Use elimination to solve and match each system of equations to the correct solution

9x+4y=-72
2x-3y=-16

Answer:

Sample response: The absolute value symbol in the equation indicates two solutions because absolute value is the distance from a number to zero on a number line. Two different directions, to the right and to the left, will determine the

Step-by-step explanation:

Answer:

  24 cm

Step-by-step explanation:

Since the triangles are similar, their dimensions are proportional. The base DC is half the base AE, so we know the ratio of triangle heights is 1 : 2.

Then the bottom height (h) ratio to the overall height is ...

  h : 36 = 2 : (1+2) = 2 : 3 = 24 : 36

The height h is 24 cm.

Answer:

6.5

Step-by-step explanation:

|-6.5| = 6.5

Answer:

6.5

Step-by-step explanation:

Points play a crucial role in defining distances, angles, and relationships between different geometric objects, providing a foundation for the study of geometry.

In geometry, a point is a fundamental concept that represents a precise location in space. It is a basic building block from which geometric figures and shapes are constructed. A point has no size, shape, or dimensions. It is often denoted by a dot or a small letter, such as point A (A). Points are used to describe the positions of other geometric elements, such as lines, curves, and polygons. They serve as reference markers and can be connected to form line segments and rays.

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Answer:

An integer number is one that can be written without using fractions or decimals, and it is an expression of ( 1.2.3..... ) and 0, and negative numbers (- 1-2-3...... )

Answer:

x + y

Step-by-step explanation:

In these examples, a and b are positive numbers.

- a + ( - b) = - (a+ b)

- a - ( - b) = - a + b

- a * - b = a * b

- a / -b = a/b

Hope this helps understanding.

Answer:

Please check explanation

Step-by-step explanation:

Here, in this question, we are interested in identifying the error made by Jillian in his solution of the equation.

This error is traceable to the second step of his solution. Adding 4.3 to 7.05 and subtracting again is the same thing as not adding anything or just adding zero only.

What he should have done is to subtract the value of 4.3 from both sides of the equation. In that manner, he would have been able to isolate v on the left hand side of the equation

Answer:

a. i. x ≤ 25 ii. 16 < x < 35 iii. 25 < x ≤ 95  

b. The second and third car seats are appropriate for a 35 lb child.

Step-by-step explanation:

a. Model those ranges with compound inequalities

Let x represent the car seat.

i. A car seat designed for a child weighing up to  and including 25 lb is described by the inequality.

x ≤ 25

ii. A car seat designed for a child weighing between 16 lb  and 35 lb is described by the inequality.

16 < x < 35

iii. A car seat designed for a child weighing between 25 lb  and 95 lb inclusive is described by the inequality.

25 < x ≤ 95

b. Which car seats are appropriate for a  33-lb child?

Since 35 lb is included in the range of the inequalities for the second and third card seats, the second and third car seats are appropriate for a 35 lb child.

Answer:4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

Answer: It's good to think about things before doing them because it is more thought out and you have a better chance of getting things correct whereas without thinking your most likely going to get it wrong. Without thinking through your options you are basically guessing the answer. I hope this helped you have a great day and god bless you :D

Answer:

t = [tex]\frac{l}{pr}[/tex]

Step-by-step explanation:

Formula or literal equation used to calculate the simple interest is,

l = prt

where 'l' = Simple interest

p = principle amount invested

r = rate of interest

t = time or duration of the investment

If we have to calculate the time of investment form the given formula,

l = prt

By the division property of equality,

[tex]\frac{l}{pr}=\frac{prt}{pr}[/tex]

[tex]t=\frac{l}{pr}[/tex]

Therefore, formula to be used is, [tex]t=\frac{l}{pr}[/tex]

Answer:

[tex]MP= (-5,7.5 )[/tex]

Step-by-step explanation:

[tex]MP= (\frac{x_1+x_2}{2} )(\frac{y_1+y_2}{2} )[/tex]

[tex]MP= (\frac{-7+-3}{2} )(\frac{6+9}{2} )[/tex] -7+-3= -10   6+9=15

[tex]MP= (\frac{-10}{2} )(\frac{15}{2} )[/tex] -10/2=-5 15/2=7.5

[tex]MP= (-5,7.5)[/tex]

-5 < -3 and the second inequality is -3 > -5

Answer:

210 divided 2 1/2= 84....

The 210 divided by 2 1/2 is 84.

To calculate 210 divided by 2 1/2, first, we need to convert the mixed number 2 1/2 to an improper fraction. The improper fraction for 2 1/2 is (2 * 2 + 1) / 2 = 5/2.

