If triangle TOY is equal to triangle STU, then what corresponding side is congruent to side US?

Answer:  The answer is given below.

Step-by-step explanation:  As shown in the attached figure, the prism-shaped roof has equilateral triangular bases, one of which is ΔABC. We need to  create an equation that models the height of one of the roof's triangular bases in terms of its sides. Let ii be AD.

SEe the figure attached herewith, ΔABC forms an equilateral triangle, in which AD is the height. So, D will be the mid-point of BC and ∠ADB = ∠ADC = 90°.

Now, in ΔADB, we have

[tex]AD^2=AB^2-BD^2\\\\\\\Rightarrow AD^2=AB^2-\left(\dfrac{1}{2}AB^2\right)^2\\\\\\\Rightarrow AD^2=\dfrac{3}{4}AB^2\\\\\\\Rightarrow AD=\dfrac{\sqrt 3}{2}AB.[/tex]

Thus, with the help of this model, we can find the height of any one of the roof's triangular bases.

Answer:

Copy and Paste Version

ADsqaured = ABsquared - BDsquared

ADsqaured = ABsquared - (1/2AB squared) 2

AD squared = 3/4AB squared

AD = square root 3/2 AB

​Now we can find the height of any of the bases

Step-by-step explanation:

The equivalent value of the fraction is A = 83 / 4 = 20.75

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the numerator of the fraction be p

where the value of p = 83

Let the denominator of the fraction be q

where q = 4

Now , the fraction is A = p/q

On simplifying the expression , we get

So , the left hand side of the equation is equated to the right hand side by the value of p/q

A = 83 / 4

A = 20.75

On further simplification , we get

A = 20.75

Therefore , the value of A = 20.75

Hence , the expression is A = 20.75

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Answer:

-1 < x < 0

AND

0 < x < 1

Step-by-step explanation:

graph is decreasing when x increases, y decreases

so the part of graph that is decreasing is between x = -1 n 1

ans is

-1 < x < 0

AND

0 < x < 1

Answer:

I would say the answer is c

Answer: the best answer is c

If the line has a slope = 0,  then it's a horizontal line

with the equation y = constant.

The line passes through (0, -3) → y= -3

Answer:

1/25

Step-by-step explanation:

Answer:

thousands

hope it helps

Step-by-step explanation

Answer:

17.3

Step-by-step explanation:

tens  ones. tenths hundredths thousandths

1        7       .   2          5                    3

We are rounding to the nearest tenth

We are rounding the 2 so we look at the 5.  If it is 5 or above we round up.

Since it is, we will round the 2 to a 3

17.3

Answer:

x + 2y = 0

Step-by-step explanation:

Answer:

y < 9

Step-by-step explanation:

y - 2 < 7

This is a one-step inequality. You have y - 2 on the left side. You want y alone on the left side. If you add 2 to the left side, you eliminate the -2. You must do the same operation to both sides of an inequality, so add 2 to both sides of the inequality to eliminate the -2 on the left side.

y - 2 + 2 < 7 + 2

y < 9

Answer: y < 9

Answer:

this is to help im not sure To find the perimeter of a rectangle or square you have to add the lengths of all the four sides. x is in this case the length of the rectangle while y is the width of the rectangle. The area is measurement of the surface of a shape.

Step-by-step explanation:

Answer:

Step-by-step explanation: 2(12+20)= 44ft hope this helps :) correct me if I am wrong pls

Answer:

60

Step-by-step explanation:

The perimeter of the triangle is found by adding up the 3 sides

5+5+ unknown side = 15

10+unknown side = 15

Subtract 10 from each side

10-10 +unknown side = 15-10

unknown side = 5

All 3 sides are length 5

Since all 3 sides are the same, it is an equilateral triangle.

If it is an equilateral triangle, all 3 angles will be the same.

There are 3 angles and they add up to 180

x+x+x = 180

3x = 180

Divide by 3

3x/3 =180/3

x = 60

Answer:

Step-by-step explanation:-22

A(-2, 2), B(4, 2), C(-6, -1), D(0, -1)

AB = CD = 4 - (-2) = 4 + 2 = 6

BD = AC. Use the formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute the coordinates of the points B and D:

[tex]d=\sqrt{(-1-2)62+(0-4)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]

BD = AC = 5

The perimeter of parallelogram ABCD:

P = 2 · 6 + 2 · 5 = 12 + 10 = 22

Rounded to the nearest whole number, approximately 5 students must attend summer school for U.S. history.

Here, we have,

To determine the number of students who must attend summer school for U.S. history, we need to calculate the proportion of students who earned a grade less than or equal to 62.9.

