The points (14,22) and (49,77) form a proportional relationship. Find the slope of the line through
the points. Then use the slope to graph the line.
The slope is

Answer:

[tex]x =3[/tex] or [tex]x = 7[/tex]

Step-by-step explanation:

Given

[tex]x^2 - 10x = -21[/tex]

Required

Solve by factoring & quadratic formula

By Factoring:

[tex]x^2 - 10x = -21[/tex]

Equate to 0

[tex]x^2 - 10x +21 = 0[/tex]

Expand:

[tex]x^2 - 7x -3x+21 = 0[/tex]

Factorize:

[tex]x(x-7)-3(x-7) = 0[/tex]

[tex](x-3)(x-7) = 0[/tex]

[tex]x -3 = 0[/tex] or [tex]x - 7 = 0[/tex]

[tex]x =3[/tex] or [tex]x = 7[/tex]

By quadratic

[tex]x^2 - 10x = -21[/tex]

Equate to 0

[tex]x^2 - 10x +21 = 0[/tex]

For

[tex]ax^2 + bx + c = 0[/tex]

x is solved using:

[tex]x = \frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

where

[tex]a = 1[/tex]; [tex]b = -10[/tex]; [tex]c = 21[/tex]

So:

[tex]x = \frac{-(-10)\±\sqrt{(-10)^2-4*1*21}}{2*1}[/tex]

[tex]x = \frac{10\±\sqrt{100-84}}{2}[/tex]

[tex]x = \frac{10\±\sqrt{16}}{2}[/tex]

[tex]x = \frac{10\±4}{2}[/tex]

Split

[tex]x = \frac{10+4}{2}[/tex] or [tex]x = \frac{10-4}{2}[/tex]

[tex]x = \frac{14}{2}[/tex] or [tex]x = \frac{6}{2}[/tex]

[tex]x = 7[/tex] or [tex]x =3[/tex]

Answer:

I think it is the second one, flown by women

Step-by-step explanation:

Answer:

i think its 48

Step-by-step explanation:

u can split it into 2 triangles

Answer:

Its A

Step-by-step explanation:

Answer:que?

Step-by-step explanation:

Answer:

· Dibuja la cancha de Baloncesto con medidas a escala #escudomania #aprenderadibujar #dibujarfacil Hola, bienvenido a este canal #escudomania, aqui encontraras...

Step-by-step explanation:

Answer:

x(x-8)(x+8)

Step-by-step explanation:

it ends with a negative 64 and the only one that also end with that would be C because -8×8 = 64

Answer:

m = 2

Step-by-step explanation:

Answer:

8x-20

Step-by-step explanation:

Answer:

You should use 0.6 cups of pineapple juice if you only have 1 cup of orange juice.

Step-by-step explanation:

With the information provided about the recipe, you can use a rule of three to find the cups of pineapple you should use if you only have 1 cup of orange juice given that the recipe calls for 30 cups of orange juice and 18 cups of pineapple juice:

30 cups of orange juice → 18 cups of pineapple juice

 1 cup of orange juice    →                    x

x=(1*18)/30=0.6 cups of pineapple juice

According to this, the answer is that you should use 0.6 cups of pineapple juice if you only have 1 cup of orange juice.

Step-by-step explanation:

2x+x=.3+.8

3x= 1.1/:3

x=0.366

Answer:

x = -2.566667

Step-by-step explanation:

simplify both sides

8 + 2x = 0.3 - x

8 + 2x = 0.3 + - x

2x + 8 = - x + 0.3

add x to both sides

2x + 8 + x = - x + 0.3 + x

3x + 8 = 0.3

subtract 8 from both sides

3x  + 8 - 8 = 0.3 - 8

3x = -7.7

divie both sides by 3

3x/3 = -7.7/3

x = -2.566667

Answer:

slope of p= -7/12

slope of q= -3/6.8

slope of r= -16/6.4

slope of m= 6.2/15.5

slope of n= 6.8/17

Step-by-step explanation:

The slopes of the line are given as 2.5 for p and q and -2.5 for r, m and n respectively.

