A boy earned $435, $230, and $562 for 3 consecutive months. How much did he earn in the fourth month so that he gets an average earning of $500 in these 4 months?

Answer:

(- 2, - 2 )

Step-by-step explanation:

the solution to the system is at the point of intersection of the 2 lines.

the 2 lines intersect at (- 2, - 2) , then

solution to the system is (2, - 2 )

[tex]12^2+9^2=x^2\\144+81=x^2\\x^2=225\\x=15[/tex]

Answer:

1

Step-by-step explanation:

[tex] log_{3}(5) \times log_{25}(9) = \frac{ log(5) }{ log(3) } \times \frac{ log(9) }{ log(25) } = \frac{ log(5) }{ log(3) } \times \frac{2 log(3) }{ 2log(5) } = \frac{2}{2} = 1[/tex]

Answer: it's D

Step-by-step explanation:

Answer:

335.16 ft

Step-by-step explanation:

Answer:

888

Step-by-step explanation:

let the number be n then divide by 8 , that is [tex]\frac{n}{8}[/tex]

now add 8 to this

[tex]\frac{n}{8}[/tex] + 8 and finally multiply this by 8 and equate to 952

8([tex]\frac{n}{8}[/tex] + 8) = 952 ( divide both sides by 8 )

[tex]\frac{n}{8}[/tex] + 8 = 119 ( subtract 8 from both sides )

[tex]\frac{n}{8}[/tex] = 111 ( multiply both sides by 8 to clear the fraction )

n = 888

the number chosen was 888

Answer:

In order to make the function continuous, the first and second pairs of lines should have common points.

1. Intersection of the first two lines:

This determines the value of a:

2. Intersection of the second two lines:

This determines the value of b:

See the graph attached

Answer:

-163

Step-by-step explanation:

-2,-25,-163

-2×6=-12 -12-13=-25

-25×6=-150 -150-13=-163

Answer:

The third term is = -163

Step-by-step explanation:

The first term is = -2

The second term = -2 ×6 = -12 Then - 13 = - 25

The second term = - 25

The third term = -25 × 6 = - 150 Then -13 = -163

The third term is -163

Mark brainliest

A fraction is a way to describe a part of a whole. The value of x is 6.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The value of x can be written as,

[tex]\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{x}}} = \dfrac{7}{13}\\\\\\\dfrac{1}{1+\dfrac{1}{\dfrac{x+1}{x}}} = \dfrac{7}{13}\\\\\\\dfrac{1}{1+\dfrac{x}{x+1}} = \dfrac{7}{13}\\\\\\\dfrac{1}{\dfrac{x+1+x}{x+1}}= \dfrac{7}{13}\\\\\\\dfrac{x+1}{x+1+x}= \dfrac{7}{13}\\\\[/tex]

13x + 13 = 7x + 7 + 7x

13x + 13 = 14x + 7

x = 6

Hence, the value of x is 6.

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From the calculations, the height of the tower is 26.4 Km

If we know that the base of the tower is B and he top of the tower is T then to find the  shortest distance between the pilot and the base of the control tower;

Sin 41 = 10.5//BP/

/BP/ = 10.5/Sin 41

/BP/ = 15.9 Km

Now, the height of the control tower is obtained from;

First /AB/ = √(15.9)^2 - (10.5)^2

/AB/ = 11.9 Km

Given that;

Tan 36 = 10.5//BT/

/BT/=  10.5/Tan 36

/BT/=  14.5 Km

Hence the height of the tower is 11.9 Km + 14.5 Km = 26.4 Km

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Answer:

1/14

Step-by-step explanation:

Let A represent the event First person getting red velvet cake
Let B represent the event Second person getting red velvet cake

P(A) = Total number of Red Velvet Cakes ÷ Total Number of Cakes =

6/21 = 2/7

If the first person gets a red velvet cake, then there are 5 red velvet cakes and 20 total cakes

Therefore P(B|A) = Number of red velvet cakes left ÷ total number of cakes left = 5/20 = 1/4

P(A and B) == probability of both getting red velvet cake P(A∩B) = P(A).P(B|A) = 2/7 × 1/4 = 2/28 = 1/14

Answer:

D. x=1

Step-by-step explanation:

8-2x = -8x + 14

First, add 8x to both sides.

