. Write an equation for the line parallel to y = 7x + 11 that contains P(-5, 7).
a. x - 7 = -76y + 5)
c. y - 7 = 7(x + 5)
b. y - 7 =-7(x + 5)
O
d . y + 7 = 7(x + 5)

Answer:

y=4x-4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(0-8)/(1-3)

m=-8/-2

m=4

y-y1=m(x-x1)

y-8=4(x-3)

y=4x-12+8

y=4x-4

Answer:y - 4x + 4 = 0

Step-by-step explanation: Formula for equation of a line passing through two coordinates is

y - y₁                 y₂ - y₁

______  =       ______

x - x₁                  x₂ - x₁

Therefore,            y₂ -y₁                                                                                                  

        y - y₁      =      ____      ×    ( x - x₁ )

                             x₂ - x₁

where x₁ =3, y₁ =8, x₂ = 1 and y₂ 0

Now substitute for the value

y - 8 = 0 - 8

         ______    x     ( x - 3 )

           1 - 3

Therefore y - 8 = -8/-2 × (x - 3 )

y - 8 = -8/-2 × (x - 3)

y -8 = 4 × (x - 3 )

y - 8 = 4( x - 3 )

y - 8 = 4x - 12, when the brackets are open,

So y = 4x - 12 + 8

    y = 4x - 4

Therefore the equation of the line is

y - 4x + 4 = 0

Answer:

C

Step-by-step explanation:

The function is formed of 2 straight lines

The equation of a straight line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate the slope using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (2, - 2) ← endpoints of left line

m = [tex]\frac{-2+5}{2+4}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

Note the line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = [tex]\frac{1}{2}[/tex] x - 3 for x <  2 ( arrow on line points left )

Repeat

with (x₁, y₁ ) = (2, - 2) and (x₂, y₂ ) = (3, 1) ← 2 points on right line

m = [tex]\frac{1+2}{3-2}[/tex] = [tex]\frac{3}{1}[/tex] = 3, thus

y = 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 1), then

1 = 9 + c ⇒ c = 1 - 9 = - 8

y = 3x - 8 for x ≥ 2 ( arrow on line points right )

Answer:

100,000,000

Step-by-step explanation:

did some research to solve this one, i recommend looking more into to it to ensure that this is the correct answer ;)

The sum of the first 1000 consecutive odd counting numbers is 1,000,000.

To find the sum of the first 1000 consecutive odd counting numbers, we need to recognize a pattern and utilize a simple formula.

Step 1: Identify the Sequence of Odd Numbers

The first few odd counting numbers are:

1, 3, 5, 7, 9, 11, 13, ...

Step 2: Determine the Formula for the Sum

The sum of the first n odd counting numbers can be calculated using the formula:

Sum = n²

This means that the sum of the first n consecutive odd numbers is equal to the square of n.

Step 3: Apply the Formula to Our Problem

In this case, we want to find the sum of the first 1000 odd numbers. Therefore, we set n to 1000:

Sum = 1000²

Step 4: Calculate the Value

Now, we perform the calculation:

Sum = 1000 * 1000 = 1,000,000

Answer:

The volume of required foam is 0.1 cm³  

Step-by-step explanation:

Given as :

The volume of box = v = 113.14 cm³

The radius of the crystal ball = r = 3 cm

Let The volume of required foam = V cm³

According to question

Volume of  crystal ball = [tex]\dfrac{4}{3}[/tex] × π × radius³                        where π = 3.14

i.e Volume of ball = [tex]\dfrac{4}{3}[/tex] × π × 3³

Or, Volume of ball = [tex]\dfrac{4}{3}[/tex] × π × 27

Or, Volume of ball = [tex]\dfrac{4}{3}[/tex] × 3.14 × 27

Or, Volume of ball = 4 × 3.14 × 9

Or, Volume of ball = 113.04 cm³

Again

∵ volume of crystal ball = v' = 113.04 cm³

So ,  The volume of required foam = volume of box - volume of crystal ball

Or, V =  v - v'

Or, V = 113.14 cm³ -  113.04 cm³

∴   V = 0.1 cm³

So, The volume of required foam = V = 0.1 cm³

Hence, The volume of required foam is 0.1 cm³  . Answer

Answer:

B and B for plato

Step-by-step explanation:

Answer:

1 unit

Step-by-step explanation:

If point J is the midpoint of segment FG with endpoints F(1,4) and G(5,12), then its coordinates are

[tex]x_J=\dfrac{x_F+x_G}{2}=\dfrac{1+5}{2}=3\\ \\y_J=\dfrac{y_F+y_G}{2}=\dfrac{4+12}{2}=8[/tex]

If point K is the midpoint of segment GH with endpoints G(5,12) and H(-1,4), then its coordinates are

[tex]x_K=\dfrac{x_G+x_H}{2}=\dfrac{5+(-1)}{2}=2\\ \\y_K=\dfrac{y_G+y_H}{2}=\dfrac{12+4}{2}=8[/tex]

The measure of JK is

[tex]JK=\sqrt{(3-2)^2+(8-8)^2}=\sqrt{1^2+0^2}=1\ unit[/tex]

Given the coordinates of their endpoints, you find that the points of interest, J and K, have coordinates J(3,8) and K(2,8), respectively. You can then apply the distance formula to find the distance between these two points, resulting in 1.

