The base of an isosceles triangle is represented by the expression 3x - 1. Each of the legs of the isosceles triangle is twice the base. Write an expression for the perimeter of the triangle listing each side. Simplify the expression. (if possible show your work.)

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Explanation:

For any parallelogram, the opposite sides are parallel and are the same length.

AB = CD

9x+2 = 12x-4

2+4 = 12x-9x

6 = 3x

x = 6/3

x = 2

Which leads to

Side AD is opposite BC, so AD = BC = 9

Answer:

[tex]7y=-5x-11[/tex]

Step-by-step explanation:

Since it says the lines are parallel both of their gradients will be same.

so gradient of line 1 = [tex]y=\frac{14-5x}{7}[/tex] = [tex]y=\frac{14}{7}-\frac{5x}{7}[/tex]= [tex]-\frac{5}{7}[/tex]

so equation of line 2 = [tex]y-y_{1}=m(x-x_{1} )[/tex]

                                   = [tex]y-(-3)_{}=\frac{-5}{7} (x-(-2)_{} )[/tex]

                                   = [tex]y +3=-\frac{5}{7}x+\frac{10}{7}[/tex]

                                   = [tex]y =-\frac{5x+10}{7}-3[/tex]

                                   = [tex]7y=-5x-11[/tex]

Step-by-step explanation:

basically a line equation typically looks like

y = ax + b

with a being the slope, and b bent the y-intercept (y value when x = 0).

5x + 7y = 14

7y = -5x + 14

y = -5/7 x + 14/7 = -5/7 x + 2

so, wie know the slope of the original line : -5/7 .

any line parallel to it must have the same slope.

our desired line looks like

y = -5/7 x + b

to get b we use the provided point (-2, -3).

-3 = -5/7 × -2 + b = 10/7 + b

-21/7 = 10/7 + b

-31/7 = b

and the full equation is

y = -5/7 x - 31/7

7y = -5x - 31

5x + 7y = -31

Answer:

y = 2

Step-by-step explanation:

   5y - 3y + 1 = -4y + 13

We only have addition and subtraction so move the terms on the other side of the equal sign with changed sign. +1 will be -1 and -4y will be +4y

terms with y = terms without y

    5y -3y +4y = 13 -1

                 6y = 12

                   y = 12/6

                  y = 2

Answer:

864 cm²

Step-by-step explanation: Volume of cube Side^3

Side of Cube= (1728)^1/3 = 12cm Total surface area = 6 x Side^2= 6 x 144 = 864 cm²

Answer:

The base is a triangle with a base length of 11 m and a corresponding height of 7 m. The height of the prism is 14 m. 12.

Answer:

18

Step-by-step explanation:

Intersecting Secant-Tangent Theorem

The square of the tangent is equal to the product of the external secant segment and the secant.

Given:

AE² = EC · ED

⇒ 12² = 8(18 + x)

⇒ 144 = 144 + 8x

⇒ 0 = 8x

⇒ x = 0

ED = 18 + x

     = 18 + 0

     = 18

Now

[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{22}{H}=sin77[/tex]

[tex]\\ \rm\Rrightarrow H=22/sin77[/tex]

[tex]\\ \rm\Rrightarrow H=22.59ft\approx 23ft[/tex]

The length of the extension ladder that is against the outside wall of the house is 22.58 feet.

When the ladder lies against a house, a right triangle is formed. The length of the ladder is the hypotenuse. The distance from the base of the ladder to the house is the base. The lenfth off the house is the length.

To find the length of the ladder, Sin would be used:

Sin = opposite / hypotenuse

Sin 77 = 22 / h

h = 22 / 0.9743 = 22.58 feet

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Answer:

261.05

Step-by-step explanation:

A=½ bh

The base is 22.7

The height is 23

22.7×23=522.1

Since the shape is a triangle we divide it by 2!!

522.1÷2=261.05

The perimeter of the figure is 261.05. Hope you understand how to solve it now :))

Answer:

Step-by-step explanation:

hello : 12=4x   and   x-3=0

Answer:

17190 years.

Step-by-step explanation:

The half-life of carbon-14 is

5730 years.

Therefore, after1 half-life there is 50%=12 of the original amount left.2half-lives there is 25%=14of the original amount left.3 half-lives there is 12.5%=18 of the original amount left.

