solve the following simultaneous linear equations by the substitution method.
2p + 3q = 10
p - 2q = -2​

Answer:

28o

Step-by-step explanation:

Given:

In the given figure [tex]m\parallel n\parallel p[/tex].

[tex]m\angle 10=2x+70[/tex]

[tex]m\angle 7=5x-20[/tex]

To find:

The [tex]m\angle 3[/tex].

Solution:

If a transversal line intersect two parallel lines, then the alternate exterior angles are equal.

[tex]m\angle 7=m\angle 10[/tex]          (Alternate exterior angle)

[tex]2x+70=5x-20[/tex]

[tex]70+20=5x-2x[/tex]

[tex]90=3x[/tex]

Divide both sides by 3.

[tex]\dfrac{90}{3}=\dfrac{3x}{3}[/tex]

[tex]30=x[/tex]

Now,

[tex]m\angle 3=m\angle 7[/tex]               (Corresponding angles)

[tex]m\angle 3=5x-20[/tex]

[tex]m\angle 3=5(30)-20[/tex]

[tex]m\angle 3=150-20[/tex]

[tex]m\angle 3=130[/tex]

Therefore, the measure of angle 3 is 130 degrees.

Answer:

10 plants

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

He planted 10 this year because last year he planted 12, and 1/3 of that is 4. He planted 6 more than that this year, so 4+6=10.

Answfirst one

Step-by-step explanation:

hope it helps thank u

Answer:

first one

Step-by-step explanation:

2 students have the same age but different heights.

since age is the input and height is the output. in order to be a function one must have exact one output for one input.

since the heights of students in Tessa 's class are not a function of their ages (one input must have two outputs) two students of same age must have different heights.

Answer:

graph c

Step-by-step explanation:

it is the longest one

Answer:

178m squared

Step-by-step explanation:

make 3 rectangular shapes

shape 1 ) 18×5=90

shape 2) 13×6= 78

shape 3) 5×2=10

Add up all the answers and that's the ans

90+78+10=178

Answer:

7.Mean=Ex/n

= 88+96+92+84+86+92+98/7

=90

(b). Median = {84,86,88},92,{92,96,98}

=92

(C).Mode=92 ; it is the number with the highest frequency

9.Mean=Ex/n

=28+26+32+24+27+32+29/7

=28

(b).Median={24,26,27},28,{29,32,32}

=28

(c).Mode=32;it is the number with the highest frequency.

8.Mean=Ex/n

=3.5+5.7+9.8+7+12.4+10.2/6

=8.1

(b).Median={3.5,5.7},7,9.8,{10.2,12.4}

=7+9.8/2

=8.4

(c).Mode=no mode

10.Mean=Ex/n

=2+6+9+8+8+2+8+7+5+4/10

=5.9

(b).Median={2,2,4,5},6,7,{8,8,8,9}

=6+7/2

=6.5

(c).Mode= 8;it is the number with the highest frequency.

I hope this helps.

Answer:

We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

8x = 180  - 148                           [ corresponding angles are equal ]

8x = 32

x = 4

Answer:

(S-2πr^2)/ 2πr = h

Step-by-step explanation:

S = 2πrh + 2πr^2

Subtract 2 pi r^2 from each side

S-2πr^2  = 2πrh + 2πr^2 -2πr^2

S-2πr^2  = 2πrh

Divide each side by 2 pi r

(S-2πr^2)/ 2πr = 2πrh/2πr

(S-2πr^2)/ 2πr = h

It is given that,

→ S = 2πrh + 2πr²

Now subtract 2πr² from the both sides,

→ S - 2πr² = 2πrh + 2πr² - 2πr²

→ S - 2πr² = 2πrh

Then divide both sides by 2πr,

→ (S-2πr²)/2πr = 2πrh/2πr

→ (S-2πr²)/2πr = h

Hence, (S-2πr²)/2πr = h is the result.

Answer:

2

Step-by-step explanation:

X^2+Y^2=4=2^2

Answer:  2.50 dollars

Explanation:

Locate 5 on the x axis, which corresponds to buying 5 kgs of apples.

Draw a vertical line through 5 on the x axis until you reach the blue line. Mark this as point P.

From point P, draw a horizontal line until you reach the y axis. You should arrive at y = 2.5

This tells us that buying x = 5 kgs of apples will cost a total of y = 2.50 dollars.

Answer:

14

Step-by-step explanation:

[tex]f(x) = {x}^{2} + 10 \\ \therefore \: f(2) = {2}^{2} + 10 \\ \therefore \: f(2) = 4 + 10 \\ \therefore \: f(2) = 14 \\ \\ g(x) = |x| \\ \therefore \:g(2) = |2| \\ \therefore \:g(2) = 2 \\ \\ f(2) + g(2) = 14 + 2 \\ \red{ \bold{(f + g)(2) = 14}}[/tex]

Step by step Explanation:

[tex]f(x) = x2 + 10g(x) = 1[/tex]

[tex](f + g)(2).[/tex]

Step 1

The equation is in standard form.

Step 2

Divide both sides by x.

Step 3

Dividing by x undoes the multiplication by x.

Step 4

Divide x 2 + 10 g x by x.

My Answer is.

The values that complete the table are -14, -8, -2 and 4

Given the function y = 3x - 8, we are to complete the given table.

If x = -2

y = 3(-2) - 8

y = -14

If x = 0

y = 3(0) - 8

y = -8

If x = 2

y = 3(2) - 8

y = -2

If x = 4

y = 3(4) - 8

y = 4

Hence the values that complete the table are -14, -8, -2 and 4

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Answer:

7B + (36 * 4) = 184

Step-by-step explanation:

In a family restaurant there are 36 tables and 7 booths.

