Question content area top Part 1 The length of the base of an isosceles triangle is 2x-6. The length of a leg is x. The perimeter of the triangle is 43 . Find x.

Answer:

1. 95=8x+55  8x=40  x=5  Reason: Since m and n are parallel, and a line traverse through it, they are corresponding angles, meaning that their angle is the same.

2. 200-2x=130  200-130=2x  2x=70  x=35  Reason: The two angles are the same because the "130-degree" angle's corresponding angle is the vertical angle of the "200-2x" angle.

3. Yes, we can use the corresponding angle theorem to prove that m and n are parallel.

4. No, there's not enough information to determine because both given angles are on line m, we need an angle on line n as well.

5. No, the same explanation as 4^^^ Vertical angles do not necessarily prove that two lines are parallel.

6. Yes, we can use the corresponding angles theorem, and then use the vertical angles theorem.

Good luck, and comment on anything you don't understand. I suggest you watch some help videos.

The length and the width vary inversely.

A variation is a relation between a set of values of one variable and a set of values of other variables.

In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.

If first rectangle length = 72cm and width = 56cm

Then, area = length x width = 72 x 56 = 4032[tex]cm^{2}[/tex]

If length of second rectangle = x

and width = 21

Area of second rectangle = 21x

so both areas are equal, which means

21x = 4032

x = 4032/21

x = 192cm

Since the first rectangle had a width of 56cm and length, 72 and second rectangle has a reduced width 21 cm and an increased length 192cm. it means that the length and the width vary inversely since the reduction in width led to an increase in length.

In conclusion, the two quantities length and width vary inversely.

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Answer:

x = 59/10 aka 5 9/10 or 5.9

Step-by-step explanation:

Answer:

X= 59/10

Step-by-step explanation:

First, we can turn 6 1/2 into a improper fraction (when the numerator is greater than the denominator)

So,

[tex]6\frac{1}{2}[/tex]  

Turns into

[tex]\frac{13}{2}[/tex]

Now we have:

[tex]X+\frac{3}{5} =\frac{13}{2} \\\\[/tex]

Next, we subtract 3/5 from both sides of the equation which equals:

[tex]X =\frac{13}{2}-\frac{3}{5} \\\\[/tex]

Simplify we get:

[tex]X= \frac{59}{10}[/tex]

or X = 5.9

Answer:

This can go both ways but out of 124 black women and only 10 selected you have a chance at least one experienced IPV

Step-by-step explanation:

Answer:

Step-by-step explanation:

Proportional relationship equation:

Use the given point (3, 1) to find the value of k:

Answer:

k = 1/3

Step-by-step explanation:

Now we have to,

→ find the constant of proportionality.

Formula we use,

→ y = kx

The constant of proportionality is,

→ y = kx

→ 1 = k × 3

→ 3k = 1

→ [ k = 1/3 ]

Hence, required answer is 1/3.

Answer:

Step-by-step explanation:

You are sorta on the right track, but .... ∠3+81°+∠4 =180°

along with 88°+∠1=180°

∠1-92°

I know why  you put 88° for ∠2 but , it's only 88° from a line parallel to that top line,  not the hypotenuse of the triangle.  But good idea, just not able to apply that here.  

you've nicely marked the two parallel lines so we know that ∠3 will math the other 64° angle ,  now you can solve for ∠2

∠1=92° and ∠3=64°  so ∠2 must equal 180-92-64=24°

∠2=24°

now solve for ∠4

180-64-81=∠4

∠4=35°

finally we can get ∠5

180-35-64=∠5

∠5=81°

and , we should have also seen that ∠5 would be the same as the 81° angle above it by ∠3 and ∠4  since those lines are parallel.

Hope that helps :)

The point we get after 180 degree clockwise rotation is E' (-3,-1)

When rotating 180° clockwise about the origin the coordinates of the image will be the same x and y numbers but the opposite sign of the pre-image.

Using the above as an example, pre-image E is located at (3,1) so the rotated image would be E' (-3,-1).

Pre-image D is located at (-1,3) so the rotated image would be D' (1,-3).

Pre-image F is located at (2,-2) so the rotated image would be F' (-2,2).

Hence we get the required point.

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The value of 1.735 to nearest hundred is 1.74.

What is nearest hundredth form?

The second digit following the decimal point is the nearest hundredth.

