please help me with this problem!

Answer:

Value of x is 20.

Step-by-step explanation:

The angle opposite to 4x is also 4x.

Similarly, the angle opposite to 5x is also 5x.

So, 4x+4x+5x+5x=360

18x=360

x=360/18

x=20

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Step-by-step explanation:

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The number of gallons of paint needed to paint the entire fence is 26.4 gallons.

Area = length × width

= 33 m × 2 m

= 66 square meter.

Number of gallons of paint needed = 66 square meter / 2.5 m²

= 26.4 gallons

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The correct answer is option B which is Sn = -111974.

When there is a constant between the two successive numbers in the series then it is called a geometric series.

Here we have the following data:-

[tex]\sum_{n=1}^7-2.6^{n-1}[/tex]

[tex]a_n = a_1r^{n-1}\ \ \ \ \ S_n = a_1(\dfrac{1-r^n}{1-r})[/tex]

Here we need to calculate the first term second term and common ratio to calculate the sum of the series.

a₁ = -2.(6¹⁻¹) = -2

a₂ = -2.( 6²⁻¹) = -2 (6) =-12

Common ratio:-

[tex]a_n = a_1r^{n-1}[/tex]

[tex]-12 = -2r^{2-1}[/tex]

r = 6

Put all the values in the sum formula:-

[tex]S_n = -2(\dfrac{1-6^7}{1-6})[/tex]

[tex]S_n = -2(\dfrac{279935}{5})=-2\times 55987[/tex]

[tex]S_n[/tex] = -111974

Therefore the correct answer is option B which is Sn = -111974.

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Answer:

Step-by-step explanation:

AFR = VFN (opposite angle rule)

7x + 33 = 9x + 7

33 - 7 = 9x - 7x

26 = 2x

x = 26 : 2

x = 13°

-----------------

check

7 * 13 + 33 = 9 * 13 + 7   (remember PEMDAS)

91 + 33 = 117 + 7

124 = 124

the answer is good

Answer:x = 6 , y = 18

Step-by-step explanation:

The length of the rectangle is 60 feet and the width of the rectangle is 45 feet.

Let L be the length and W be the width of the rectangle.

Then the area of the rectangle will be

Area of the rectangle = L×W square units

A farmer’s rectangular pen has an area of 2,700 square feet, and the width is 15 feet shorter than the length.

L = W + 15

Then we have

2700 = W(W + 15)

W² + 15W - 2700 = 0

W² + 60W - 45W - 2700 = 0

(W + 60)(W - 45) = 0

W = 45, -60

Then the dimension of the rectangle will be

W = 45 feet

L = W + 15

L = 45 + 15

L = 60 feet

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Answer:

f(2) = 2

Step-by-step explanation:

Given function:

f(x) = 5x - 12

To Find:

f(2)

Solution:

Well,it is absolutely clear from the problem,that x = 2.So just substitute 2 in x's place on the function,then simplify using PEMDAS.

[tex]f(x) = 5x - 12[/tex]

[tex]f(2) = 5(2)- 12[/tex]

[tex]f(2) = 10 - 12[/tex]

[tex]\boxed{f(2) = - 2}[/tex]

Hence,f(2) is equal to -2.

Answer:

[tex]x^{-\frac{2}{7} }[/tex]

Step-by-step explanation:

→ Add the powers together

[tex]x^{\frac{3}{7} {-\frac{5}{7} }[/tex]

→ Simplify

[tex]x^{-\frac{2}{7} }[/tex]

Answer:

d) 150%

Step-by-step explanation:

[tex]x=25*300\%=25*3=75\\[/tex]

[tex]y=25\%*40+40=50[/tex]

[tex]x/y*100\%=75\div50*100\%=150\%[/tex]

Answer:d

150%

Step-by-step explanation:

Answer:

20.4 years (nearest tenth)

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\implies \sf 15000=6000\left(1+\frac{0.045}{12}\right)^{12t}[/tex]

[tex]\implies \sf \dfrac{15000}{6000}=\left(1.00375\right)^{12t}[/tex]

[tex]\implies \sf 2.5=\left(1.00375\right)^{12t}[/tex]

[tex]\implies \sf \ln (2.5)=\ln \left(1.00375\right)^{12t}[/tex]

[tex]\implies \sf \ln (2.5)=12t \ln \left(1.00375\right)[/tex]

[tex]\implies \sf t=\dfrac{\ln (2.5)}{12 \ln (1.00375)}[/tex]

[tex]\implies \sf t=20.40017123[/tex]

Therefore, it would take 20.4 years (nearest tenth) for the investment to reach $15,000.

