Write an inequality to model the situation.
A number exceeds 21.
n ≤ 21
n < 21
n > 21
n ≥ 21

Answer:

3.716 m²

Step-by-step explanation:

10⁻² = 0.01, so 9.29 x 0.01 = 0.0929

multiple 0.0929 by 40 to get 3.716 m²

Answer:

-2 is a zero of the polynomial. 2 is not a zero of the polynomial.

Step-by-step explanation:

A value of x is a zero of a polynomial if when it is substituted for x in the polynomial, it makes the polynomial evaluate to zero.

The polynomial is x + 2

Let x = -2:

x + 2 = -2 + 2 = 0

-2 is a zero of the polynomial.

Let x = 2:

x + 2 = 2 + 2 = 4

2 is not a zero of the polynomial.

x² - 8x + 12 = 0

First of all we need to find the roots

Δ = b² - 4.a.c

Δ = (-8)² - 4 . 1 . 12

Δ = 64 - 4. 1 . 12

Δ = 16

Has 2 real roots

x = (-b +- √Δ)/2a

x' = (--8 + √16)/2.1    

x'' = (--8 - √16)/2.1

x' = 12 / 2    

x'' = 4 / 2

x' = 6    

x'' = 2

So our equation can be solved with x = 6 and x = 2, therefore we can create two other equations with the same roots

x - 6 = 0

and

x - 2 = 0

Answer:

(x – 4)2 = 4

Step-by-step explanation:

Answer:

Refeect circle A over the the y line = x

Step-by-step explanation:

Answer:

F(x) = [tex]\frac{x^3}{3} - \frac{7x^2}{2} + 5x + c[/tex]

Step-by-step explanation:

The antiderivative of a function (also called the integration of a function) is the reverse of the differentiation of that function. Given a function f(x), its integration, F(x), can be calculated as follows;

F(x) = [tex]\int\limits{f(x)} \, dx[/tex]

From the question, f(x) = x² - 7x + 5

Therefore,

F(x) = [tex]\int\limits {(x^2 - 7x + 5)} \, dx[/tex]

F(x) = [tex]\frac{x^3}{3} - \frac{7x^2}{2} + 5x + c[/tex]

Where c is the constant of the integration (antiderivative).

PS: The constant of integration is used for indefinite integrals and allows to express integration of a function in its most general form.

Answer:

Step-by-step explanation:

No figure supplied, so lots of assumptions needed.

Assume side length of triangle is 4 cm.  

( If = 4 cm  means ??)

Assume ABC is equiangular, all three angles are 60 degrees.

(This is a cross-sectional view, but don't see any)

Side length = 4

altitude of triangle = 4 sin(60) = 2sqrt(3)

radius of circumscribed circle of equilateral triangle

R = (2/3) altitude

= (2/3)*2sqrt(3)

= (4/3)sqrt(3)

Diameter

D = 2R

= (8/3) sqrt(3)

Answer: 8 cm

Step-by-step explanation:

The figure in the image attached below shows that there are two specific angles that are congruent to each other, angles AD and CD.

We are given the length of one of these angles:

AD= 4 cm so we must multiply 4 by 2, since there are TWO angles measuring 4 cm.

4 cm x 2 angles (AD and CD) =8 cm.

Proof of answer is shown below!

Answer:

The answer is

Step-by-step explanation:

The above variation is written as

[tex]y = \frac{k}{ {x}^{2} } [/tex]

where k is the constant of variation

when y = 9

x = 4

We have

k = yx²

k = 9(4)²

k = 9 × 16

k = 144

So the formula for the variation is

[tex]y = \frac{144}{ {x}^{2} } [/tex]

when y = 1

[tex]1 = \frac{144}{ {x}^{2} } [/tex]

Cross multiply

x² = 144

Find the square root of both sides

x = √144

x = 12

Hope this helps you.

±2

Step-by-step explanation:

Answer:

[tex]\sqrt{x-4} +5[/tex]

Step-by-step explanation:

the conjugate of [tex]\sqrt{x-4} -5[/tex]  is the term that completes a²-b² when multiplied by each other

a²-b² = (a+b)(a-b)

Answer:

The answer is (1,-5). (i.e x=1 and y=-5).

Hope it helps..

Answer:

(1,-5)

Step-by-step explanation:

Answer:

5 and 1 over 6

Step-by-step explanation:

Simplifying the given:

Correct choice is the last one: 5 and 1 over 6

5 and 1 over 6    .......................................                        

Answer:

59°

Step-by-step explanation:

A triangle adds up to 180°. A right triangle has a 90° angle.

1. Set up the equation

90 + 31 + x = 180

2. Simplify

121 + x = 180

3. Solve for x by subtracting 121 from both sides

x = 59

Answer:

The correct option is (C).