To find the distance between two points, we can apply the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Given that J is the midpoint of FG, the coordinates of J can be found using the midpoint formula ((x1 + x2) / 2, (y1 + y2) / 2). By applying this formula, we find that J = ((1 + 5) / 2, (4 + 12) / 2) = (3,8).

Similarly, the coordinates of K, as the midpoint of GH, are K = ((5 + (-1)) / 2, (12 + 4) / 2) = (2,8).

Now we can plug the coordinates of J and K into the distance formula to find JK: d = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((2 - 3)^2 + (8 - 8)^2) = sqrt((1)^2 + 0) = sqrt(1) = 1.

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Answer:

1. Translation 5 units to the left and 1 unit down

2. Reflection across the x-axis

Step-by-step explanation:

Triangle XYZ has its vertices at points X(-6,2), Y(-4,7) and Z(-2,2).

1. Translate triangle XYZ 5 units to the left and 1 unit down. This translation has the rule:

[tex](x,y)\rightarrow (x-5,y-1)[/tex]

Then

[tex]X(-6,2)\rightarrow X'(-11,1);[/tex]

[tex]Y(-4,7)\rightarrow Y'(-9,6);[/tex]

[tex]Z(-2,2)\rightarrow Z'(-7,1).[/tex]

2. Reflect triangle X'Y'Z' across the x-axis. This reflection has the rule:

[tex](x,y)\rightarrow (x,-y)[/tex]

Then

[tex]X'(-11,1)\rightarrow X''(-11,-1);[/tex]

[tex]Y'(-9,6)\rightarrow Y''(-9,-6);[/tex]

[tex]Z'(-7,1)\rightarrow Z''(-7,-1)[/tex]

These points are exactly the vertices of the triangle X''Y''Z''.

The sequence of transformations is translation, rotation, reflection, and dilation.

The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is:

Translation: Move the triangle in a linear direction without rotating it.

Rotation: Rotate the triangle about a fixed point or axis.

Reflection: Mirror the triangle across a line known as the axis of reflection.

Dilation: Increase or decrease the size of the triangle while preserving its shape.

By applying these transformations in the specified sequence, triangle XYZ can be mapped onto triangle X"Y"Z".

The correct option will the new price is 120% of the old one because the price increases by 20%, which is added to 100%.

Percent of change is determined by the difference between the two values divided by the orginal one, then multiplied by 100.

i.e. percent of change=(change in value/original value)*100

So according to the asked question,

old value of the shoes=$25

new value of the shoes=$30

change in value=30-25=$5

percent of change=((30-25)/25)*100=20%

hence price increases by 20%.

If the old price is 100 and price increases by 20% then new price will be 120.

So the new price is 120% of the old one.

in another way we can calculate that

old value*x%=new value

⇒old value*x/100=new value

⇒x=new value*100/old value=30*100/25=120%

Therefore the new price is 120% of the old one because the price increases by 20%, which is added to 100%.

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The greatest whole possible whole number length of the unknown side is 9 inches

Solution:

Two sides of an acute triangle measure 5 inches and 8 inches

The length of the longest side is unknown

We have to find the length of unknown side

The longest side of any triangle is a hypotenuse

For a acute triangle we know:

If c is the longest side of a acute triangle, a and b are other two sides of a acute triangle then the condition that relates these three sides are given as:

[tex]c^2<a^2+b^2[/tex]

Here in this sum,

a = 5 inches

b = 8 inches

c = ?

Substituting we get,

[tex]c^2< 5^2+8^2\\\\c^2 < 25 + 64\\\\c^2 < 89\\\\c < 9.4[/tex]

On rounding to nearest whole number,

c < 9

Hence, to the greatest whole possible whole number length of the unknown side is 9 inches

Answer:

The greatest whole possible whole number length of the unknown side is 9 inches

Step-by-step explanation:

Answer:

[tex]4(x+3.5)^{2}=0[/tex]

Step-by-step explanation:

we have

[tex]4x^{2}+28x+49=0[/tex]

step 1

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](4x^{2}+28x)=-49[/tex]

step 2

Factor the leading coefficient

[tex]4(x^{2}+7x)=-49[/tex]

step 3

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]4(x^{2}+7x+3.5^2)=-49+(3.5^2)(4)[/tex]

