Lines m and n are perpendicular. If the slope of m is zero, then the slope of n is
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Word Problem #1:

You are in a submarine at a depth of some unknown value x. The submarine rises 15 feet. After this point, you are able to record the depth to be 18 feet below sea level.

x = original depth

15 = height you rise up

-18 = final depth

x+15 = final depth

x+15 = -18 is the equation we solve to find the value of x

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Word Problem #2:

You are in debt to your friend. Debt is represented by negative numbers. For example, writing -2 means you are 2 dollars in debt. If you start off being x dollars in debt, but pay off $15, then you will have a balance of x+15 dollars. If this new final balance is -18, then we can say x+15 = -18

So in short: you go from x dollars in debt to 18 dollars in debt after paying off $15 to your friend.

77.99+7.00+9.99=96.98

96.98 times 8.75% or 0.0875=8.48575 or 8.49                    8.49+96.98=$105.47

Answer: 20

Step-by-step explanation:

Given: Point [tex]\text{G}[/tex] is on line segment [tex]\text{FH}[/tex]. Given [tex]\text{FH}[/tex] is [tex]4\text{x}+8[/tex] , [tex]\text{FG}[/tex]. is [tex]\text{x}[/tex], and [tex]\text{GH}[/tex] is [tex]5\text{x}[/tex].

To Find: the numerical length for [tex]\text{GH}[/tex].

Solution:

Point [tex]\text{G}[/tex] is on the line segment [tex]\text{FH}[/tex]

therefore,

[tex]\text{FH}=\text{FG}+\text{GH}[/tex]

putting the values

[tex]4\text{x}+8=\text{x}+5\text{x}[/tex]

[tex]4\text{x}+8=6\text{x}[/tex]

[tex]8=2\text{x}[/tex]

[tex]\text{x}=4[/tex]

Now,

[tex]\text{GH}=5\text{x}[/tex]

[tex]\text{GH}=5\times4[/tex]

[tex]\text{GH}=20[/tex]

Hence numerical length of line segment [tex]\text{GH}[/tex] is [tex]20[/tex]

The numerical length of GH is 20

If Point G is on the line segment FH, this means that:

Given the following parameters:

FH=4x+8

FG=x

GH=5x

Substitute the given values into the formula as shown:

x + 5x = 4x + 8

6x = 4x + 8

6x - 4x = 8

2x = 8

Divide both sides by 2

2x/2 = 8/2

x = 4

Get the length of GH

GH = 5x

GH = 5(4)

GH = 20

Hence the numerical length of GH is 20

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The calculated value of y in this linear system is 18

How to determine the value of y in this linear system?

From the question, we have the following parameters that can be used in our computation:

x + y + z = 62

x - y = 12

2x + y + z = 92

Subtracting the equations 1 and 2, we have

2x - x = 92 - 62

x = 30

In equation (2), we have

x - y = 12

This gives

y = x - 12

Substitute the known values into the equation

y = 30 - 12

Evaluate

y = 18

Hence, the value of y is 18

Answer:

[5, 0]

Step-by-step explanation:

x-intercept is where 0 = y. Just simply plug in 0 for y, then your x is given to you in your face.

Answer:

Third Option: $2.07

Step-by-step explanation:

Sales tax is the tax that is applied on the sales of goods by the government paid by the public. Here,

Given

Amount = $29.50

And

Sales tax rate = 7%

The formula for calculation of tax is:

Sales tax = Amount * tax rate

= 29.50 * 7/100

= 29.50*0.07

= 2.065

Rounding off will give

$2.07

So third option is correct ..

Answer:

$2.07

Step-by-step explanation:

Answer:

maybe number 2

Step-by-step explanation:

because if 2+k=18 then there is no other k there and where did the additional 2 come from ?and 2k=18 then value of k is 9 + there is balance.I may be wrong correct me but i think it is no.2

Answer:

2k = 18

k = 9

Step-by-step explanation:

First we have to look at each side of the hanger.

There are 2 k's, which can be represented as "2 times the value of k" or 2k.