Now, we can perform the division:

210 ÷ 5/2

To divide by a fraction, we multiply by its reciprocal:

210 * 2/5

Now, perform the multiplication:

(210 * 2) / 5 = 420 / 5

Next, simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 5:

420 ÷ 5 = 84

The result of 210 divided by 2 1/2 is 84. So, 210 ÷ 2 1/2 = 84.

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What is that supposed to mean

Answer:  see proof below

Step-by-step explanation:

Given: A + B = C                → A = C - B

                                          → B = C - A

Use the Double Angle Identity:     cos 2A = 2 cos² A - 1

                                             → (cos 2A + 1)/2 = cos² A

Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · 2 cos [(A - B)/2]

Use Even/Odd Identity: cos (-A) = cos (A)

Proof LHS → RHS:

LHS:                     cos² A + cos² B + cos² C

[tex]\text{Double Angle:}\qquad \dfrac{\cos 2A+1}{2}+\dfrac{\cos 2B+1}{2}+\cos^2 C\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg(2+\cos 2A+\cos 2B\bigg)+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\dfrac{1}{2}\bigg(\cos 2A+\cos 2B\bigg)+\cos^2 C[/tex]

[tex]\text{Sum to Product:}\quad 1+\dfrac{1}{2}\bigg[2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A-2B}{2}\bigg)\bigg]+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\cos (A+B)\cdot \cos (A-B)+\cos^2 C[/tex]

[tex]\text{Given:}\qquad \qquad 1+\cos C\cdot \cos (A-B)+\cos^2C[/tex]

[tex]\text{Factor:}\qquad \qquad 1+\cos C[\cos (A-B)+\cos C][/tex]

[tex]\text{Sum to Product:}\quad 1+\cos C\bigg[2\cos \bigg(\dfrac{A-B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{A-B-C}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+(C-B)}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-(C-A)}{2}\bigg)[/tex]

[tex]\text{Given:}\qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+A}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-B}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1+2\cos C \cdot \cos A\cdot \cos (-B)[/tex]

[tex]\text{Even/Odd:}\qquad \qquad 1+2\cos C \cdot \cos A\cdot \cos B\\\\\\.\qquad \qquad \qquad \quad =1+2\cos A \cdot \cos B\cdot \cos C[/tex]

LHS = RHS: 1 + 2 cos A · cos B · cos C = 1 + 2 cos A · cos B · cos C   [tex]\checkmark[/tex]

Answer:

[tex]\boxed {\tt f(5)=101}[/tex]

Step-by-step explanation:

We are given the function:

[tex]f(x)=18x+11[/tex]

and asked to find f(5). Therefore, we must substitute 5 in for each [tex]x[/tex].

[tex]f(5)=18(5)+11[/tex]

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Multiply 18 and 5.

[tex]f(5)=90+11[/tex]

Add 90 and 11.

[tex]f(5)=101[/tex]

f(5) is equal to 101.

Answer:

in 3/4 year tree had grown 2/3

in 1 year tree had grown (2/3)/0.75 =8/9 feet

Step-by-step explanation:

Step-by-step explanation:

9868866858566586575765578

Answer:

[tex]x > \frac{16}{3} [/tex]

Step-by-step explanation:

[tex]4x - 8 > 24 - 2x \\ 4x + 2x > 24 + 8 \\ 6x > 32 \\ x > \frac{16}{3} [/tex]

Answer:

11 hours and 22 minutes

Answer:

2 months for $175

Step-by-step explanation:

2x5 is 10 so 2x50 = 100 and since 75 was already in the bank when he started doing deposits, it took him 2 month to deposit 100

Answer:

50

Step-by-step explanation:

i got this one wrong 175 isnt correct

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

To solve for x, we can use the Exterior Angle Theorem.

The Exterior Angle Theorem states that the exterior angle is equivalent to the sum of the two opposite, interior angles.

So, we can write the following equation:

[tex](6+25x)=(44)+(18x-3)[/tex]

Now, we just have to solve for x.

On the right, let's subtract. So:

[tex]6+25x=18x+41[/tex]

Now, let's subtract 18x from both sides. This gives:

[tex]6+7x=41[/tex]

Now, let's subtract 6 from both sides. This will yield:

[tex]7x=35[/tex]

And, finally, let's divide both sides by 7, giving us:

[tex]x=5[/tex]

And we're done!

We can use the Exterior Angle Theorem.

6 + 25x = 44 + 18x - 3

6 + 25x = 18x + 41

25x = 18x + 35

7x = 35

x = 5

Best of Luck!

Answer:

+ or - $9

Step-by-step explanation:

Step-by-step explanation:

35•32 or 1120 there you go

Refer to the attachment for solution.