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.

The negative slope indicates the rate of decrease while the positive shows the rate of increase.

The slope of the given lines can be obtained as follows,

(a) In order to find slope of line p,

Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,

m = (-3 - 8)/(0.4 - (-4))

⇒ m = -2.5

(b)  In order to find slope of line q,

Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,

m = (13 - 0)/(6.8 - 12)

⇒ m = -2.5

(c)  In order to find slope of line r,

Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,

m = (13 - (-3))/(6.8 - 0.4)

⇒ m = 2.5

(d) In order to find slope of line m,

Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,

m = (-15.5 - 0)/(0 - 6.2)

⇒ m = 2.5

(e)  In order to find slope of line n,

Use the formula m = (x₂ - x₁)/(y₂ - y₁) and substitute the corresponding values to get,

m = (-5 - 12)/(- 6.8 - 0)

⇒ m = 2.5

Hence, the slopes of first two lines are 2.5 and of the remaining three are 2.5.

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Answer: 3.25 + 5.50s ≤ 30

Step-by-step explanation:

The following information can be gotten from the question.

Cost of chocolate milk = $3.25

Cost of stack pancake = $5.50

Maximum amount to be spent by Benjamin = $30

Number of stacks of pancakes to be bought = s

First, we need to calculate the stacks of pancakes that Benjamin can buy. This will be:

= $5.50 × s

= 5.50s

Therefore, the total money that Benjamin will spend will be:

= 3.25 + 5.50s

Since he wants to be able to be at most $30 before tax, the inequality can be written as:

= 3.25 + 5.50s ≤ 30

Answer:

Remote Control Car Fast RC Cars Toys for 6-12 Years Old Boys,High Speed RC Truck Offroad Remote Control Truck RC Rock Crawler All Terrain RC Car Toys for Boys Kids Gift (Green) 3.6 out of 5 stars 141 More Buying Choices $14.62 (1 used offer)

Step-by-step explanation:

Histogram attached

Answer and explanation:

To find the center of the distribution, we find the mean of the distribution.

Mean= sum of all values/number of values

To calculate the mean of the distribution using the histogram(attached) with given frequencies, we find the mid point of each class and multiply by its frequency to get the sum of the values(estimated) and then divide by the number of values(sum of the frequencies of the classes)

midpoint of 50-60=50+60/2=55

midpoint of 70-80=150/2= 75

midpoint of 80-90=170/2=85

midpoint of 90-100=190/2=95

midpoint of 100-110=210/2=105

Midpoint of 110-120=230/2=115

Midpoint of 120-130=250/2=125

Midpoint of 130-140=270/2=135

Midpoint of 140-150=290/2=145

Midpoint of 150-160=310/2=155

Sum of the values= 55*frequency= 55*3+75* 2+85*1+95*7+105*17+115*29+125*10+

135*2+145*3+155*3

Sum of all values =8605

Number of values= 3+2+1+7+17+29+10+2+3+3=77

Mean= 8605/77= 111.753

Therefore the center of the distribution is between 110 and 120 calories.

Answer:

I'm pretty sure its obtuse triangle

Step-by-step explanation:

A ={1,2,3,4,6,12}

B={4,6,8,10

[tex]A \cup B=[/tex]{1,2,3,4,6,8,10,12}

Answer:

Ok. I'm sorry Jules lost a golf ball. Is there a question?

Answer:

jus buy a new one

Step-by-step explanation:

they lost the golf ball so they need to buy a new one cuh

Answer:

A. By the Side-Side-Side (SSS) Congruence Theorem, ΔABC ≅ ΔDEF.

B. [tex] \overline{AB} \cong \overline{DE} [/tex]

[tex] \overline{BC} \cong \overline{EF} [/tex]

[tex] \overline{AC} \cong \overline{DF} [/tex]

Step-by-step explanation:

a. From the diagram given, it shows that all three sides of ∆ABC are congruent to all the three corresponding sides of ∆DEF.

