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2 years ago

In the diagram, m CD = 128° and m DA = 76°. What is m∠ABC?

2 answers:

7 0

Angle ABC is an inscribed angle.

Inscribed angle = 1/2 * Intercepted Arc

The intercepted arc is arc CD + arc DA, which would be 128 + 76 = 204

m<ABC = 1/2(204)

m<ABC = 102 degrees

You answer is D) 102

Vikki [24]2 years ago

6 0

Answer: The value of m∠ABC is 102° .

Step-by-step explanation:

Since we have given that

m CD = 128°

m DA = 76°

We need to find the m∠ABC, Angle subtended at the center is half of the sum of the measure of the arc intercepted by it.

$\frac{m\ CD+m\ DA}{2}=\angle ABC\\\\\frac{128^\circ+76^\circ}{2}=\angle ABC\\\\102^\circ=m\angle ABC$

The value of m∠ABC is 102° .

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Since they mowed $\frac{8}{9}$ of the lawn in two equal parts, we need to split the pieces that were mowed into two equal groups. We know that in total they mowed 8 out of the total 9 pieces of lawn, so two equal groups that make 8 would be of size 4, since $\frac{8}{2}=4$ . Then they each mowed $\frac{4}{9}$ of the lawn.

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2 years ago

A 2-column table with 10 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1,

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Answer- A,D,E

Step-by-step explanation:

A two column table with 5 rows. The first column, x, has the entries, negative 2, 0, 2, 4. The second column, y, has the entries, 6, 3.5, 1, negative 1.5.

Which equations represent the data in the table? Check all that apply.

y – 6 = y minus 6 equals StartFraction negative 5 Over 4 EndFraction left-parenthesis x plus 2 right-parenthesis.(x + 2)

y – 2 = –y minus 2 equals negative StartFraction 5 Over 4 EndFraction left-parenthesis x minus 1 right-parenthesis.(x – 1)

y + 2 = y plus 2 equals StartFraction negative 5 Over 4 EndFraction left-parenthesis x minus 6 right-parenthesis.(x – 6)

y – 1 = –y minus 1 equals negative StartFraction 5 Over 4 EndFraction left-parenthesis x minus 2 right-parenthesis.(x – 2)

y – 3.5 = –1.25x

Im just rephrasing the question

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2 years ago

Read 2 more answers

Quincy feeds his dog 2.75 cups food each day each cup of dog food costs $1.25. He multiplies the numbers together to determine h

Flura [38]

2times1 because 2.75 take the 75 off and 1.25 take the 25 off so you multiply 2 and 1 so 2times1 equals 2

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2 years ago

Find the coefficient of x2 in (3x2 – 5) (4 + 4x2), expand using algebraic expressions and answer

Scilla [17]

Answer:

- 8

Step-by-step explanation:

Given

(3x² - 5)(4 + 4x²)

Each term in the second factor is multiplied by each term in the first factor, that is

3x²(4 + 4x²) - 5 (4 + 4x²) ← distribute both parenthesis

= 12x² + 12 $x^{4}$ - 20 - 20x² ← collect like terms

= 12 $x^{4}$ - 8x² - 20

The coefficient of the x² term is - 8

7 0

2 years ago

6. Two observers, 7220 feet apart, observe a balloonist flying overhead between them. Their measures of the

MaRussiya [10]

Answer:

The ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

Step-by-step explanation:

Let's call:

h the height of the ballonist above the ground,

a the distance between the two observers,

$a_1$ the horizontal distance between the first observer and the ballonist

$a_2$ the horizontal distance between the second observer and the ballonist

$\alpha _1$ and $\alpha _2$ the angles of elevation meassured by each observer

S the area of the triangle formed with the observers and the ballonist

So, the area of a triangle is the length of its base times its height.

$S=a*h$ (equation 1)

but we can divide the triangle in two right triangles using the height line. So the total area will be equal to the addition of each individual area.

$S=S_1+S_2$ (equation 2)

$S_1=a_1*h$

But we can write $S_1$ in terms of $\alpha _1$ , like this:

$\tan(\alpha _1)=\frac{h}{a_1} \\a_1=\frac{h}{\tan(\alpha _1)} \\S_1=\frac{h^{2} }{\tan(\alpha _1)}$

And for $S_2$ will be the same:

$S_2=\frac{h^{2} }{\tan(\alpha _2)}$

Replacing in the equation 2:

$S=\frac{h^{2} }{\tan(\alpha _1)}+\frac{h^{2} }{\tan(\alpha _2)}\\S=h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})$

And replacing in the equation 1:

$h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})=a*h\\h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}$

So, we can replace all the known data in the last equation:

$h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}\\h=\frac{7220 ft}{(\frac{1 }{\tan(35.6)}+\frac{1}{\tan(58.2)})}\\h=3579,91 ft$

Then, the ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

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2 years ago