The last digit of the fractional part of 1.735 should be eliminated if it is less than 5 in order to complete the calculation. and If the fractional part of 1.735 has a last digit that is 5 or more and a second digit that is less than 9, we will add 1 to the second digit of a fractional part and remove the third digit. If the fractional part of 1.735 has a last digit that is 5 or greater, a second digit that is 9, and a first digit that is 9, then you can add 1 to the integer part to make the fractional part 00.

Hence, The hundredth form is 1.74.

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She put decimals incorrectly. The correct product of the decimal numbers is 7.8 and 0.3 will be 2.34.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

Janelle composed 23.4 for the result of 7.8 x 0.3. Utilize number sense to choose if Janelle put the decimal point perfectly located in the item.

Then the multiplication of the numbers 7.8 and 0.3 will be given by putting a cross sign between them. Then we have

⇒ 7.8 x 0.3

⇒ 2.34

She put decimals incorrectly. The correct product of the decimal numbers is 7.8 and 0.3 will be 2.34.

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Expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

As given in the question,

Condition for the expression:

Sally and Anne both went for a movie.

Each one purchased a drink.

Shared one popcorn and one veggie bought by them.

Consider movie ticket price = 9

drink price = 1.35

Popcorn price = 3.50

Veggie price = 1.74

Explanation for different expressions are:

1. one-half (9 + 1. 35 + 3. 50 + 1. 74)

Here sum of all the amount is divided equally, which is not correct as movie ticket and drink they have purchased individually.

2.  9 + 1. 35 + one-half (3. 50 + 1. 74)

This is correct option as it represents :

Movie ticket price = 9

Drink = 1.35

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

3. 18 + 2. 70 + one-half (3. 50 + 1. 74)

As per consideration of price this is not correct option.

Movie ticket price =18

Drink = 2.70

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

4. 9+1. 35+2(3. 50+1. 7)

This is not correct option as popcorn and veggie price is doubled.

Therefore, expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

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The cost of materials for the least expensive such container is 245.31 dollars .

Suppose the width of container is x (m),

length of the base of container is 2x (m)

the base area of container is (length × width)sq. m i.e 2x² meter².

Since the volume of container is 10 m³.

the height of container = area of container/ volume of container

height of container= 10/2x² m = 5/x² m

The cost of making such container is cost of base = 2x²*10 = 20x².

cost of sides of container = (2×2x × 5/x² + 2× x × 5/x²)×6 = 180/x

The overall cost is hence the sum of the base and the sides: f(x) = 20x² + 180/x

The get the minimum,

df(x)/dx = 20×(2x - 9/x²) = 0

so 2x = 9/x^2 => 2x = 2.0800 ==> x = 1.651 m

f(x) = 245.31 dollars

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The sum of the interior angles of a 17-sided polygon is 2700 °.

Given:

sum of the interior angles of a 17-sided polygon.

we know that:

sum of interior angles = n-2 * 180

n = 17

= (17-2)*180

= 15*180

= 2700 °

Therefore the sum of the interior angles of a 17-sided polygon is 2700 °.

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Answer:

2067.5

Step-by-step explanation:

divide each number and when you get to the end add a zero for the decimal.

Answer:

Step-by-step explanation:

let's go back to making 1 loaf.  

1 cup water                                  1*x1

1/4 cup white sugar                 1/4*x2

3/4 teaspoon dry yeast          3/4*x3

1/4 teaspoon salt                     1/4*x4

1/8 cup vegetable oil              1/8*x5

2.5 cup flour                           5/2*x6

now just multiply by 13   :)

13*x1        cups water                 13

13/4*x2  cups white sugar        3.25

39/4*x3 Tspoon dry yeast       9.75

13/4*x4  Tspoon salt                3.25

13/8*x5  cups veggie oil         1.625

65/2*x6 cups flour                  32.5

If the 5-day simple moving average was $54.27, then the stock's closing price on Thursday was $56.24.

The table shows the closing stock prices of a new energy company for the past 5 days. One of the closing prices is missing from the table. The 5-day simple moving average is $54.27. The closing price of the stock on Monday, Tuesday, Wednesday, and Friday was $52.45, $53.18, $52.37, and $57.11. We need to find the closing price on Thursday. Let the missing value of the stock price be denoted by the variable "x". The average is the sum of all the values divided by the total number of values. We can solve the given equation.

A = (52.45 + 53.18 + 52.37 + x + 57.11)/5

54.27 = (52.45 + 53.18 + 52.37 + x + 57.11)/5

54.27*5 = (52.45 + 53.18 + 52.37 + x + 57.11)

271.35 = 215.11 + x

x = 271.35 - 215.11

x = 56.24

Hence, the closing price of the stock on Thursday is $56.24.