8+6x=14

Next, subtract 8 from both sides.

6x=6

Lasty, divide 6 from both sides.

x=1

Hope this helps!

If not, I am sorry.

Answer:

5/7 or D

Step-by-step explanation:

i just know

Answer:

C: 1/2

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: C. \cfrac{1}{2}[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \textsf{Slope of line - } [/tex]

[tex]\qquad \tt \rightarrow \: m = \cfrac{rise}{run} [/tex]

[tex]\qquad \tt \rightarrow \: m = \cfrac{0 - ( - 4)}{8 - 0} [/tex]

[tex]\qquad \tt \rightarrow \: m = \cfrac{ 4}{8 } [/tex]

[tex]\qquad \tt \rightarrow \: m = \cfrac{ 1}{2} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

2

Step-by-step explanation:

because it's for the point s

The radical equation from the following equation is 3+x√7=13, the correct option is C.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that;

Four equations

x+√5=12, x² = 16, 3+x√7=13, 7√x = 14

Now,

Out of the four options you gave, only one is a radical equation:

Ox+√5=12 O x² = 16 O 3+x√7=13 O 7√x = 14

Only 3+x√7=13 because x is under a cube root sign. The other options are not radical equations because they do not have variables under radicals.

Therefore, the radical equation will be 3+x√7=13.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:\approx 9.2 \:\: units [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \textsf{Using distance formula : - } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{(2 - 0) {}^{2} + (0 - 9) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{(2) {}^{2} + (- 9) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{ 4 + 81} [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{85} \: \: units[/tex]

[tex]\qquad \tt \rightarrow \: \approx 9.2 \: \: units[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The distance between points A and B is 9.2 units.

We have,

To find the distance between two points (a, b) and (c, d) in a coordinate plane, you can use the distance formula:

Distance = √[(c - a)² + (d - b)²]

In this case, point A is (2, 0) and point B is (0, 9).

Now, plug the values into the distance formula:

Distance = √[(0 - 2)² + (9 - 0)²]

Distance = √[(-2)² + 9²]

Distance = √[4 + 81]

Distance = √85

Now, round the answer to the nearest tenth:

Distance ≈ √85 ≈ 9.2 (rounded to the nearest tenth)

Thus,

The distance between points A and B is 9.2 units.

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Answer:

B. 1:18

Explanation Down Below

Step-by-step explanation:

Hello!

First, let's find the volume of each cylinder by plugging in the given values.

Volume of a Cylinder: [tex]V = \pi r^2h[/tex]

Since the variables are the same as given in the formula, we can just use the formula as the volume.

[tex]\implies{\boxed{{V = \pi r^2h}}[/tex]

We have to plug in 3r for the radius, and 2h for the height.

[tex]\implies \boxed{ V = 18\pi r^2h}[/tex]

We can see that the Volume of Cylinder B is just 18 times the Volume of Cylinder A, but we can find the same ratio using equations.

The answer is Option B. 1:18.

Answer:

See below

Step-by-step explanation:

The first one IS decay...as 'x' increases the function decreases

the second and third are NOT ...as 'x' increases the value increases

radioactive decay IS decay (obviously)

the one with e^2x   is not ....it grows exponentially as x grows

and finally the last one is decay because as x gets larger the value of y gets smaller

The multiplication law states that

So

Answer:

1 = 1

Step-by-step explanation:

We all know the law of exponents,the one we'll use to solve this is the multiplication law:

Solved:

x^0 = 1

Alternate method:

5^3 and 5^3 cancels, which results to

The length of the three congruent sides is 7 cm and the fourth side length is 12cm.

Given quadrilateral has three congruent sides and perimeter of quadrilateral is 33 cm.

A quadrilateral can be expressed as ABCD and three congruent sides are AB, BC, CD and the fourth side is AD.

