Two parallel lines are intersected by another line, as shown below.



What is the measure of ∠1?

A
61°

B
74°

C
81°

D
119°

52; 64

So the train is going the opposite direction so the two train add to 232 which is model by this formula:

x+12 = y

2(y+x) = 232

so the x is the slower train mph and the y is the faster train mph, you can substitute y with x+12:

2((x+12)+x) = 232

2(2x+12) = 232

4x + 24 = 232

4x + 24 = 232 - 24

4x = 208

4x/4 = 208/4

x = 52

52 + 12 = y

y = 64

so the slower train is 52 and the faster train is 64

Answer:

52

Step-by-step explanation:

Answer:

Hailey walked 70 miles last month.​

Step-by-step explanation:

Consider the provided information.

Hailey walks at an average rate of 3.5 miles  per hour.

She walked 3 weeks  at her regular rate for 6 hours per week.

[tex]3\times (6\times 3.5)=3\times 21=63[/tex]

Hence, she walk 63 miles in last 3 weeks.

She walked 1 week at one-half her regular  rate for 4 hours.

Half of her regular  rate is [tex]3.5\div2[/tex]

Therefore, the distance covers

[tex]1\times (3.5\div2)4=7[/tex]

The sum of distance is: 63+7=70

Hailey walked 70 miles last month.​

Answer:

a. $18.36 for 3 pizzas  :   k  = 6.12

b. $4.17 for 3 pounds of bananas .   k  = 1.39

c. $16.48 for 4 pounds of potatoes .  k  = 4.12

d. 2 cups of flour to make 24 cookie .  k  = 2

Step-by-step explanation:

PROPORTIONALITY:

Two quantities x and y are said to proportional to each other

if for x ∝ y , x = y k.

Here, k i s called the PROPORTIONALITY CONSTANT.

⇒  [tex]x \propto y \implies  k = \frac{x}{y}[/tex]

Now, for the given quantities:

a.  $18.36 for 3 pizzas [box]    

Here,[tex]k =  \frac{18.36}{3} = 6.12[/tex]

So, the proportionality constant is 6.12.

b. $4.17 for 3 pounds of bananas [box]

Here,[tex]k =  \frac{4.17}{3} = 1.39[/tex]

So, the proportionality constant is 1.39.

c. $16.48 for 4 pounds of potatoes [box]

Here,[tex]k =  \frac{16.48}{4} = 4.12[/tex]

So, the proportionality constant is 4.12.

d. 2 cups of flour to make 24 cookies

Here,[tex]k =  \frac{24}{2} = 12[/tex]

So, the proportionality constant is 12

Answer:

[tex]Angle\ b= 70\°[/tex]

Step-by-step explanation:

The correct question is

Angle a and angle b are vertical angles

Angle a =8x+6

Angle b= 4x+38

Solve for x and find the measure of angle b

we know that

Vertical Angles are the angles opposite each other when two lines cross. They are always congruent.

m∠a=m∠b -----> by vertical angles

substitute the given values

[tex](8x+6)\°=(4x+38)\°[/tex]

solve for x

[tex]8x-4x=38-6[/tex]

[tex]4x=32[/tex]

[tex]x=8[/tex]

Find the measure of angle b

[tex]Angle\ b= (4x+38)\°[/tex]

substitute the value of x

[tex]Angle\ b= (4(8)+38)\°[/tex]

[tex]Angle\ b= 70\°[/tex]

Where the above parameters are given, the measure of angle b is 70°.

Given:

Angle a = 8x + 6

Angle b = 4x + 38

Since angle a and angle b are vertical angles, they are equal:

8x + 6 = 4x + 38

Now, let's solve for x:

8x - 4x = 38 - 6

4x = 32

x = 32 / 4

x = 8

Now that we've found x, we can substitute it back into the equation for angle b to find its measure:

Angle b = 4x + 38

= 4 * 8 + 38

= 32 + 38

= 70

So, the measure of angle b is 70°.

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Answer:

98.75%.

Step-by-step explanation:

On March 20, 2011, a $1000 bond had a selling price of $987.50.

We are asked what will be the quoted price for the bond.

Now, the quoted price of a bond is the price at which the bond was last traded and it is expressed as the percentage of the original bond value.

