The second angle of a triangle is 3 times as large as the first. The third angle is 50° more than the first. Find the measure of the smallest angle

Her house to school is 5 miles.

The distance on the map is 2.5 inches, so we know 2.5 inches equals 5 miles.

Divide 5 miles by 2.5 inches to find miles per inch:

5 / 2.5 = 2 miles per inch.

Now you can multiply the other dimensions on the map by 2 to find total miles:

School to Library = 3 x 2 = 6 miles.

Library to Park = 1.5 x 2 = 3 miles.

Total distance traveled: 5 + 6 + 3 = 14 miles.

subsitute 3 as x

f(3) = (1/7) × (7^3)

f(3) = 1/7 × 343

f(3) = 343 ÷ 7

f(3) = 49

The required value of f(3) = 49.

f(x)= (1/7)(7^x)

The function which is in format f(x) =   where, a is constant and x is variable,  the domain of this exponential function  lies   (-∞, ∞).  

f(x)= (1/7)(7^x)
f(3) = 1/7(7^3)

f(3) = 1/7 x 7³
f(3) = 7² = 49

Thus the required value for f(3) = 49

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Answer:

The answer is D. 5

Step-by-step explanation:

Answer:

The side b is 5 units

Step-by-step explanation:

Given the two sides of triangle and one angle of triangle we have to find the remaining side of triangle.

a=12 units

c=10 units

∠B=24°

we have to find the side b of triangle ABC

By cosine law,

[tex]\cos B=\frac{a^2+c^2-b^2}{2ac}[/tex]

[tex]\cos 24^{\circ}=\frac{12^2+10^2-b^2}{2(12)(10)}=\frac{144+100-b^2}{240}[/tex]

[tex]b^2=244-240\cos 24^{\circ}=24.7490901658[/tex]

[tex]b=4.97\sim 5units[/tex]

Answer:

a. 6

b. 9

c. 4

Step-by-step explanation:

a.

Range = greatest - smallest

Range = 85 - 79

Range = 6

b.

b > 81

82, 83, 84...

3 82s

4 83s

2 85s

3 + 4 + 2 = 9

c.

b = 83

4 83s

4

Answer:

2.0*10^5 meters

Step-by-step explanation:

To answer this question, multiply

2.0*10^(-2) meters by 10 million, that is:

2.0

------ * 10*10^6 meters

10²

This expression simplifies to:

2.0*10^5 meters (which corresponds to answer D).

An ant is 2.0x10^-2 meters long. If you put 10 million ants in a line, the total length of the line would be 200,000 meters.

An ant is 2.0x10^-2 meters long. If you put 10 million ants in a line, the total length of the line would be 200,000 meters (D).

Answer:

Step-by-step explanation:

In a 30-60-90 triangle, the ratio of the lengths of the angles' opposite sides are 1-√3-2.

If the long leg is 8, then the short one is 8/√3, or 8√3/3.

Therefore, the hypotenuse, which is double the short leg, is 16√3/3.

In a 30-60-90 triangle, the long leg is √3 times the short leg and the hypotenuse is twice the short leg. By knowing the long leg and using these relationships, we can work out the short leg and then the hypotenuse. In this specific problem, the hypotenuse of the triangle is approximately 9.24.

In a 30-60-90 triangle, the ratio of the side lengths is consistent. The length of the long leg is always √3 times the length of the short leg. The hypotenuse, which is the longest side of the triangle, is always twice the length of the short leg. If the length of the long leg is 8, the formula of this triangle can be used to find the length of the hypotenuse.

However, in your question, the length of the short leg isn't given. But based on the formulas for a 30-60-90 triangle, we can work it out. As long as we know that the long leg is √3 times the short leg, we can solve for the short leg, hence it's 8/√3.

Then, as the hypotenuse is twice the short leg, so hypotenuse = 2 * (8/√3) = 16/√3 ≈ 9.24.

