For each function, what is the output of the given input?
For f(x)= 4x+7, find f(4)

Answer:

Step-by-step explanation:

First, let's look at the pie-shaped segment defined by the 123° angle and the 18.6 m radius.

The area of the entire circle is given by A = πr² = 3.14159(18.6 m)², or A = 1086.865 m².

The area of the "pie slice" is (123/360) of that, or 371.346 m².

Next, we must find the area of the triangle and subtract this area from this 371.346 m²:

Use the Law of Cosines to find the area of this triangle.  The Law of Cosines in appropriate form is

c² = a² + b² -2ab*cos C.

In this case C is 123° and a and b are both 18.6 m in length.  Thus,

c² = (18.6 m)² + (18.6 m)² - 2(18.6 m)(18.6 m)*cos 123°

Thus,

c² = 691.92 m² - 691.92*cos 123°, or

    = (691.92 m²)(1 - cos 123°)

     =  (691.92 m²)(1 - [-0.5446] ) = (691.92 m²)(1.5446) = 1068.767

Taking the square root of this result, we get c = +32.6920 m.

Subdivide the triangle shown to form a new triangle with hypotenuse 18.6 m, adjacent side 32.6920 m  / 2, or  16.3460 and opposite side h.

Then 18.6² = h² + 16.3460², which leads to h²2 = 18.6² - 16.346², or 78.768.

Then h = √78.768 = 8.875 (m).

We now use this info to find the area of the illustrated triangle, using the formula A = (1/2)(base)(height).  That comes out to:

A = (1/2)(16.3460 m)(8.875 m) = 72.535 m²

Finally, we subtract twice that from the area of the 'pie' to get the area of the yellow (shaded) area:

pie area - area of triangle shown in the diagram =

371.346 m² - 145.071 m² = 226.3 m² (to the nearest tenth)

Answer:

226.4

Step-by-step explanation:

NOT 226.3 !!

The expression is 5(40+80)

The sum of 40 and 80 can be written as

(40+80)

and when we take the 5 times of the sum

we can write as

5(40+80)

Answer:

Number 7 is A and Number 8 is D.

Answer:

The correct answers are

A) 2+10h

D) 40

Answer:

= [tex]\dfrac{1}{5^{9}}[/tex]

Step-by-step explanation:

When dividing values with exponents, we simply need to subtract the numerators exponent to the denominators exponent.

So we have:

[tex]\dfrac{5^{-6}}{5^{3} }[/tex]

= [tex]5^{-6 - 3}[/tex]

= [tex]5^{-9}[/tex]

Now since we have a negative exponent, we can get the reciprocal of the value to make it positive.

= [tex]\dfrac{1}{5^{9}}[/tex]

Answer:

The answer is 1 / 5^(9)

Step-by-step explanation:

We just need to divide both numbers and find the result

(5)^-6 / (5)^3

(5)^(-6-(3)) =

(5)^(-9) =

1 / 5^(9) = 5,120 .10^(-7)

Answer:

Step-by-step explanation:

[tex]\frac{4^{10}}{4^2} = 4^{10 - 2} = 4^8[/tex]

Alternative A

I hope I helped you.

Answer:

A. 4^8

Step-by-step explanation:

When you divide powers with the same base, use the same base, and subtract the exponents.

Here is the rule:

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

Here is your problem:

[tex] \dfrac{4^{10}}{4^2} = 4^{10 - 2} = 4^8 [/tex]

the answer is quadratic model :)

Answer: 4 hours

Step-by-step explanation:

10+6=16

16+6=22

22+6=28

28+6=34

Factor the polynomial

7(x-3)(x+5)

Answer:

Step-by-step explanation:

first solve the volume of the rectangular prism

V = l x w x h

where l is the length

w is the width

h is the height

V = 7 x 4 x 2.5

v = 70 cu cm

then solve the volume of the box

v = e^3

v = 0.5^3

v = 0.125

number of cubes = 70 / 0.125

number of cubes = 560 cubes

Answer:

