If m<9=97° and m<12=114°, find each measure. I have to show my work.

Answer:

The first one is acute, the second is right, and the third is obtuse.

Step-by-step explanation:

Hope this helps :)

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Answer:

Angle 1 - acute angle

Angle 2 - right angle

Angle 3 - obtuse angle

Step-by-Step Explanation:

The acute angle is smaller than right angles, right angles are 90 degrees, and obtuse angles have larger degree angle than right angles.  

Answer:

0,2

Step-by-step explanation:

The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.

The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.

As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:

When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).

As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.

For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.

The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.

Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.

The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.

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Answer:

The answer to this problem is 170.300

The given expression can be written in a single radical as q³ .   \(\sqrt[]{ q^{\frac{7}{6} } }\). The solution has been obtained by solving the radical expressions.

What are radical expressions?

An expression which contains a square root is referred to as a radical expression. The 'V'-shaped portion of the radical sign will have a superscript number when it is used to represent any root other than a square root.

We are given √q³ \(\sqrt[3]{q^{8} }\).

On simplifying the expression, we get

⇒√q² . q \(\sqrt[3]{q^{3} . q^{3} . q^{2} }\)

⇒q . √q . q² .  \(\sqrt[3]{ q^{2} }\)

⇒q³ . √q  \(\sqrt[3]{ q^{2} }\)

⇒q³ . \(\sqrt[]{ q^{\frac{1}{2} + \frac{2}{3} } }\)

⇒q³ . \(\sqrt[]{ q^{\frac{7}{6} } }\)

Hence, the given expression can be written  in a single radical as q³ . \(\sqrt[]{ q^{\frac{7}{6} } }\).

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The graph that shows the image of ∠B after a rotation of 180∘ about the origin has the coordinates B' - (-1, 8)(attached)

The 180-degree rotation, whether clockwise and anticlockwise, is one of the most basic and frequent geometric transformations. The coordinates of B (x, y) after the rotation will only have the opposite signs of the initial values if B (x, y) is a point that needs to be rotated 180 degrees the about origin.

The camera may move wherever on its side in accordance with the 180-degree rule, but it must not cross the axis. The performers maintain the same left/right interaction with one another while the camera is on one side of the 180-degree line.

It is demonstrated to rotate 180 degrees around the origin.

From the question:

The coordinates of B are - B(1, -8).

Thus, the formula is (x,y)→(−x,−y)  for a 180° rotation of the origin.

B' - (-1 ,-(- 8))

B' - (-1, 8)

The graph that shows the image of ∠B after a rotation of 180∘ about the origin has the coordinates B' - (-1, 8): . (attached)

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Answer:b

Step-by-step explanation:

Answer:157.5

Step-by-step explanation:becuase mutilpy 4.5x35 that equals 157.5

Answer:

it's obtuse angle...

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= Obtuse triangle

 (a triangle in which one of the interior angles measures more than 90° degrees.)

We need to identify which is the correct shape. We are told that it has a vertex. A vertex is a point where two or more lines, curves or edges met. In three dimensional shapes a vertex is a corner of the shape. As you can see, from the three shapes we have in the picture the only one with a corner is the cone. It is also important to note that this corner is in the opposite side of the base and this base has a circular shape.

As we discussed above the shape that meets these characteristics is the cone. Therefore the answer is the cone.

The area of the forest will be approximately 1396 km sq. after 10 years.

Given that, a forest covers an area of 2100 km sq and that each year this area decreases by 4%..

If the area of the forest decreases by 4% each year, then after one year it will be 96% of the original size.

After two years, it will be 96% of 96% of the original size, or 0.96² of the original size.

After ten years, it will be 96% of itself ten times, or 0.96¹⁰ of the original size.

So the area of the forest after 10 years will be:

Area = Initial area × 0.96¹⁰

Area = 2100 km sq × 0.96¹⁰

Area = 1396 km sq

Therefore, the area of the forest cover in 10 years will be 1396 km sq.

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Answer:

11/12

Step-by-step explanation:

3/4=.75

11/12=.91666......

