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2 years ago

Write an equation of a line that passes through the point (8, 4) and is parallel to the line y = 4x + 2.

Mathematics

2 answers:

IRINA_888 [86]2 years ago

8 0

y = 4x - 28 is the equation of a line that passes through the point (8, 4) and is parallel to the line y = 4x + 2.

NemiM [27]2 years ago

4 0

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Find Slope :
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y = 4x + 2
Slope = 4
Slope of the Parallel line = 4

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Substitute slope = 4 :
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y = mx + b
y = 4x +b

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Find y-intercept :
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y = 4x + b
At point (8, 4), x = 8 when y = 4
4 = 4(8) + b
4 + 32 + b
b = 4 - 32
b = -28

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Substitute y-intercept into the equation :
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y = 4x - 28

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Answer : y = 4x - 28 (Answer A)
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Mr and Mrs Thomas buy tickets for themselves and their four children The cost of an adult ticket is £7 more than the cost of a c

Evgen [1.6K]

Let's call the prices a and c, a for adult...

The cost of an adult ticket is £7 more than the cost of a child ticket:

a = 7 + c

The total cost of the six tickets is £86.

86 = 2a + 4c

c = a-7

86 = 2a + 4(a-7) = 6a - 28

114 = 6a

a = 19

Answer: £19

Check:

That implies c=12.

2a+4c = 2(19)+4(12) = 38 + 48 = 86, good

8 0

2 years ago

The track team is trying to reduce their time for a relay race. First they reduce their time by 2.1 minutes. Then they are able

konstantin123 [22]

Answer: 15.7 minutes

Step-by-step explanation:

Let x be the time in the beginning (in minutes).

Given: The track team is trying to reduce their time for a relay race.

First they reduce their time by $t_1=$ 2.1 minutes.

Then they are able to reduce that time by $t_2=$ 10

If their final time is 3.96 minutes, then

$x-t_1-t_2=3.6\\\Rightarrow\ x=3.6+t_1+t_2\\\Rightarrow\ x=3.6+2.1+10\\\Rightarrow\ x= 15.7$

Hence, their beginning time was 15.7 minutes.

7 0

2 years ago

What is the value of x if g^x-1-2= 25?

SVETLANKA909090 [29]

Answer:

Third option: $x=\frac{5}{2}$

Step-by-step explanation:

<h3> The correct exercise is attached.</h3>

The equation given is:

$9^{x-1}-2=25$

The steps to find the value of "x" are shown below:

1. Add 2 to both sides of the equation:

$9^{x-1}-2+2=25+2\\\\9^{x-1}=27$

2. Descompose 9 and 27 into their prime factors:

$9=3*3=3^2\\27=3*3*3=3^3$

3. Substitute them into the equation:

$3^{2(x-1)}=3^3$

4. Knowing that If $a^n=b^m$ , then $n=m$ , we get:

$2(x-1)=3$

5. Apply Distributive property:

$2x-2=3$

6. Add 2 to both sides:

$2x-2+2=3+2\\\\2x=5$

7. Divide both sides of the equation by 2:

$\frac{2x}{2}=\frac{5}{2}\\\\x=\frac{5}{2}$

3 0

2 years ago

Read 2 more answers

An artist cuts 4 squares with sides of length x ft from the corners of a 12 ft-by-18 ft rectangular piece of sheet metal. She be

ehidna [41]

Answer:

$V = 216x - 60x^2 + 4x^3$

Step-by-step explanation:

The volume V of the fountain is equal to:

V = L*W*h

Where L is the lenght of the fountain, W is the width of the fountain and h is the high of the fountain

We already know that h is equal to x. On the other hand, if we cut a square with side of length x, L and W are calculated as:

L = 18 - 2x

W = 12 - 2x

So, replacing L, W and h on the equation of the volume, we get:

V = (18-2x)*(12-2x)*x

Finally, simplifying the function we get:

$V = ((18*12)+(18*(-2x))+(-2x*12)+((-2x)*(-2x)))*x$

$V = (216-36x-24x+4x^2)*x\\V = (216-60x+4x^2)*x\\V = 216x - 60x^2 + 4x^3$

6 0

2 years ago

A contractor has submitted bids on three state jobs: an office building, a theater, and a parking garage. State rules do not all

german

Answer:

The following are the answer to this question:

Step-by-step explanation:

In the given question the numeric value is missing which is defined in the attached file please fine it.

Calculating the probability of the distribution for x:

$\to f(x) = 0.19\ for \ x=14\\\\\to f(x) = 0.29 \ for\ x=7\\\\\to f(x) = 0.38\ for \ x=1\\\\\to f(x)=0.14 \ for \ x=0\\$

The formula for calculating the mean value:

$\bold{ E(X)= x \times f(x)}$

$=14 \times 0.19+7 \times 0.29+1 \times 0.38+0\times 0.14\\\\=2.66 + 2.03+0.38+ 0\\\\=5.07$

$\bold{E(X^2) = x^2 \times f(x)}$

$=14^2 \times 0.19+7^2 \times 0.29+1^2 \times 0.38+0^2 \times 0.14 \\\\=196 \times 0.19+ 49 \times 0.29+1 \times 0.38+0 \times 0.14\\\\= 37.24+ 14.21+ 0.38+0 \\\\=51.83$

use formula for calculating the Variance:

$\to \bold{\text{Variance}= E(X^2) -[E(X)]^2}$

$= 51.83 - (5.07)^2\\\\= 51.83 - 25.70\\\\=26.13$

calculating the value of standard deivation:

Standard Deivation (SD) = $\sqrt{Variance}$

$= \sqrt{26.13} \\\\=5.111$

6 0

2 years ago