What is the equation of a line parallel to y = 4/5x + 2 that passes through (1, 2)?

Answer: D

Step-by-step explanation:

m = - 7/4

Point (4, -2)

y - - 2= -7/4(x-4)

y + 2 = - 7/4x + 7

y = - 7/4x +7-2

y = - 7/4 x + 5

The equation of the line that is parallel to the given line is option (D) [tex]y=-\frac{7}{4}x+5[/tex] is the correct answer.

The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.

For the given situation,

The line is [tex]y=-\frac{7}{4} x-2[/tex] ------ (1)

The general equation of line in slope intercept form is

[tex]y = mx + c[/tex] ------ (2)

On comparing the equation 1 and 2, we get the slope as

⇒ [tex]m=-\frac{7}{4}[/tex] and

When two lines are parallel, then the slope of the parallel line is equal to the slope of the given line.

So, the slope of the parallel line is [tex]m = -\frac{7}{4}[/tex]

Thus the equation of the parallel line passing through the point (x1,y1) is (4,-2) as,

⇒ [tex]y-y1=m(x-x1)[/tex]

⇒ [tex]y-(-2)=-\frac{7}{4} (x-4)[/tex]

⇒ [tex]y+2=-\frac{7}{4} (x-4)[/tex]

⇒ [tex]y=-\frac{7}{4}x+\frac{7}{4} (4)-2[/tex]

⇒ [tex]y=-\frac{7}{4}x+7-2[/tex]

⇒ [tex]y=-\frac{7}{4}x+5[/tex]

Hence we can conclude that the equation of the line that is parallel to the given line is option (D) [tex]y=-\frac{7}{4}x+5[/tex] is the correct answer.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\dfrac{-12}{-2} \times24-24(6)-6}\\\\\\\boxed{\rightarrow 6(24) - 24(6) - 6}\\\\\\\huge\boxed{\rightarrow{144 - 144 - 6}}\\\\\\\huge\boxed{\rightarrow 0 -6}\\\\\\\huge\boxed{= -6}\\\\\\\\\huge\boxed{\textsf{Therefore, your answer is: \mathsf{-6 }}}\huge\checkmark[/tex]

Answer:

76.25

Step-by-step explanation:

Answer: Base = 3    Height = 8

Step-by-step explanation:

Base

9 to 1/3 = 3

Height

24 to 1/3 = 8

Answer:

Step-by-step explanation:

( C ). 112°

Answer:

31

Step-by-step explanation:

You divide, 372 divided by 12

the actual number of vans needed is 31 vans to accommodate the entire camp. To estimate the number of vans needed to accommodate the entire camp, we can use the concept of rounding up to the nearest whole number.

The number of vans required will be the total number of campers divided by the capacity of each van (12 passengers), rounded up to the nearest whole number.

Estimate:

Number of vans needed =[tex]\(\frac{372}{12}\)[/tex](rounded up to the nearest whole number)

[tex]\(\frac{372}{12} \approx 31\)[/tex]

So, the estimate suggests that around 31 vans will be needed to accommodate the entire camp.

To calculate the actual number of vans needed, we can use the exact division without rounding up.

Actual number:

Number of vans needed = [tex]\(\frac{372}{12} = 31\)[/tex] vans

Thus, the actual number of vans needed is 31 vans to accommodate the entire camp.

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Figure 1,

When 1 unit = 1 cm

Perimeter = Boundary of the figure

                = 3+3+6

                = 12 cm

Area of one square = side * side

                                    = 1*1

No. of squares in the figure = 6 squares

Area = Space occupied inside the figure

        = 6 cm^2

Hope it helped :)

Answer:

We have 12 mL of 11% alcohol.

How much water do we add to make it a 6% solution?

We have 1.32 mL alcohol and 10.68 mL water

x is the water to add

(1.32) / (12 + x) = .06

1.32 = .72 + .06x

.6 = .06x

x = 10 mL

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

substitute for the the given variables.

a=2

b=-4

sqrt 2^3-7=sqrt 8-7=sqrt1=1

1+absolute value of -4 = 1+4=5

answer 5

Answer:

Multply both side by 3

Step-by-step explanation:

Answer:

Recall that the height of the object, in meters, is a function of elapsed time, in seconds. Thus what [tex]f(8)=12[/tex] means is that the object is at a height of 8 meters when 12 seconds have passed since its launch.

Best interpretation of the given f(8) = 12 is 8 seconds after the object is launched it is at a height of 12meters.

" Interpretation is defined as the explanation of something in your own words or as per your understanding."

According to the question,

Given,

H = f(t)

H represents the height in meters of an object

t represents the time in seconds

Interpretation of the given situation,

f(8) = 12

time = 8seconds

height of the object = 12meters

Hence, interpretation of the given situation is  8 seconds after the object is launched it is at a height of 12meters.

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9514 1404 393

Answer:

  (0, -3)

Step-by-step explanation:

The y-intercept is the point where the graph crosses the (vertical) y-axis. That point is halfway between grid lines marked -2 and -4, so is at the grid line with the value -3. The x-coordinate there is 0, so the y-intercept point is ...

  (x, y) = (0, -3)

_____

Since the y-intercept always has an x-coordinate of 0, we sometimes refer to the y-intercept using only the y-value: -3.

Answer:

hope this helps

Step-by-step explanation:

3*2 * 1 = 24 ways . It is called arrangement or permutations, while if you need to group some objects it is called combination and there we need to consider unique groups only.

Answer:

292 yd²

Step-by-step explanation:

First you split the composite shape into two rectangle.

a) Horizontal rectangle - L × W

7 × 26 = 182 yd²

b) Vertical rectangle - L × W

5 × 22 = 110 yd²

Therefore 182 + 110 = 292 yd²

Answer:

Angle AED = Angle CEB —> Opposite angles

So; Angle CEB = 95°

I hope I helped you^_^

∠AED and ∠CEB are opposite angles so they will be the same so ∠CEB will also 95°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

Two opposite angles become by the intersection of two lines will always same.