Answer:

11/12

Step-by-step explanation:

3/4 = 9/12

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

0.1286 miles

Step-by-step explanation:

.9/7=.1286 [rounded]

Answer:

Step-by-step explanation:

x - 12 ≤ 3 - 2x

3x ≤ 15

x ≤ 5

To graph this, just draw a VERTICAL line passing through x = 5, then shade the area to the LEFT

Answer:

5 meters : 1 gallon

fuel efficiency of Car is 7 meters per gallons

Step-by-step explanation:

Given Tanya car goes 45 meters on 7 gallons.

In terms of ratio  of distance traveled and fuel consumed

45 meters : 7 gallons

since both 45 and 7 are multiple of 7 dividing both side by 7

45/7 meters : 7/7 gallons

5 meters : 1 gallon

Thus, fuel efficiency of Car is 7 meters per gallons.

The value of "a" will be 30 for the given Algebraic expression.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, a algebraic expression 6a -4a +5a = 210

Simplifying the equation in terms of a

6a -4a +5a = 210

adding or subtracting the terms with the same variables

7a = 210

divide by 7 on both sides

a = 30

Therefore, the value of "a" will be 30 for the given Algebraic expression.

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The student council raised $2,790 and they have to shared equally among 3 comittees, then:

Each commitee has a budget of $930, then for the sports committee that wants to purchase t-shirts and each t-shirt costs $12, we can create the following expression:

Let x be the greatest number of t-shirts

Rounding, the sport commitee can purchase 77 t-shirts.

Answer:

Anna owes $3600 to the bank

Step-by-step explanation:

12/100 * 6000 = 720 * 5 years

= $3600

Hence Anna owes $3600 to the bank

3) The given inequality is

The inequality symbol is that of less than. Since it has an equal to sign attached, then, the meaning is h is less than or equal to 9. In words, h is at most 9, no more than 9.

Answer:

Length of one piece = 6 cm

Length of second piece = 16 cm

Step-by-step explanation:

Total Length of board = 22 cm

The board is divided into 2 pieces.

Let length of one piece = l

Length of second piece = 2l + 4

We need to find length of both pieces.

We can write the equation:

Total length = Length of one piece + Length od second piece

Putting values and finding length

\(22 = l+(2l+4)\\22=l+2l+4\\22=3l+4\\3l=22-4\\3l=18\\l=\frac{18}{3}\\l=6\)

So, we get l= 6

Length of one piece = l =6 cm

Length of second piece = 2l + 4 = 2(6)+4 = 12+4 = 16 cm

Therefore,

Length of one piece = 6 cm

Length of second piece = 16 cm

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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Answer:

C.  \(x=-9 \textsf{ and }x=1\)

Step-by-step explanation:

\((x+4)^2=25\)

\((x+4)(x+4)=25\)

expand the brackets:

\(x^2+8x+16=25\)

subtract 25 from both sides:

\(x^2+8x-9=0\)

factor:

\(x^2+9x-x-9=0\)

\(x(x+9)-1(x+9)=0\)

\((x-1)(x+9)=0\)

solve for x:

\(x-1=0 \implies x=1\)

\(x+9=0 \implies x=-9\)

Answer:

2sqr3, the first option

Step-by-step explanation:

Answer:

A. r²

Step-by-step explanation:

The formula for the area of a circle is π r²,

thus the π is multiplied by the r²

To multiply mixed numbers, we first need to convert them to improper fractions, then we can multiply them and simplify the result back to a mixed number.

Converting the first mixed number to an improper fraction:

-3 5/7 = -3 × 7/7 + 5/7 = -21/7 + 5/7 = -16/7

Converting the second mixed number to an improper fraction:

-2 1/2 = -2 × 2/2 + 1/2 = -4/2 + 1/2 = -3/2

Multiplying the two improper fractions:

(-16/7) × (-3/2) = (16/7) × (3/2) = 48/14 = 24/7

Simplifying the result to a mixed number:

24/7 = 3 3/7

Therefore, -3 5/7 x -2 1/2 = 3 3/7.

Answer:

Step-by-step explanation:

Answer:1 1/3

Step-by-step explanation:

There is your answer! :)