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Answer: 17

Step-by-step explanation: To find the radius of Q, you'd have to solve for x. So, 4x+3=7x-6, which results in x equaling 3. Next, bisect the chord EF, so it will be 8. Solve for QA, which is 15 and use the pythagorean theorem to solve: x^2=15^2+8^2 -> x=17

3p/8 - 13 = -25

3p/8 = -12 | * 8

3p = -96 | : 3

P = -32

The value of p is -32

see the image

C . Permutation number of ways = 1

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[tex]0.888 = 111/125 = 88.8percent[/tex]

I just gave you 0.888 is it's fraction and percentage.

First, 111/125 is the simplified answer and is over the 100th and is not big enough for the 1,000's.

Second, 111/125 as a percentage is 88.8%.

Have a great day.

Answer:

a

Step-by-step explanation:

Answer:

A, B, and C

I think. Please let me know if wrong.

Heres what i did:

1.8 x 100 = 180.

180 - 80 = 100

(they made over 10 in profit)

A. 1.2 x 0 = 0

B. 1.2 x 40 - 48

C. 1.2 x 60 = 72

D. 1.2 x 70 = 84

E. 1.2 x 80 =96

D and E bot Exceed 80 so it has to be AB and C

Hope this Helps ☺

Answer:

A,b,c

Step-by-step explanation:

P=1.8d-1.2s

P=180-1.2s

100=180-1.2s

-80=-1.2s

66.7=s

If they sold ≥67 sandwiches, p<100

If they sold ≤66 sandwiches, p>100

Therefore A, B and C are correct

the number of candy bars (x) divided by 16 kids is less than or equal to 66 canyldy bars

Answer:

1/4

Step-by-step explanation:

Let's find the value of c.

                              1         2^2        1

2^(-4)*2^2 = c = --------- * -------- = -------- = 1/4

                             2^4          1         2^2

this result matches the fourth given possible answer choice.

For this case we have that by definition of power properties:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

We have the following expression:

[tex]2 ^ {- 4} * 2 ^ 2 = a ^ b = c[/tex]

It can be rewritten as:

[tex]\frac {2 ^ 2} {2 ^ 4}[/tex]

By definition of power properties we have:

[tex]\frac {a ^ m} {a ^ n} = a ^ {m-n}[/tex]

So:

[tex]\frac {2 ^ 2} {2 ^ 4} = 2 ^ {2-4} = 2 ^ {- 2} = \frac {1} {2 ^ 2} = \frac {1} {4}[/tex]

Thus, [tex]c = \frac {1} {4}[/tex]

Answer:

Option D

To find out how long it takes to earn $25 in interest on a principal of $500 at a 5% annual interest rate, use the simple interest formula. The calculation reveals it takes 1 year.

The question asks us to determine the time it takes to earn $25 in interest on a principal of $500 at an annual interest rate of 5% using simple interest. The formula for simple interest is Interest = Principal × Rate × Time. We can rearrange this formula to solve for time (Time = Interest / (Principal × Rate)).

Given that the interest earned is $25, the principal is $500, and the rate is 5% (0.05 in decimal form), we substitute these values into our rearranged formula to find the time.

Substituting these into the formula gives us:

Time = $25 / ($500 × 0.05) = $25 / $25 = 1 year

Therefore, it takes 1 year to earn $25 in interest at a 5% annual rate on a $500 principal using simple interest.

Answer: [tex]x=-\dfrac{3}{2}, 7[/tex]

Step-by-step explanation:

[tex]2x^2-10x-26=x-5[/tex]

[tex]2x^2-10x-26-x+5=0[/tex]  Move all terms to one side

[tex]2x^2-11x-21=0[/tex] Simplify [tex]2{x}^{2}-10x-26-x+5[/tex]

[tex]2x^2+3x-14x-21=0[/tex] Split the second term

[tex]x(2x+3)-7(2x+3)=0[/tex]  Factor out common terms in the first two terms, then in the last two terms.