Let AD=x

then AB=BC=CD=x-5

This means if all the sides of a quadrilateral are known, we can get its perimeter by adding all its sides.

So, Perimeter = AB + BC + CD + DA.

Substitute values

(x-5)+(x-5)+(x-5)+x=33

4x-15=33

    4x= 48

     x=12

Hence the fourth side length is 12cm and the other sides are 7 cm longer.

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The asymptote and the y-intercept of the function is asymptote: y = 2

y-intercept: (0,8) , Option A is the answer.

Asymptote is a straight line that approaches the curve but does not meet even at infinite distance.

It is given that f(x) = 6 (0.5)ˣ +2

The horizontal asymptote is at y = c

y = 2

From the curve it can be seen that

The intercept of y axis is determined when x = 0

then f(0) = 6 * (0.5)⁰ + 2

f(0) = 8

Therefore the y intercept is at (0,8)

Therefore Option A is the right answer.

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Answer:

C

Step-by-step explanation:

thats what i got

The solution will be the point of intersection of the two lines. The solution to the system is (1.1, 1.3)

Inequalities are expression not separated by an equal sign. Given the following inequalities

x+2y<4

3x-y >2

They are both written in standard form. The first line will be a dashed line and shaded below the graph while the second line will be a dashed line and shaded above.

The solution will be the point of intersection of the two lines as attached

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Answer:

Graph D is the correct one.

Step-by-step explanation:

The number of  days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days

Since from the question, we see that the number of pennies double with each day. It forms a geoemetric progression with

Since the number of pennies after n days equals N = 2ⁿ

Let

So, after n days, the length of the stack of pennies is the geoemetric progression D = 2ⁿ × L

Making n subject of the formula, we have

n = ㏒(D/L)/㏒2

Substituting the values of the variables into the equation, we have

n = ㏒(D/L)/㏒2

n = ㏒(3 × 10¹⁶ m/1.5 × 10⁻³ m)/㏒2

n = ㏒(3/1.5 × 10¹⁹)/㏒2

n = ㏒(2 × 10¹⁹)/㏒2

n = ㏒2 + ㏒10¹⁹/㏒2

n = (19㏒10 + ㏒2)/㏒2

n = (19 + 0.3010)/0.3010

n = 19.3010/0.3010

n = 64.1

n ≅ 64 days

So, the number of  days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days

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Answer:

auto correlation is the answer to the question

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ y{ }^{2} }{(p - y) {}^{y} }[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} }{(p - y) {}^{y} } + \cfrac{ - 2p}{(p - y) {}^{y - 1} } + \cfrac{1}{(p - y) {}^{y - 2} } [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} + ( - 2p)(p - y) + 1(p - y) { }^{2} }{(p - y) {}^{y} } [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2}- 2p {}^{2} + 2py + p {}^{2} + y{ }^{2} - 2py}{(p - y) {}^{y} } [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} + {p}^{2} - 2p {}^{2} + 2py - 2py + y{ }^{2} }{(p - y) {}^{y} }[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{ y{ }^{2} }{(p - y) {}^{y} }[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

2^12

Step-by-step explanation:

16^3 can be rewritten as (2^4)^3 which can then be rewritten as 2^12 by multiplying the exponents

Use the change-of-basis identity,

[tex]\log_x(y) = \dfrac{\ln(y)}{\ln(x)}[/tex]

to write

[tex]xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}[/tex]

Use the product-to-sum identity,

[tex]\log_x(yz) = \log_x(y) + \log_x(z)[/tex]

to write

[tex]xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}[/tex]

Redistribute the factors on the left side as

[tex]xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}[/tex]

and simplify to

[tex]xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)[/tex]

Now expand the right side:

[tex]xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}[/tex]

Simplify and rewrite using the logarithm properties mentioned earlier.

[tex]xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1[/tex]

[tex]xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}[/tex]

[tex]xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}[/tex]

[tex]xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)[/tex]

[tex]\implies \boxed{xyz = x + y + z + 2}[/tex]

(C)

Answer:

60

Step-by-step explanation:

10(2 + 2) + 20

=10(4)+20

=40+20

=60