So, in our case the quoted price will be [tex]\frac{987.50}{1000} \times 100 = 98.75[/tex] %. (Answer)

Answer:

D.6x-7

Step-by-step explanation:

Answer:

B. 6x-49

Step-by-step explanation:

36x2-49

36x2=72

72-49=23

18%-7= (-6.82)

6x-49=(-43)

18% - 49=(-50.26)

23-(-6.82)=16.18

23-(-43)=66

23-(-50.26)=73.26

Answer:

The guy wire is 7.2111 ft long

Step-by-step explanation:

Notice that we are in the presence of a right angle triangle formed by: the height (the standing 6 ft pole), the base (the distance from the pole to the anchoring point on the ground), and the actual guy wire. See attached image for reference.

Notice that since pole and ground are perpendicular to each other (at 90 degrees) , the guy wire forms what is called the "hypotenuse" (longest side) of the right angle triangle. We can therefore use the Pythagorean Theorem to solve this problem with the formula for the hypotenuse:

[tex]Hypotenuse=\sqrt{side1^2 +side2^2} \\Hypotenuse= \sqrt{6^2+4^2}\\Hypotenuse=\sqrt{36+16} \\Hypotenuse=\sqrt{52} \\Hypotenuse=7.2111\, ft[/tex]

Answer:

Step-by-step explanation:

4/(x+23)

The quotient of four and a number increased by 23 will be (x/4) + 23.

The divisor and the number being divided by it are referred to as the dividend and the number being divided by it, respectively. The result of division is the quotient.

Mathematical operations, such as number addition, subtraction, multiplication, and division, must be applied. It has the fundamental operators +, -, ×, and ÷.

It is given that the quotient of four and a number increased by 23.

Let the number be x.

The quotient indicates division as x/4.Further, it increases by 23 as,

(x/4) + 23.

Thus, the quotient of four and a number increased by 23 will be (x/4) + 23.

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Answer:

OPTION B

Step-by-step explanation:

3 and 'a' are multiplied and 5 is subtracted from the result.

OPTION B says 5 less than 3 times a number would fit perfectly.

Other options talk about adding or taking ratios and clearly do not fit the case.

Hence, the right answer is Option B.

Answer:

x= -2

Step-by-step explanation:

Because both functions are equal to y wr can set the equations equal to each other and solve for x

-3x-10=6x+8

-3x=6x+18.

-9x=18

x=-2.

Answer:

The total number of social worker doing part time work is 9  .

Step-by-step explanation:

Given as :

The percentage of social worker on which Cole surveyed = 20 %

I.e 20 % of the social worker

Or the number of social worker = 45

Let The number of social worker working part time = x

So, x = 20 % of the total social worker

I.e x = 0.2 × 45

∴ x = 9

So , out of total 45 social worker , the number of social worker working part time = 9

Hence The total number of social worker doing part time work is 9  . Answer

Cole surveyed 225 social workers in total.

Understanding Employment Percentages

To find the total number of social workers that Cole surveyed, we can use a simple proportion based on the information given:

→ 20% of the total number of surveyed social workers = 45.

→ Let N be the total number of social workers surveyed.

Write the equation representing the percentage:

→ 0.20 * N = 45

→ Solve for N by dividing both sides of the equation by 0.20:

N = 45 / 0.20

  = 225

So, Cole surveyed a total of 225 social workers.

Answer:

the answer is b

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{Put the coordinates of the given point A(2, 3)}\\\text{to the equation of a line}\ kx-2y+k=0:\\\\A(2,\ 3)\to x=2,\ y=3\\\\(k)(2)-(2)(3)+k=0\\2k-6+k=0\qquad\text{add 6 to both sides}\\2k+k=6\\3k=6\qquad\text{divide both sides by 3}\\\boxed{k=2}[/tex]

The value of k will be 3.

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The point A(2,3) lies on the line given by equation kx- 2y + k = 0

Since, Point A is lies on the equation.

Hence, Point A(2,3) is satisfy by the equation;

The equation of line,

kx - 2y + k = 0

Substitute (x, y) = (2, 3) in above equation;

k × 2 - 2 × 3 + k = 0

2k - 6 + k = 0

3k - 6 = 0

3k = 6

k = 3

Thus, The value of k will be 3.