Answer:

Step-by-step explanation:

Given polynomials:

(6x+7+x²)+(2x²-3)

Solution:

Removing brackets,

Collecting like terms,

Simplifying ,

Done!

Hence option 3 is correct.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:  ax² + bx + c = 0.

The given expression is;

(6x+7+x²)+(2x²-3)

Now add the like term in the given expression,

⇒   x² + 2x² + 6x + 7 - 3

⇒ 3x² + 6x + 4

Hence,

The sum of polynomial is 3x² + 6x + 4.

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Answer:

After solving this question I got and 120 tokens

Answer:

Pythagoras was the Greek geometer .

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Using a system of equations, it is found that Wilma is 50 years old and Yvonne is 10 years old.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

Wilma is 5 times as old as yvonne, hence:

x = 5y.

In ten years, yvonne's age will be a third of wilma's age, hence:

[tex]y + 10 = \frac{1}{3}(x + 10)[/tex]

Since x = 5y:

[tex]y + 10 = \frac{1}{3}(x + 10)[/tex]

[tex]y + 10 = \frac{1}{3}(5y + 10)[/tex]

3y + 30 = 5y + 10

2y = 20.

y = 10.

Then:

x = 5y = 5 x 10 = 50.

Wilma is 50 years old and Yvonne is 10 years old.

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Answer:

Like terms are mathematical terms that contain the same variables. We combine like terms, because it simplifies algebraic expressions.

Closure property is the term for when you add or multiply two whole numbers together, and the result is always just a whole number. It is related to adding, subtracting, and multiplying polynomials, because when something is closed, the output will result in being the same type of object as the inputs.

Step-by-step explanation:

Like terms: When combining like terms, we add their coefficients. For instance, if we have 3y and 4y, we get 7y. That is because we added (3+4) to get 7, and plugged in the variable "y".

Closure property: Adding, subtracting, or multiplying two polynomials will output a polynomial.

Answer:

the sum of all exterior angle is 360 degree

A fraction is a way to describe a part of a whole. The correct option is C.

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

The choice that is equivalent to the fraction  can be found by rationalizing the denominator of the fraction. Therefore, we can write,

[tex]\dfrac{2}{2-\sqrt{6x}}\\\\\\=\dfrac{2}{2-\sqrt{6x}} \times \dfrac{2+\sqrt{6x}}{2+\sqrt{6x}}\\\\\\= \dfrac{4+2\sqrt{6x}}{4-6x}\\\\\\=\dfrac{2(2+\sqrt{6x})}{2(2-3x)}\\\\\\= \dfrac{2+\sqrt{6x}}{2-3x}[/tex]

Hence, the correct option is C.

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Answer:

35 miles/hour

Step-by-step explanation:

See attached image.

Answer:

36.2

Step-by-step explanation:

Assuming that the dotted line is a perpendicular bisector, we can say that it splits the side that is 30 units long into 2 sets of 15 units. Then, we can use the pythaogrean theorem to solve (Leg A is 33 and Leg B: 15). a^2+b^2=c^2

33^2+15^2=c^2

1089+225=c^2

1314=c^2

Square root of 1314 = square root of c^2

36.2 aapproximately c

Step-by-step explanation:

Hi There! Let me help you :)

To answer this question, we have to know about the way to simplify it. First, you find the factor of 48.

[tex] = {48}^{ \frac{1}{2} } [/tex]

[tex] = {(16 \times 3)}^{ \frac{1}{2} } [/tex]

[tex] = {16}^{ \frac{1}{2} } \times {3}^{ \frac{1}{2} } [/tex]

[tex] \: [/tex]

—Use the general formula of the exponential, where a^m/n = ^n√a^m.

[tex] \: [/tex]

[tex] = {16}^{ \frac{1}{2} } \times {3}^{ \frac{1}{2} } [/tex]

[tex] = \sqrt[2]{16} \times {3}^{ \frac{1}{2} } [/tex]

[tex] = 4 \times {3}^{ \frac{1}{2} } [/tex]

The answer is C.