On the other side, we have the value of 18. The question states that the two sides are balanced. Therefore, the correct equation that represents the image is:

2k = 18.

To find the value of k that makes the equation true, we must isolate the variable k. To do this, we divide 2 from each side of the equation.

2k ÷ 2 = 18 ÷ 2

k = 9.

The value of k that makes the equation true is 9.

Answer:

it is 2

Step-by-step explanation:

Hello There!

The slope of this line would be 3.

The slope is gradually increasing so starting from the Y intercept value, its consistently going up 3 on the Y axis and going over 1 on the X axis

Answer:

A. Buying socks and buying shoes are dependent events.

Step-by-step explanation:

We are given that

The probability that a customer buys socks ,P(A)=0.15

The probability that a customer socks given that the customer buys shoes P(A\B)=0.20

The probability that a customer buys shoes,P(B)=1-0.15=0.85

By using formula P(E')=1-P(E)

Where P(E)= Probability of an event that is happened

P(E')=Probability of an event that is not happened

We have to find [tex]P(A\capB)[/tex]  for two events

[tex]P(A)\cdot P(B)[/tex]

[tex]=0.85\times 0.15=0.1275[/tex]

We know that conditional probability of an event when given that the probability of an event B is given

[tex]P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}[/tex]

[tex] 0.20=\frac{P(A\cap B)}{0.85}[/tex]

[tex]P(A\cap B)=0.20\times 0.85=0.17[/tex]

[tex]P(A\cap B)\neq P(A)\cdot P(B)[/tex].

Therefore, the two events are dependent .Hence, Buying socks and buying shoes are dependent events.

Therefore, option A is true.

Answer: A. Buying socks and buying shoes are dependent events.

Step-by-step explanation:

Answer:

(b - 2)(3b + 7)

Step-by-step explanation:

Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term

product = 3 × - 14 = - 42 and sum = + 1

The factors are - 6 and + 7

Use these factors to split the b- term

3b² - 6b + 7b - 14 ( factor the first/second and third/fourth terms )

= 3b(b - 2) + 7(b - 2) ← factor out (b - 2) from each term

= (b - 2)(3b + 7) ← in factored form

ANSWER

[tex]k = 17[/tex]

EXPLANATION

The given function is

[tex]f(x) = 2x + 3[/tex]

The translation that shifts this function 10 units to the right is

[tex]f(x - 10)[/tex]

This implies that

[tex]f(x - 10) = 2(x - 10) + 3[/tex]

We expand the parenthesis to get:

[tex]f(x - 10) = 2x -20+ 3[/tex]

[tex]f(x - 10) = 2x - 17[/tex]

Comparing this equation with

[tex]f(x) = 2x - k[/tex]

we have

[tex]k = 17[/tex]

k=17

The new function would be f(x)=2x-17

In the previous function when u put x=0 you got 3.

Now when the function moves 10 units to the right you still have to get y=3 for x=10. So

2x-k=3 substitute 10 for x

20-k=3 solve for k

K=17.

Answer:

15

Step-by-step explanation:

Substitute x = - 5 into f(x)

f(- 5) = 5(- 5) + 40 = - 25 + 40 = 15

Answer:

Option C.

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem triangles HEF and EGE are similar  

because

[tex]EF/GF=HF/EF[/tex]

substitute the values

[tex]\frac{\sqrt{3}}{1}=\frac{3}{\sqrt{3}}\\ \\3=3[/tex]

Is true

The sides are proportional

and

∠HFE=∠GFE

∠EHF=∠GEF

∠HEF=∠EGF

The angles are congruent

The scale factor is equal to

[tex]EF/GF[/tex]

[tex]\frac{\sqrt{3}}{1}[/tex]

Answer:

Option C

Step-by-step explanation:

Two triangles are similar if they have at least 2 equal angles

Note that the HEF triangle has angles of 90 °, 60 ° and 30 °

Note that the EGF triangle has angles of 90 ° and 30 ° so the third angle must be 60 °

Then HEF and EGF are similar triangles.

