Which ordered pairs make both inequalities true? Select two options.
y < 5x + 2 y>=1/2x+1

(-1,3)
(0,2)
(1,2)
(2,-1)
(2,2)

Answer:

A

Step-by-step explanation:

Lets say x=1

y: 3(1)+1=4

x: 4(1)-1=3

Final answer:

The correct option is (D) (2,7). To solve the system of equations, set them equal to each other and solve for x, which is 2, and then substitute x back into either equation to find y, which is 7. Hence, the intersection point is (2, 7).

Explanation:

To find the solution to a system of equations when graphed, you look for the point where the two lines intersect. The given equations are y=3x+1 and y=4x-1.

Since both equations equal y, you can set them equal to each other to find the point of intersection:

3x + 1 = 4x - 1.

To solve for x, subtract 3x from both sides:

1 = x - 1.

Then, add 1 to both sides to isolate x:

x = 2.

To find the corresponding y value, substitute x into one of the original equations, let's use the first one:

y = 3(2) + 1,

which simplifies to y = 6 + 1 = 7.

Therefore, the solution to the system of equations and the point of intersection is (2, 7).

Answer:

-2a²

Step-by-step explanation:

The question is  2a × -a

This means 2a(-a)

= -2×(a×a)

=-2(a²)

=-2a²

Answer:

10) Exact Answer: 36

Estimate: 36

11) Exact Answer: 2001

Estimate: 1900

Step-by-step explanation:

10a) To find the exact answer, simply divide the given numbers.

10b) To find the estimated answer, use compatible numbers. We know that any "hundred" number is easily divisible by 5. Therefore, 900/5 = 36.

It is possible for the estimate to be the same as the exact answer.

10a) To find the exact answer, simply divide the given numbers.

10b) To find the estimated answer, use compatible numbers. There is no pattern we can look for, so round to the nearest whole number.

We know that if we rounded .38 to 0 or 1, the answer would not be nearly as close as if we rounded .38 to .4.

Therefore, 760/.4 = 1900

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Answer:

8y³ + 6y² - 29y + 15

Step-by-step explanation:

Take each separate term in the second set of parentheses and multiply it by the terms in the first set of parentheses. Put them altogether, and you will arrive at the above answer.

I am joyous to assist you anytime.

Hence, the product is [tex]8y^3+6y^2-29y+15[/tex]

The product of two numbers is the result you get when you multiply them together. So 12 is the product of 3 and 4, 20 is the product of 4 and 5, and so on.

multiplying corresponding terms,

[tex](4y-3)(2y^2+3y-5)\\8y^3+12y^2-20y-6y^2-9y+15\\8y^3+6y^2-29y+15[/tex]

Hence, the product is [tex]8y^3+6y^2-29y+15[/tex]

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Answer:

  F ≥ 45

Step-by-step explanation:

"No less than" means "greater than or equal to", so you can write the expression as ...

  F ≥ 45 . . . . . miles per gallon

Answer:

87.88 ft^2.

Step-by-step explanation:

Area = 1/2 * base * height

= 1/2 * 16.9 * 10.4

= 87.88 ft^2.

Answer:

87.88 ft²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 16. 9 and h = 10.4, so

A = 0.5 × 16.9 × 10.4 = 87.88 ft²

Answer:

The correct answer would be option A, 21.37

Step-by-step explanation:

In order to find out the percentage change of price of a product, either increase of decrease, that is found by finding the change in the price and then divide it by the base price and then finding the percentage of that price. The whole process is as follows:

Original price of iPod: $210.95

New Price of iPod: $165.88

Decrease in the price of iPod: 210.95-165.88= 45.07

Now dividing decreased price with the original price we get:

45.07/210.95=0.213652

Now to find the percentage, we need to multiply it with 100

0.213652*100=21.3652% which is approximately 21.37%

Answer:

Choice 4.