Step-by-step explanation:

The exponential function representing decay is as follows:

[tex]y=y_{0}\cdot e^{kt};\ k<0[/tex]

Here,

y = final value  

y₀ = initial value  

k = growth rate  

t = time passed

The graph represents exponential decay is:

"On a coordinate plane, a graph approaches y = 0 in quadrant 1 and curves up into quadrant 2."

Thus, the correct option is (C).

Answer:

The answer is C

Step-by-step explanation:

I  just took the test on edge

Answer:

10,341

Step-by-step explanation:

[tex]S_{n}=\frac{n}{2} (a_1}+a_{n})\\S_{54}=\frac{54}{2} (6+377)=27 \times 383=10,341[/tex]

Answer:

HI = 13

Step-by-step explanation:

The triangle that is shown is a 45-45-90 triangle, so we know that GH = GJ = 9 and IJ = 13, we are able to solve for HI.

Technically, IJ = HI, since both triangles are congruent. Both IJ and HI will be 13.

Answer:

Option D.

Step-by-step explanation:

The given quadratic equation is

[tex]y=x^2+7x+10[/tex]

We need to draw the graph of given equation by using graphing calculator as shown below.

From the graph it is clear that the parabola intersect the x-axis at points (-2,0) and (-5,0). So, the x-intercepts are (-2,0) and (-5,0).

Therefore, the correct option is D.

Answer:

Step-by-step explanation:

if x=0 then f(x)=2 (0,2)

if f(x)=0 then x=-1 (-1,0)

If x = 0, then f(0) =  

✔ 2.25

.

If f(x) = 0, then x =  

✔ –1

.

Answer:

A. 1 4/6 cups of blueberries

Step-by-step explanation:

1 -- 2/3                      

Proportion, Batches to Blueberries

1*(2 1/2) -- (2/3)( 2 1/2)              

Because we are now multiplying the 1 batch to 2 1/2 batches. So to keep the proportion balanced/equal we are using the same operation on the right side of the proportion

2 1/2 -- (2/3)( 5/2 )      

2 1/2 -- 5/3

2 1/2 -- 1 2/3

Simplify

On the right side shows the blueberries for 2 1/2 batches. 1 2/3 = 1 4/6    

Hope that helps! Tell me if you need more info

Answer:

the actual answer is 78750

Step-by-step explanation:

summation of 2-176 in the equation 5n+5

Answer: C) For every original price, there is exactly one sale price.

For any function, we always have any input go to exactly one output. The original price is the input while the output is the sale price. If we had an original price of say $100, and two sale prices of $90 and $80, then the question would be "which is the true sale price?" and it would be ambiguous. This is one example of how useful it is to have one output for any input. The input in question must be in the domain.

As the table shows, we do not have any repeated original prices leading to different sale prices.

Answer:

C STAY SAFE!!!

Step-by-step explanation:

Ok we know this cant be A the reason is It says tha the original price is increasing so thats FALSE... its trying to trick you so no

The second choice says The sale price is always less than the original price. well take a look at the sale prices are they? Obiously not so False

Ok the third option For every original price, there is exactly one sale price. well this is true ask yourself each it helps.

Last option The sales price is never less than zero. erm   FALSE OBIOUSLY THIS IS TRUE JUST NOT TRUE ITS WRONG        

THE ANSER IS C

Answer:

Step-by-step explanation:

Since the above sequence is a geometric sequence

An nth term of a geometric sequence is given by

[tex]A(n) = a(r)^{n - 1} [/tex]

where a is the first term

r is the common ratio

n is the number of terms

From the question

a = 10

To find the common ratio divide the previous term by the next term

That's

r = 30/10 = 3 or 90/30 = 3 or 270/90 = 3

Since we are finding the 12th term

n = 12

So the 12th term is

[tex]A(12) = 10( {3})^{12 - 1} [/tex]

[tex]A(12) = 10 ({3})^{11} [/tex]

Hope this helps you

The correct answer is 180 oranges

Explanation:

In mathematics, a ratio expresses two or more numbers that are related. In the case fo the ration 9: 40 this expresses 9 oranges are used to serve fruit salad for 40 people. Now, if you need to determine what is the number of oranges not for 40 people but for 800 people you can use cross multiplication. This process is explained below:

[tex]\frac{9}{40} = \frac{x}{800}[/tex]   - 1. Multiply  9 x 800 and 40 x x (cross multiplication)

[tex]7200 = 40x[/tex] - 2. Solve the equation by diving 7200 into 40

[tex]\frac{7200}{40} = x[/tex]

[tex]x = 180[/tex] - 3. 180 represents the number of oranges to serve 800 people, which   can be expressed as 180: 800

Answer:

28

Step-by-step explanation:

140 calories over 5 ounce

= 28

The unit rate of calories per ounce will be 28 calories/ ounce

What is proportion ?

A proportion is an equation based on the equality of two ratios.

