Consider the line y=7x+4.
Find the equation of the line that is parallel to this line and passes through the point ( -3, 5)
Find the equation of the line that is perpendicular to this line and passes through the point ( -3, 5)

9514 1404 393

Answer:

  (x -4)² +(y -2)² = 20

Step-by-step explanation:

The circle is the circumcircle of triangle OAB. Then OA will be a diameter if angle OBA is a right angle. We can check that by looking at the slopes of AB and BA.

  B-O = (6, 6)-(0, 0) = (6, 6)   ⇒   slope = Δy/Δx = 6/6 = 1

  A-B = (8, 4) -(6, 6) = (2, -2)   ⇒   slope = -2/2 = -1

These slopes have a product of -1, so OB ⊥ BA. The hypotenuse (OA) of ΔOBA is the diameter of the circle.

Then the midpoint of the hypotenuse is the center of the circle.

  C = (O +A)/2 = ((0, 0) +(8, 4))/2 = (4, 2)

The equation is ...

  (x -h)² +(y -k)² = r² . . . . . circle with center (h, k) and radius r

The radius is the distance from O to C, so is ...

  r² = 4² +2² = 20

and the equation of the circle is ...

  (x -4)² +(y -2)² = 20 . . . . equation of the circle

Answer:

x = 1

Step-by-step explanation:

4x - 5/5 = 3

4x - 1 = 3

add 1 to each side of the equation:

4x = 4

divide both sides by 4:

x = 1

Answer:

4x=3+5/5

Step-by-step explanation:

like term

4x=8/5

20x/20=8/20

x=2/5

Answer:

A.

Step-by-step explanation:

42/48=7/8

40/48=5/6

(お役に立てれば！)

Answer:

f(x)= 2 ³√x+4

Step-by-step explanation:

Thats the answer

The equation of the function is f(x) = 2∛x -4.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We will take two points from the graph substitute in each function.

So, the points are (0, -4) and (1, -2).

1. f(x) = ∛x -4

For x= 0

f(x) = ∛0 -4 = -4

and, For x= 1

f(x) = ∛1 -4 = 1 -4 = -3  (False)

2. f(x) = 2∛x -4

For x= 0

f(x) = 2∛0 -4 = -4

and, For x= 1

f(x) = 2∛1 -4 = 2 -4 = -2 (True)

3. f(x) = 2∛x +4

For x= 0

f(x) = 2∛0+4 = 4

and, For x= 1

f(x) = 2∛1 +4 = 2+4 = 6 (False)

4. f(x) = ∛x +4

For x= 0

f(x) = ∛0 +4 = 4

and, For x= 1

f(x) = ∛1 +4 = 1 +4 = 5 (False)

Thus, the required function is f(x) = 2∛x -4.

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Length of a text can be measured with ruler. Therefore, option C is the correct answer.

Everything around us has a measurement value, from the amount of sugar you put in a cake to the size of a football field. Each thing is measured differently based on its length, weight, volume, or duration. With these measurements, the idea of "Metric System" is introduced.

A ruler, sometimes called a rule, line gauge, or scale, is a device used in geometry and technical drawing, as well as the engineering and construction industries, to measure distances or draw straight lines.

Length of a text can be measured with ruler.

Therefore, option C is the correct answer.

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Answer:

C

Step-by-step explanation:

Step-by-step explanation:

Given that,

Half of Robert's piece of wire is equal to of Maria's wire i.e.

[tex]\dfrac{R}{2}=M[/tex] ....(1)

Total length of the wires = 10 feet

ATQ,

[tex]R+M=10[/tex] ....(2)

Use equation (1) in (2).

[tex]R+\dfrac{R}{2}=10\\\\\dfrac{3R}{2}=10\\\\R=\dfrac{20}{3}\\\\R=6.67\ ft[/tex]

So,

[tex]M=\dfrac{6.67}{2}\\\\M=3.33\ ft[/tex]

Hence, this is the required solution.

Answer:

1.12838m or 1.13m

Step-by-step explanation:

hope this helps

Answer:

X = 5.9 (in degree mode)

Step-by-step explanation:

Do the following:

12(tan26) = X

Plugging this into a calculator, you will get:

X = 5.9 (in degree mode)

Answer:

Select a card from a set of cards with the letters A through D, then spin this once.

Spin this and roll an 8-sided number cube with the digits 1 to 8.

Answer:

6 inches

Step-by-step explanation:

If 3 blocks equals 2 inches, then we must first find out how many times 3 can fit into 9. We do this by dividing 9 by 3 to get 3. To get your final answer just multiply 2 by 3 and you will get 6 inchs. I hope this helped :0

The probability computed shows that the point estimate of the population is 6.2%.