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Answer:

13.12%

Step-by-step explanation:

Answer:

1. 0

2. 7

3. -2

4. 10

5. -7

6. -8

7. -2

8. -6

9. -4

10. -5

11. 2

12. -9

13. -9

14. -9

Step-by-step explanation:

The non-real solutions according to the equation is (1 + √5 i)/3 and (1 - √5 i)/3.

A polynomial can be factored, and its roots can be discovered using the factor theorem. The polynomial residual theorem is indeed a special instance of this one.

A polynomial f(x) has a factor (x-a), as was noted in the beginning, if and only if f(a) = 0.

As per the given equation in the question,

3x⁵ + 25x⁴ + 26x³ - 86x² + 76x - 48

The function can be written as:

f(x) = g(x).h(x)  (i)

The real solutions from the graph is,

x₁ = -6, x₂ = -4 and x₃ = 1.

So,

g(x) = (x + 6) × (x + 4) × (x - 1)

g(x) = (x² + 10x + 24) × (x - 1)

g(x) = x³ + 9x² + 14x - 24.

Now, substitute the values in (i)

3x⁵ + 25x⁴ + 26x³ - 86x² + 76x - 48 = (x³ + 9x² + 14x - 24) × (ax² + bx + c)

Therefore,

ax⁵ = 3⁵

a = 3.

-24c = -48  

c = 2.

-24(bx) + 14(cx) = 76x

-24b + 28 = 76

b = -2.

The equation for non-real solution:

h(x) = 3x² - 2x + 2.

Δ = b² - 4ac = (-2)² - 4(3)(2) = -20

x₁ = (2 + √20)/6 = (1 + √5 i)/3

x₂ = (2 - √20)/6 =  (1 - √5 i)/3

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Answer:

$48,000

Step-by-step explanation:

Answer:

[tex] G [/tex]eometric.

Step-by-step explanation:

To get the common ratio in a Geometric Progression (GP), T2/a(T1). a(T1) = 1000, T2 = 500.

So, 500/1000 = 1/2. Therefore, common ratio = 1/2

Now, multiply by the the given term to find the next term i.e

1/2 × 1000 = 500, 1/2 × 500 = 250, 1/2 × 250 = 125, 1/2 × 125 = 62.5, etc.

The appropriate fraction produced by the expression is -32/9.

Any function that can be expressed as a rational fraction, which is an algebraic fraction in which both the numerator and the denominator are polynomials, is referred to as a rational function.

Given the function below:

6x-5/3 = 5x + 9

Cross multiply

6x - 5 = 3(5x + 9)

Expand to have:

6x - 5 = 3(5x) + 3(9)

6x - 5 = 15x + 27

6x - 15x = 27 + 5

-9x = 32

Divide both sides by -9

-9x/-9 = 32/-9
x = -32/9

Hence the result of the expression as an improper fraction is -32/9.

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Absolute value of Complex Number -2 + 3i is [tex]\sqrt{13}[/tex]

Absolute value of complex number:

                                                          z = x + iy is the general form of the complex number where x is real part and y is the imaginary part.

                 If we talk about absolute value of complex number z = x + iy then it is represented by |z| = |x + iy|.It is also rad as modulus of z.Absolute value is always going to be a positive value.

              and,

                       |z| = |x + iy|

                            = [tex]\sqrt{x^{2} + y^{2} }[/tex]

Now,

      We have to find the absolute value of complex number, 3i - 2

             z = 3i - 2

                = -2 + 3i

  Absolute value of z is,

                                     |z| = | -2 + 3i |

                                          = [tex]\sqrt{(-2)^{2} + 3^{2} }[/tex]

                                          = [tex]\sqrt{4 + 9}[/tex]

                                          = [tex]\sqrt{13}[/tex]

Thus,

       Absolute value of  Complex number  -2 + 3i is [tex]\sqrt{13}[/tex]

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To reach the break-even point, the publisher should sell 40,000 books.

A break-even point (BEP) is the point where revenues = total cost. Hence, at this point, the company does not gain profit or loss.

On the other hand, total cost is calculated as:

Total cost = fixed cost + variable cost

Where variable cost depends on the number of units produced.