[tex]4(x^{2}+7x+12.25)=0[/tex]

step 4

Rewrite as perfect squares

[tex]4(x+3.5)^{2}=0[/tex]

The equation by completing the square is [tex]\[ (x + \frac{7}{2})^2 = 0 \].[/tex]

To complete the square for the quadratic equation [tex]\(4x^2 + 28x + 49 = 0\)[/tex], we need to follow these steps:

Divide the entire equation by the coefficient of [tex]\(x^2\)[/tex] to make it equal to 1. This gives us:

[tex]\[ x^2 + 7x + \frac{49}{4} = 0 \][/tex]

Next, we need to find the value to complete the square. This is done by taking half of the coefficient of [tex]\(x\)[/tex], which is [tex]\(\frac{7}{2}\)[/tex], and squaring it:

[tex]\[ \left(\frac{7}{2}\right)^2 = \frac{49}{4} \][/tex]

We add and subtract this value to the equation to complete the square:

[tex]\[ x^2 + 7x + \frac{49}{4} - \frac{49}{4} + \frac{49}{4} = 0 \][/tex]

Now, we can rewrite the equation as a perfect square trinomial and a constant:

[tex]\[ (x + \frac{7}{2})^2 - \frac{49}{4} + \frac{49}{4} = 0 \][/tex]

Simplify the equation by combining the constants:

[tex]\[ (x + \frac{7}{2})^2 = 0 \][/tex]

Answer:

Dividing 4 × 1  by 4 × 0.01 = [tex]\dfrac{ 4 \times 1}{4 \times 0.01}[/tex] = 100

Step-by-step explanation:

i) the value of 4 in 64.723 is given by 4 × 1 = 4, because 4 is the one's place

ii) the value of 4 in 9.048 is is given by 4 × 0.01 = [tex]\dfrac{4}{100}[/tex] = 0.04, because 4 is in the hundredth's place

iii) the value of 4 in 64.723 is 100 times the value of 4 in 9.048 which we get by dividing 4 × 1  by 4 × 0.01 = [tex]\dfrac{ 4 \times 1}{4 \times 0.01}[/tex] = 100

Answer:

100

Step-by-step explanation:

Solving by elimination...

4x=14-3y ---> 12x=42-9y

               ×3

3x-3y=11 ----> 12x-12y=44

               ×4

  12x=42-9y

-(12x-12y=44)

--------------------

12y=-2-9y

21y=-2

y=-2/21

3x-3(-2/21)=11

3x+2/7=11

3x=10 5/7

x=25/7

Answer:

4x=14-3y 3x-3y=11

Step-by-step explanation:

Answer:

$ 150

Step-by-step explanation:

Given:

Cost price of a microwave = $105

Discount % = 30

Question asked:

what was the price of the microwave before sale = ?

Solution:

Let the price of the microwave before sale = [tex]x[/tex]

Price before sale - 30 % discount = cost price of  microwave (by Javier)

[tex]x - 30\% of x = 105[/tex]

[tex]x - \frac{30x}{100} = 105[/tex]

[tex]\frac{70x}{100} = 105\\[/tex]

Multiplying both side by 100

[tex]70x = 105 \times 100[/tex]

[tex]70x = 10500[/tex]

Dividing both side by 70

[tex]x = \frac{10500}{70} \\x = 150[/tex]

x = price of the microwave before sale = $ 150

Thus, price of the microwave before the sale = $150

A right circular cylinder with radius 4 cm and height 3 cm-150.72 cu cm

A cone with radius 5cm and height 12 cm-314 cu cm

A pyramid with base area 16 sq cm and height 30 cm-160 cu cm

A pyramid with a square base of length 3 cm and height 16 cm-48 cu cm

Explanation

volume of cylinder=[tex]\pi r^2h[/tex][tex]3.14*4^2*3=150.72[/tex] cu cm

volume of cone=[tex]1/3 \pi r^2 h[/tex]=314 cu cm

volume of pyramid=[tex](base area*height)/3=(16*30)/3[/tex]=160 cu cm

volume of pyramid=

=[tex](base area*height)/3\\square base length=3 cm\\base area=a^2 =3^2 =9\\volume=(9*16)/3=48cm^3[/tex]

Answer:

The slope of the least squares regression line is:

0.32

The units of the slope of the line are:

centimeters per day.

The slope of the line tells you that for each new day you can predict that a plant's height will increase by about 0.32 centimeters.

The y-intercept of the least square regression line is:

-1.72

The units of the y-intercept of the line are:

centimeters.

The y intercept:

Typical height compared to the soil line.