It is given that 5-ounce container of Greek yogurt contains 140 calories and it is to calculate for one ounce calories contain in Greek yogurt :

[tex]\begin{aligned}5 \text{\:ounce}&\rightarrow 140 \text{\:calories}\\1 \text{\:ounce}&\rightarrow \frac{140}{5}\text{\:calories} \\&\rightarrow 28 \text{\:calories}\end{aligned}[/tex]

Therefore, the unit rate of calories per ounce will be 28 calories/ ounce

Read more about ratio at:

https://brainly.com/question/17869111

#SPJ2

Answer:

True

Step-by-step explanation:

Inverse variation on a graph is depicted by the movement of the graph diagram (line) in a downward motion

Answer:true

Step-by-step explanation:

Answer:

probability that the other side is colored black if the upper side of the chosen card is colored red = 1/3

Step-by-step explanation:

First of all;

Let B1 be the event that the card with two red sides is selected

Let B2 be the event that the

card with two black sides is selected

Let B3 be the event that the card with one red side and one black side is

selected

Let A be the event that the upper side of the selected card (when put down on the ground)

is red.

Now, from the question;

P(B3) = ⅓

P(A|B3) = ½

P(B1) = ⅓

P(A|B1) = 1

P(B2) = ⅓

P(A|B2)) = 0

(P(B3) = ⅓

P(A|B3) = ½

Now, we want to find the probability that the other side is colored black if the upper side of the chosen card is colored red. This probability is; P(B3|A). Thus, from the Bayes’ formula, it follows that;

P(B3|A) = [P(B3)•P(A|B3)]/[(P(B1)•P(A|B1)) + (P(B2)•P(A|B2)) + (P(B3)•P(A|B3))]

Thus;

P(B3|A) = [⅓×½]/[(⅓×1) + (⅓•0) + (⅓×½)]

P(B3|A) = (1/6)/(⅓ + 0 + 1/6)

P(B3|A) = (1/6)/(1/2)

P(B3|A) = 1/3

Answer:

160 adults and 80 students

Step-by-step explanation:

With the information from the exercise we have the following system of equations:

Let x = number of students; y = number of adults

I want to maximize the following:

z = 3 * x + 6 * y

But with the following constraints

x + y = 240

y / 2 <= x

As the value is higher for adults, it is best to sell as much as possible for adults.

So let's solve the system of equations like this:

y / 2 + y = 240

3/2 * y = 240

y = 240 * 2/3

y = 160

Which means that the maximum profit is obtained when there are 160 adults and 80 students, so it is true that added to 240 and or every two adults, there must be at least one student.

Answer:

= A

explanation :

On moving day, Guyton needs to rent a truck. The length of the cargo space is 10 ft , and the height is 1 ft less than the width. The brochure indicates that the truck can hold 420 ft3 . What are the dimensions of the cargo space? Assume that the cargo space is rectangular shape.

Answer:

The dimensions; width w is 7 ft and height is 6 ft

Step-by-step explanation:

L = 10 ft the length of the cargo space

w = the width of the cargo space

h = the height of the cargo space the height is 1 ft less than the width

h = w - 1

The truck can hold 420 ft^3 - this means the volume of the space V = 420 ft^3

But V = L*w*h

Substitute h = w - 1 into the Volume equation

Therefore,

10*w*(w - 1) = 420

10w^2 - 10w - 420 = 0

By Using quadratic equation formula to solve and considering positive answer,

w = {-b +- √(b^2 - 4ac)}/2a

Where;

a = 10, b = -10 and c = -420

w = {-(-10) +- √(-10^2 - 4(10)(-420)}/2(10)

w = {-(-10) +- 130}/20

w = (10 + 130)/20 = 140/20 = 7

Or

w = (10 -130)/20 = -120/20 = -6

Here,

I take positive answers and the width is 7 ft

Also, from h = w - 1

height = 7 - 1 = 6 ft

As per the question on a moving day, the Guyton is renting a truck and the length of his cargo the height of which is less than the width. The brochure indicates the trick that he can hold.

The dimension of the cargo will be based on the amount of capacity of the cargo and the amount of cargo that needs to be moved. On the day of the move, he rent a truck. The L of all cargo space is given as 10 feet, and that of height is 1 foot which is less than the width. This brochure tells us that the truck can hold 420 feet.

Find out more information about the length of the cargo space.

brainly.com/question/1170096.

Answer:

20.8 hours

Step-by-step explanation:

2 3/5 = 2.6.The painter will take (2.6 × 8) = 20.8 hours to paint a wall.

Hope this helps and pls mark as brianliest :)

Answer:

20.8, 20 4/5, and 104/5

We are given the equation y = 3x - 6

The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.

The b value in this equation is -6, thus the y-intercept is -6.

Let me know if you need any clarifications, thanks!

Answer:

c

Step-by-step explanation:

im not too sure