Therefore,

Total cost = fixed cost + number of unit produced x cost per unit

Parameters given in the problem:

fixed cost = h. 400,000

unit cost = h. 35

selling price = h.45 per unit

Let p be the number of books sold. Then,

Revenues = 45 x p

Total cost = 400,000 + 35 x p

At break-even point:

Revenues = total cost

45 x p = 400,000 + 35 x p

10 p = 400,000

p = 40,000

Hence, the break-even point is 40,000 books

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Phil invests £800 for 3 years at the rate of 2% then the total amount after 3 years is £848.

The simple interest method, which adds interest to the starting principal amount at the same rate every day, is a quick and easy technique to calculate the interest on that money.

Simple interest is a way to calculate the amount of interest that will be charged on a certain amount of money at a certain rate and for a certain period of time.

As per the given information in the question,

Principal amount, P =  £800

Time, T = 3 years.

Rate, R = 2%

[tex]SI=(Principle*Rate*Time)/100[/tex]

SI = (800 × 2 × 3)/100

SI = 4800/100

SI = £48

Then, the total amount at the end of 3 years,

= £48 + £800

Total amount = £848

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The algebraic expression is 2n - 3 if Julie runs three miles less than twice the number n that Hannah runs. So option (a) is correct

An algebraic expression is a mathematical expression made up of variables, constants, and algebraic operations.

It is assumed:

"Julie runs three miles less than twice as far as Hannah runs," the expression goes.

It states three miles less than a number, so you get a -3 and twice the number n, which is the same as 2n, and then you rearrange it to get 2n-3

The expression is 2n - 3

Thus, the algebraic expression is 2n - 3, if Julie runs three miles less than twice the number n that Hannah runs.

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Answer:

Step-by-step explanation:

V = 64

a = ∛V = ∛ 64 = 8

Sum = 12·a = 12·8 = 48

The situation can be represented in a linear equation using a slope-intercept form as y = 2x - 58

A linear equation is an algebraic equation of the form y = mx + b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Data;

We can find the slope of the line using

m = y₂ - y₁ / x₂ - x₁

Substituting the values into the equation

m = 116 - 102 / 87 - 80

m = 2

We can find the y-intercept using any point.

y = mx + c

102 = 2(80) + c

102 = 160 + c

c = -58

The equation in slope-intercept form will be y = 2x - 58

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Using the area of rectangle, the dimensions of the rectangle with maximum area are 5√2 and 5/√2.

In the given question we have to find the dimensions of the rectangle with maximum area.

Given Semicircle Radius is 5.

As we know that standard equation of circle is [tex]x^2+y^2=a^2[/tex]

a=5, so the equation is [tex]x^2+y^2=(5)^2[/tex]

[tex]x^2+y^2=25[/tex]

Therefore, Half circle y=[tex]\sqrt{25-x^2}[/tex]

Area of Rectangle(A) =xy

Because Half of the rectangle is lies in first quadrant and half lies in second quadrant

Therefore,

Area of Rectangle(A) = 2xy

Now putting the value of y

Area(A) = 2x[tex]\sqrt{25-x^2}[/tex]

Here we need to maximize the area of Rectangle, so find derivative and set equal to zero.

A'= [tex]\frac{d}{dx}(2x\sqrt{25-x^2})[/tex]

A'= 2[tex][x\frac{d}{dx}\sqrt{25-x^2}+\sqrt{25-x^2}\frac{d}{dx}x][/tex]

A'= 2[tex][x\cdot\frac{-x}{\sqrt{25-x^2}}+\sqrt{25-x^2}\cdot1][/tex]

A'= 2[tex][\frac{-x^2}{\sqrt{25-x^2}}+\sqrt{25-x^2}][/tex]

A'= 2[tex](\frac{-x^2+25-x^2}{\sqrt{25-x^2}})[/tex]

A'= 2[tex](\frac{25-2x^2}{\sqrt{25-x^2}})[/tex]

For critical Number A' = 0

2[tex](\frac{25-2x^2}{\sqrt{25-x^2}})[/tex] = 0

25-2x^2 = 0

2x^2=25

x^2=25/2

x=±√25/2

x=±5/√2

Therefore,

Base of the Rectangle = 2x

Base of the Rectangle = 2×5/√2

Base of the Rectangle = 5√2

and

height of rectangle = [tex]\sqrt{25-x^2}[/tex]

height of rectangle = [tex]\sqrt{25-(5/\sqrt{2})^2}[/tex]

height of rectangle = [tex]\sqrt{25-(25/2)}[/tex]

height of rectangle = √(50-25)/2

height of rectangle = √25/2

height of rectangle = 5/√2

Hence, the dimensions of the rectangle with maximum area are 5√2 and 5/√2.

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