pyramid height.

Hence,

             [tex]H=\frac{3*V}{S_{base}}\\[/tex].

Since the pyramid is square, its base is a square.        ⇒

[tex]S_{base}=a^2\\S_{base}=(5\ inch)^2\\S_{base}=25\ inch^2\\H=\frac{3*50}{25} \\H=3*2\\H=6\ (inch).[/tex]

Good luck!    

Step-by-step explanation:

To write a polynomial in standard form, put the degree that are the greatest first

So here it would be

[tex] {x}^{5} + 4 {x}^{3} - 3 {x}^{2} + 10[/tex]

Remember constant are numbers that you learned back in elementary,

Numbers like 10,90,4,1,0,-3 etc.

Remember that constant are basically represented like this

[tex]k \times {x}^{0} [/tex]

For example, 10 is represented like

[tex]10 \times {x}^{0} [/tex]

Since 0 is the smallest degree possible, for a polynomial, constants are the last term of a polynomial in standard form

Answer:

$470

Step-by-step explanation:

Add all the amounts given.

200+140+130=470

They spent $470 that day.

Hope this helps!

If not, I am sorry.

Answer:

470

Step-by-step explanation:

140+130+200= 470

They said that day, which means all together. So we add.

Answer:

If the exterior of the house is 2000 square feet and each gallon of paint covers 350 square feet.

Then she needs to buy 6 gallons of paint.

Step-by-step explanation:

Dividing the total area by the area that each gallon of paint covers we get,

[tex]$\frac{2000}{350} \times \frac{50}{50}=\frac{40}{7}$$[/tex]

Now, performing long division we get,

[tex]$7\overset{5}{\overline{\left){\begin{align} & 40 \\ & \underline{35} \\ & \underline{05} \\ \end{align}}\right.}}$$[/tex]

She needs five gallons of paint fully and some amount of the sixth gallon because we get a remainder.

She can't buy paint in fraction, hence she has to buy 6 gallons of paint.

The standard form of a line passing through the points (-1, -3) and (2, 1) is 4x - 3y = 5.

The slope of the given line, m = (1 - (-3))/(2 - (-1)) = (1 + 3)/(2 + 1) = 4/3.

Computed using the formula for the slope of a line, m = (y₂ - y₁)/(x₂ - x₁), when a line passes through the points (x₁, y₁) and (x₂, y₂).

The point intercept form of a line is y - y₁ = m(x - x₁) when the line passes through the point (x₁, y₁) and has the slope m.

Thus, the given line in the point intercept form can be written as:

y - 1 = (4/3)(x - 2).

The standard form of a line is ax + by = c.

To convert the point intercept form to the standard form, we do as follows:

y - 1 = (4/3)(x - 2),

or, 3(y - 1) = 3(4/3)(x - 2) {Multiplying both sides by 3},

or, 3y - 3 = 4x - 8 {Simplifying},

or, 8 - 3 = 4x - 3y {Rearranging},

or, 4x - 3y = 5 {Rearranging and simplifying}.

Thus, the standard form of a line passing through the points (-1, -3) and (2, 1) is 4x - 3y = 5.

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The value of y is 2

The complete question is in the image

From the complete question, we have:

rs + st = rt

This gives

8y + 4 + 4y + 8 = 36

Evaluate the like terms

12y = 24

Divide by 12

y = 2

Hence, the value of y is 2

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Answer: D. 26 units

Step-by-step explanation: perimeter is the distance around the figure, or all the sides added together.
With a rectangle it is known that the opposite sides are congruent, or the same, so 8+8+5+5 = 26

The slope(m) of the given set is -3.

The slope(m) of a pair of the given ordered set is the change in the rise over the run. The rise is the y-axis while the run is the x-axis.

Mathematically;

[tex]\mathbf{Slope(m) = \dfrac{\Delta y}{ \Delta x}}[/tex]

[tex]\mathbf{Slope(m) = \dfrac{y_2-y_1}{x_2-x_1} }[/tex]

Here:

[tex]\mathbf{Slope(m) = \dfrac{12-9}{1-2} }[/tex]

[tex]\mathbf{Slope(m) = \dfrac{3}{-1} }[/tex]

Slope (m) = -3

Therefore, we can conclude that the slope of the given set is -3. From the given option, kindly find out which of the slope is equivalent to -3.

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Answer:

32.75 inches

Step-by-step explanation:

Pythagoras' theorem. The long length squared minus the short length squared gives you the answer squared, so square root it :)

By using a graphing calculator, the solution set that would be found in the overlapping areas of a graph of Jill's sales is (15, -4).

First of all, we would assign variables to the blend of brownies that were made by Jill for the bake sale as follows:

Since Jill sold more than 11 plates in total, we have:

x + y > 11.

Also, Jill sold less than $66.50 worth of brownies:

5.50x + 4.00y < 66.50.

By using a graphing calculator, the solution set that would be found in the overlapping areas of a graph of Jill's sales is (15, -4).

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The coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)

An equation is an expression that shows the relationship between two or more variables and numbers.

Let (x, y) represent the coordinate of the midpoint E. Point E is the midpoint of CD, hence:

x = [(-7) + (-3)] / 2 = -5

y = [(-2) + (-5)] / 2 = -3.5

The coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)

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Answer:

9%

Step-by-step explanation:

percent increase is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

increase = $3.87 - $3.54 = $0.33 , then

% increase = [tex]\frac{0.33}{3.54}[/tex] × 100% ≈ 9% ( to the nearest whole percent )

Answer:

9 %  (rounded to the nearest whole percent)

Step-by-step explanation:

the amount of increase:

3.87 - 3.54 = 0.33

Then

the percent increase for the cost of gas :

[tex]=\frac{0.33}{3.54} \times 100\\\\= 0.093220338983 \times 100\\\\=9.3220338983 \ \%[/tex]

The transformations which map f(x) to g(x) according to the equation are; Translation of f(x) 2 units to the left and 3 units upwards.

