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3 years ago

22. The measures of the angles of ADEF are in the ratio 2:4:4. What are the

Mathematics

1 answer:

denis23 [38]3 years ago

3 0

The measures of the angles of Δ DEF are 36° , 72° , 72°

Step-by-step explanation:

The sum of the measures of the interior angles in any triangle is 180°

In Δ DEF

The ratio between the measures of its interior angles is 2 : 4 : 4

To find the measure of each angle

1. Find the sum of the ratio between the measures of its angles

2. Divide 180° by the sum of the ratio

3. Multiply the quotient by each ratio

∵ The ratio between the measures of the angles of Δ DEF = 2 : 4 : 4

∴ The sum of the ratio = 2 + 4 + 4 = 10

→ m∠D : m∠E : m∠F : sum of the ratio

→ 2 : 4 : 4 : 10

→ ? : ? : ? : 180°

Divide 180 by 10, then multiply the quotient by the components of

the ratio to find the measure of each angle

∵ m∠D = $(2)\frac{180}{10}$

∴ m∠D = 36°

∵ m∠E = $(4)\frac{180}{10}$

∴ m∠D = 72°

∵ m∠F = $(4)\frac{180}{10}$

∴ m∠F = 72°

The measures of the angles of Δ DEF are 36° , 72° , 72°

Learn more:

You can learn more about the ratio in brainly.com/question/2707032

#LearnwithBrainly

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Tina spends $50.86 at the craft store. She buys 5 yards of fabric at $8.98 per yard and 2 spools of thread. What is the price of

irina1246 [14]

She spends $50.86.
Cost for 1 yard of fabric is $8.98.
So to find the the cost of 5 yards of fabric, multiply $8.98 x 5 = $44.9. Therefore for the 5 yards of fabric she paid $44.9.

To find how much she paid for 2 spools of thread subtract the amount she spent at the craft store and the cost for the 5 yards of fabric.
&50.86 - $44.9 = $5.96.
Therefore the cost of 2 spool of thread is $5.96 / 2 = $2.98

Therefore the cost of 1 spool of thread is $2.98.

To check if it’s correct just add the cost of the 5 yards of fabric and the 2 spools of thread.
$44.9 + $5.96 = $50.86

4 0

3 years ago

Is (-3, 2) a solution of -4r - 10y< - 9?

Blizzard [7]

Answer:

The point (-3,2) is not a solution of the inequality

Step-by-step explanation:

Inequality

Inequalities relate the left and the right side of an expression with an operator other than the equal sign.

The inequality given in the question is

$-4r - 10y< - 9$

There are many combinations of r and y that make inequality be true. For example, for r=1 and y=1

$-4(1) - 10(1)< - 9$

$-14< - 9$

This relation is true since -14 is less than -9.

Also, there are many combinations that make the given inequality be false.

For example, for r=2 and y=-1

$-4(2) - 10(-1)< - 9$

$-8+10$

$2$

This inequality is false.

Let's test the point (-3,2)

$-4(-3) - 10(2)< - 9$

$12-10$

$2$

Which is false, thus the point (-3,2) is not a solution of the inequality

3 0

3 years ago

Tony and Cleo are donating some of their books to a hospital. If Tony contributes half of his books and Cleo gives one third of

liraira [26]

Short Answer: Tony 40 Cleo 30
Givens
T = Tony
C = Cleo

Equations
1/2 T + 1/3 C = 30 (1)
2/5 T + 1/2 C = 31 (2)

Adjustments
Multiply (1) by 3
Multiply (2) by 2

New Equations
3/2 T + C = 90 (1a)
4/5 T + C = 62 (2a) Subtract (2a) from (1a)
(3/2 - 4/5)T = 28 the common multiple of 2 and 5 = 10.
(15/10 - 8/10)T = 28
7/10 T = 28 Multiply by 10
7T = 28*10
7T = 280 Divide by 7
T = 280/7 = 40

Put T = 40 into (1)
1/2 T + 1/3 C = 30
1/2 (40) + 1/3 C = 30
20 + 1/3 C = 30 Subtract 20 from both sides.
1/3 C = 30 - 20
1/3 C = 10 Multiply through by 3
C = 10 * 3
C = 30

Answer:
Cleo has 30 books.
Tony has 40 books.

Check
Use Equation 2
2/5 T + 1/2 C = 31
2/5*40 + 1/2 * 30 = ? 31
16 + 15 =?3`
31 = 31 They are equal.

4 0

3 years ago

4y-x=5+2y; 3x+7y=24 solve systen by using substitution

jek_recluse [69]

4y - x = 5 + 2y ..... (1)
3x + 7y = 24 ..... (2)

by grouping like terms in (1)
4y - x = 5 + 2y
4y - 2y - x = 5
-x + 2y = 5 ..... (1a)

by multiplying (1a) through by -3
(-3)(-x) + 2(-3)y = 5(-3)
3x - 6y = -15 ..... (1b)

by subtracting 1a from 2
3x -3x + 7y - (-6y) = 24 - (-15)
13y = 39
⇒ y = 3

by substituting y=3 into (2)
3x + 7(3) = 24
3x = 24 - 21
3x = 3
⇒ x = 1

∴ solution to the system is x=1 when y = 3

6 0

3 years ago

Construct the confidence interval for the population mean. c=. 95 x=6. 4 o=. 3 and n=42.

Damm [24]

The confidence interval is (63.909, 64.0907).

The confidence interval of a population mean is found using the formula:

CI = x ± z(σ/√n), where CI is the confidence interval, x is the mean, z is the z-score corresponding to the confidence level, σ is the standard deviation, and n is the population size.

In the question, we are given the confidence level, c = 95%.

Z-score corresponding to this, z = 1.96.

The mean of the population, x = 6.4.

The standard deviation of the population, σ = 0.3.

The population size, n = 42.

Thus, using the formula, the confidence interval is:

CI = 6.4 ± 1.96(0.3/√42),

or, CI = 6.4 ± 0.09073037.

Thus, the confidence interval is (64 - 0.09073037, 64 + 0.09073037), or, (63.909, 64.0907).

Learn more about the confidence interval at

brainly.com/question/17097944

#SPJ4

3 0

2 years ago