Work out the surface area of the solid
cuboid.
7m
6m
3m

[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-9)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-8)}}} \implies \cfrac{-4 +9}{3 +8} \implies \cfrac{ 5 }{ 11 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-9)}=\stackrel{m}{ \cfrac{ 5 }{ 11 }}(x-\stackrel{x_1}{(-8)}) \implies {\large \begin{array}{llll} y +9= \cfrac{ 5 }{ 11 } (x +8) \end{array}}[/tex]

Answer:

x = 1/2, y = 4

Step-by-step explanation:

2x + 3y = 13----------> 2x + 3y = 13

4x - y = -2------------> 12x - 3y = -6

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

14x = 7

x = 1/2, y = 4

Answer:

4 * 5 * 6 = 120  possible meals can we order.

Step-by-step explanation:

given that-

If you go to a restaurant and there are 4 choices for main dishes, 5 choices for sides, and 6 choices for drinks

4 * 5 * 6 = 120 combinations or Ways to Order

we can order the main dish in 4 different ways. Then, we can choices for sides in 5 different ways and the drinks in 6 different ways.

(The outcome of the selection of the first does not influence the second or third)

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The values of the expressions are

Expression 1

5-(-1 - 2)^2

Evaluate the difference in the expression

So, we have

5 - (-1 - 2)^2 = 5 - (-3)^2

Evaluate the exponent in the expression

So, we have

5 - (-1 - 2)^2 = 5 - 9

Evaluate the difference in the expression

So, we have

5 - (-1 - 2)^2 = -4

Expression 2

|x/x+y| - x^2 + y

When x = 2 and y = -3

Substitute x = 2 and y = -3 in |x/x+y| - x^2 + y

So, we have

|x/x+y| - x^2 + y = |2/2 - 3| - 2^2 - 3

Evaluate the difference in the expression

So, we have

|x/x+y| - x^2 + y = |2/-1| - 2^2 - 3

Evaluate the quotient and the exponent in the expression

So, we have

|x/x+y| - x^2 + y = |-2| - 4 - 3

Remove the absolute bracket

|x/x+y| - x^2 + y = 2 - 4 - 3

Evaluate the difference in the expression

So, we have

|x/x+y| - x^2 + y = -5

Hence, the solutions to the expressions are -4 and -5

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The unit rate of the graph is is inches per hour

A graph will hold as many information as the plotter will wish to give it. The information the graph has the more compicated wit will be

The graph plotted is a graph of snowfall in inches against time in hours. The input values of the graph is the time in hours while the snow fall in inches is the output values

The unit rate of graphs is gotten from the the units plotted against the other unit. Here it is inches against hours

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The given exponential function represents the growth in function with a percentage increase as 57.3%.

Given we have the exponential function as :

y=8800(1.573)ˣ

it is in the form of: y=k.aˣ

therefore, if a>2 then the function represents growth.

and if a<1 then the function represents decay.

now, x=1.573

1.573 > 1

so, the function represents change in growth.

therefore, 1.573 - 1

= 0.573

= 57.3%

hence the change in growth of the function is increased by 57.3%.

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Answer: $3.25 an hour.

Step-by-step explanation: If the server wants to make 184 dollars and they already made 164.50, you subtract 184 by 164.50. 184-164.50= 19.50

That is how much the server made without tips over the course of 6 hours, and we want the amount they made in 1 hour. So we now divide 19.50 by 6. 19.50/6=3.25

Answer:

Step-by-step explanation: the answer is .75. your welcome

the answer is 3/4 or 0.75

The power of the kettle if it takes 70 seconds to boil is 4 kilowatts.

It is given in the question that the  number of seconds that it takes for a kettle to boil, n, is inversely proportional to its power in kilowatts, p.

Also, The equation of proportionality is n = 280/p.

We have to find the power of the kettle if it takes 70 seconds  to boil.

According to the data given in the question, we can write,

n ∝ 1/p

n = k/p

Where k is the constant of proportionality.

Hence, k = 280

n = 280/p

Putting n = 70 seconds in the equation, we get,

70 = 280/p

p = 280/70

p = 4 kilowatts.

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Answer:

200.96 square inches

Step-by-step explanation:

it's asking for the area of a circle

we know that the radius is 8, so we can just plug it into the circle area formula which is

area = (pi) r^2

you plug in 8 for r (r stands for radius)

8^2 is 64

64 times pi is 200.96 (because pi=3.14)

The correct option regarding the central limit theorem is given as follows:

The average survival time of a large number of guinea pigs has a distribution that is close to normal.