First, we need to standardize the cutoff grade using the z-score formula:

z = (x - μ) / σ

Where:

x is the cutoff grade (62.9 in this case)

μ is the mean grade (79)

σ is the standard deviation (7)

Substituting the values into the formula:

z = (62.9 - 79) / 7

z ≈ -2.3

Next, we need to find the proportion of students with a z-score less than -2.3 using a standard normal distribution table or calculator. The corresponding proportion is approximately 0.0107.

To find the number of students who must attend summer school, we multiply this proportion by the total number of students:

Number of students attending summer school = 0.0107 * 440

Number of students attending summer school ≈ 4.7

Rounded to the nearest whole number, approximately 5 students must attend summer school for U.S. history.

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Final answer:

By calculating the Z-score for a grade of 62.9 and consulting a Z-table, approximately 4 students out of 440 at Thomas Paine high school must attend summer school for U.S. history.

Explanation:

To find out how many students at Thomas Paine high school must attend summer school for U.S. history based on their grades, we'll use the properties of the normal distribution. The distribution of grades is normally distributed with a mean of 79 and a standard deviation of 7. We are interested in the students scoring less than or equal to 62.9.

First, we need to calculate the Z-score for a grade of 62.9, which indicates how many standard deviations an element is from the mean. The Z-score is calculated as follows: (X - mean) / standard deviation, where X is the grade. For a grade of 62.9, Z = (62.9 - 79) / 7 = -2.3.

Next, we consult a Z-table to find the proportion of students scoring this Z-score or lower. A Z-score of -2.3 corresponds to approximately 1.01% of the distribution.

Finally, to find the number of students, we multiply this proportion by the total number of students taking U.S. history, which is 440. Therefore, roughly 0.0101 * 440 = 4.44, which when rounded to the nearest whole number, results in 4 students needing to attend summer school for U.S. history.

Answer:

84 people

Step-by-step explanation:

Since 30% of the people came from Germany then 84 people came from Germany.

On a flight from London with 280 passengers, 30% of the passengers, or 84 passengers, came from Germany.

To find out how many passengers came from Germany, we need to calculate 30% of the total number of passengers. Given that there were 280 passengers in total, we can find the number of passengers from Germany by multiplying 280 by 30/100:

Number of passengers from Germany = 280 × 30/100
= 84

Therefore, 84 passengers came from Germany on the flight from London.

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Answer:

x = 1

y = 2

Step-by-step explanation:

y = 2x

-6x + 6y = 6

-6x + 6(2x) =6    Substitute the fist equation for the value of y

-6x + 12x = 6     Combine like terms

6x = 6     divide

x = 1

Then, substitute the value of x in the equation for y

y = 2x    y = 2(1)

              y = 2

So with using the substitution method, to be able to do so you must have one of the equations isolated with one of the variables. In this case, we see that the first equation has the y variable isolated. Now with this, we are going to substitute y in the second equation for 2x since y = 2x:

[tex]-6x+6(2x)=6[/tex]

From here, we can solve for x:

[tex]-6x+6(2x)=6\\-6x+12x=6\\6x=6\\x=1[/tex]

Since we have the x-value, substitute x for 1 into either equation to solve for y as such:

[tex]y=2*1\\y=2\\\\-6(1)+6y=6\\-6+6y=6\\6y=12\\y=2[/tex]

In short:

Answer:

4 scrunchies

Step-by-step explanation:

GIVEN :

Sara can spend up to $24.98.

She already spent $12.99

She wants scrunchies that are $3.00 each.

To Find : No. of scrunchies She can purchase.

Solution :

Since she can spend up to  $24.98.

She already spent $12.99

So, amount she can spend further = $24.98-$12.99 = $11.99

Now she wants to buy scrunchies

No. of scrunchies of $3.00 = 1

No. of scrunchies of $1.00 = 1/3

No. of scrunchies of  $11.99 :

= [tex]\frac{1}{3} *11.99[/tex]

⇒ [tex]3.99[/tex]

Thus no. of scrunchies of $11.99 =3.99≈4

Hence she can buy 4 scrunchies

Answer:

1/6 is the scale factor

Step-by-step explanation:

If two figures are similar, then we can relate different characteristics of the figure by using the scale factor.   The scale factor is a measure of proportion with the original figure.

Obviously only similar figures can be compared using a scale factor.  We know that similar figures are proportional and constant of proportionality of different dimensions in linear form such as length, height, width, perimeter etc is called scale factor.