The number of cubes are needed to fill the rectangular prism = 448 cubes

Step-by-step explanation:

It is given that,

A rectangular prism has a length of 7 cm, a width of 4 cm, and a height of 2 cm. The prism is filled with cubes that have edge lengths of 1/2 cm

To find the volume of rectangular prism

Volume of rectangular prism = Length x Width X Height

Length = 7 cm, Width = 4 cm and height = 2cm

Volume = 7 x 4 x 2 = 56 cm³

To find the volume of small cubes

Volume of cube = a³

a = 1/2 cm = 0.5³ = 0.125

To find the number of cubes needed to fill prism

Number of cubes = Volume of prism/  volume of cube

 = 56/0.125 = 448 cubes

Therefore the correct answer is 448 cubes

Hi. if you have acces to a ti-84 plus or a virtual to plug it into Y= and click 2nd and graph which will take you to the data table

Answer:

The correct option is 1.

Step-by-step explanation:

The system of equations is

[tex]f(x)=2(3)^x[/tex]

[tex]g(x)=10\log (x+3)[/tex]

Using graphing tool we can draw the graph as shown below.

From the below graph it is clear the graph of f(x) and g(x) intersect at (-1.944,0.236) and (1.004,6.025).

[tex](-1.944,0.236)\approx (-2,0.2)[/tex]

[tex](1.004,6.025)\approx (1,6)[/tex]

The approximate solutions of the given system of equations are (-2,02) and (1,6). Therefore only option 1 is correct.

Answer:

To calculate exponential growth, use the formula y(t) = a__ekt, where a is the value at the start, k is the rate of growth or decay, t is time and y(t) is the population's value at time t.

Mark as brainliest please..

To calculate the time for exponential growth, use the formula n = ln(M) / ln(b) for a specific multiple (M) and growth rate (b), or the Rule of 70 for estimating doubling time.

Understanding Exponential Growth

The formula to calculate the time for exponential growth depends on the growth rate and the factor by which a quantity increases. If the growth rate is constant and represented as a percentage or fraction, the growth is exponential. For example, if a bacterial population doubles every hour, starting with 1000 bacteria, it will grow to 2000 after one hour, 4000 after two hours, and so on.

Calculating Time for Exponential Growth

One formula to find the time (n) to reach a certain multiple (M) of the original amount at a specific growth rate (b) is:

n = ln(M) / ln(b)

For instance, to calculate the time to increase by a factor of 1000 with an annual growth rate of 7% (b = 1.07):

n = ln(1000) / ln(1.07) ≈ 102 years

This equation shows that it would take approximately 102 years for the quantity to grow by a factor of 1000.

The Rule of 70

t = 70 / growth rate

t = 70 / 2.9 ≈ 24 years

The time it takes for exponential growth can vary significantly based on the growth rate and the factor of increase desired.

your answer is 2,700 cubic centimeters

Answer:

2340

Step-by-step explanation:

-2 and 8 are the roots of that problem found by factoring.

The answer of the question is A

Answer: The answer to ur question is 60.84

Have a good one and can I get brainliest pls

Answer:

144 out of 180 days.

Step-by-step explanation:

180/30 is 6. That means that 30 * 6 = 180. So, 24 * 6 = 144, which is our answer.

Answer:

See below  

Step-by-step explanation:

Integer exponents are a subset of rational exponents

Integer exponents

An integer exponent is an exponent that is an integer. For example, in the expression y = 5³, the 3 is an integer exponent.

An integer exponent is a power. Thus, 5³ = 5× 5× 5.

Rational exponents

Rational exponents can be expressed as a ratio of integers with nonzero denominators.

Thus, in the expression [tex]y = 5^{\frac{ 2}{3 }}[/tex], the fraction ⅔ is a rational exponent.