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Answer:

6 kitchen remodels

The drawing will help

Answer: it is already in standard form

Step-by-step explanation: for example

To write a linear equation in standard form, move each variable term to the left side of the equation and simplify.

A x+/-By=c and in this case it is 2x-8y=16

The equation 2x-8y=16 is already in the standard form of a linear equation, which is represented as Ax + By = C, where A is 2, B is -8, and C is 16.

In Mathematics, the equation you provided, 2x-8y=16, is already in the standard form. The standard form of a linear equation is usually represented as Ax + By = C, where A, B, and C are integers, and A and B are not both zero. In your equation, 'A' corresponds to 2 (the coefficient of x), 'B' corresponds to -8 (the coefficient of y), and 'C' is equal to 16.

The equation describes a line on a two-dimensional space or plane, and it is used to define the relationship between two variables, x and y. The standard form allows you to quickly identify the x-intercept and y-intercept, which are used to graph the line.

The equation you provided does not need any further adjustments or transformations since it is already in its standard form.

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Answer:

[tex]x=12[/tex]

Step-by-step explanation:

we have

[tex]-8(8-x)=\frac{4}{5}(x+28)[/tex]

solve for x

Applying distributive property both sides

[tex]-8(8)-8(-x)=\frac{4}{5}(x)+\frac{4}{5}(28)[/tex]

[tex]-64+8x=\frac{4}{5}(x)+\frac{112}{5}[/tex]

Multiply by 5 both sides to remove the fractions

[tex]-64(5)+8x(5)=4x+112[/tex]

[tex]-320+40x=4x+112[/tex]

subtract 4x both sides

[tex]-320+40x-4x=4x+112-4x[/tex]

[tex]-320+36x=112[/tex]

Adds 320 both sides

[tex]-320+36x+320=112+320[/tex]

[tex]36x=432[/tex]

divide by 36 both sides

[tex]x=12[/tex]

Answer:

Define the two numbers as

x

x+7

2(x+7) + 1 = 5x

2x + 14 + 1 = 5x

15 = 3x

3x = 15

x = 5

x+7 = 12

One number is 7 less than another. 5 is 7 less than 12.

Twice the second number = 2*12 = 24

Is 24, 1 less than 5 times the first number.

5*5 = 25

25-24 = 1

The smaller of the two numbers is 5.

Answer:

The correct answer is 17 weeks.

Step-by-step explanation:

First, write an equation:

total cost = (30)weekly + deposit

Let's solve:

1004.51 = 30w + 500

504.51 = 30w                          Subtract 500 from both sides

16.817 = w                                Divide both sides by 30

17 = w                                      Round up (money always rounds up)

Hope this helps,

♥A,W,E,S.W.A.N.♥

Answer: The height of hill is 125 feet.

Step-by-step explanation:

Given that velocity of the rollercoaster is [tex]v= \sqrt{(v_\limit{0}^{2} )+64h}[/tex]

Where, [tex]v_\limit{0}[/tex] is initial velocity and h is height from top of hill.

and v is velocity at height h.

Initial Velocity [tex]v_\limit{0}[/tex] is 10feet/sec at top of hill.

Also, Velocity at bottom of the hill is 90feet/sec.

Therefore, the value of h at top of the hill is h=0 and value of h at bottom of the hill is h=h

[tex]v= \sqrt{(v_\limit{0}^{2} )+64h}[/tex]

[tex]90= \sqrt{(10)^{2} +64h}[/tex]

[tex]90^{2}= 10^{2} +64h[/tex]

8100=100+64h

8000=64h

h=125 feets.

Thus, The height of hill is 125 feet.