If scale factor >1 then there is dilation of enlargement otherwise shrink

Here drawing is having dimensions as 9x7 instead of original 54x42

Proportion is the same as 1/6

So scale factor = 1/6

Answer:  [tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

The formula to find the scale factor(k) :

[tex]k=\dfrac{\text{length of side in image}}{\text{length of corresponding side in pre-image}}[/tex]

From the given table, the height of statue of drawing = 9 inches

The height of statue of real statue = 54 inches

Then, the scale factor : [tex]k=\dfrac{9}{54}=\dfrac{1}{6}[/tex]

Similarly for length , the scale factor = [tex]k=\dfrac{7}{42}=\dfrac{1}{6}[/tex]

Hence, the  scale factor of the drawing to the real statue = [tex]\dfrac{1}{6}[/tex]

The question requires understanding of real estate value, equity, and mortgage calculations related to buying a house. Freda's equity is the entire value of her house at $250,000. Ben has paid off a portion of his loan and has an equity of $100,000 in his home.

The question provided deals with the financial aspects of purchasing a house and understanding real estate value, equity, and mortgage calculations. Helena purchasing a house for $210,000 would fall under the mathematics or business subject area as it involves financial calculations.

Freda's house situation, where she bought a house for $150,000 in cash and its current value is $250,000, tells us that her equity in the property would be the entire value of the house, which is $250,000, since she owes nothing to the bank.

As for Ben, he initially purchased his house for $100,000 and made a 20% down payment. He took a loan from the bank to cover the remaining 80%, later paid off $20,000 of it, and his house value has increased to $160,000. Ben's remaining loan balance would be the original borrowed amount minus what he has already paid back. Since he had taken 80% of $100,000, that would have been $80,000 initially, minus the $20,000 paid, leaves him with a $60,000 debt. The equity that Ben has in his house is the current market value minus the debt, which is $160,000 - $60,000, giving him an equity of $100,000.

In another scenario provided, Joanna is looking to determine how much she can afford in terms of a house loan with yearly payments of $12,000 at an interest rate of 4.2% over a 30-year period. She would need to apply the formula for calculating a mortgage payment and the total amount paid over the course of the loan.

Helena's total monthly payments are approximately $2,361.17. The closest answer choice is C. $2330.20.

Principal and Interest:

Down payment = 5% of $210,000 = $10,500

Loan amount = $210,000 - $10,500 = $199,500

Using a mortgage calculator, the monthly principal and interest payment for a 15-year loan at 4.5% interest on $199,500 is $1595.54.

PMI (Private Mortgage Insurance):

Loan-to-value ratio (LTV) = $199,500 / $200,000 = 99.75%

Based on the table, the PMI premium for a 15-year fixed-rate loan with an LTV of 95.01% to 97% is 0.79%.

Annual PMI premium = 0.79% of $199,500 = $1575.05

Monthly PMI premium = $1575.05 / 12 = $131.25

Property Taxes:

Annual property taxes = 3.5% of $200,000 = $7000

Monthly property taxes = $7000 / 12 = $583.33

Homeowners Insurance:

Monthly homeowners insurance = $600 / 12 = $50

Total Monthly Payments:

Principal and Interest: $1595.54

PMI: $131.25

Property Taxes: $583.33

Homeowners Insurance: $50 Total: $2350.12

Complete Question:

Helena is purchasing a house for $210,000, with a 15 -year fixed-rate mortgage at 4.5% interest. She has made a 5% down payment. The house is valued at $200,000, and the local tax rate is 3.5%. Her homeowners insurance is $600 per year. What are her total monthly payments? (Use the table below to calculate PMI premiums.)

[tex]\begin{tabular}{lcccl} Base-To-Loan\% & \multicolumn{2}{c}{ Fixed Rate Loan } & \multicolumn{2}{c}{ ARM 2\%+1 Year Cap } \\& $30 {yrs}$ & $15 {yrs}$ & $30 {yrs}$ & $15 {yrs}$ \\$95.01 \%$ to $97 \%$ & $0.90 \%$ & $0.79 \%$ & ${n} / {a}$ & ${n} / {a}$ \\$90.01 \%$ to $95 \%$ & $0.78 \%$ & $0.26 \%$ & $0.92 \%$ & $0.81 \%$ \\$85.01 \%$ to $90 \%$ & $0.52 \%$ & $0.23 \%$ & $0.65 \%$ & $0.54 \%$ \\$85 \%$ and Under & $0.32 \%$ & $0.19 \%$ & $0.37 \%$ & $0.26 \%$\end{tabular}[/tex]

A. 2654.23

B. 2894.71

C. 2330.20

D. 2202.72

Answer:

3

Step-by-step explanation:

2/3 divided by 2/9

flip 2/9 to 9/2

2/3 mutilplied by 9/2

2 cancels 2 and 9 divides 3

equals 3

Answer:

Feline Flavor is less expensive per pound.