[tex](2x+3)(x-7)=0[/tex] Factor out the common term [tex]2x+3[/tex]

[tex]x=-\dfrac{3}{2}, 7[/tex]

Answer:

x = -3/4 and 7/2 will be your final answer, but check below for a correction on your work

Step-by-step explanation:

***Your work is incorrect, it should be

2x² - 11x - 21 = 0

you need to subtract an 'x' from both sides, and add 5 to both sides...you added an x to the left side and subtracted a 5 from the left side instead***

I'll solve this so in case you will need help on it too.

Now you'll have

x = (11 ± √[(-11²) - 4(2)(-21)])/([4(2)]

x = (11 ±  √289)/8

x = (11 ± 17)/8

x = (11 + 17)/8 = 28/8 = 7/2

or

x = (11 - 17)/8 = -6/8 = -3/4

not to sure on  how to tell you to answer this one but it looks like 4 inches :)

The pants are $38.06 and the television is $1,147.50.

The sales tax on the pair of pants is calculated by multiplying $35 x .0875 = $3.06

The total cost is $35 + 3.06 = $38.06.

The sales price of the television is calculated by multiplying $1,250 x .85, (100 - .15 discount = .85) = $1,062.50 is the sales price

The sales tax is calculated by multiplying $1,062.50 x .08 = $85

The total price is $85 + $1,062.50 = $1,147.50

Answer: [tex]f(7)=-4[/tex]

Step-by-step explanation:

1. You have the following function given in  the problem:

[tex]f(x)=10-2x[/tex]

2. Then, to find [tex]f(7)[/tex] asked in the exercise, you only need to substitute [tex]x=7[/tex] (which is the input value) into the given function.

3. Therefore, keeping the above on mind, you obtain that [tex]f(7)[/tex] is:

[tex]x=7[/tex]

[tex]f(7)=10-2(7)[/tex]

[tex]f(7)=10-14[/tex]

[tex]f(7)=-4[/tex]

Answer:

The correct answer is,

f(7)  -4

Step-by-step explanation:

It is given that,

f(x) = 10 - 2x

To find f(7)

To find f(7) we have to put 7 instead of x in f(x).

Here  f(x) = 10 - 2x,

Step 1: substitute the value x = 7 we get ,

f(7) = 10 - (2 * 7)    

 = 10 - 14 = -4

Therefore we get the answer  f(7) = -4

The correct answer is first option.

Answer:

2,2 dimethyl propane

Step-by-step explanation:

To name such an organic compound, first identify the longest carbon chain in the provided table, the fourth compound, its longest carbon chain has three carbon atoms thus, the prefix prop-

Then we find the other substituents attached to the carbon chain. In the given compound it has two methyl (CH₃) groups attached to the second carbon atom.

thus 2,2 since there are two attached.

Answer:

2.5 * 10^-5

Step-by-step explanation:

2.5 * 10^-5

If the number is between 1 and -1 excluding 0. Then

count the number of zeros

add 1 more

write the notation of where you put the decimal place

The power is minus and equal to the number of zeros + 1

0.000025

zeros: the number of zeros = 4

Add 1: 4 + 1 = 5

Decimal goes between the 2 and the 5

2.5

Power: = - 5

Answer: 2.5 * 10^-5

Answer:

The answer is [tex]2x^{3}y^{-2}\sqrt{6}[/tex]

Step-by-step explanation:

∵ √24 = 2√6

∵ [tex]\sqrt{x^{6}}=(x^{\frac{1}{2}})^{6}=x^{3}[/tex]

∵ [tex]\sqrt{y^{-4}}=(y^{\frac{1}{2}})^{-4}=y^{-2}[/tex]

∴ [tex]\sqrt{24x^{6}y^{-4}}=2x^{3}y^{-2}\sqrt{6}[/tex]

8 divided by 2=4 then square the 4

16

Answer:

16

Step-by-step explanation:

A perfect square trinomial is a three-term polynomial (also called a trinomial) that results from squareing a binomial. Every trinomial of the form: [tex]a^{2} +2ab+b^{2}[/tex], It is a perfect square trinomial.