By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a ', b' c' then

[tex]\frac{a}{a'}=\frac{b}{b'}=\frac{c}{c'}=k[/tex]

Where the constant k is known as "scale factor"

In this case

[tex]\frac{HF}{EF}=\frac{HE}{EG}=\frac{FE}{GF}=k[/tex]

[tex]k=\frac{3}{\sqrt{3}}=\frac{2\sqrt{3}}{2}=\frac{\sqrt{3}}{1}=\sqrt{3}[/tex]

[tex]\frac{FE}{GF}=\frac{\sqrt{3}}{1}[/tex]

or

[tex]\sqrt{3}:1[/tex]

The answer is Option C

Answer:

[tex]X\leq -8[/tex]

This solution provides a step-by-step explanation to solve the inequality x – 1 ≤ -9, which results in the solution x ≤ -8. This solution indicates that all numbers x that are less than or equal to -8 will satisfy this inequality.

To solve the given inequality x – 1 ≤ – 9, you should first isolate the variable on one side of the inequality:

So, the solution to the inequality is x ≤ -8, which means all numbers x that are less than or equal to -8 will satisfy this inequality.

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Answer:

The y-intercept is the point (0,5)

Step-by-step explanation:

step 1

Find the slope of the line perpendicular to the line y=(3/4)x+3

Remember that

If two lines are perpendicular, then the product of their slopes is equal to -1

m1*m2=-1

we have

m1=3/4 -----> the slope of the line y=(3/4)x+3

Find m2

substitute

(3/4)*m2=-1

m2=-4/3

step 2

Find the equation of the line into point slope form

The equation is equal to

y-y1=m(x-x1)

we have

m=-4/3

(x1,y1)=(3,1)

substitute

y-1=-(4/3)(x-3) ----> equation of the line into point slope form

step 3

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

substitute in the equation of the line and solve for y

y-1=-(4/3)(0-3)

y-1=4

y=4+1=5

The y-intercept is the point (0,5)

Final answer:

The y-intercept of the line perpendicular to y = 3/4x+3 that includes the point (3, 1) is 5.

Explanation:

To find the y-intercept of the line perpendicular to the line y = 3/4x+3 that includes the point (3, 1), we first need to determine the slope of the perpendicular line. Since the given line has a slope of 3/4, the slope of the perpendicular line will be the negative reciprocal, which is -4/3. We then use the point-slope form of a line equation, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope.

Substituting the point (3, 1) and the slope -4/3 into the equation gives us y - 1 = -4/3(x - 3). Simplifying, we get y = -4/3x + 5. The y-intercept of this line is the y-value when x is zero, which in this case is 5.

Answer:

f(3) = 64/3

Step-by-step explanation:

f(x)=1/3•4^x

Let x = 3

f(3) = 1/3* 4^3

    = 1/3 * 64

   = 64/3

Answer:

64/3 (APEX)

Step-by-step explanation:

Answer:

6√2

Step-by-step explanation:

A 45 45 90 right triangle, so ratio of leg : leg: hypotenuse = a: a : a√2 (a = value of leg)

Given: leg = 6

So the ratio of leg : leg: hypotenuse = 6 : 6 : 6 √2

Answer:

x = 6√2

Answer:

B

Step-by-step explanation:

Since the triangle is right use the sine ratio to solve for x

and the exact value for sin45° = [tex]\frac{1}{\sqrt{2} }[/tex], then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex]

Multiply both sides by x

x × sin45° = 6 ( divide both sides by sin45° )

x = [tex]\frac{6}{sin45}[/tex] = [tex]\frac{6}{\frac{1}{\sqrt{2} } }[/tex] = 6[tex]\sqrt{2}[/tex]

Answer:

c- shifted 3 units right and 4 units up

Step-by-step explanation:

In this problem, we have a quadrilateral named as ABCD. Recall that a quadrilateral is a two-dimensional shape having four sides. So, we need to identify what transformation has been performed to get A'B'C'D', which is the same quadrilateral shifted certain units right and up. So take one point, say, B, so how do we need to do to obtain point B'? well, we need to move that point 3 units right and 4 units up, but how can we know this? just count the number of squares you need to move from B to B' horizontally and vertically, which is in fact  3 units right and 4 units up.

