50 Points! Multiple choice algebra question. Photo attached. Thank you!

The domain of the function (t) in h = - 16t² + 56t should be greater than

or equal to 43.5 seconds as the height of the rocket can not be negative.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given that;

A rocket is launched into the air. Its height in feet is given by

h = - 16t² + 72t.

Where t represents time in seconds and h represents the height in feet.

We know that height can not be negative.

h ≥ 0.

So,  - 16t² + 56t ≥ 0.

- 16t² ≥ -56t.

16t² ≥ 56t.

16t ≥ 56.

t ≥ 56/16.

t ≥ 3.5 seconds.

Therefore, the domain of the function (t) in h = - 16t² + 56t should be greater than or equal to 3.5 seconds.

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Answer: Lara

Step-by-step explanation:

convert yards into feet

yards*3= feet

89 yards * 3 = 267 feet

Since 270 is greater than 267 Lara. Lara's distance is greater by 3 feet since 270-267 is 3

Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, - 5 ) and (x₂, y₂ ) = (3, - 2 )

m = [tex]\frac{-2-(-5)}{3-4}[/tex] = [tex]\frac{-2+5}{-1}[/tex] = [tex]\frac{3}{-1}[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, - 2 )

- 2 = - 3(3) + c = - 9 + c ( add 9 to both sides )

7 = c

y = - 3x + 7 ← equation of line

I did some research and found that for quadratic equations in the form of [tex]y = ax^2 + bx + c[/tex], you can find the minimum value using the equation [tex]$\text{minimum} = c - \frac{b^2}{4a}[/tex] .

We can substitute our given values in the formula and get the following: [tex]$37 = 118 - \frac{b^2}{4}$[/tex] .

We can go ahead and solve it, and get the following:

[tex]-81 = -\frac{b^{2}}{4}[/tex]

[tex]324 = b^2[/tex]

[tex]\pm{18} = b[/tex]

Now we know that the equation is either [tex]$f(x)=x^2+18x+118$[/tex]  or [tex]$f(x)=x^2-18x+118$[/tex] .

We will solve using both equations, but we will solve the one with a positive b-value first. Substituting [tex]f(x)[/tex] for [tex]$37$[/tex], the minimum or y-value of the vertex, we can now solve for the x-value of the vertex.

We have:

[tex]37 = x^2+18x+118[/tex]

[tex]0=x^2+18x+81[/tex]

[tex]0=(x+9)^2[/tex]

[tex]x+9=0\\x=-9[/tex]

Doing the same thing with the second equation, we get:

[tex]37 = x^2-18x+118[/tex]

[tex]0=x^2-18x+81[/tex]

[tex]0=(x-9)^2[/tex]

[tex]x-9=0\\x=9[/tex]

After all of this, we know our vertex's x-values are either [tex]9[/tex] or [tex]-9[/tex], and that our y-value is [tex]37\\[/tex].

We can conclude that our k-value (y-value of the vertex in vertex form) is [tex]37[/tex], and our h-value (x-value of the vertex in vertex form) is [tex]9[/tex] or [tex]-9[/tex].

Conclusion:         [tex]h = -9, 9[/tex]

                            [tex]k=37[/tex]

Answer: y=4x+7

Step-by-step explanation:

-8x+2y=14

Convert to y=kx+b

2y=8x+14

y=4x+7

The points that are solutions to the equation [tex]2x^2 + y = 4[/tex] are:

I. (3, -14)

III. (-3, -14)

To determine which of the given points are solutions to the equation [tex]2x^2 + y = 4[/tex], we need to substitute the x and y values of each point into the equation and check if the equation holds true.

Let's evaluate each point one by one:

I. (3, -14)

Substituting x = 3 and y = -14 into the equation:

[tex]2(3)^2 + (-14) = 4[/tex]

18 - 14 = 4

4 = 4

Since both sides of the equation are equal, the point (3, -14) is a solution to the equation.

II. (-3, 14)

Substituting x = -3 and y = 14 into the equation:

[tex]2(-3)^2 + 14 = 4[/tex]

18 + 14 = 4

32 = 4

Since the equation is not satisfied (32 is not equal to 4), the point (-3, 14) is not a solution to the equation.

III. (-3, -14)

Substituting x = -3 and y = -14 into the equation:

[tex]2(-3)^2 + (-14) = 4[/tex]

18 - 14 = 4

4 = 4

Since both sides of the equation are equal, the point (-3, -14) is a solution to the equation.