Step-by-step explanation:

f(g(x))

Replace g(x) with x^2+8 since g(x)=x^2+8.

f(g(x))

f(x^2+8)

Replace old input,x, in f with new input, (x^2+8).

f(g(x))

f(x^2+8)

2(x^2+8)+5

Distribute:

f(g(x))

f(x^2+8)

2(x^2+8)+5

2x^2+16+5

Combine like terms:

f(g(x))

f(x^2+8)

2(x^2+8)+5

2x^2+16+5

2x^2+21

Answer:

D

Step-by-step explanation:

Took the test

Answer:

964.62

Step-by-step explanation:

Let x = the original price

35% less than means we pay 65% of  the original price

627 = 65% x

Changing to decimal form

627 = .65x

Divide each side by .65

627/.65 = .65x/.65

964.6153846 =x

Rounding to the near cent

964.62

Answer:

4

Step-by-step explanation:

Start by multiplying both sides by 4.

[tex]\frac{1}{4} x-\frac{1}{8} =\frac{7}{8} +\frac{1}{2} x\\x-\frac{1}{2} =\frac{7}{2}+2x[/tex]

Next, combine like terms.

[tex]x-\frac{1}{2} =\frac{7}{2}+2x\\-\frac{1}{2} =\frac{7}{2} +x\\x=\frac{8}{2} \\x=4[/tex]

Answer:

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

Step-by-step explanation:

4x-6=10x-3 (add 6 to both sides)

4x=10x+3 (subtract 10x from both sides)

-6x=3 (divide both sides by -6)

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

Answer: X = -1/2

Step-by-step explanation: Your goal is to isolate x. First, subtract 4x from each side.

-6 = 6x - 3

Add 3 on both sides.

-3 = 6x

Divide by 6 on each side.

X = -1/2

Answer:

14, 18, 20, and 24 are not perfect squares.

The numbers that are not perfect squares are:

1. 20

2. 18

3. 14

4. 24

These numbers do not have integer square roots, which means they are not perfect squares.

A perfect square is a number that can be expressed as the product of an integer multiplied by itself. For example, 25 is a perfect square because [tex]\(5 \times 5 = 25\).[/tex]

Let's examine each number:

1. 25 - This is a perfect square because  [tex]\(5 \times 5 = 25\).[/tex]

2. 20 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.

3. 18 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.

4. 36 - This is a perfect square because [tex]\(6 \times 6 = 36\).[/tex]

5. 16 - This is a perfect square because [tex]\(4 \times 4 = 16\).[/tex]

6. 14 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.

7. 24 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.

Therefore, the numbers that are not perfect squares are 20, 18, 14, and 24. They cannot be represented as the square of an integer. The other numbers, 25, 36, and 16, are perfect squares as they can be expressed as the square of an integer.

The complete question is here.

Which numbers are not perfect squares? 25 20 18 36 16 14 24

Answer:

A=1512

Step-by-step explanation:

The area of a rectangle with a length of 27 and a height of 56 is 1512.

Formula: A=wl

A=wl=56·27=1512

Answer: 1,512 units^2

Step-by-step explanation: To find the area of a rectangle, multiply the length by the width. 27 x 56 =1512. Since you are finding the area, the answer would be squared.

Answer:

54

Step-by-step explanation:

Answer:

54 square units

Step-by-step explanation:

In order to calculate the surface area of the prism you have to calculate the area of each face of the prism, and you have to remember the different formulas to calculate the areas:

[tex]Rectangle=Length*Width[/tex]

[tex]Triangle=\frac{Base*Height}{2}[/tex]

So you just have to insert the values into the formulas:

[tex]Rectangle1=4*3.5[/tex]

[tex]Rectangle1=14[/tex]

[tex]Rectangle2=5*3.5[/tex]

[tex]Rectangle2=17.5[/tex]

[tex]Rectangle3=3*3.5[/tex]

[tex]Rectangle3=10.5[/tex]

[tex]Triangle1=\frac{4*3}{2}[/tex]

[tex]Triangle1=6[/tex]

[tex]Triangle2=\frac{4*3}{2}[/tex]

[tex]Triangle2=6[/tex]

If you add up all the faces, you get the surface area of the prism:

14+17.5+10.5+6+6=54

Answer:

C 90

Step-by-step explanation:

Answer: OPTION B.

Step-by-step explanation:

You can observe in the figure provided that the angle 3 and the angle that measures 70° , share the same vertex, therefore, you can conclude that they are Vertical angles and they are congruent. Then:

[tex]m\angle 3=70\°[/tex]

You can notice that the angle 1 and the angle that measures 70° are Complementary angles (They add up to 90°), then you can find the measure of the angle 1:

[tex]m\angle 1+70\°=90\°\\\\m\angle 1=90\°-70\°\\\\m\angle 1=20\°[/tex]

Then:

[tex]m\angle 3-m\angle 1=70\°-20\°\\\\m\angle 3-m\angle 1=50\°[/tex]

Answer:

corresponding angles

Step-by-step explanation:

Corresponding angles are in matching corners .