A rational exponent is both a power and an nth root. The numerator is the power, and the denominator is the root. Thus,

[tex]5^{\frac{ 2}{ 3}} = \sqrt[3]{5^{2}} = (\sqrt[3]{5}})^{2}[/tex]

Answer:

9 12 15

Step-by-step explanation:

9²+12²=15²

81+144=225

The product after multiplying 8 x 1/5 in the simplest form is 1.6.

Given a multiplication expression, 8 x 1/5.

We have to find the product of this in the simplest form.

Here 8 and 1/5 are the numbers which are to be multiplied.

The simplest fractional form of the product is,

8 x 1/5 = 8/5

This fraction cannot be simplified further.

Now we have to find the result in decimal form.

8 x 1/5 = 1 3/5 = 1 + 0.6 = 1.6

Hence the product is 1.6.

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There is a 150% increase.

Work is attached in the image provided.

Have a great day!

Answer:

the zero product property because you can set them to 0

Answer:  The correct option is

(C) Zero product property.

Step-by-step explanation:  The given problem is

[tex](x+2)(x+6)=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To conclude that x+2=0 or x+6=0, one must use which of the given properties.

We know that

for any two expressions E and F, we have

[tex]EF=0~~~\Rightarrow E=0~\textup{or}~F=0.[/tex]

This property is known as Zero product property.

Therefore, to conclude x+2=0 or x+6=0 from the given problem (i), we must use the Zero product property.

Thus, (C) is the correct option.

Answer:

1) [tex](x+1)(x+2)[/tex]

2) [tex](x+5)(x+10)[/tex]

Step-by-step explanation:

You can factorize the quadratics equations by applying the proccedure shown below:

1) [tex]x^2+3x+2[/tex]

Find two number whose sum is 3 and whose product is 2.

These would be 1 and 2.

Rewrite it as folowing:

[tex](x+1)(x+2)[/tex]

 2) [tex]x^2+15x+50[/tex]

Find two number whose sum is 15 and whose product is 50.

These would be 5 and 10.

Therefore, you can rewrite it as folowing:

[tex](x+5)(x+10)[/tex]

The 1st one is (x+2)(x+1)

The 2nd one is (x+5)(x+10)

Answer:

V=a^3 is the answer

The value of the volume of a cube with an edge of 6cd³ is,

⇒ V = 216c³d⁹

A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.

We have to given that;

An edge of cube is,

⇒ 6cd³

Since, We know that;

Volume of cube is,

⇒ V = side³

Hence, The value of the volume of a cube with an edge of 6cd³ is,

V = (6cd³)³

V = 216c³d⁹

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Answer:

Step-by-step explanation:

24n+32=0

24n= -32

24n=-32 all over 8

3n= -4

n= -4/3

Answer:

Step-by-step explanation:

The formula fo an area of a triangle:

[tex]A=\dfrac{bh}{2}[/tex]

b - base

h - height

We have

x - base

6x - height

Substitute:

[tex]A=\dfrac{(x)(6x)}{2}=\dfrac{6x^2}{2}=3x^2[/tex]

Answer:

[tex]\large\boxed{x=2\sqrt{21}\ and\ y=4\sqrt3}[/tex]

Step-by-step explanation:

Look at the picture.

ΔADC and ΔCDB are similar. Therefore the sides are in proportion:

[tex]\dfrac{AD}{CD}=\dfrac{CD}{DB}[/tex]

We have

[tex]AD=14-8=6\\CD=y\\DB=8[/tex]

Substitute:

[tex]\dfrac{6}{y}=\dfrac{y}{8}[/tex]         cross multiply

[tex]y^2=(6)(8)[/tex]

[tex]y^2=48\to y=\sqrt{48}\\\\y=\sqrt{16\cdot3}\\\\y=\sqrt{16}\ cdot\sqrt3\\\\\boxed{y=4\sqrt3}[/tex]

For x use the Pythagorean theorem:

[tex]x^2=6^2+(4\sqrt3)^2\\\\x^2=36+48\\\\x^2=84\to x=\sqrt{84}\\\\x=\sqrt{4\cdot21}\\\\x=\sqrt4\cdot\sqrt{21}\\\\\boxed{x=2\sqrt{21}}[/tex]

Answer:

Step-by-step explanation:

Hello, this is a factorization algebra case:

a) 7(X+6)

b) 11y + 7

Best regards

Answer:

What is this question?