In summary, the points that are solutions to the equation [tex]2x^2 + y = 4[/tex]are:

I. (3, -14)

III. (-3, -14)

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Answer:

16 and 4

Step-by-step explanation:

To divide 20 in the ratio 4:1, we need to divide the quantity into 5 parts (4 parts for the first ratio and 1 part for the second ratio) and then allocate the parts accordingly.

The total number of parts is 4+1=5. So, each part represents 20/5 = 4.

To find the share of the first ratio, we multiply the first ratio (4) by the number of parts it represents (4). So, the first share is 4*4 = 16.

To find the share of the second ratio, we multiply the second ratio (1) by the number of parts it represents (1). So, the second share is 1*4 = 4.

Therefore, the quantities in the ratio 4:1 that add up to 20 are 16 and 4, respectively.

The 97% confidence interval for the proportion of college freshmen who would report cheating if they witnessed it in class is (0.0728, 0.1482).

The point estimate is the proportion of students who responded "yes" out of the total sample.

In this case, the point estimate is 19/172, which is approximately 0.1105.

b. Margin of Error:

To calculate the margin of error, we need the standard deviation. Since we don't have the population standard deviation, we'll use the formula for the estimated standard deviation of a proportion:

Margin of Error (ME) = z√[(p(1 - p)) / n]

Where z is the z-score corresponding to the desired confidence level. For a 97% confidence level, the z-score is approximately 1.96, p is the point estimate of the proportion and n is the sample size.

Using the given values, we can calculate the margin of error:

ME = 1.96√[(0.1105(1 - 0.1105)) / 172]= 0.0377

c. Confidence Interval:

The confidence interval is calculated by subtracting and adding the margin of error from the point estimate.

Confidence Interval = Point Estimate ± Margin of Error

Confidence Interval = 0.1105 ± 0.0377

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hello

the answer to the question is:

y = a tan(bx – c) + d

a = 1, b = 1, c = π/2

the midline is y = d, so y = 0 and there's no vertical shift

the vertical stretch is 1, so label the y-axis so the inflection point of the curve is 1 above the midline, 1, and the other inflection point is 1 below the midline, −1

the period is:

T = π/b ----> T = π

the phase shift is:

PS = c/b ----> PS = π/2

and also, there's no amplitude for tangent and cotangent, there is only the vertical stretch that takes the place of an amplitude

The option that would create an appropriate strata is given as follows:

Four teachers from each school in the district are chosen at random to complete a survey on the topic.

Samples may be classified as follows:

An appropriate strata is created when stratified sampling is used that is, the population is divided into groups(each school in the district), and then an equal amount(four teachers from each school) is surveyed.

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Answer:

C

Step-by-step explanation:

[tex]9\sqrt{x} + 3\sqrt{3x} + \sqrt{9x} \\= \sqrt{x} ( 9 + 3\sqrt{3}+3)\\ = 12\sqrt{x} + 3\sqrt{3x}[/tex]

Answer:

  (B)  sin(60°) = 4/x

Step-by-step explanation:

You want an equation for finding the hypotenuse of a 30°-60°-90° triangle with the middle-length side being 4 units.

The trig relation between the side opposite and angle and the hypotenuse of the right triangle is ...

  Sin = Opposite/Hypotenuse

In this triangle, this relation means ...

  sin(60°) = 4/x . . . . . matches choice (B)

__

Additional comment

The middle-length side is opposite the middle length angle.

This is a "special" right triangle with sides in the ratios 1 : √3 : 2. The length x will be 4(2/√3) = (8/3)√3. It can be useful to remember the side length ratios for this triangle.

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Answer:

21

Step-by-step explanation:

Answer:

The square root of 50 is approximately 7.07.

Answer:

7.07106781187...

Step-by-step explanation:

its an irrational number

The solution is; C. x² + 2x - 1 = 3 equation could be solved using this application of the quadratic formula.

Here,

Quadratic formula: x = -b±√b²-4ac/2a     [ +/-   is   ± ]    

You can find the value of a, b, c  -->  ax² + bx + c = 0  

we have,

x = -2±√2² - 4×1× -4 / 2×1    

Since this is not simplified, you can find a, b, c:

a = 1

b = 2

c = -4

A.)  x² + 1 = 2x − 3   Make the equation into ax² + bx + c = 0.