Both 5 and 6 are in the lower left corner

Answer:

5.

Step-by-step explanation:

1 1/3 * 3 3/4

= 4/3 * 15/4

= 60/12

= 5.

First we simplify,

[tex]1\dfrac{1}{3}\cdot3\dfrac{3}{4}[/tex]

to

[tex]\dfrac{4}{3}\cdot\dfrac{15}{4}[/tex]

Then we continue simplifying,

[tex]

\dfrac{4\cdot15}{4\cdot3}=\dfrac{15}{3}=\boxed{5}

[/tex]

Hope this helps.

r3t40

Answer:

Option A is the correct answer.

Step-by-step explanation:

Period of simple pendulum is given by the expression,

            [tex]T=2\pi \sqrt{\frac{l}{g}}[/tex]

Where l is the length of pendulum, g is acceleration due to gravity.

Here given for Venus

         Period, T = 2.11 s

        Length of pendulum, l = 1 m

     We need to find acceleration due to gravity, g

Substituting

            [tex]2.11=2\pi \sqrt{\frac{1}{g}}\\\\\sqrt{g}=\frac{2\pi}{2.11}\\\\g=8.87m/s^2[/tex]

Acceleration due to gravity of Venus = 8.9 m/s²

Option A is the correct answer.

Answer:

Explanation:

You can create the graph by determining the expression that shows the relationship between the variables and then drawing the graph in a coordinate system.

1. Determine the expression that relates the variables.

a) The name of the variables is given:

b) Point rules:

In conclusion, it has been determined that the expression that rules the system of points is the inequality 2x + y ≥ 4.

2) Building the graph

In conclusion, you can use the points (2,0) and (0,4) to draw the line that is the border of your graph.

        x ≥ 0 and y ≥ 0

The resulting graph is attached.

Answer:

D

Thank me later!! Just did the test on edge

Answer:

420 minutes

Step-by-step explanation:

1 hour = 60 minutes

7 * 1 hour = 7 * 60 minutes

7 hours = 420 minutes

We know that 1 hour = 60 minutes

To find how many minutes is in seven hours, we can multiply 60 by 7 and we will get a product of 420.

1 hour = 60 minutes

2 hours = 120 minutes

3 hours = 180 minutes

4 hours = 240 minutes

5 hours = 300 minutes

6 hours = 360 minutes

7 hours = 420 minutes

Answer:

25

Step-by-step explanation:

If the mean of the temperatures in the chart is 24° with standard deviation of 4º, there has been 25 years within one  standard deviation of the mean.

27° is the temperature value that is within one standard deviation of mean.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Given

Mean of the temperatures in the chart [tex]\mu[/tex] [tex]\mew[/tex]= 24°

Standard deviation [tex]\sigma[/tex] = 4º

The lower and upper bound for temperature within one standard deviation of the mean is given as:

Lower bound =  [tex]\mu[/tex] -  [tex]\sigma[/tex] = 24° - 4º =  20°

Thus, the lower bound is  = 20°

Upper bound =  [tex]\mu[/tex] + [tex]\sigma[/tex] = 24° + 4º =  28°

Thus, the upper bound is  = 28°

Now, the temperature value between (Lower bound, Upper bound) that is (20°, 28°) is said to be within one standard deviation of the mean.

Hence, 27° is the temperature value that is within one standard deviation of mean.

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Answer:

The answer is -3.

Step-by-step explanation:

-3(-3+2)-6

First solve the parenthesis. -3+2= -1.

-3(-1)-6

-3 times -1 is 3. Two negatives always equal a positive.

3-6 = -3.

Answer:

-1½ = b

Step-by-step explanation:

Combining all like-terms on the right side of the equivalence symbol will give you this:

4b + 6 = 0

- 6 -6

------------

4b = -6 [Divide by 4]

b = -1½ [OR -1,5]

I am joyous to assist you anytime.

If there was an illustration, I would be happy to assist you.