The equation given in the task content is as follows;

It therefore follows that the transformations which would produce function g(x) from f(x) involves a 2 units translation to the left and a 3 units translation upward.

Remarks:

The complete question requires that the transformations from f(x) to g(x) be identified.

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Answer:

1/18

Step-by-step explanation:

P(Orange AND Red)

= P(Orange socks)*P(Red shirt)

= 1/3*1/6

= 1/18

The price of the stock is expected to increase in the long run correctly describes it and is denoted as option D.

This is defined as the pictorial representation of date or variables in an organized manner.

From the graph provided , we can infer that after a while the stock began to rise which is the same as it increasing in the long run.

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Answer: A, C, E

Step-by-step explanation:

These are not polynomials because there is one term where the variable has an exponent that is not a positive integer.

Resolviendo un sistema de ecuaciones, vemos que se venden 6 libros de secundaria 4 y 6 libros de secundaria 1.

Primero definimos dos variables:

Sabemos que se venden 12 libros en total, entonces:

x + k = 12

Tambien sabemos que se recauda un total de $82, entonces:

x*$8 + k*$6 = $82

Entonces tenemos dos ecuaciones.

a) Usando la primer ecuacion, podemos aislar x para tener:

x = 12 - k

b) Ahora podemos reemplazar eso en la otra ecuación para solucionar el sistema.

(12 - k)*$8 + k*$6 = $82

$96 - $2*x = $82

$2*x = $12

x = $12/$2 = 6

Es decir se venden 6 libros de secundaria 4, y como se venden 12 libros en total, los otros 6 libros vendidos son de secundaria 1.

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Answer:

126 ft^2

Step-by-step explanation:

The area of a rectangle is just its length times its width. We are given that the length is 14 ft, and the width is 9 ft. If we multiply the two quantities, we get that the area is 14*9 or 126 ft^2

Answer: 126ft^2

Step-by-step explanation:

area of rectangle=length*width

here

length=14 ft

width=9ft

area=14*9

area= 126 ft^2

Answer:

chord

Step-by-step explanation:

a chord is a line drawn from one part of a circle's circumference to another without passing through the centre.

If the line passed through the centre then it would be a diameter

Answer:

The answer would be A

Step-by-step explanation:

1^2=1×1= 1

2^2 =2×2=4

3^2=3×3=9

4^2=4×4=16

Therefore,

√11  lies between 3 and 4

Answer:

A

Step-by-step explanation:

[tex]since 3 is \sqrt{9} and 4 is \sqrt{16} then it follows that \sqrt{11} is between the two[/tex]

The quadratic equation ax²+bx+c = 0 is given and this is illustrated below.

ax²+bx+c = 0

Step 1: Subtract c from both sides

ax²+bx+c-c = 0-c

ax²+bx = -c

Step 2: Divide both sides of the equation by a

ax²/a + bx/a = -c/a

x² + bx/a = -c/a

Step 3: Complete the square and add the quantity (b/2a)² times a squared to both sides

x² + bx/a +  (b/2a)² = -c/a +  (b/2a)²

Step 4: Square the quantity b/2a on the right side of the equation

x² + bx/a +  (b/2a)² =  -c/a +  b²/4a²

Step 5: Find a common denominator on the right side of the equation which is 4a²

x² + bx/a +  (b/2a)² =  -4ac/4a² +  b²/4a²

Step 6: Add the fractions together on the right side of the equation

x² + bx/a +  (b/2a)² =  (-4ac+  b²)/4a²

Step 7: The equation on the left is to be written as a perfect square as shown

(x+b/2a)² =  (-4ac+  b²)/4a²

Step 8: Take the square root of both sides

√(x+b/2a)² = √ (-4ac+  b²)/4a²

(x+b/2a) =  √(-4ac+  b²)/2a

Step 9: subtract b/2a from both sides

x+b/2a - b/2a =  -b/2a + √(-4ac+  b²)/2a

x =  -b/2a + √(-4ac+  b²)/2a

Step 10: Add the fractions together on the right-hand side

x =  -b±√(-4ac+  b²)/2a

This will then gives the required equation.

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This is an exponential function due to the presence of exponent

Exponential functions are inverse of logarithmic functions. Given the function below;

f(x) = 2^x - 14

This is an exponential function due to the presence of exponent and since the standard form of an exponential function is y = ab^x

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The length of EF is 3.8

To do this, we make use of the following law of sines

EF/sin(D)= DE/sin(F)

So, we have:

EF/sin(75)= 3/sin(50)

This gives

EF = sin(75) * 3/sin(50)

Evaluate the product

EF = 3.8

Hence, the length of EF is 3.8

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Considering the given function and the asymptote concept, we have that:

In this problem, the function is:

[tex]f(x) = \frac{5x}{x - 25}[/tex].

The vertical asymptote is found as follows:

x - 25 = 0 -> x = 25.

The horizontal asymptote is found as follows:

[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = \lim_{x \rightarrow \infty} 5 = 5[/tex].

Hence the end behavior is that as [tex]x \rightarrow \infty, f(x) \rightarrow 5[/tex].

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