It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean given by [tex]\mu[/tex] and standard deviation given by [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, as is the case in this problem, the sampling distribution is also approximately normal, as long as n is at least 30.

For this problem, we have that the distribution is strongly skewed, hence it will only be normal for large sample sizes, and the last option is correct.

The options are given by the image at the end of the answer.

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Error might the student have made was in angle 147 as acute angle means angle less than 60°

Acute angles are those that range in size from 0 to 90 degrees and are smaller than 90 degrees. Examples include 60, 30, 45, and other angles. An acute triangle is a triangle with all of its internal angles smaller than 90 degrees. An equilateral triangle, for instance, is an acute triangle because the internal angles are 60°.

Less than 90° of an angle is referred to be an acute angle. An acute angle, for instance, is formed when the time is 11 o'clock between the hour hand and the minute hand. Consequently, acute angles include 30°, 40°, 57°, and others.

Given that : The students are guvena right triangle. One of the acute angles has a measure of 33°. One student saha tbe measure kf the other acute angle is 147°.

As the acute angles are angles less than 90°

and they have measure as 147°

So the error was in measure angle as 147°

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Answer:

all those that give 12p as a result (look at the examples)

Step-by-step explanation:

Which expression is equivalent to 5p+7p

5p + 7p = 12p

The sum of the expression 10,000 + 2,000 + 60 + 1 is 12061

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

10,000 + 2,000 + 60 + 1

The sum of the expression can be calculated using a calculator

So, we have

10,000 + 2,000 + 60 + 1 = 12061

Hence, the value of the sum 10,000 + 2,000 + 60 + 1 is 12061

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Answer:

perimeter of triangle = a + b + c

perimeter = 3x-5+2x+19-x

                = 6x + 14

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Answer: P=2a + b which = A- 3x - 5

Step-by-step explanation:

The value of x in the triangle extended through W to X is 39.5°.

It should be noted that a triangle has a total angle of 180° and also has three sides. Based on the information given, the following can be deduced:

Angle 1 = 3x - 4.

Angle 2 = 6x + 6

Angle 3 = x + 20

Therefore, the value of x will be gotten by adding the values and equating to 180°. This will be:

3x - 4 + 6x + 6 + x + 20 = 180

4x + 22 = 180

Collect like terms

4x = 180 - 22

4x = 158°

Divide

x = 158/4

x = 39.5°

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Answer: 39.5°

Step-by-step explanation:

The total amount received at the end of 1 year will be 242000

The amount available in Austin's saving account: $100,000

Rate of interest = 142% per year

Simple interest: Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

The formula for simple interest is given:

Simple Interest = P*R*T/100

where P = principal amount invested

R = rate of interest per year

T = time in years for which the amount is invested

Substituting the values in the formula we get:

Simple interest = 100000*142*1/100

= 142000

Total amount after 1 year = Principal invested + Simple interest earned

= 100000 + 142000

= 242000

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Answer:

82 because 102.50/1.25=82

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Step-by-step explanation:

Check the picture below.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~7 - (-2)~~)^2 + (~~9 - 7~~)^2} \implies d=\sqrt{(7 +2)^2 + (9 -7)^2} \\\\\\ d=\sqrt{( 9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }[/tex]

Answer:

FM and GB

Step-by-step explanation:

the angles are corresponding meaning that the lines must be parallel

The simplification of number 17/0 gives the undefined form.

For the given question;

The expression is 17/0

Let us say that 17/0 = x

Its means; 17 = x ×0

17 = 0

But , 17 ≠ 0

As, given expression 17/0 can not be defined by any number.

Thus, 17/0 is an undefined term.

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Answer:

211a+9x

Step-by-step explanation:

first, calculate the exponents (the number times itself) of each number

9a +81a +121a+9x

the reason they are positive is that a negative times a negative equals a positive ex: -3 x -3 = 9

next, combine the coefficients

starting with the variable for a

9a+81a+121a= 211a

x has no other coefficients so it would remain 9x

so the simplified answer would be

211a+9x

The value of m in the right triangle to the nearest tenth is 7.2 units.

The figure above is a right triangle.

The right triangles are similar.

Therefore, right triangle ABC is similar to right triangle BDC.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Therefore, let's find the value of m using the similar triangle principle,

m / 13 = 4 / m

cross multiply

m × m  = 13 × 4

m² = 52

square root both sides

√m² = √52

m = 7.21110255093

Therefore,

m = 7.2 units.

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For an equivalent expression for [tex]18^{-7}\\[/tex] * [tex]18^5\\[/tex] it is option 4 that is correct that means the equivalent expression can be seen as [tex]\frac{1}{18} ^{2}[/tex].

Expressions that can be considered are equivalent do the same thing even when they have distinct appearances. When we get to enter the same value(s) for the same variable, two algebraic expressions that are equivalent have the same value (s).

Calculating the equivalent expression,

[tex]18^{-7}\\[/tex] * [tex]18^5\\[/tex]

= [tex]18^{-7+5}[/tex]

=[tex]18^{-2}[/tex]

=  [tex]\frac{1}{18} ^{2}[/tex]

An expression that can be considered equivalent to another phrase but then differs in appearance is the one that has the same value or worth. In algebra, we can say 2(2x – 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.

When two expressions can be reduced to a single thread expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. You can also determine whether two expressions are equivalent.

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Step-by-step explanation:

The answer is 8+2x . This is the correct answer .

The formula for y in terms of x is y = [tex]\frac{16}{25} x^{3}[/tex]

Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.

Given that,

Y is inversely proportional to a³ When a = 2, y = 10

A is directly proportional to x when x = 4, a = 20

If y is inversely proportional to a³

[tex]\frac{y}{x^{3} }[/tex]∝1

y = [tex]\frac{k}{a^{3} }[/tex], where k is the proportionality constant

Given, a=2, y=10, then 10 = [tex]\frac{k}{2^{3} }[/tex]

k = 10 × 2³

k = 80

Substituting k = 80 back into the formula;

y = [tex]\frac{80}{a^{3} }[/tex]............. 1

Similarly, if a is directly proportional to x, then a ∝ x i.e a = kx

If x=4, a=20 then;

20 = 4k

k = [tex]\frac{20}{4}[/tex]

k = 5

Substituting k = 5 back into the formula;

a = 5x ....... 2

Substitute equation 2 into 1;

y = [tex]\frac{80}{a^{3} }[/tex]

y = [tex]\frac{80}{5x^{3} }[/tex]

y = [tex]\frac{80}{125x^{3} }[/tex]

y = [tex]\frac{16}{25x^{3} }[/tex]

Therefore, the formula for y in terms of x is y = [tex]\frac{16}{25} x^{3}[/tex]

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SOLUTION:

Step 1:

In this question, we have the following question:

A rock is dropped from a height of 10 feet. The height of the rock is modeled by the graph shown.

Part A



​​What is the height of the rock 0.5 seconds after being dropped? The height of the rock 0.5 seconds after being dropped is ........... feet

6 .

Step 2:

Part B



To the nearest tenth of a second, how many seconds after being dropped does the rock hit the ground?The rock hits the ground approximately ...............................seconds after being dropped.

0.8



Answer:

2600 meters

Step-by-step explanation:

2.6x1000

for the different values of x, we have found the values of the function f (x) = x² + 2 x + 1.

We are given the function:

f (x) = x² + 2 x + 1

We need to complete the given table of values for x and f (x)

For x = - 3:

f (- 3) = (- 3)² + 2 (- 3) + 1

f (- 3) = 9 - 6 + 1

f (- 3) = 4

For x = - 2:

f (- 2) = (- 2)² + 2 (- 2) + 1

f (- 2) = 4 - 4 + 1

f (- 2) = 1

For x = - 1:

f (- 1) = (- 1)² + 2 (- 1) + 1

f (- 1) = 1 - 2 + 1

f (- 1) = 0

For x = 0:

f (0) = (0)² + 2 (0) + 1

f (0) = 0 + 0 + 1

f (0) = 1

For x = 1:

f (1) = (1)² + 2 (1) + 1

f (1) = 1 + 2 + 1

f (1) = 4

For x = 2:

f (2) = (2)² + 2 (2) + 1

f (2) = 4 + 4 + 1

f (2) = 9

For x = 3:

f (3) = (3)² + 2 (3) + 1

f (3) = 9 + 6 + 1

f (2) = 16

Table:

x     - 3      - 2      - 1      0      1      2      3

y       4         1        0      1      4      9     16

Therefore, for the different values of x, we have found the values of the function f (x) = x² + 2 x + 1.

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