Let r = amount customer gets back

r = 1000 - (1000)(0.03)

r = 1000 - 30

r = $970

For this case we have the following polynomial:

[tex]-24a ^ 6b ^ 4-40a ^ 3[/tex]

We must find the greatest common factor of the terms of the polynomial.

The GCF of the coefficients is given by:

[tex]24 = 3 * 8\\40 = 5 * 8[/tex]

Then we look for the GFC of the variables:

We have then:

[tex]a ^ 6 = a ^ 3a ^ 3\\a ^ 3 = a ^ 3[/tex]

Finally rewriting we have: [tex]-24a ^ 6b ^ 4-40a ^ 3 = -8a ^ 3 (3a ^ 3b ^ 4 + 5)[/tex]

Answer:

the complete factored form of the polynomial is:

[tex]-8a ^ 3 (3a ^ 3b ^ 4 + 5)[/tex]

[tex]\bf \stackrel{mixed}{-3\frac{3}{8}}\implies -\cfrac{3\cdot 8+3}{8}\implies \stackrel{improper}{-\cfrac{27}{8}}~\hfill \stackrel{mixed}{-1\frac{3}{4}}\implies -\cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{-\cfrac{7}{4}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{from left to right}}{-\cfrac{\stackrel{9}{~~\begin{matrix} 27 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{4}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\times -\cfrac{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\div -\cfrac{7}{4}}\implies \cfrac{9}{4}\div -\cfrac{7}{4}[/tex]

[tex]\bf \cfrac{9}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\times-\cfrac{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{7}\implies -\cfrac{9}{7}[/tex]

Answer:

C. [tex]y=(x-3)^2[/tex] and [tex]y=x^2-6x+9[/tex]

Step-by-step explanation:

before answering the problem let us remind the formula for square of sum and differences

[tex](a+b)^2=a^2+2 \times a \times b + b^2[/tex]

[tex](a-b)^2=a^2-2 \times a \times b + b^2[/tex]

We are going to use the above two formulas to solve each part and come to an answer

A. [tex]y = (x + 3)^2[/tex]

[tex](x + 3)^2=x^2+2 \times x \times 3 + 3^2[/tex]

[tex](x + 3)^2=x^2+6x+9[/tex]

Hence this option is not correct pair

B. [tex]y = (x-5)^2[/tex]

[tex](x - 5)^2=x^2-2 \times x \times 5 + 5^2[/tex]

[tex](x -5)^2=x^2-10x+25[/tex]

Hence this option is also not correct pair

C. [tex]y = (x -3)^2[/tex]

[tex](x - 3)^2=x^2-2 \times x \times 3 + 3^2[/tex]

[tex](x -3)^2=x^2-6x+9[/tex]

Hence this option is correct as it have equivalent pair

D. [tex]y = (x + 5)^2[/tex]

[tex](x + 5)^2=x^2+2 \times x \times 5 + 5^2[/tex]

[tex](x + 5)^2=x^2+10x+25[/tex]

Hence this option is also not correct pair

To solve (sin(x))^2 = 1/36, we find the arcsine of ±1/6. The solutions are sin⁻¹(1/6), π - sin⁻¹(1/6), 2π - sin⁻¹(1/6), and π + sin⁻¹(1/6) within the interval [0,2π].

To solve the equation (sin(x))^2 = 1/36 in the interval [0,2π], we first take the square root of both sides to get sin(x) = ±1/6. The sine function oscillates between -1 and 1 every 2π radians, which means that we are looking for angles where the sine value is ±1/6.

To find the specific angles, we use the arcsine function or inverse sine function. The principal value of sin⁻¹(1/6) gives us one of the solutions, and considering the symmetry of the sine function, the other solutions can be found in the second and fourth quadrants, where the sine function is positive and negative, respectively.

The solutions to sin(x) = 1/6 in the interval [0,2π] are x = sin⁻¹(1/6) and x = π - sin⁻¹(1/6). For sin(x) = -1/6, the solutions are x = 2π - sin⁻¹(1/6) and x = π + sin⁻¹(1/6). Thus, the solutions to the original equation (sin(x))^2 = 1/36 within [0,2π] are sin⁻¹(1/6), π - sin⁻¹(1/6), 2π - sin⁻¹(1/6), and π + sin⁻¹(1/6), all of which can be calculated to find the exact values.