MATHEMATICS HIGH SCHOOL

6. What type of triangle has all acute angles?

Answers

Answer 1
Answer:

Answer:

equilateral triangle is always all acute nothing else
Answer 2
Answer:

Answer:

Acute triangles or also called as acute-angled triangles

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What is the correct label for the angle?
Can you help please?​
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Tony has $727.29 in his checking account. He must maintain a $500 balance to avoid a fee. He wrote a check for $248.50 today. Write and solve an inequality to solve for the least amount of money he needs to deposit to avoid a fee.

Answers

The required inequality for the least amount of money he needs to deposit to avoid a fee is 727.29 - 248.50 + x ≥ 500 and he needs to deposit at least $21.21 in her account to avoid a fee.

What is inequality?

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now it is given that,

Amount in the account = $727.29

Amount in the check = $248.50

Amount need to maintain = $500

Now let x be the Tony needs to deposit.

So, total balance in the account =  727.29 - 248.50 + x

Since, he must maintain a $500 balance to avoid a fee. That means the balance can be greater than or equal to $500.

Thus the required inequality is:

727.29 - 248.50 + x ≥ 500

Adding alike terms,

468.79 + x ≥ 500

Subtracting 468,79 both the side we get,

x ≥ 500 - 468.79

Solving we get,

x ≥ 21.21

Therefore, he needs to deposit at least $21.21 in her account to avoid a fee.

Thus,the required inequality for the least amount of money he needs to deposit to avoid a fee is 727.29 - 248.50 + x ≥ 500 and he needs to deposit at least $21.21 in her account to avoid a fee.

To learn more about inequality:

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inequality is
727.29-248.50+x>500
x=how much she needs to deposit
478.79+x>500
subtract 478.79 from both sides
x>21.21


at least $21.21

Indra baked and frosted a rectangular cake to sell at a bake sale for the Model UN club. The cake, including frosting, was 4 inches high, 16 inches wide, and 12 inches long. She centered the cake on a circular tray. The circular tray had a radius of 10 inches. What is the area, to the nearest square inch, of the tray that is not covered by the cake?A. 100
B. 114
C. 122
D. 314
E. 192

Answers

Answer:

C. 122

Step-by-step explanation:

Given,

Dimension of the cake:

Length = 12 in      Width = 16 in      Height = 4 in

We have to find out the area of the tray that is not covered by the cake.

Indra centered the cake on a circular tray.

Radius of the tray = 10 in.

So area of the tray is equal to π times square of the radius.

Framing in equation form, we get;

Area of tray =\pi* r^2=3.14*{10}^2=3.14* 100=314\ in^2

Since the cake is placed in circular tray.

That means only base area of cake has covered the tray.

Base Area of cake = length* width=12* 16=192\ in^2

Area of the tray that is not covered by the cake is calculated by subtracting area of base of cake from area of circular tray.

We can frame it in equation form as;

Area of the tray that is not covered by the cake = Area of tray - Base Area of cake

Area of the tray that is not covered by the cake =314-192=122\ in^2

Hence The area of the tray that is not covered by the cake is 122 sq. in.

Chad washes windows after school to make some extra money. He charges $5.50 to wash each window. If the customer provides the supplies, Chad deducts $3.25 from the total cost. One customer paid a total of $27.50 and did not provide supplies. Which equation could be used to find the number of windows, w, that Chad washed for this customer? 5.5w + 3.25 = 27.5 5.5w - 3.25 = 27.5 5.5w = 27.5 5.5 - 3.25w = 27.5

Answers

Answer:

\$5.50w=\$27.50

Step-by-step explanation:

We know that Chad charges $5.50 per window washed, and he deducts $3.25 from the total cost if the costumer provides the supplies. However, in this case, the costumer doesn't provide the supplies, so Chad will charge $5.50 per window.

This relation can be expressed as

\$5.50w

Where w represents windows.

If he charges $27.50, the relation is

\$5.50w=\$27.50

Therefore, the right answer is the third choice \$5.50w=\$27.50

If you want to find the number of windows Chad washed, you just have to solve the expression

\$5.50w=\$27.50\nw=(\$27.50)/(\$5.50)\n w=5

Chad washed 5 windows.
3.25w=27.5 is the correct answer.

In a pot worth $2.35, there are 6 quarters, 5 dimes, 5 pennies, and the rest of the coins are nickels. What is the ratio of nickels to dimes?

Answers

Answer:

6:5

Step-by-step explanation:

It is given that a pot worth $2.35 and there are 6 quarters, 5 dimes, 5 pennies, the rest of the coins are nickels.

We know that

$1 = 100 cents

1 penny = 1 cent = $0.01

1 nickel = 5 cents. = $0.05

1 dime = 10 cents. = $0.10

1 quarter = 25 cents = $0.25

The value of 6 quarters is

6* 0.25=1.50

The value of 5 dimes is

5* 0.10=0.50

The value of 5 pennies is

5* 0.01=0.05

Let x be the number of nickels. So, the value of x nickels is

x* 0.05=0.05x

Total value of 6 quarters, 5 dimes, 5 pennies, and x nickels is

Total =1.50+0.50+0.05+0.05x

Total =2.05+0.05x

It is given that the pot worth is $2.35.

2.05+0.05x=2.35

Subtract 2.05 from both sides.

0.05x=0.30

Divide both sides by 0.05.

x=6

The number of nickels is 5.

(Nickel)/(Dimes)=(6)/(5)=6:5

Therefore, the ratio of nickels to dimes is 6:5.

In a pot worth $2.35 containing 6 quarters, 5 dimes, 5 pennies, and some nickels, the ratio of nickels to dimes is 6:5.

To find the ratio of nickels to dimes, we need to determine the number of nickels and dimes in the pot. We know that there are 6 quarters, 5 dimes, and 5 pennies in the pot, which is a total of 16 coins. Therefore, the number of nickels should be the difference between the total number of coins and the sum of quarters, dimes, and pennies.

The total value of the coins in the pot is $2.35. Since 6 quarters are worth $1.50, 5 dimes are worth $0.50, and 5 pennies are worth $0.05, the remaining value should come from the nickels.

Thus, the value of the nickels is $2.35 - $1.50 - $0.50 - $0.05 = $0.30. Since each nickel is worth $0.05, the number of nickels is $0.30 ÷ $0.05 = 6.

The ratio of nickels to dimes is therefore 6:5, which means that for every 6 nickels, there are 5 dimes.

Learn more about ratios here:

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What is the sale price of a shirt that was originally $25 but that has been marked down by 33 percent?

Answers

100% = 25, 67% = 16.75

Factor completely, the expression: 2x^3-2x^2-12x

Answers

2x^3-2x^2-12x=2x(x^2-x-6)=(*)\n\n------------------------------\nx^2-x-6\n\na=1;\ b=-1;\ c=-6\n\n\Delta=(-1)^2-4\cdot1\cdot(-6)=1+24=25\n\n\sqrt\Delta=√(25)=5\n\nx_1=(1-5)/(2\cdot1)=(-4)/(2)=-2;\ x_2=(1+5)/(2\cdot1)=(6)/(2)=3\n\nx^2-x-6=(x+2)(x-3)\n\n------------------------------\n\n(*)=2x(x+2)(x-3)
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