Each table can seat 4 people.

Let the number of people who can be seated in a booth be represented by B.

Total seating capacity of the restaurant is 184 people.

Expressing this as an equation:

Among the given options, this relation is expressed in the second option, namely, 7B + (36 * 4) = 184

Answer:

they exceeded their goal by 668 cans.

Step-by-step explanation:

multiplying 524 by 7 you get 3668, then subtracting 3,000 from that you get 668.

Answer:

23.1948270095

Step-by-step explanation:

Answer:

Step-by-step explanation:

Rule defining the reflection across the line x = -2 has been given as,

[tex]r_{x=-2}[/tex]

Line x = -2 will work as a mirror for the given triangle J, K, L.

That means distance of the vertices J, K and L and image points J', K' and L' will be equidistant from the line x = -2,

Vertices of the image triangle J'K'L' will be,

J' → (-5, 2)

K' → (-3, 2)

L' → (-4, 1)

Answer:

see below

Step-by-step explanation:  7  1  16  15  

Meal  Alone                      =    393.16

Tax      393.16 × 0.0625   =    24.57        Recall 6.25% = 6.26 / 100 =  0.0625

Tip      393.16 × 0.18         =     70.77        Recall 18% = 18 / 100 =  0.18

Add up the three values  =  488.50        Total

an easier way to do this !!!!!!     use the distributive rule

               393.16 ( 1 + 0.0625 + 0.18)

               393.16 ( 1.2425)

 Total   =  488.5013    or $488.50

Answer:

???

Step-by-step explanation:

Answer: nose

Step-by-step explanation:

Answer:

strange question...

I assume it is asking which ones can be expressed as "5x"

those are all the ones that are a multiple of 5

5, -5x , & 5x^2 satisfy that

Step-by-step explanation:

The terms that are like 5x are: -8x and 4x as they both have the variable x raised to the power of 1 (x).

Given are some algebraic terms 9x², -8x, 5x², 3, 4x, 5 and -5, out of these we need to choose the terms which are like 5x.

To determine the terms with properties similar to 5x, we need to look for terms that have the same variable (x) raised to the same power (1).

The terms that have similar properties to 5x are those with the variable x raised to the power of 1 (x) or simply x.

From the given terms:

9x² - This term has x raised to the power of 2, not 1.

-8x - This term has x raised to the power of 1 (x), similar to 5x.

5x² - This term has x raised to the power of 2, not 1.

3 - This is a constant term and does not have x.

4x - This term has x raised to the power of 1 (x), similar to 5x.

5 - This is a constant term and does not have x.

-5 - This is a constant term and does not have x.

Hence the terms that are like 5x are: -8x and 4x.

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Hello!

9x + 4 + x = 54 <=>

<=> 9x + x + 4 = 54 <=>

<=> 10x + 4 = 54 <=>

<=> 10x = 54 - 4 <=>

<=> 10x = 50 <=>

<=> x = 50 : 10 <=>

<=> x = 5 => 9 × 5 + 4 + 5 = 54

Good luck! :)

Answer:

x = 5

Step-by-step explanation:

First, combine like terms. Like terms are terms with the same variables as well as same amount of said variables:

9x + x + 4 = 54

(9x + x) + 4 = 54

10x + 4 = 54

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do tot he other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

-

First, subtract 4 from both sides of the equation:

10x + 4 (-4) = 54 (-4)

10x = 54 - 4

10x = 50

Next, divide 10 from both sides of the equation:

(10x)/10 = (50)/10

x = 50/10 = 5

x = 5 is your answer.

~

Answer:

103.23 square feet

Step-by-step explanation:

Area of the largest room = length × width

Each centimeter was equal to 1.5 feet

7.4 cm = 1.5 × 7.4 = 11.1 feet

6.2 cm = 1.5 × 6.2 = 9.3 feet

Length = 11.1 feet

Width = 9.3 feet

Area of the largest room = length × width

= 11.1 feet × 9.3 feet

= 103.23 square feet

Answer:

vertically opposite angles

Step-by-step explanation:

supplementaries angles

The measure of angle B is 45° since option F. is correct in the given question.

Any two angles (say X & Y), are said to be supplementary when their summation (X + Y) is equal to 180°.

Angle A and Angle B are supplementary, which implies A+B=180°.

Angle B is one-third angle A, which implies

[tex]B=\frac{1}{3} A[/tex]

or, 3B = A

Using the value of A in the previous equation, we get 3B + B = 180°.

4B = 180°

or, B = 45°.

Thus, the measure of angle B is 45°. The correct answer is option F.

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Answer:

[tex](60\times 50)\div 3[/tex]

Step-by-step explanation:

We are given that

Length of roll of sod, l=3 feet

Width of roll of sod, b=1 feet

Length of courtyard, L=60 feet

Breadth of courtyard, B=50 feet

Area of rectangle=[tex]Length\times breadth[/tex]

Using the formula

Area of roll of sod=[tex]3\times 1 feet^2[/tex]

Area of roll of sod=3 square feet

Area of courtyard=[tex]60\times 50[/tex] square feet

Number of rolls of sod needed=[tex]\frac{Area\;of\;courtyard}{area\;of\;roll\;of\;sod}[/tex]

Using the formula

Number of rolls of sod needed=[tex]\frac{60\times 50}{3}[/tex]

Number of rolls of sod needed=[tex](60\times 50)\div 3[/tex]

This is required expression which represents the number of rolls of sod needed.