1−78=18

So, your answer would be the time it takes for carbon-14 to elapse 3 half-lives.

5730⋅3=17190

Answer:

D. (-1, 3)

Step-by-step explanation:

Substitute the points for x and y, until you find the one that makes the equation true.

A. (-5, 3)

-3x + 4y < 20 <== substitute

-3(-5) + 4(3) < 20

15 + 12 < 20

27 < 20

This statement is false (27 is greater than 20, not less than)

B. (-3, 5)

-3x + 4y < 20

-3(-3) + 4(5) < 20

9 + 20 < 20

29 < 20

This statement is false (29 is greater than 20, not less than)

C. (1, 7)

-3x + 4y < 20

-3(1) + 4(7) < 20

-3 + 28 < 20

25 < 20

This statement is false (25 is greater than 20, not less than)

D. (-1, 3)

-3x + 4y < 20

-3(-1) + 4(3) < 20

3 + 12 < 20

15 < 20

This statement is true (15 is less than 20)

Therefore, the correct answer is D

Hope this helps!

Answer:

[D] (-1,3)

Step-by-step explanation:

To know which ordered pair is in the solution set of -3x+4y < 20 we first need to identify the x-value in the ordered pair and plug it into the equation. When simplify, on the condition the y-value you get is identical as the y-value in the ordered pair, then that ordered pair is a solution to the equation.

Now let's solve:  

To find the solution of the equation is ordered pair substitute the value of x and y co-ordinate to check set of ordered pair is the solution of the given equation.

Given:

-3x + 4y < 20

[A] (-5,3)

-3(-5)+4(3)<20

The left side 27 is not less than the right side 20, which means the statement is false

-3x + 4y < 20

[B] (-3,5)

-3(-3)+4(5)<20

The left side 29 is not less than the right side 20, which means the statement is false

-3x + 4y < 20

[C] (1,7)

-3(1)+4(7)<20

The left side 25 is not less than the right side 20, which means that the given statement is false.

-3x + 4y < 20

[D] (-1,3)

-3(-1)+4(3)<20

The left side 15 is less than the right side 20, which means that the given statement is always true.

Hence, Answer is [D] (-1,3)

[RevyBreeze]

Answer:

42.63mm²

Step-by-step explanation:

Base times height:

8.7 times 4.9 is 42.63mm².

So

Area:-

[tex]\\ \rm\rightarrowtail lw[/tex]

[tex]\\ \rm\rightarrowtail (8.7)(4.9)[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{87}{10}\times \dfrac{49}{10}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{4963}{100}[/tex]

[tex]\\ \rm\rightarrowtail 49.63mm^2[/tex]

Answer: 95% of the customers have to wait.

Answer: 68%

Step-by-step explanation:

Answer:

8x+7

Explanation:

f(x) = x + 3

g(x) = 7x + 4

==========

Put values

Done!

Answer:

  f(x) = 2(1/3)^x

Step-by-step explanation:

To find the parameters of this exponential equation, follow the instructions given in the hint.

__

  b = 6/18 = 1/3 . . . . . divide 6 by 18 to find 'b'

  18 = a(1/3)^-2 . . . . . substitute a point and 'b' in the equation

  18(1/3)^2 = a = 2 . . . . multiply by (1/3)^2

The equation is ...

  f(x) = ab^x

  f(x) = 2(1/3)^x

The equation of the blue line is y = 7x - 8 and the equation of the red line is y = -2x + 2

Equations are written as a function of two or more variables with input and output.

The standard linear equation is given in the form y = mx + b

m is the slope

b is the y-intercept

For the red line, the y-intecept is 2

Using the coordinate point on the red line (0,2) and (1, 0)

Slope = -2/1
Slope = -2

Equation of the  red line is y = -2x + 2

For the blue line, we will use the coordinate points (2, 6) and (1, -1)
m = -7/-1

m = 7

-1 = 7(1) + b

-1 - 7 = b

b = -8

Hence the equation of the blue line is y = 7x - 8

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Answer:

Step-by-step explanation:

[tex]\sf \sqrt{x^{10}}=\sqrt{x^{2*5}}\\\\[/tex]

