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3 years ago

Use the substitution method to solve the system of equations. Choose the

Mathematics

1 answer:

Ksivusya [100]3 years ago

8 0

Answer:

x = 1

y = 3

Step-by-step explanation:

We can solve this problem by inputting the second equation into the first equation by replacing the y variable with the second equation.

x + 3y = 10

y = x + 2

x + 3(x + 2) = 10

Now, distribute three with x and 2

3 * x = 3x

3 * 2 - 6

x + 3x + 6 = 10

4x + 6 = 10

Subtract 6 from both sides

4x = 4

So, x = 1

Solve for y by replacing x in the second equation with 1.

y = 1 + 2

y = 3

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Solve. 90<img src="https://tex.z-dn.net/?f=x" id="TexFormula1" title="x" alt="x" align="absmiddle" class="latex-formula"> = 27.

Irina-Kira [14]

Answer: $x$ ≈ $0.732$

Step-by-step explanation:

You need to find the value of the variable "x".

To solve for "x" you need to apply the following property of logarithms:

$log(m)^n=nlog(m)$

Apply logarithm on both sides of the equation:

$90^x=27\\\\log(90)^x=log(27)$

Now, applying the property mentioned before, you can rewrite the equation in this form:

$xlog(90)=log(27)$

Finally, you can apply the Division property of equality, which states that:

$If\ a=b,\ then\ \frac{a}{c}=\frac{b}{c}$

Therefore, you need to divide both sides of the equation by $log(90)$ . Finally, you get:

$\frac{xlog(90)}{log(90)}=\frac{log(27)}{log(90)}\\\\x=\frac{log(27)}{log(90)}$

$x$ ≈ $0.732$

7 0

3 years ago

I dont know which two chose

pshichka [43]

- Points J, K, and Q are collinear
- There is only one line that can be drawn through points L and P

7 0

3 years ago

Can anyone help with the answers to all these questions with an explanation please?

saveliy_v [14]

ANSWER:

1) 25.70 cm 2) 30.84 cm 3) 10.71 km 4) 1.07 km 5) 6.71 cm 6) 10.07 mm

EXPLANATION:

1. Know that the circumference formula for a full circle is:

$C = 2\pi r$

The value of pi ( $\pi$ ) = 3.14

The radius ( $r$ ) will be given in the diagrams.

2. Now we can figure out the perimeters.

Shape One: Semi-circle

C = 2 x 3.14 x 5

C = 31.4 cm

Divide the circumference by 2 because it is a semi-circle. Then add 10 cm to this (because the flat side is 10 cm).

P = $\frac{31.4}{2} +10$

P = 25.7 cm ≈ 25.70 cm

Shape Two: Semi-circle

C = 2 x 3.14 x 6 (the picture shows the diameter so we need to half that to get the radius)

C = 37.68 cm

Divide the circumference by 2 because it is a semi-circle. Then add 12 cm to this (because the flat side is 12 cm).

P = $\frac{37.68}{2}+12$

P = 30.84 cm

Shape Three: Quadrant

C = 2 x 3.14 x 3

C = 18.84 km

Divide the circumference by 4 because it is a quadrant. Then add 6 km to this (because the two flat sides are 3 km each and so it is 6 km total).

P = $\frac{18.84}{4} +6$

P = 10.71 km

Shape Four: Quadrant

C = 2 x 3.14 x 0.3

C = 1.884 km

Divide the circumference by 4 because it is a quadrant. Then add 0.6 to this (because the two flat sides are 0.3 km each and so it is 0.6 km total).

P = $\frac{1.884}{4} + 0.6$

P = 1.071 km ≈ 1.07 km

Shape Five

C = 2 x 3.14 x 1

C = 6.28 cm

For this shape, we need to subtract the circumference of the missing sector from the circumference of the full circle to obtain the circumference for this shape. So, the circumference for the shape would be:

C = $6.28 - \frac{6.28}{4}$

C = 6.28 - 1.57

C = 4.71 cm

Then add the flat sides (1 cm + 1 cm = 2 cm) to this circumference to get the perimeter.

P = 4.71 + 2

P = 6.71 cm

Shape Six

C = 2 x 3.14 x 1.5 (Divide the 3 mm diameter by 2 to get the radius)

C = 9.42 cm

Do the same thing you did for Shape 5.

C = $9.42 - \frac{9.42}{4}$

C = 7.065 mm

Then add the flat sides (1.5 + 1.5 = 3) to this circumference.

P = 7.065 + 3

P = 10.065 mm ≈ 10.07 mm

7 0

3 years ago

hailey borrowed $100 from here friend she is paying here 20 per week how many weeks will it take here to pay here back?

romanna [79]

Answer: 5 weeks

Step-by-step explanation:

100 divided by 20 equals 5

4 0

2 years ago

Read 2 more answers

A $387.50 item is marked down by 49%. What is the new cost of the item?

Free_Kalibri [48]

Initial(1-markdown)
387.50(1-49%)=197.625

final answer: $197.63

5 0

3 years ago