Divide the number of events by the number of possible outcomes. After determining the probability event and its corresponding outcomes, divide the total number of ways the event can occur by the total number of possible outcomes.

a. The point estimate of the population will be calculated thus:

= 62% = 62/100 = 0.62

b. The margin of error of the population will be:

= z value × [✓0.62 × ✓0.38 / ✓200]

= 1.96 × (0.78 × 0.61 / 14.14)

= 0.0672

Therefore, the interval estimate is 6.72%.

c. The margin of error of the population proportion is found using half the range will be:

= [0.76 - 0.46] /2

= 0.30/2

= 0.15

d.  The community action group’s claim is likely based on either interval estimate of the true population proportion since the confidence interval value is greater than 0.45.

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Answer:

a = 65 yd is the answer.

Step-by-step explanation:

a = ?

b = 72 yd

c = 97 yd

According to the Pythagoras theorem,

a² + b² = c²

a² + 72² = 97²

a² + 5184 = 9409

a² = 9409 - 5184

a² = 4225

a = 65 yd

∴ a = 65 yd is the length of the missing leg.

Answer:

Try B

Step-by-step explanation:

9514 1404 393

Answer:

  11.1

Step-by-step explanation:

The tangent makes a right angle with the diameter at the point of tangency. So, the triangle is a right triangle, and the Pythagorean theorem can be used to find the length of x. The radius is shown as 7.1, so the diameter will be 14.2.

  x^2 + 14.2^2 = 18^2

  x^2 = 122.36

  x = √122.36 ≈ 11.1

The length of the tangent is about 11.1 units.

Answer:

y = |x| - 4

Step-by-step explanation:

this translates the function y down by 4 as is required

Answer:

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = 0.5188

The percentage of that Delta car batteries last between three and four years

P(3≤X≤4) = 52%

Step-by-step explanation:

Step(i):-

Given that the sample size n =12 -volt car batteries

Let  'X' be a Random variable in a normal distribution

Given that mean of the normal distribution = 45 months

Given that the Standard deviation of the normal distribution = 8months

Step(ii):-

Let  X₁ = 3 years = 12 × 3 = 36 months

[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{36-45}{8} = -1.125[/tex]

Let X₂ = 4 years  = 12 × 4 = 48 months

[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{48-45}{8} = 0.375[/tex]

Step(iii):-

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = P(-1.125≤Z≤0.375)

                   = P(Z≤0.375) - P(Z≤-1.125)

                   = 0.5 +A(0.375) - (0.5-A(1.125)

                   = 0.5 + 0.1480 - (0.5 -0.3708)

                  = 0.1480 + 0.3708

                 = 0.5188

Final answer:-

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = 0.5188

The percentage of that Delta car batteries last between three and four years

P(3≤X≤4) = 52%

Answer:

See attachment for plot

Step-by-step explanation:

The attachment has enough information to solve for only question (4).

Solving (4), we have:

[tex]W = (-1,-1)[/tex]

[tex]X = (4,1)[/tex]

[tex]Y = (4,5)[/tex]

[tex]Z =(1,7)[/tex]

Required

Reflect over the x-axis

When a point (x,y) is reflected over the x-axis, the resulting point is (x,-y)

i.e.

[tex](x,y) => (x,-y)[/tex]

So, we have:

[tex]W = (-1,-1)[/tex] ==> [tex]W' =(-1,1)[/tex]

[tex]X = (4,1)[/tex] ==>[tex]X' = (4,-1)[/tex]

[tex]Y = (4,5)[/tex] ==> [tex]Y' =(4,-5)[/tex]

[tex]Z =(1,7)[/tex] ==> [tex]Z' = (1,-7)[/tex]

So, we plot on a grid, the following points:

[tex]W' =(-1,1)[/tex]

[tex]X' = (4,-1)[/tex]

[tex]Y' =(4,-5)[/tex]

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

See attachment for plot

Answer:

Step-by-step explanation:

I think it could be D

Sorry if not correct

Answer:

11

Step-by-step explanation:

Find the length of the hypotenuse of the right triangle with sides 9 and 6

[tex]a^{2} +b^{2} =c^{2} \\9^{2} +6^{2} =c^{2} \\81+31=c^{2} \\\sqrt{117} =c[/tex]

Use c and the height 2 to find the hypotenuse of the triangle with the dotted line

[tex]\sqrt{117} ^{2} +2^{2} =c^{2} \\117+4=c^{2} \\221=c^{2} \\11=c[/tex]

the dotted line is 11

Answer:

15.1666666667

Step-by-step explanation:

Answer: I think C.

Step-by-step explanation:

Answer:

-77.625

Step-by-step explanation:

How to find

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations. Therefore, the value of the expression 6 3/4 (- 11.5) is -77.625.

Answer:the first one opn and qps

Step-by-step explanation:

Answer:

x = 19

z = 102°

Step-by-step explanation:

✔️5x - 17 = 78 (vertical angles area congruent)

5x - 17 + 17 = 78 + 17

5x = 95

5x/5 = 95/5

x = 19

✔️78 + z = 180° (angles on a straight line).

78 + z - 78 = 180 - 78

z = 102°

Answer:

I would say B

Step-by-step explanation:

sorry if the answer was wrong i am bad at math