Since E is the intersection point so ∠AED and ∠CEB are opposite angles.

So,

∠AED = ∠CEB

∠CEB = 95°.

Hence "∠AED and ∠CEB are opposite angles so they will be the same so ∠CEB will also be 95°".

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Answer:

The problems listed are all the formulas for 2d figures:

Area of a Triangle: 1/2 B*H

Area of a Square: S^2

Area of a Rectangle: l*w

Perimeter of a Square: 4s

Perimeter of a Triangle: a+b+c

Perimeter of a Rectangle: 2l+2w

Answer:

21

Step-by-step explanation:

6*3 = 18

1/2 = 0.5

6*0.5 = 3

18 + 3 = 21

Answer:

21

Step-by-step explanation:

The simplified expression for the perimeter of the rectangle is 16x - 4. The perimeter of a rectangle is given by the formula: P = 2 * (length + width).In this case, the length of the rectangle is given as 7x + 1, and the width is given as x - 3.

So, the perimeter can be expressed as: P = 2 * (7x + 1 + x - 3)

Now, let's simplify this expression: P = 2 * (8x - 2)

P = 16x - 4

Therefore, the simplified expression for the perimeter of the rectangle is 16x - 4.

A rectangle is a type of quadrilateral with specific properties that distinguish it from other shapes. Here are some key properties of a rectangle:

Opposite Sides are Equal in Length: In a rectangle, the opposite sides are always equal in length. This means that the length of one pair of parallel sides is the same as the length of the other pair.

Opposite Angles are Equal: The opposite angles in a rectangle are equal in measure. This property makes all angles in a rectangle right angles (90 degrees).

Consecutive Angles are Supplementary: Consecutive angles in a rectangle are supplementary, meaning that the sum of any two consecutive angles is 180 degrees. This property is a consequence of the fact that opposite angles are equal, making each pair of consecutive angles form a linear pair.

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Step-by-step explanation:

1) let the number=x

six times a number=6x

Condition:

6x+4=22

2) eleven times a number=11x

Condition:

11x-5=50

3) 9 times a number=9x

Condition:

9x-7=-16

Note:if you need to ask any question please let me know.

Answer:

(-11 , -16)

Step-by-step explanation:

The midpoint will always be, as the term suggests, in the middle of the line segment. You simply need to find the distance for both x & y, and to apply that to the midpoint. In this case:

Endpoint (x₁ , y₁): (5 , 10)

Midpoint (x₂ , y₂): (-3 , -3)

Note that when finding distance, you will subtract the point₂ from point₁:

x: 5 - (-3) = 8

y: 10 - (-3) = 13

Therefore, each time you plot another point, you will be subtracting 8 from the x value, and 13 from the y value:

Endpoint (x₃ , y₃) = Midpoint (-3 , -3) + (_ - 8 , _ - 13) = (-11 , -16)

(-11 , -16) is your answer.

~

Using midpoint formula

[tex]\boxed{\sf (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}[/tex]

[tex]\\ \rm\longmapsto (-3,-3)=\left(\dfrac{5+x_2}{2},\dfrac{10+y_2}{2}\right)[/tex]

Firstly

[tex]\\ \rm\longmapsto \dfrac{5+x_2}{2}=-3[/tex]

[tex]\\ \rm\longmapsto 5+x_2=2(-3)=-6[/tex]

[tex]\\ \rm\longmapsto x_2=-6-5[/tex]

[tex]\\ \rm\longmapsto x_2=-11[/tex]

Now

.[tex]\\ \rm\longmapsto \dfrac{10+y_2}{2}=-3[/tex]

[tex]\\ \rm\longmapsto 10+y_2==2(-3)[/tex]

[tex]\\ \rm\longmapsto 10+y_2=-6[/tex]

[tex]\\ \rm\longmapsto y_2=-6-10[/tex]

[tex]\\ \rm\longmapsto y_2=-16[/tex]

Hence the coordinates are

Answer:

x = 3

Step-by-step explanation:

Given

[tex]2^{3x+1}[/tex] = [tex]2^{10}[/tex]

Since bases on both sides are equal, both 2, then equate the exponents

3x + 1 = 10 ( subtract 1 from both sides )

3x = 9 ( divide both sides by 3 )

x = 3

Answer:

Angle BAD corresponds to Angle FEH in the scaled copy.

Angle ABC corresponds to Angle EFG in the scaled copy.

Angle BCD corresponds to Angle FGH in the scaled copy.

Angle ADC corresponds to Angle EHG in the scaled copy.

Answer:36

Step-by-step explanation:

It says he typed 36 words in a paragraph in a minute which means he types 36 per minute

Answer:

the answer is -1445.05.

Answer:

Step-by-step explanation:

the answer is -1445.05.

Answer:

That’s simple 10

Step-by-step explanation

Let me know if I’m correct

hope this helps

Answer:

It’s a rational number

Step-by-step explanation:

Answer:

im not sure

Step-by-step explanation:

Answer:

0.32

Step-by-step explanation:

Step-by-step explanation:

(X)^2 - (6)^2

= (x-6)(X+6)

Answer:

[tex](x - 6) \times (x + 6)[/tex]

Step-by-step explanation:

[tex] {x}^{2} - 36[/tex]

write in exponential form.

[tex] {x}^{2} - {6}^{2} [/tex]

factor:

[tex](x - 6) \times (x + 6)[/tex]

Answer:

12 is the answer

Step-by-step explanation:

18- 3×2= 18- 6 = 12