Step-by-step explanation:

I'm not sure what you are asking.

Answer:

Step-by-step explanation:

1. Add 1 to both the sides

2. 3x=12

3. Divide both the sides by 3

4. X=4

Answer:

Step-by-step explanation:

[tex]3x-1=11\qquad\text{add 1 to both sides}\\\\3x-1+1=11+1\\\\3x=12\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}=\dfrac{12}{3}\\\\\boxed{x=4}[/tex]

Chloe should purchase at least 6 arrangements from Blooms to get a better value compared to Petals Plus, as this is the smallest whole number of arrangements where the total cost at Blooms becomes less than that at Petals Plus.

To determine how many arrangements Chloe should purchase from Blooms to get a better value, we need to compare the total cost of floral arrangements from both stores for varying quantities. We'll calculate the breaking point where the total cost from Blooms becomes less than that from Petals Plus.

Let the number of arrangements Chloe is considering purchasing be denoted by n. The total cost at Petals Plus for n arrangements would be:

Total cost at Petals Plus = $33.04n + $63.00

Similarly, the total cost at Blooms for n arrangements would be:

Total cost at Blooms = $25.07n + $112.00

Chloe gets a better value from Blooms when the total cost at Blooms is less than at Petals Plus:

$25.07n + $112.00 < $33.04n + $63.00

To find the value of n, we'll solve the inequality:

$8.97n > $49.00

n > $49.00/$8.97

n > 5.46

Since Chloe can't purchase a fraction of an arrangement, the smallest whole number of arrangements she should purchase from Blooms to get the better value is 6. Therefore, the answer is option A: 6.

Answer:

Table 2

Step-by-step explanation:

The given frequency distribution table is

X  :   1           2           3            4           5

f   :   11          1            2           4           2

The sum of frequencies is

[tex]\sum f=11+1+2+4+2=20[/tex]

The formula for probability is

[tex]P_i=\frac{f_i}{\sum f}[/tex]

where, [tex]f_i[/tex] is frequency and [tex]\sum f[/tex] in the sum of frequencies.

For X=1,

[tex]P_1=\frac{11}{20}=0.55[/tex]

For X=2,

[tex]P_2=\frac{1}{20}=0.05[/tex]

For X=3,

[tex]P_3=\frac{2}{20}=0.1[/tex]

For X=4,

[tex]P_4=\frac{4}{20}=0.2[/tex]

For X=5,

[tex]P_5=\frac{2}{20}=0.1[/tex]

The probability distribution table corresponds with the given frequency distribution table is

X  :   1           2           3            4           5

P   :   0.55    0.05    0.1          0.2       0.1

Therefore, the correct option is 2.

The only probability distribution table that corresponds with the frequency distribution table is; Second table

From the given frequency distribution table, let's find the sum of the given frequencies. Thus;

Σf = 11 + 1 + 2 + 4 + 2

Σf = 20

Now,the probability for each value of x will be;

P_x = f_x/Σf

Where f_x represents the frequency of the given value of x.

Thus;

P_1 = 11/20

P_1 = 0.55

P_2 = 1/20

P_2 = 0.05

P_3 = 2/20

P_3 = 0.1

P_4 = 4/20

P_4 = 0.2

P_5 = 2/20

P_5 = 0.1

Looking at the tables in the options, in conclusion the only tables that have their P value corresponding with those we got for each value of x is Option B which is the second table.

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