The lines shown below are perpendicular. If the green line has a slope of
2
-3, what is the slope of the red line?
3'
-5
10+
1
-10-
5
10
++
15
OA 3/2
O B. 3
O C. - 13/
D. -13/1
OD.

Answer: x=5

Step-by-step explanation:

3x + y = 13 ------- (1)

2x - 4y =18 ------- (2)

2x = 4y + 18 ------- (3)

(3) x 3

6x = 12y + 54 ------- (4)

(1) x 2

6x + 2y = 26 --------- (5)

sub (4) into (5)

12y + 54 + 2y =26

14y + 54 = 26

14y = -28

y = -2 --------- (6)

sub (6) into (1)

3x - 2 = 13

3x = 15

x = 5

The result of the definite integral by substitution is 214440.6.

In this problem we find the case of a definite integral, that is, an integral with definite limits, that must be simplified by algebraic substitution to be solved quicker. First, write the substitution formula and its derivative:

u = 6 · x - 7

du = 6 dx

f(u) = u⁴

Second, define the new limits of the definite integral:

a = 6 · 2 - 7

a = 5

b = 6 · 5 - 7

b = 23

Third, simplify the integral by means of the substitution formula:

[tex]\frac {1}{6}\int\limits^{23}_{5} {u^{4}} \, du[/tex]

Fourth, integrate the expression:

[tex]I = \frac{1}{30} \cdot u^{5}\left|_{5}^{23}[/tex]

I = (1 / 30) ·  (23⁵ - 5⁵)

I = 214440.6

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The percent of 18 that equals 23 rounded to the nearest tenth is 127.8%.

Percentage is simply number or ratio expressed as a fraction of 100.

Given the data in the question;

Let x% represent the percentage of 18 that is equal to 23.

Note that x% is the same as x/100

Hence;

x/100 × 18 = 23

Solve for x

18x/100 = 23

Cross multiply

18x = 23 × 100

18x = 2300

Divide both sides by 18

18x/18 = 2300/18

x = 2300/18

x = 127.8

Therefore, the required percentage is 127.8%.

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Answer:

93.75min

Step-by-step explanation:

Solution:

The rate of fill up is, Rate = 3.2 Gallons / minute = 3.2 g/min

The hut tub volume is 300 Gallons

You can set up this problem as follows:

Every 3.2 gallons require 1 minute, How many minutes 300 gallons require?

3.2  g    1min

300 g     ? min    = (300 gallons x 1min/ 3.2 gallons)=(300/32)min

= 93.75 min

or simply the number minutes is the time required (T) the rate is (R) and the volume is (V)

such that T=V/R= (300g/3.2 g/min)= 93.75 min

There is no conversion of units in this problem, but manipulation of units

Answer:

[tex]x2 + 4x + 4 = 0 [/tex]

The solution for the system of equations is negative one fourth comma three fourths.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Slope intercept form of a line is y = mx + c, where m is the slope and c is the y intercept.

Given two lines on a graph.

Let y = m₁x + c₁ and y = m₂x + c₂ are the equations of two lines.

One line passes through (0, 1) and (1, 2).

m₁ = (2 - 1) / (1 - 0) = 1

Substituting m₁ = 1 and a point (x, y) = (0, 1) in y = m₁x + c₁,

1 = c₁

Equation of one line is y = x + 1.

Other line passes through (0, 0) and (1, -3).

m₂ = (-3 - 0) / (1 - 0) = -3

Substituting m₂ = 1 and a point (x, y) = (0, 0) in y = m₂x + c₂,

0 = c₂

Equation of second line is y = -3x

Solving both the equations y = x + 1 and y = -3x,

-3x = x + 1

-4x = 1

x = -1/4

y = -3x = 3/4

Solution is (-1/4, 3/4).

Hence the solution of the system of equations is the point (-1/4, 3/4).

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The sum of the angles of the triangle below are angle A = 34.91°, angle B = 86.41°, and angle C = 58.68°.

According to the triangle sum theorem, a triangle's internal angles can be added up to 180 degrees. The triangle sum theorem, often referred to as the angle sum theorem of the triangle, states that the total of the measures of a triangle's internal angles in a Euclidean space adds up to 180 degrees, whether the triangle is acute, obtuse, or right.

Let a = 8, b = 14 and c = 12 for the given triangle.

Then,

cos (A) = (b² + c² − a²) / 2bc

cos (A) = (14² + 12² - 8²)/ (2)(14)(12)

cos (A) = (196 + 144 - 64)/ 336

cos (A) = 0.82

A = cos⁻¹ (0.82)

A = 34.91°

Similarly, for angle B.