        [tex]\sf = \sqrt{(x^{5})^{2}}\\\\ = \sqrt{x^{5}*x^{5}}\\\\ = x^{5}[/tex]

so hmmm from the equation we can see that is in "x terms" so the independent variable is "x", that tells us the parabola is a vertical one, leading term's coefficient is "2", that means it opens upwards like a bowl.

on a vertical parabola the axis of symmetry is the x-coordinate of its vertex, let's find the vertex of this one.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+4} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 12}{2(2)}~~~~ ,~~~~ 4-\cfrac{ (12)^2}{4(2)}\right)\implies \left( -3~~,~~4-\cfrac{144}{8} \right) \\\\\\ (-3~~,~~4-18)\implies (\stackrel{x}{-3}~~,~~-14)~\hfill \stackrel{\textit{axis of symmetry}}{x=-3}[/tex]

The perimeter of the flag Akihiro draws is the sum of the flag's side lengths

The perimeter of the flag Akihiro draws is 20 units

From the coordinate plane, the side lengths of the flag are:

6 units, 4 units, 6 units and 4 units

Add up the side lengths, to determine the perimeter (P)

P = 6 units + 4 units + 6 units + 4 units

Evaluate the sum

P = 20 units

Hence, the perimeter of the flag Akihiro draws is 20 units

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Answer:

20 units

Step-by-step explanation:

The system of equations has two distinct equations

The solution to the system of equations is (-2,-1)

The system of equation is given as:

y = 2x + 3

And

y = 3x + 5

Start by plotting the graphs of the equations

From the graph (see attachment), we have:

(x,y) = (-2,-1)

Hence, the solution to the system of equations is (-2,-1)

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Answer :

⠀

Step-by-step explanation :

⠀

Here,

⠀

We know that,

[tex]{\longrightarrow \qquad{ \mathfrak{ \pmb{Base \times Height = Area_{(Parallelogram)}}}}}[/tex]

⠀

Now, Substituting the values in the formula :

⠀

[tex]{\longrightarrow \qquad{ \sf{ {13 \times Height = 104}}}}[/tex]

⠀

[tex]{\longrightarrow \qquad{ \sf{ {Height = \dfrac{104}{13} }}}}

[/tex]

⠀

[tex]{\longrightarrow \qquad{ \pmb { \frak{Height \: \: {= 8}}}}}[/tex]

⠀

Therefore,

Question :-

Answer :-

Explanation :-

As per the provided information in the given question, we have been given that the Area of Parallelogram is 104 units² . Its Base is given as 13 units . And, we have been asked to calculate the Height of the Parallelogram .

For calculating the Height , we will use the Formula :-

[tex] \bigstar \: \: \: \boxed{ \sf{ \: Area \: _{Parallelogram} \: = \: Base \: \times \: Height \: }} [/tex]

Therefore , by Substituting the given values in the above Formula :-

[tex] \dag \: \: \: \sf { Area \: _{Parallelogram} \: = \: Base \: \times \: Height } [/tex]

[tex] \longmapsto \: \: \: \sf { 104 \: = \: 13 \: \times \: Height } [/tex]

[tex] \longmapsto \: \: \: \sf { \dfrac {104}{13} \: = \: Height} [/tex]

[tex] \longmapsto \: \: \: \sf { 8 \: = \: Height} [/tex]

[tex] \longmapsto \: \: \: \textbf {\textsf {Height \: = \: 8 }} [/tex]

Hence :-

[tex] \underline {\rule {204pt} {4pt}} [/tex]

Additional Information :-

[tex] \begin{gathered} \begin{gathered} \begin{gathered}\begin{gathered}\boxed{\begin{array}{c} \\ \underline{ { \textbf {\textsf \red{ \dag \: \: More \: Formulas \: \: \dag}}}} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Square} = Side \times Side} \\ \\ \\ \footnotesize\bigstar \: \bf{Area \: _{Rectangle} = Lenght \times Breadth} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Triangle} = \frac{1}{2} \times Base \times Height } \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Parallelogram} = Base \times Height} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Trapezium} = \frac{1}{2} \times [ \: A + B \: ] \times Height } \\ \\ \\ \footnotesize \bigstar \: \bf {Area \: _{Rhombus} = \frac{1}{2} \times Diagonal \: 1 \times Diagonal \: 2}\end{array}}\end{gathered}\end{gathered} \end{gathered} \end{gathered} [/tex]

Answer:

My answer is The diameter is 24

Reflecting the polygon FGHI across the line involves flipping the line across the line y = -1

The coordinates are given as:

F(2, – 1), G(5,2), H(8, 3), and I(6, 0)

The line of reflection is given as:

y = -1

To reflect the line, we apply the following rule of reflection

(x,y) [tex]\to[/tex]  (x,-y-2)

So, we have the following coordinates of the image

F' = (2, – 1)

G' = (5,-4)

H' = (8, -5)

I' = (6, -2)

See attachment for the image of the reflected polygon

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Roy bought 35 pounds of pet food.