Answer:

Simplification of algebric expression is [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]

Step-by-step explanation:

Simplify any algebric expression means to write an equivalent expression in which all similar terms combined and remove all symbols such as brackets.

The given algebraic equation is [tex]x^{2} -\frac{4}{x^{2} } +2x[/tex]

now for simplifying it

First of all take L.C.M of [tex]x^{2}[/tex]

= [tex]\frac{x^{2} (x^{2}) -4 + 2x(x^{2} )}{x^{2} }[/tex]

We get [tex]\frac{x^{2} -4+2x^{3}}{x^{2} }[/tex]

Further we can write it as  [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]

Simplification of algebric expression is [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]

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Answer:

x = 5.00 cm

Step-by-step explanation:

• area of the rectangle = [tex]x[/tex]   x   [tex](x + 1)[/tex]

                                     = [tex]x^2 + x[/tex]

• area of the circle = π r²

                               = [tex]\frac{22}{7}[/tex]   x   [tex](x + 2)^2[/tex]

                               = [tex]\frac{22}{7}[/tex]   x   [tex](x^2 + 4x + 4)[/tex]

∴   [tex]x^2 + x[/tex]   +    [tex]\frac{22}{7}[/tex]   x   [tex](x^2 + 4x + 4) = 184[/tex]  

⇒  [tex]x^2 + x[/tex]      +   [tex]\frac{22}{7} x^2 \space\ + \space\ \frac{88}{7} x \space\ + \space\ \frac{88}{7} = 184[/tex]

⇒  [tex]\frac{29}{7}x^2 \space\ + \space\ \frac{95}{7}x \space\ - \frac{1200}{7} = 0[/tex]

• Using quadratic formula, where

a = [tex]\frac{29}{7}[/tex]

b = [tex]\frac{95}{7}[/tex]

c = [tex]\frac{-1200}{7}[/tex] ,

[tex]x=\frac{-b \pm \sqrt{b^2-4c}}{2}[/tex]

[tex]x = \frac{-\frac{95}{7}\pm \sqrt{(\frac{95}{7})^2 - 4(\frac{29}{7})(\frac{-1200}{7} ) } }{2(\frac{29}{7})}[/tex]

[tex]x = 5.00 \space\ \space\ \space\ or \space\ \space\ \space\ x = -8.28[/tex]

As length (x) cannot be a negative number,

x = 5.00 cm

Sum of triangle angles = 180

smallest angle = x

second angle = 3x

third angle = x +35

180 = x + 3x + x + 35

145 = 5x

x = 29 is the smallest

the second is 87

the third is 64

Answer:

y=(-5x)+(-7)

Step-by-step explanation:

The equation for slope is y=mx+b

so you would say -5x as the mx in the equation and -7 as the u intercept.

Hii!

_________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

y=-5x-7

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

For this question we will use the slope intercept form equation, because we are provided with the slope and the y-intercept.

The slope intercept form equation is [tex]\large\textsf{y=mx+c}[/tex]. In this formula m denotes the slope and c denotes the y-intercept.

Since we have both m and b, we can stick them into the formula. Upon doing this we obtain

[tex]\twoheadrightarrow\sf y=-5x+(-7)[/tex]

[tex]\bullet[/tex] Simplify

[tex]\twoheadrightarrow\sf y=-5x-7[/tex]

[tex]\bullet[/tex] Great job! We found the equation

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

--

Answer:

rounded is $207.66

Step-by-step explanation:

you start by doing 349(0.30) which would be 104.7

349-104.7=244.3

next you do 244.3(.15)=36.645

244.3-36.645= $207.655

Answer: 30 buttons

Step-by-step explanation:

If there were 8 kids, and 7 more joined, then there were 15 kids making snowmen (8+7 = 15).  Each child used 2 buttons for the eyes, so 30 buttons were used (15 x2 = 30).  This is assuming no other buttons were used on the snowmen for anything else

Answer:

okay

Step-by-step

no of yards they cut in an hour

Jacob = 2 yard

jenny 3/4 of a yard

no of yards it will take jenny to cut 3 yards =  4 hours

The intercept is 3 and 5

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

To find x- intercept, y=0

x² + 2x -15=0

x² -5x + 3x -15=0

x(x-5) - 3(x-5) = 0

(x-5)(x-3)=0

Hence, the x- intercept is 3 and 5.

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