The coordinates of point P are: (1/5 , -12/5)

Step-by-step explanation:

Here

R(-3,-4) = (x1,y1)

S(5,0) = (x2,y2)

The ratio is: 2:3

The coordinates of a point that divides the line in ratio m:n are given by:

Let P be the point then

[tex](x_P, y_P) = (\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]

Putting values

[tex](x_P, y_P) = (\frac{(2)(5)+(3)(-3)}{2+3},\frac{(2)(0)+(3)(-4)}{2+3})\\= (\frac{10-9}{5},\frac{0-12}{5})\\=(\frac{1}{5},\frac{-12}{5})[/tex]

Hence,

The coordinates of point P are: (1/5 , -12/5)

Keywords: Coordinate geometry

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Answer:

-2x^2-3x-9+-3x^2-4+6

16x - 3x - 9 + 9x - 4 + 6

13x - 9 + 9x  + 2

13x + 9x -9 + 2

21x -7

Step-by-step explanation:

-2x^2-3x-9+-3x^2-4+6

16x - 3x - 9 + 9x - 4 + 6

13x - 9 + 9x  + 2

13x + 9x -9 + 2

21x -7

Answer:

Step-by-step explanation:

Area of side walk = (106 * 81) - (100 * 75)

Area of side walk = 8586 - 7500 = 1086 square foot.

Answer:

5 blue tiles

Step-by-step explanation:

Answer: 5 blue tiles are in each row

Step-by-step explanation:

If Gia has 80 tiles and puts them in all in 8 equal rows there would be 10 rows because 80÷8=10. So considering the fact that there is a equal number of blue and white tiles I divided 10 by 2 and I got 5 so I came to the conclusion that there is 5 blue tiles in each row and there is 5 white tiles in each row.

I'm not sure, so I won't answer it, in case you get it wrong

Answer:

(x-7) (x-4)

Step-by-step explanation:

3x²-33x+84 can be factored into

3 (x-7) (x-4)

Answer:

24000

Step-by-step explanation:

2000 * 12

= 2 * 12 *(1000)

=24*1000

If we want to multiply by 1000 we "tack" three zeros onto the end.

24000.

Answer: 24,000

Step-by-step explanation: if 2,000 multiplied by 10 = 20,000, and 2,000 multiplied by 2 = 4,000, then if you add those together you get 24,000

Answer:

The time taken by smaller pipe to fill the tank alone is 74.2 min

Step-by-step explanation:

Given as :

The time taken by two pipes to fill tank = 19 min

Let the time taken by larger pipe to fill tank = y

And the time taken by smaller pipe to fill tank = x

According to question

The smaller pipe takes 49 minutes longer than larger pipe

I.e x = y + 49

Now,

[tex]\dfrac{1}{x}[/tex] + [tex]\dfrac{1}{y}[/tex] = [tex]\dfrac{1}{49}[/tex]

Or, [tex]\dfrac{1}{y + 49}[/tex] + [tex]\dfrac{1}{y}[/tex] = [tex]\dfrac{1}{49}[/tex]

Or, [tex]\dfrac{y + 49 + y}{y^{2} + 49 y }[/tex] = [tex]\dfrac{1}{49}[/tex]

Or, 2 y + 49 = [tex]\dfrac{y^{2}+49y }{19}[/tex]

Or, 19 × ( 2 y + 49 ) = y² + 49 y

Or, 38 y + 931 = y² + 49 y

Or, y² + 49 y - 38 y - 931 = 0

or, y² + 11 y - 931 = 0

Or, Applying quadratic equation method to calculate the value of y

so, y = [tex]\frac{- b \pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]

Or,  y = [tex]\frac{- 11 \pm \sqrt{11^{2}-4\times 1\times (-931)}}{2\times 1}[/tex]

Or, y = [tex]\frac{- 1 \pm \sqrt{121+3724}}{2}[/tex]

or, y = [tex]\frac{- 1 \pm \sqrt{3845}}{2}[/tex]

or, y = [tex]\frac{- 1 \pm 62.008}{2}[/tex]

∴   y = 25.2 , - 36.5

So, The time taken by larger pipe = y = 25.2 min

and the time taken by smaller pipe to fill the tank = y + 49 = 25.2 + 49 = 74.2 min

Hence The time taken by smaller pipe to fill the tank alone is 74.2 min answer

Answer:

50.8 centimeters

Step-by-step explanation:

So, if Shannon's chair is 20 inches tall, you would multiply that by 2.54 in order to get the length in centimeters.

20 x 2.54 = 50.8.

So Shannon's char is 50.8 centimeters tall.

Answer:

B) 2/11

Step-by-step explanation:

(4/2a)(a/11)

4/2a=2/a

(2/a)(a/11)=2/11