Cos (B) = (c² + a² − b²)/2ca

Cos (B) = (12² + 8² - 14²)/ (2)(12)(8)

A = cos⁻¹ (0.0625)

B = 86.41°

The sum of all the angles of a triangle is 180:

A + B + C = 180°

34.91° + 86.41° + C = 180°

C = 58.68°

Hence, the sum of the angles of the triangle below are angle A = 34.91°, angle B = 86.41°, and angle C = 58.68°.

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Answer:

192 in²

Step-by-step explanation:

The surface area of a square pyramid can be calculated by summing up the area of its base and four lateral faces.

The base area of the square pyramid is 8 x 8 = 64 in².

The area of each lateral face is a triangle with base 8 in and height 8 in, so its area is 1/2 x 8 x 8 = 32 in².

So the total surface area of the pyramid is 64 + 4 x 32 = 192 in².

192in²

Step-by-step explanation:

Each side of the base of a square pyramid measures 8 inches.The height of each lateral face of the pyramid is also inches.

What is the surface area of the pyramid?

192in²

A

The graph of the function g(x) = 1/x + 13 is a transformation of the graph of f(x) = 1/x. The transformation that has been applied is a vertical shift of 13 units upward. This means that every point on the graph of f(x) has been moved upward by 13 units along the y-axis, resulting in the new graph of g(x). In other words, the graph of g(x) will be parallel to the graph of f(x) but shifted upward by 13 units.

The inequality nature is discussed below.

Given is a inequality.

Assume the inequality to be -

ax + b > g

Now, if for the value of g = - 7, the expression - (ax + b) is greater than g       {for any specific value of x} then the inequality is said to be true.

Therefore, the inequality nature is discussed above.

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Answer:

Step-by-step explanation:

...........

Answer: X divided by 5

               X/5

Step-by-step explanation:

if x is the cost of the dinner each person pays x divided by 5 because there are 5 people

The vertex of the absolute value function y = |3x - 9| is at (3, 0).

The actual name is the vertex, and to find the vertex we first need to find the value of x such that the argument of the absolute value part becomes zero, then we need to solve:

3x - 9 = 0

3x = 9

x = 9/3 = 3

x = 3

Now we can evaluate the absolute value function there:

y = |3*3 - 9|

y = 0

The vertex is at (3, 0).

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Kelly flew a total of [tex]6\frac{17}{42}[/tex] hours..

A fraction represents a part of a whole.

Given that Kelly took  2 4/7 hours to fly from City A to City B

Again Kelly took another 3 5/6 hours to fly from City B to City C.

We have to find the total time taken by Kelly to fly from City A to city B

To find this we have to add the fractions.

[tex]2\frac{4}{7} +3\frac{5}{6}[/tex]

Convert mixed fractions to proper fraction and solve.

18/7 + 23/6

The LCM of 7 and 6 is 42

108+161/42

269/42

[tex]6\frac{17}{42}[/tex]

Hence, Kelly flew a total of [tex]6\frac{17}{42}[/tex] hours.

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Answer:

D. 74

Step-by-step explanation:

Answer:

D=74

Step-by-step explanation:

10 + (8/2)^3

10 + 512/8

10 + 64

Answer: 74

The formula holds true for matrices A and B.

The formula (A + B)^2 = A^2 + 2AB + B^2 holds true for all matrices A and B that are of the same size and can be added and multiplied. To prove this, we calculate the left-hand side and the right-hand side of the equation:

(A + B)^2 = (A + B)(A + B) = A^2 + AB + BA + B^2

Since AB = BA, we can simplify the equation to:

(A + B)^2 = A^2 + 2AB + B^2

So, the formula holds true for matrices A and B.

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Based on the proportionate equation of the selling price (S), cost price (C), and profit (P), the change in S caused by decrease of C and increase of P is decrease by 4%

Based on the given information, we know that:

S ∝ √C --> S directly varies as the square root of C

S ∝ 1/P³ --> S inversely as the cube of P

We can combine both relationships to make a proportionate equation:

S = √C / P³

We know from the case that:

ΔC = - 2%

ΔP = 1%

Then:

C' = C + ΔC

C' = C + (-0.02)P

C' = 0.98C

P' = P + ΔP

P' = P + (0.01)P

P' = 1.01P

S' = √C' / P'³

S' = √(0.98C) / (1.01P)³

S' = 0.96 √C/P³

S' = 0.96S

ΔS = S' - S

ΔS = 0.96S - S

ΔS = - 4%

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Answer:

Step-by-step explanation:

since there are 60 seconds in 1 minute, we can do

5.85 = 60second

5.85/60  to show how many cm happened in 1 second.