In this case, it is necessary to divide the intermediate value of 8 by 2, and then square it, obtaining the result.

Answer:

22.35 m/s

Step-by-step explanation:

The distance is always a positive unit, so distance traveled (d) = 15 miles

Time (t) = 0.3 hours

Time (t) = 0.3 * 60 = 18 minutes

(1 hour = 60 minutes)

Velocity (v) = ?

The formula of distance is: d = v*t

=> v = d/t = 15/18 = 0.83 miles/minute

we can also calculate velocity is meter/sec, for that

1 minute = 60 sec

=> 18 mins = 18*60 = 1080 sec

1 mile = 1609.34 meters

=> 15 miles = 15 * 1609.34 = 24,140 m

hence,

v = 24,140/1080 = 22.35 m/s

Answer:

£6,000 and  £15,000.

Step-by-step explanation:

This split works out to 2 fractions:  2 / (2 + 5) = 2/7 and  5/(2+5) = 5/7.

So the required amounts are £21,000 * 2/7 = £6,000 and 5/7 * 21,000

= £15,000.

the answer will be -11/5. i

Answer:

x=  - 2 and 1/5

Step-by-step explanation:

Given a sphere and a cylinder with the same radius, r, and the height of the cylinder equal to the radius, the sphere has a greater volume. This is concluded by comparing the volume formulas for a sphere (4/3πr³) and a cylinder (πr³).

The sphere and cylinder have the same radius, r, and the height of the cylinder, h, is equal to its radius, r. We'll calculate the volumes of both an apply our given conditions to see which figure has a greater volume.

The formula for the volume of a cylinder is Vcylinder = πr²h. In this case given that h=r, it becomes Vcylinder = πr³.

The formula for the volume of a sphere is Vsphere = 4/3πr³.

Comparing both, we definitely see that the sphere with a volume of 4/3πr³ is greater than the cylinder with a volume of πr³

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B) Translate 4 units down and rotate 180°

Rule for 180° = (x, y) ---- (-x, -y)

Pick one point on Triangle A. (I picked the pointiest point)

(-5, 6)

Now translate 4 units down.

You will now be on (-5, 2)

Rotate 180°

You will now have (5, -2)

And the pointiest point on Triangle B is (5, -2)

So, B is the correct answer.

Option B is correct. The required transformation that will map triangle A to triangle B and illustrate the similarity between the two triangles is translating 4 units down and rotate 180° about the origin

In order to determine the transformation that will map triangle A to B, we need to do the following:

If the coordinate is translated 4 units down as seen from the figure, the resulting coordinate of the vertex on triangle B will be at (5, -6+4) i.e. (5, -2)

We can see that it tallies with a similar coordinate on triangle B. Hence the required transformation that will map triangle A to triangle B and illustrate the similarity between the two triangles is translating 4 units down and rotate 180° about the origin

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a.would be the best answer to me because base in the table is you look carefully.you would see that it is double by yen and it is a constant. rate of change a linear function. that is why I think it's the best answer.

Answer:

A

Step-by-step explanation:

It can not be B, because the statement in the reasoning is false.

Nor can it be C, the statement is irrelevant and unnecessary.

Nor D, it makes no sense.

It's A because it is true and makes sense.

Answer:

Step-by-step explanation:

The formula of a volume of a cube:

[tex]V=a^3[/tex]

a - edge

Cube A:

a = 8in. Substitute:

[tex]V_A=8^3=512\ in^3[/tex]

Cube B:

a = 5in. Substitute:

[tex]V=5^3=125\ in^3[/tex]

[tex]\dfrac{V_A}{V_B}=\dfrac{512}{125}=4.096\approx4.1[/tex]