Step-by-step explanation:

A unit price has  a 1 in the denominator

To find the unit price, we take the price  and divide by the amount.

Kitty Kibbles:  $24 for 16 lbs

$24/16 = $1.50 per lb

Feline Flavor:  $11.20  for 8 lbs

$11.20 / 8 = $1.40 per lb

Feline Flavor is less expensive per pound.

Final answer:

After 20 years, the amount in the account with an initial deposit of $7,000 at a 2% interest rate compounded monthly would be $10,408.98.

Explanation:

To find the amount in the account after 20 years with no withdrawals, we use the formula for compound interest:

[tex]A = P(1 + \(\frac{r}{n}\))^nt[/tex]

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount ($7,000)

r = the annual interest rate (decimal) (2%, or 0.02)

n = the number of times that interest is compounded per year (monthly, so 12)

t = the number of years the money is invested or borrowed for (20 years).

Plugging in the values, we get:

[tex]A = 7000(1 + \(\frac{0.02}{12}\))^(12*20)[/tex]

After calculating the values inside the parentheses and raising them to the power of 240 (12 times 20), we find:

A = 7000(1 + 0.00166667)^240

A = 7000(1.00166667)^240

A = 7000 * 1.48685385

A = $10,408.98

Therefore, after 20 years, the amount in the account would be $10,408.98 with no withdrawals, given a 2% interest rate compounded monthly.

Answer:

y=5

Step-by-step explanation:

1

Subtract 4 from both sides

8y=5y+19-4

2

8=5y+15

3

8-5y=15

4

3y=15

5

y=15/3

6

y=5

Answer:

1563

Step-by-step explanation:

x= 1 bag of bananas

so, 4x=2084

Divide 2084 by 4 to find how much 1 bag of bananas would cost. 2084/4= 521.

To find how much 3 bags of bananas would cost, multiply 521 (the price of one bag) by 3. 521x3= 1563

3 bags of bananas are $1563

Answer:

3. - 1 52/57

4.  -1 23/135

5. -3 31/36

Step-by-step explanation:

3.  Note the answer will be a negative number because one of the numbers is negative and the other is positive. When we do the division  use positive numbers . Then we can just plug in  the negative.

It looks like  114 will only divide once into 218  because 2*114 = 228 .

So the whole number part is 1. Now subtract 114 from 218  we get  104.

So we have the mixed number 1 104/114. These numbers in the fraction are positive so we divide by 2 to simplify.

This gives us 1 52/57

Finally plug in the negative and we have -1 52/57 (answer)

Q4. In a similar fashion to the above  158 / 135 = 1 and the fraction part is (158-135) / 135 =  23/135,so the answer is  -1 23/135  ( note its negative because of the -135).

Q5.

-834 / 216

216 divides 3 times into 834 and the remainder is 834 - 3 * 216

= 834 - 648 =  186

so the mixed number is -3 186/216

Now simplify 186/216:-

divide each number by 2 , we get  93/108

3 will divide into 93 and 108 giving 31/36

Now plug in the negative.

So the answer is -3 31/36

Answer:

3. [tex]-1\tfrac{52}{57}[/tex]

4. [tex]-1\tfrac{23}{135}[/tex]

5. [tex]-3 \tfrac{31}{36}[/tex]

Step-by-step explanation:

3.

To find :  the quotient when we divide -218 by 114

Solution : As in −218÷114 one of the numbers is negative and the other is positive, quotient must be negative .

[tex]\frac{-218}{114}=\frac{-109}{57}=-1\tfrac{52}{57}[/tex] ( mxed fraction )

( see fig (i) )

4.

To find : the quotient when we divide 158 by 135

Solution: As in 158÷(−135) one of the numbers is negative and the other is positive, quotient must be negative .

[tex]\frac{158}{-135}=-1\tfrac{23}{135}[/tex] ( mixed fraction )

( see fig (ii) )

5.

To find : −834÷216

Solution :

As in −834÷216 one of the numbers is negative and the other is positive, quotient must be negative .

[tex]\frac{-834}{216}=\frac{-417}{108}=\frac{-139}{36}=-3 \tfrac{31}{36}[/tex]

( see fig iii )

Answer:

9 feet

Step-by-step explanation:

18 x 1/2 = 9

      or

18 / 2 = 9