Subtract 2x on both sides, and add 3 on both sides to set the equation equal to 0

x² + 1 - 2x + 3 = 2x - 2x - 3 + 3

x² - 2x + 4 = 0      

a = 1

b = -2

c = 4    This is not the answer because b = 2 not -2, and c = -4 not 4

B.) x² - 2x − 1 = 3     Subtract 3 on both sides to set the equation = 0

x² - 2x - 4 = 0

a = 1

b = -2

c = -4      This is not the answer because b = 2 not -2

C. x² + 2x - 1 = 3    Subtract 3 on both sides to set the equation = 0

x² + 2x - 4 = 0

a = 1

b = 2

c = -4    This is your answer

D. x² + 2x - 1 = -3      Add 3 on both sides to set the equation = 0

x² + 2x + 2 = 0

a = 1

b = 2

c = 2    

This is not the answer because c = -4 not 2

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complete question:

Which equation could be solved using this application of the quadratic formula?

x = -2±√2² - 4×1× -4 / 2×1    

Answer:

Step-by-step explanation:

lets solve all the equations and check:

1 ) 8 - x = 11

 -x = 11 - 8

  x = -3 ------------- not this one

2 ) x + 7 = 4

    x = 4 - 7

    x = -3 -------------not this one

3 ) 5 + x = 9

    x = 9 - 5

    x = 4 ------------- not this one

4 ) x - 2 = 1

    x = 1 + 2

    x = 3 ----------- this is the correct option

                hope this helps!

Answer:

A = 30 cm

B = 14 cm

C = 15 cm

D = 41 cm

Step-by-step explanation:

You can find A by multiplying 10 times 6 (because the other side of the square is ten and the side of A already has that 4 there it would be 6) which would be 60, then since it is a right triangle, you can divide that by two and get 30.

You can find B by multiplying 4 by 7 (because the other part of that side of the square is 3 so that part would be 7) which would be 28, then since it is a right triangle, you can divide that by two and get 14.

You can find C by multiplying 10 times 3 and getting 30, then since it is a right triangle, you can divide that by two and get 15.

You can find D by multiplying 10 by 10 (because it is a square) then you'll get 100 from that. Then you can subtract the rest of the triangles from it which would be 100 minus 30 minus 14 minus 15 and you would get 41 which would be triangle D.

Hope this helps!! Let me know if you need more explanation

The solution to the proportional equation 5/8 = 8/a is a = 64/5 or a = 12.8.

To solve the proportional equation 5/8 = 8/a, we can cross-multiply.

Cross-multiplying means multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa.

We have:

5 × a = 8 × 8

5a = 64

To isolate the variable a, we divide both sides of the equation by 5:

a = 64/5

We may cross-multiply the proportional equation 5/8 = 8/a to find the solution.

Cross-multiplication is the process of multiplying the denominator of the second fraction by the first fraction's numerator, and vice versa.

We possess

5 × a = 8 × 8 5a = 64

We divide both sides of the equation by 5 to identify the variable a:

a = 64/5.

We may cross-multiply to find the solution to the proportional equation 5/8 = 8/a.

Cross-multiplication is the process of multiplying one fraction's numerator by another's denominator and vice versa.

There are:

5 × a = 8 × 8 5a

= 64

By multiplying both sides of the equation by 5, we may separate the variable a:

a = 64/5.

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Answer:

x ≈ 12.7

Step-by-step explanation:

since the triangle is isosceles then the 2 legs are congruent, both 9

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² = 9² + 9² = 81 + 81 = 162 ( take square root of both sides )

x = [tex]\sqrt{162}[/tex] ≈ 12.7 ( to the nearest tenth )

Answer:

Solution is in the attached photo.

Step-by-step explanation:

This question tests on the concept of triangles, as this is an isosceles triangle, the other 2 unknown angles are the same, as well as the sine rule.

Answer:

The original number was 4.

Step-by-step explanation:

We can construct an equation to model the given situation, using a variable x to represent the original number:

"the quantity of 6 minus a number"

[tex](6 - x)[/tex]

"four times the quantity"

[tex]4(6 - x)[/tex]

"is 8"

[tex]4(6 - x) = 8[/tex]

We can solve for x in this equation.

[tex]4(6 - x) = 8[/tex]

↓ applying the distributive property ... [tex]A(B+C) = AB + AC[/tex]

[tex]24 - 4x = 8[/tex]

↓ adding 4x to both sides

[tex]24 = 8 + 4x[/tex]

↓ subtracting 8 from both sides

[tex]16 = 4x[/tex]

↓ dividing both sides by 4

[tex]4 = x[/tex]

[tex]\boxed{x = 4}[/tex]

So, the original number was 4.

The proportion that correctly defines θ is BC/PC = DE/PE = θ.

option  C.