0.0975 cm per second.  

Step-by-step explanation:

x = 2 3/4

y = -1 1/4

I think this is the answer

The 5th term of the geometric sequence described by an = 5(1.5)-1 is 6.5

Geometric progression,  which is also called geometric sequence, is defined as a sequence with non-zero numbers where all of the terms after the first is determined by multiplying the previous one by a fixed, non-zero number that is termed the common ratio.

The general formula for a geometric sequence is given as;

an = ar^n-1

From the information given, we have that the nth term of the geometric sequence is expressed with the equation;

an = 5(1.5)-1

expand the bracket

an = 7.5 - 1

Now, subtract the value, we get;

an = 6.5

Hence, the value of the term of the geometric sequence is 6.5

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Answer:

M

Step-by-step explanation:

Answer: $675

Step-by-step explanation:

To calculate the monthly payment, we need to determine the number of $2,000 increments that the car costs. $30,000 ÷ $2,000 = 15.

So, the car costs 15 $2,000 increments.

Next, we need to multiply the number of increments by the $45 increase in payment per increment to find the monthly payment. 15 increments × $45/increment = $675.

Therefore, the monthly payment for a $30,000 car would be $675.

All the correct statements are,

a) 3 lb plaster / 1 qt water is a unit rate for the mis.

c) Using the same rate, the potter mixes 9 pounds of plaster with 3 quarts of water.

e) Using the same rate, the potter mixes 12 pounds of plaster with 4 quarts of water.

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

A potter mixes 6 pounds of pottery plaster with 2quarts of water.

Now, We get;

The unit rate for the mis = 6/2

                                      = 3/1

Thus, 3 lb plaster / 1 qt water is a unit rate for the mis.

And, Using the same rate, the potter mixes 9 pounds of plaster with 3 quarts of water.

Using the same rate, the potter mixes 12 pounds of plaster with 4 quarts of water.

Thus, All the correct statements are,

a) 3 lb plaster / 1 qt water is a unit rate for the mis.

c) Using the same rate, the potter mixes 9 pounds of plaster with 3 quarts of water.

e) Using the same rate, the potter mixes 12 pounds of plaster with 4 quarts of water.

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The complete question is shown in figure.

[tex]\stackrel{mixed}{24\frac{1}{2}}\implies \cfrac{24\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{49}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]300\cdot 24\frac{1}{2}\implies 300\cdot \cfrac{49}{2}\implies 7350\qquad \textit{now let's add the 1\% for the broker} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{1\% of 7350}}{\left( \cfrac{1}{100} \right)7350}\implies 73.5~\hfill \stackrel{7350~~ + ~~73.5}{\text{\LARGE 7423.5}}[/tex]

The surface area of the pyramid is 3136 square inches.

A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.

Given:

Each side of the base of a square pyramid measures 8 inches.

The height of each lateral face of the pyramid is also 8 inches.

The perimeter of the base P is 32 inches.

The base area B = 8 x 8 = 64 square inches.

The surface area of the pyramid,

= B + 12(P x L)

= 64 + 12(32 x 8)

= 3136 square inches.

Therefore, the surface area is, 3136 square inches.

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The probability the firm will lose money from 10 wells is 0.99 and the probability the firm will gain 1.5 million from the ten wells is  1 minus the CDF of 4 successful wells.

1.

The expected profit from each well is $1 million - $60,000 = $940,000. The expected profit from all ten wells is $940,000 * 10 = $9,400,000. The probability of losing money on all ten wells is 1 - (0.1)^10 = 0.99

2.

To calculate the probability of gaining $1.5 million or more, we can use the cumulative distribution function (CDF) of the binomial distribution, which models the number of successful wells out of ten. The CDF gives the probability of getting a certain number of successful wells or fewer. To get the probability of getting more than a certain number of successful wells, we subtract the CDF of that number from 1. To get the probability of getting 2 or more successful wells, we subtract the CDF of 1 from 1, and so on. To get the probability of getting 5 or more successful wells, we subtract the CDF of 4 from 1, and so on. To get the probability of getting $1.5 million or more, we need to find the probability of getting 5 or more successful wells, since 5 wells at $1 million each give $5 million. The CDF of 4 successful wells can be found using statistical software or by using tables or approximations. The final answer is 1 minus the CDF of 4 successful wells.

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Answer: this is like multiplying. this is way to easy.the answer is 25.

Step-by-step explanation:

the answer is 25 bc its just saying

whats 5 times 5 which the answer is 25 right ?

Answer:

30,000 ÷6=

5,000 a month