Addition is one of the four basic operations of arithmetic, The addition of two whole numbers results in the total amount or sum of those values combined.

Addition is the process of finding the total, or sum, by combining two or more numbers.

An example of addition is: 5 + 11 + 3 = 19.

Given that, Roy bought a 25 pound bag and a 10 pound bag of pet food we need to find that how many pounds of pet food did he buy

Since, we are required to find what amount of pet food did Roy bought from the market, here we will simply add both the amounts to get the total amount.

Total food =  25 pound bag + 10 pound bag

= 35 pound bag

Hence, Roy bought 35 pounds of pet food.

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Answer:

Volume of a sphere = 4/3 πr³

4/3 * 3.14 * r³ = 4000

4.19 * r³ = 4000

r³ = 4000 / 4.19

r = ∛1058

r = 10.19

Now, surface area = 4πr² = 4 * 3.14 * (10.19)²

S.A. = 12.56 * 104

S.A. = 1307

In short, Your Answer would be Option D) 1307 m²

Hope this helps!

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

As it is stated, the triangles are similar to find the length of AB we can use the proportion of sides'

Let x represent the missing length

BD/AE = CD/CE

(2.76)/22 = 5/x cross multiply expressions:

x(2.75) = 110 divide both sides by 2.75

x = 40

Answer:

Volume = 1/3 ft^3

Step-by-step explanation:

volume of prism is multiplying the dimensions

Volume = (1/3 ft)x(2/3ft)x(1 1/2ft)  

Volume = (1/3 ft)x(2/3ft)x( 3/2ft)

Volume = (1x2x3)/(3x3x2) ft^3 = 6/18 ft^3 = 1/3 ft^3

Option B is correct, the volume of the  right rectangular prism is 1/3 cubic feet.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The given figure is a right rectangular prism.

The length is [tex]1\frac{1}{2}[/tex] feet

The width is 2/3 feet

The height is 1/3 feet.

Volume=Length×width×Height

= [tex]1\frac{1}{2}[/tex] ×2/3×1/3

=3/2×2/3×1/3

=1/3 cubic feet

Hence, Option B is correct, the volume of the  right rectangular prism is 1/3 cubic feet.

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Answer:

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

Answer:

Answer is equation C

Step-by-step explanation:

They are converting Celsius temperature to Fahrenheit temperature.

F = 1.8C + 32

F = 1.8(0) + 32 = 32 Fahrenheit

F = 1.8(30) + 32 = 86 Fahrenheit

F = 1.8(100) + 32 = 212 Fahrenheit

Answer:

C) F = 1.8C + 32

Step-by-step explanation:

Hello! The easiest way to do this is to substitute the numbers from your table into your possible answer choices until you find numbers that make a true/correct statement.

For A:

F = 32C + 1.8 <== substitute any number for F and C from your table

32 = 32(0) + 1.8 <== multiply

32 = 0 + 1.8 <== add

32 = 1.8

This statement is false/incorrect

For B:

C = 1.8F + 32 <== substitute any number for F and C from your table

0 = 1.8(32) + 32 <== multiply

0 = 57.6 + 32

0 = 89.6

This statement is false/incorrect

For C:

F = 1.8C + 32 <== substitute any number for F and C from your table

32 = 1.8(0) + 32 <== multiply

32 = 0 + 32 <== add

32 = 32

This statement is true/correct

For D:

C = 32F + 1.8 <== substitute any number for F and C from your table

0 = 32(32) + 1.8 <== multiply

0 = 1024 + 1.8 <== add

0 = 1025.8

This statement is false/incorrect

As we can see, the only equation that makes a true statement is C.

Therefore, the correct answer is C.

Hope this helps!