Answer:  The correct option is

(c) shifted 3 units right and 4 units up

Step-by-step explanation:  We are given to select the correct steps that were applied o ABCD to obtain A'B'C'D' as shown in the figure.

From the graph, we note that

the co-ordinates of the vertices of quadrilateral ABCD are A(2, 3), B(4, 8), C(6, 8) and D(8, 3).

And, the co-ordinates of the vertices of quadrilateral A'B'C'D' are A'(5, 7), B'(7, 12), C'(9, 12) and D'(11, 7).

So, the transformations from the vertices of ABCD to the vertices of A'B'C'D' are as follows :

A(2, 3)    ⇒   A'(5, 7) = (2+3, 3+4),

B(4, 8)    ⇒   B'(7, 12) = (4+3, 8+4),

C(6, 8)    ⇒   C'(9, 12) = (6+3, 8+4),

D(8, 3)    ⇒   D'(11, 7) = (8+3, 3+4).

Therefore, the required rule of translation from ABCD to A'B'C'D' is

(x, y)  ⇒   (x+3, y+4). That is, 3 units right and 4 units up.

Thus, the required steps applied to ABCD to obtain A'B'C'D' are

Shifted 3 units right and 4 units up.

Option (c) is CORRECT.

Answer:

The sum of the geometric sequence is: -6665

Step-by-step explanation:

By looking at the geometric sequence, we can note that each term is multiplied by -6.

So, the fourth term is going to be: -216

The fifth term is going to be: 1296

The sixth term is going to be: -7776

The sum of the geometric sequence is: 1 - 6 + 36 - 216 + 1296 - 7776 = -6665

Answer:

The correct answer option is E. [83 + 2(79) + 4(88)] × 1/7.

Step-by-step explanation:

We are given the quiz average, test average and final average for Sabra's grades for a class.

Given that her test average counts twice as much as her quiz average and final exam counts twice as much as her test average for her overall average:

[tex](83+79+79+88+88+88+88)[/tex] ÷ [tex]7[/tex]

This can also be written as:

[83 + 2(79) + 4(88)] × 1/7

Answer:

2nd choice B.

Step-by-step explanation:

You can use the options A-D to help you eliminate pretty quickly without actually graphing

So first chose says you have the graph on the left when x<1 But you should see our visual actually says we want to include what happens at 1 (the filled dot) so this isn't the answer

Second choice Possible

Third choice... I'm just going to look at one of the parts... x^2+4 for x<=1 says we should have part of a parabola to the left of x=1 (inclusive) but there is not parabola in our visual

Fourth choice: same reason as third choice

Answer is the 2nd

Answer:  b) (2m³ - 4p⁵)(2m³ + 4p⁵)

Step-by-step explanation:

Use the difference of a square formula: a² - b² = (a - b)(a + b)

[tex]4m^6 - 16p^{10}\\\bullet a) \sqrt{4m^6}=2m^3\\\bullet b)\sqrt{16p^{10}}=4p^5[/tex]

(2m³)² - (4p⁵)² = (2m³ - 4p⁵)(2m³ + 4p⁵)

Answer:

2957

Step-by-step explanation:

Instead of just giving you a formula.. I want to show you how to understand the formula

So 2200 is the initial population

After 1st year, we are going to have an increase of 3% so 1st yr gives us 2200(1.03)=2266

After 2nd year, we are going to have increase of 3% from previous year so we could do 2266(1.03) or realize this is the same as 2200(1.03)^2 .

so you are going to keep multiplying factors of 1.03 to that per year.

So at 10 years we have 2200(1.03)^10

The formula I mentioned was really this initial population times (1.03)^(number of yrs)

So answer is 2956.616

To the nearest whole number is 2957

Answer:

1/(x+3)+7/(x+2)

Step-by-step explanation:

I'm assuming the full numerator is (8x+23)... and by making that assumption I'm assumed the fraction was (8x+23)/[(x+3)(x+2)].