Step-by-step explanation:

Answer:

A is 198

B is 22

Step-by-step explanation:

22 × 9 = 198

22 + 198 = 220

Answer:

E

Step-by-step explanation:

Answer:

[tex](x,y) -----> (x+9,y-12)[/tex]

Step-by-step explanation:

we know that

[tex]A(7, 3) ----> A'(16,-9)[/tex]

The rule of the translation is equal to

[tex](x,y) -----> (x+a,y+b)[/tex]

Find the values of a and b

[tex](7,3) -----> (7+a,3+b)[/tex]

we have that

[tex]7+a=16[/tex] ----> [tex]a=16-7=9[/tex]

[tex]3+b=-9[/tex] ---->[tex]b=-9-3=-12[/tex]

substitute the values of a and b

[tex](x,y) -----> (x+9,y-12)[/tex]

That means----> The translation is 9 units right and 12 units down

Answer:

Option D:

(x, y) -> (x + 9, y minus 12)

Step-by-step explanation: Honestly all people want are the answers so I don't really care to write an explanation.

Answer:

Yes! 4(3y-2)=12y-8

Answer:

yes 4(3y - 2) = (12y - 8)

Step-by-step explanation:

because if you should expand 4(3y - 2) by multiplying each value within the bracket by 4, you will have 12y - 8

Answer:

Step-by-step explanation:

(-3,-9) , (2,-6), (-5,4), (1,2), (6,0)

the domain is gonna be ur x values

so the domain of this function is [ -5,-3,1,2,6] <==

** the domain is ur x values and the range is ur y values

Answer: -1

Step-by-step explanation:

i just answered if off of edg.

Answer:

D.BC and Pn are corgruent.

Step-by-step explanation:

Pair of segments in the figures that are congruent : BC and PN.

In geometry, congruent means identical in shape and size. Congruence can be applied to line segments, angles, and figures. Any two line segments are said to be congruent if they are equal in length.

Given in the figure,

Two polygons ABCDEF and JKLMNP

where

AB≅MN

BC≅PN

CD≅PJ

DE≅JK

EF≅KL

FA≅LM

Hence, BC and PN is the pair of segments in the figures that are congruent.

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The measure of the angle is;

200.64 degrees ⇒ B

200 degrees 38' 24" ⇒ C

Step-by-step explanation:

To convert the measure of an angle from degrees to radians or from radians to degrees use these rules

∵ The measure of an angle is 3.5 radians

- We need to change its measure to degree, use the 2nd rule

∵ π = 3.14

∴ Its measure in degree = [tex](3.5).(\frac{180}{3.14})[/tex]

∴ Its measure in degree = 200.64°

To find its measure in degree, minutes and seconds, multiply the number before decimal point by 60 to find the number of minutes

∵ 1° = 60'

∵ 0.64 × 60 = 38.4

- That means the number of minutes is 38

∵ 1' = 60"

∵ 0.4 × 60 = 24

- That means the number of seconds is 24

∴ The measure of the angle is 200° 38' 24"

The measure of the angle is;

200.64 degrees

200 degrees 38' 24"

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Answer:

It’s FALSE

Step-by-step explanation:

Answer:

Step-by-step explanation:

No. Of quarters n(Q)= 3

No. Of dimes n(D) = 5

No. Of nickels n(N) = 2

Total T = 3+5+2 = 10

Prob(D) = n(D)/T = 5/10 = 1/2

Now there are 9 left since it is not replaced back

Prob(Q) = 3/9 = 1/3

Prob(D and Q) = 1/2 × 1/3 = 1/6

The probability you will pick a dime and then a quarter without putting the dime back in your pocket is 1/6

Probability is the likelihood or chance that an event will occur

If you have 3 quarters, 5 dimes, and 2 nickels in your pocket, the total coins you have will be:

Total outcome = 3 + 5 + 2

Total outcome = 10

Probability of picking a dime = 5/10 = 1/2
Probability of picking a quarter = 3/9 = 1/3

Pr( a dime and then a quarter without putting the dime back in your pocket) = 1/2 * 1/3 = 1/6

Hence the probability you will pick a dime and then a quarter without putting the dime back in your pocket is 1/6

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Answer:

x = y/12

Step-by-step explanation:

The function to calculate the number of illiterate people in Sylvania t years from today is P(t) = 9000 * (3/5)^t.

To write a function that gives the number of illiterate people in Sylvania, P(t), t years from today, we can use the following formula:

P(t) = 9000 * (3/5)^t

This formula represents the reduction in the number of illiterate people by 3/5 each year. To calculate the number of illiterate people t years from today, we multiply the initial number of illiterate people (9000) by the reduction factor (3/5) raised to the power of t.

Answer: 9000( 1 - 3/5 ) ^t

Answer:

I think is B .3 < x

hope it helps!

Answer:

-3< X is the correct answer. sorry if i'm to late:(

Step-by-step explanation: