Question 1

A triangle has sides of length 2 cm, 8 cm and 9 cm.
Calculate the value of the largest angle in this triangle.

For the segments to be congruent, x should be 13/2.

This is a case of congruency of segments. We know that two segments are congruent if and only if they have equal lengths.

Now, here the two line segments JK and RS have lengths 2x-9 and 30-4x respectively.

So, to be congruent, JK and RS must be of equal length.

Or in other words, 2x-9 = 30-4x

or 6x= 30 + 9 =39

i.e. 6x = 39.

Dividing both sides by 3, we get

2x=13 , which implies , x =13/2 or 6.5

Thus, for JK and RS  to be congruent  , x =13/2.

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For the segments to be congruent, x should be 13/2.

This is a case of congruency of segments. We know that two segments are congruent if and only if they have equal lengths.

Now, here the two line segments JK and RS have lengths 2x-9 and 30-4x respectively.

So, to be congruent, JK and RS must be of equal length.

Or in other words, 2x-9 = 30-4x

or 6x= 30 + 9 =39

i.e. 6x = 39.

Dividing both sides by 3, we get

2x=13 , which implies , x =13/2 or 6.5

Thus, for JK and RS  to be congruent  , x =13/2.

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Using linear function to solve this problem, for every 1 gallon of gas, Francisco travelled 27.9 miles

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2. A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. where m is slope of the line and b is the y - intercept

We can use the data given in writing out our equation

390.6 = 14x

If 14 gallons = 390.6 miles

 1 gallon = x miles

x = 390.6 / 14

x = 27.9 miles

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Answer:

Yes they are

Step-by-step explanation:

Because AE and FD both make a 50 degree angle with AC they are parallel which means that the two angles are corresponding.

Answer:

y = 7/2x - 4

Step-by-step explanation:

7/2 is the slope and -4 is the y intercept

Answer:  9v=162

Step-by-step explanation:

If you need the answer, Victors height is 18.

9v = 162

/9       /9

V = 18

Step-by-step explanation:

we are given a variable of victors height as v

according the expression

9 × v = 162

9v = 162

divide both sides by 9

v = 18

Selling price per unit minus variable cost per unit.

Option A is the correct answer.

We have,

Marginal contribution refers to the amount of revenue generated by each additional unit sold after deducting the variable costs associated with producing that unit.

It represents the incremental profit generated by selling one more unit.

Now,

To calculate the marginal contribution, you subtract the variable cost per unit from the selling price per unit.

This calculation takes into account the direct costs directly attributable to the production of each unit and provides insight into the profitability of each additional unit sold.

Thus,

Selling price per unit minus variable cost per unit.

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Mrs. Fran's average daily balance is $738.

What is average?

In everyday terms, an average is one number chosen to represent a list of numbers; it is often the sum of the numbers divided by the number of numbers in the list (the arithmetic mean).

Add the number of days in the list.

5+3+9+7+7=31

Multiply the number of days by the amount owed.

Use the arithmetic operation of multiplication -

For five days she owed $233.49 = 5 × 233.49 = $1,167.45

For three days she owed $651.11 = 3 × 651.11 = $1,953.33

For nine days she owed $991.08 = 9 × 991.08 = $8,919.72

For seven days she owed $770.00 = 7 × 770.00 = $5,390.00

For seven days she owed $778.25 = 7 × 778.25 = $5,447.75

Then add these products.

Use the arithmetic operation of addition -

1,167.45 + 1,953.33 + 8,919.72 + 5,390.00 + 5,447.75 = 22,878.25

Now divide the sum by 31.

22,878.25 / 31 = 738.008 ≈ 738

Therefore, the average balance is obtained as $738.

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Step-by-step explanation:

-3(-x -3y) = 3( x +3y) = 3x+9y

Step-by-step explanation:

Lola's pet turtle walked 10 feet, and then half that length again. This means that Lola's pet turtle walked:

= 10 + (1/2 × 10) = 10 + 5 = 15 feet

Lola's baby brother walked 3 feet, and then half that length again. Total length walked will be:

= 3 + (1/2 × 3) = 3 + 1.5 = 4.5 feet

Lola's hamster walked 6.5 feet, and then half that length again. Total length walked will be:

= 6.5 + (1/2 × 6.5) = 6.5 + 3.25 = 9.75

Lola's mom walked x feet, and then half that length again. Total length walked will be:

= x + (1/2 × x) = x + 0.5x = 1.5x

Total feet walked by the whole member of the family will be:

= 15 + 4.5 + 9.75 + 1.5x

= 29.25 + 1.5x

Answer:

turtle: 10 + 5 = 15

brother:  3 + 1 1/2 = 4 1/2

hamster: 6 1/2 + 3 1/4 = 9 3/4

Mom: x + 1/2x = 1 \(\frac{1}{2}\)x

Step-by-step explanation:

Answer:

Yes, he can.

Step-by-step explanation:

To find the sale, you need to times the sale percentage by the original price so

60 x 0.50 = 30

Then you subtract the original price by the sale price so

60 - 30 = 30

So the with the sale, the price is $30.

Now the tax

Do the same

30 x 0.045 = 1.35

Now instead of subtracting you add so

30 + 1.35 = $31.35

Yes, he can afford it.

Answer:

x = 141

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

its because B is the equilateral triangle and they are asking for a prism whose base is an equilateral angle

The smaller number is 5.5 and the larger number is 15.5.

Let's start by assigning variables to the two unknown numbers. Let x be the smaller number and y be the larger number.

From the problem statement, we know that:

x + y = 25 (the sum of the two numbers is 25)

y = 3x - 3 (the larger number is 3 less than three times the smaller)

We can use the second equation to solve for y in terms of x, by adding 3 to both sides:

y + 3 = 3x

Then, we can substitute this expression for y into the first equation:

x + (y + 3) = 25

Substituting y + 3 with 3x, we get:

x + 3x = 22

Combining like terms, we get:

4x = 22

Finally, we solve for x by dividing both sides by 4:

x = 5.5

Now that we know x, we can use the equation y = 3x - 3 to find y:

y = 3(5.5) - 3 = 15.5

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Answer:

A=12,000 m^3

Step-by-step explanation:

First, here is the area of the pyramid.

A= 1/3 Bh

Now, let's define our variables.

B= 900 m^2

h= 40 m

We will plug them into the equation.

A= 1/3 (900)(40)

I will simplify by dividing 900/3 to get rid of the fraction.

A= 300(40)

A=12,000

Hope this helps!

Step-by-step explanation:

\((6 + 5 + 5) \times 7 = 112\)

Answer:

The correct option is (B) 69.7%.

Step-by-step explanation:

The table provided represents the probabilities of a positive response to two government programs from citizens in eight cities.

The probabilities mentioned in the table are conditional probabilities, i.e. the probability of a positive response for program 1, given that the individual is from city x.

The probability a positive response for program 1 from an individual from Houston is 69.7%.

Then the conditional probability of a positive response for program 1, given that the individual is from Houston is 69.7%.

Thus, the correct option is (B).

The probability (in percentage) that a score will fall between a -3z and +2 z scores is 97.59%.

Assuming a standard normal distribution, the probability that a score falls between -3z and +2z can be calculated as the difference between the cumulative probabilities of +2z and -3z.

Using a standard normal distribution table or calculator, we find that the cumulative probability of +2z is approximately 0.9772, and the cumulative probability of -3z is approximately 0.0013.

Therefore, the probability that a score falls between -3z and +2z is:

0.9772 - 0.0013 = 0.9759

Converting to a percentage, we get:

0.9759 x 100% ≈ 97.59%

So the probability that a score falls between -3z and +2z is approximately 97.59%.

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5Step-by-step explanation:

Answer:

Step-by-step explanation:

The inverse of the function h(x)=3/4x+12 is h^-1(x)=(4x-48)/3.

The inverse of a function is found by switching the x and y variables and solving for y. In this case, the inverse of the function h(x)=3/4x+12 can be found by following these steps:

1. Switch the x and y variables:

x = 3/4y + 12

2. Isolate the y variable on one side of the equation:

x - 12 = 3/4y

3. Multiply both sides of the equation by 4/3 to get y alone:

(4/3)(x - 12) = y

4. Simplify the equation:

(4x - 48)/3 = y

5. Rewrite the equation with y on the left side:

y = (4x - 48)/3

Therefore, the inverse of the function h(x)=3/4x+12 is h^-1(x)=(4x-48)/3.

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Mrs. casen will be charged $3420 for the carpet and installation

Given that,

In her new home, Mrs. Casen intends to have three to five rolls of carpet placed. The price of the carpet, with installation included, is $450 for each half carpet roll.

It is said that it will cost,

$450 - 1/2 carpet roll

?       - 3 4/5 carpet roll

Coverting 3 4/5 into proper fraction,

3 4/5 -----> 19/5,

So now it looks like,

$450 - 1/2 carpet roll

?       -  19/5 carpet roll

By cross multiplication,

19/5 * 450 = 1/2 * ?

1710=1/2* ?

3420 = ?

Therefore, it will cost $3420 for Mrs. Casen to install carpets in her new house.

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The value of a Chi-Square goodness-of-fit test at a 5% significance level is 13.45

We need to perform a Chi-Square goodness-of-fit test at a 5% significance level.

First we need to calculate the expected count

expected value = ∑(x)/n

= (40 + 33 + 35 + 32 + 60)/5

= 200/5

= 40

Now we need tocalculate the test statistic value

Observed  expected  O - E    (O - E)^t/E       %

40                40             0            0                   0

33                40             -7          1.225          9.11

35                40             -5          0.625         4.65

32                40             -8         1.6                11.90

60                40             20        10                 74.35

Chi square test is 13.45

Therefore, the value of test statistics is 13.45.

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Answer:

oh period

Step-by-step explanation:

slay queen yaasss

Answer:

Since we are using the negative integer of -1, the answer would simply be -1. This is because 1 time any number is always going to be 1.

Step-by-step explanation:

Answer:

D) y < 1/3x - 1

Step-by-step explanation:

the equation of the line is y= 1/3x-1, then the dark part represents all the values that less than the values of y. The broken line means 'strongly', then the sign should be '<'.

Answer- 9 shelves

In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.

HOPE THIS HELPS & GOOD LUCK!

The triangles in this problem are classified as follows:

1. Isosceles.

2. Scalene.

3. Scalene.

4. Equilateral.

5. Scalene.

The classification of the triangles relative to their side lengths are given as follows:

In this problem, the side lengths are not given, hence a ruler has to be used to find the measures of the side lengths and classify the triangles.

Three of the triangles are scalene, as they have different side lengths, while triangle 1 is isosceles, as the sides of the right triangle have the same measure, and triangle 4 is equilateral, as all three side lengths are equal.

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Answer:

1) AC = 6 cm

2) AB = 16.2 cm      ( note that ^{2} is = square and \sqrt{  this is = square root)

3) BC = 12.65cm

Step-by-step explanation:

1) a^{2} + b^{2} = c^{2}

4.8^{2} + 3.6^{2} = AC^{2}

36 = AC^{2}

\sqrt{ }36 = AC

AC = 6

2)   a^{2} + b^{2} = c^{2}

AB^{2} + 6.75^{2} = 17.55^{2}

AB^{2} = 308.0025 - 25.5625

AB = \sqrt{ }262.44

AB = 16.2

3)  a^{2} + b^{2} = c^{2}

BC^{2} + 6^{2} = 14^{2}

BC^{2} = 196 - 36

BC = \sqrt{ } 160

BC = 12.65

I hope this helps a little bit.

Answer:

£15.6

Step-by-step explanation:

Method 1:

You are trying to find 30% of £52.

Therefore:

\(\frac{30}{100} * 52 = \frac{30 * 52}{100}\)

If you solve this you will find that 30 × 52 = 1560, and 1560 ÷ 100 = £15.6.

So, the answer is £15.6.

Method 2:

You can solve 30% of £52 by using an algebra equation.

By using the rule that to convert a percentage to a decimal you divide by 100, you can change 30% to be 0.3.

Now, in order to write the equation, you will have to include 0.3 and 52.

The equation is:

0.3 * 52 = x

Once you multiply, you will find that the answer is £15.6.

I hope I helped!

Answer:

it is 4/5 I'm pretty sure