(8x+23)/[(x+3)(x+2)]=A/(x+3)+B/(x+2)

8x+23=A(x+2)+B(x+3)                   I multiply both sides by (x+3)(x+2)

Set x to -2 that gives -16+23=B          so this means B=7

Set x to -3 instead that gives -24+23=A(-1)   so this means A=1

So (8x+23)/[(x+3)(x+2)]=1/(x+3)+7/(x+2)

For this case we have the following function:

[tex]f (x) = - \sqrt {x + 3} -2[/tex]

By definition, the domain is given by all the values for which the function is defined.

The given function is no longer defined if the argument of the root is negative. So:

[tex]x + 3 \geq0\\x \geq-3[/tex]

Thus, the domain of the function is given by all the values of x greater than or equal to -3.

Domain: [-3, ∞)

Substituting the values of the domain, we find the range.

[tex]f (-3) = - \sqrt {-3 + 3} -2 = -2[/tex]

The function evaluated in ∞ gives -∞. So the range is given by:

(-∞, 2]

Answer:

Domain:  [-3, ∞)

Range: (-∞, 2]

The answer for this equation is C.

Answer: 107 degrees.

Step-by-step explanation:

A quadrilateral is defined as a 2-dimensional closed shape which has four sides and four vertices.

By definition the interior angles of a quadrilateral add up 360 degrees.

We know that this quadrilateral has 2 right angles (which are angles that measure 90 degrees) and we know that the measure of the third angle is 73 degrees.

Let be "x" the measure of the fourth angle.

Then you can write this expression:

[tex]360\°=90\°+90\°+73\°+x[/tex]

And finally solve for "x":

 [tex]360\°=253\°+x[/tex]

[tex]360\°-253\°=x[/tex]

[tex]x=107\°[/tex]

The correct answer is D. (2x^2+4-7)(x)+(2x^2+4x-7)(x-2).

To use the distributive property, we need to distribute the first factor,

(2x^2 +4−7), over the two factors in the second set of parentheses, (x) and  (x−2).

This means we multiply each term in the first factor by each term in the second set of parentheses, and then add the products together.

Here is the correct distribution:

(2x^2+4-7)(x) + (2x^2+4-7)(x-2)

= (2x^3+4x-7x) + (2x^3-4x+14x-14)

= 4x^3-3x+7 + 10x-14

= 4x^3+7x-7

Therefore, the correct answer is D. (2x^2+4-7)(x)+(2x^2+4x-7)(x-2).

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Answer:

f(x) = -(x-4)^2 + 5

Step-by-step explanation:

The function [tex]f(x) = -(x-4)^2 + 5[/tex] is a quadratic function. Its graph looks like a parabola. The graph has a vertex of (4,5) and opens up downward.

Proving that [tex]f(x) = -(x-4)^2 + 5 \le 5[/tex] for all x:

[tex]x^2 \ge 0 \Rightarrow (x-4)^2 \ge 0 \Rightarrow -(x-4)^2 \le 0 \Rightarrow -(x-4)^2 + 5 \le 5.[/tex]

The function which has a range of {y | y < 5} is f(x) = -(x – 5)² + 4​.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given a range of the function, {y | y < 5}.

We want to find the corresponding function.

The range of the function contains all the values less than 5.

For the first two functions, when we substitute x = 4,

The value of the function, f(x) = 5

So this is not possible.

For the third function also, when we substitute any integers other than 5, the value of function is greater than 5.

Hence the correct option is D.

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Answer:

The value of 8m is 2

Step-by-step explanation:

step 1

Find the value of m

we know that

[tex]m^{-3} =64[/tex]

so

[tex]\frac{1}{m^{3}}=64\\ \\m^{3}=\frac{1}{64}\\ \\ m=\frac{1}{\sqrt[3]{64}}\\ \\m=\frac{1}{4}[/tex]

step 2

Find the value of 8m

[tex]8m=8(\frac{1}{4})=2[/tex]

Answer:7

Step-by-step explanation:since it has the rule f(n) =2n+1

Third term is when n=3

Therefore 2(3) +1=7