Therefore, by the Side-Side-Side (SSS) Congruence Theorem, ΔABC ≅ ΔDEF.

b. The sides that are congruent in the ∆s given that applies to the SSS Congruence Theorem are:

[tex] \overline{AB} \cong \overline{DE} [/tex]

[tex] \overline{BC} \cong \overline{EF} [/tex]

[tex] \overline{AC} \cong \overline{DF} [/tex]

Answer:

B is (4,0) and D is (8,10)

Step-by-step explanation:  Read the x and y cordinates

Answer:

(8,10)

Step-by-step explanation:

coordinates are set up like (x,y)

8 is in the x

10 is in the y

Answer:

y= x ^3 - 4x

Step-by-step explanation:

Regroup terms.

y=x^3 +2x−6x

Simplify x^3 +2x−6x  to x^3 −4x.

AAAAANNNNNnnNNND the answer  is

y= x^3 - 4x

IN GRAPH

Answer:

Arranging from longest (at top) to shortest (at bottom)

DF

EF

DE

Step-by-step explanation:

We need to place the sides of triangle DE, DF and EF from longest to shortest.

The triangle has longest side that is opposite to the largest angle

We know two angles < E= 61° , <F= 59° we need to find <D

Sum of angles of triangle = 180°

So, 61°+59°+<D=180°

120°+<D=180°

<D=180°-120°

<D=60°

So, the largest angle is <E= 61°

The longest side must be opposite to <E so, the side is DF

The second largest angle is <D=60° so, second side will be EF

The smallest angle is <F=59° so, third (shortest) side will be DE

Arranging from longest (at top) to shortest (at bottom)

DF

EF

DE

Answer:

the answer is -120

Step-by-step explanation:

trust :)

Given:

Henry can type 3500 words in 70 minutes.

Colin can type 1500 in 30 minutes.

Brian can type 2200 words in 40 minutes.

To find:

The person who types at the fastest rate of words per minute.

Solution:

We know that,

[tex]\text{Rate of words per minute}=\dfrac{\text{Number of words}}{\text{Number of minutes}}[/tex]

Using this formula, we get

[tex]\text{Henry's rate of words per minute}=\dfrac{3500}{70}=50[/tex]

[tex]\text{Colin's rate of words per minute}=\dfrac{1500}{30}=50[/tex]

[tex]\text{Brian's rate of words per minute}=\dfrac{2200}{40}=55[/tex]

Since 55>50, therefore Brian's types at the fastest rate of words per minute.

Answer:

208[tex]cm^{2}[/tex]

Step-by-step explanation:

Area of a rectangle= base x height

Find the area for each one of the rectangles and add up

2(4x8)+2(6x8)+2(4x6)

Answer:

m<BGC = 145°

Step-by-step explanation:

<AGC and <DGB are vertical angles. Vertical angles are congruent. Therefore:

m<AGC = m<DGB

[tex] 3x + 20 = 8x - 5 [/tex] (substitution)

Collect like terms

[tex] 3x - 8x = -20 - 5 [/tex]

[tex] -5x = -25 [/tex]

Divide both sides by -5

x = 5

m<BGC = 180 - (m<AGC) (linear pair)

m<BGC = 180 - (3x + 20)

Plug in the value of x

m<BGC = 180 - (3(5) + 20) = 180 - 35

m<BGC = 145°

Answer:

The total number of miles you will be traveling for the entire round trip is 125650 miles.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

The question states that 1 inch = 4 miles. Therefore, if you multiply 31412 inches by 4, you will get the total number of miles you will be traveling for the round trip.

31412 × 4 = 125650

Therefore, the total number of miles you will be traveling for the entire round trip is 125650 miles.

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Answer:

A

Step-by-step explanation:

You want to double the 3 into the right square. Then add 15. After that, move the 7 into the 10 square.And there you go. You got 19-