The length of the arcs is calculated as follows;

Length of arc = (θ/360) x 2πr

where;

For sector PCB, the length of the arc is given as;

(θ/360) x 2π(PC) = BC

(θ/360) x 2π = BC/PC

θ = BC/PC ------- (1)

Note: 2π radian = 360⁰

For sector PED, the length of the arc is given as;

(θ/360) x 2π(PE) = DE

(θ/360) x 2π = DE/PE

θ = DE/PE ------- (2)

Compare the two equations as follows;

BC/PC = DE/PE = θ

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answer is 45

400/9 = 44.44...

so with the extra employees you need another manager.

Answer:

40 managers

Step-by-step explanation:

If there is one manager for every 9 engineers, we can assume that each manager is responsible for a group of 9 engineers. To determine the number of managers in the company, we need to divide the total number of engineers by 9.

First, we need to determine the total number of engineers in the company. Since there is one manager for every 9 engineers, the ratio of engineers to managers is 9:1. This means that for every 10 people (9 engineers and 1 manager), there is 1 manager. So we can find the total number of groups of 10 people by dividing the total number of employees by 10:

400 employees / 10 = 40 groups of 10 people

This means that there are 40 groups of 10 employees (1 manager and 9 engineers) in the company. Since there is 1 manager in each group, the total number of managers in the company is equal to the number of groups:

Number of managers = Number of groups = 40

Answer:

You dont have to tell me to show my work twice

Step-by-step explanation:

To find the length of side c (the hypotenuse), we will use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (a and b) is equal to the square of the hypotenuse (c).

In this case, a = 30 feet and b = 40 feet. Therefore:

c^2 = a^2 + b^2

c^2 = 30^2 + 40^2

c^2 = 900 + 1600

c^2 = 2500

c = √2500

c = 50 feet

So the length of side c (the hypotenuse) is 50 feet. To find out how many feet of flowers will be planted along side c, we need to know the perimeter of the triangle (the sum of the lengths of all three sides). The perimeter is:

Perimeter = a + b + c

Perimeter = 30 + 40 + 50

Perimeter = 120 feet

Therefore, 120 feet of flowers will be planted along side c.

Answer:   Here, side a = 30ft.

side b = 40ft.

Hence according to, Pythagoras theorem,

h²=p²+b²

where, h= hypotenuse of the triangle

            b= base of the triangle

            p= perpendicular of the triangle

Step-by-step explanation:

hypotenuse c {according to question} - c=[tex]\sqrt{a^{2} + b^{2}[/tex]

therefore, c=[tex]\sqrt{30^{2} + 40^{2} }[/tex] = 50ft. will be the answer.

Hypotenuse means the longest side of the triangle or in other words the side opposite to the 90° angle of the triangle.

The true statement is that the box-plot indicates that:

To determine the validity of this statement, we compare the minimum weekly salary of men (represented by the lower end of the box-plot whisker) to the median of women's earnings (represented by the line inside the box).

If the median of women's earnings is less than the minimum salary of men, then more than 50% of women earn less than the minimum weekly salary of men.

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Answer:

The fraction of cupcakes they ate is:

5 / 8

The fraction of cupcakes left is:

3 / 8

Given statement solution is :- The slope (m) of the line is -2, and the y-intercept (b) is -5/4.

To find the y-intercept and slope of the line represented by the equation -8x - 4y = 5, we need to rearrange the equation into slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.

Let's begin by isolating the term with y:

-8x - 4y = 5

Subtract -8x from both sides:

-4y = 8x + 5

Next, divide both sides of the equation by -4 to solve for y:

y = (-8/4)x - (5/4)

Simplifying further:

y = -2x - 5/4

Now we can identify the slope and the y-intercept:

The slope (m) of the line is -2, and the y-intercept (b) is -5/4.

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The minimum of this quadratic function is -55.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry, Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function T = n²- 10n - 30, we have:

Axis of symmetry, Xmax = -(-10)/2(1)

Axis of symmetry, Xmax = 10/2 = 5.

For the vertex of T = n²- 10n - 30, we have:

T = n²- 10n - 30

T(5) = 5²- 10(5) - 30

T(5) = -55.

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The passing score cutoff is 39, and 22.22% of the students failed.

Using the generic formula =

Z = score - mean / standard deviation

According to the question, the results of a psychology test had a mean of 57 and a standard deviation of 9, and they were normally distributed.

Anything 2 or more standard deviations below the mean on the test was considered a failing grade,

hence z = 2/9 = 0.222.

Additionally, the falling cut-off score is determined by using the formula: Falling cut-off = mean - 2 x standard deviation,

or 57 - 2 x 9 = 39.

Hence the passing score cutoff is 39, and 22.22% of the students failed.

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