if angle ab is a right triangle then ab is perpendicular to bc

Answer:

4 1/2

Step-by-step explanation:

Add the fractions:

11/6+8/3

11/6+16/6

27/6

27/6=4.5

SOLUTION

The total cost of the books is $8

Calculating 20% off gives

Therefore the amount paid is $6.40

The reason for the required step using the property of equality are as follow:

7. Addition property of equality.

8. Symmetric property of equality.

9. Reflexive property of equality.

10.Symmetric property of equality.

As given,

The reason for the required step using the property of equality are as follow:

7. 4x - 10 = 7 - 2x

4x+2x - 10 = 7

6x -10 = 7

Here

Addition Property of Equality is applied.

If x, y,  and z are real numbers, and x=y

then

x+ z=y+ z

8. 6 = x

x = 6

Here Symmetric Property of Equality is applied.

If x and y are real numbers, then

x = y

y = x

9. 4 = 4

Here Reflexive Property of Equality is applied.

If x is a real number, then

x = x

10. -3 = x

x = -3

Here Symmetric Property of Equality is applied.

If a is a and b are real numbers then,

a = b

b = a

Therefore, The reason for the required step using the property of equality are as follow:

7. Addition property of equality.

8. Symmetric property of equality.

9. Reflexive property of equality.

10.Symmetric property of equality.

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Option(A) i.e, 60 sq. feet is an answer.

The area of a rectangle is the number of unit squares that its perimeter includes. A rectangle's area is the area it takes up within the confines of its four sides. The area of a rectangle is determined by its dimensions. A rectangle's area is essentially equal to the product of its length and breadth. A shape's area is defined as the "space enclosed within the perimeter or the boundary" of the given shape.

The area of a rectangle can be calculated using the formula Area of rectangle = length × width.

Given, length = 15 feet, width = 4 feet

put these values in given formula,

Area of rectangle =  15 * 4

                              = 60 square feet

Hence, the answer is option(A)  i.e, 60 sq. feet.

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Answer: 8 1/2

I can't give an explanation though

Answer:

A. x = 11

Step-by-step explanation:

so, the angle D corresponds to angle T.

therefore, the side BD corresponds to RT.

and CD to ST.

since both triangles are similar, they must have the same angles, and all corresponding sides and other lengths must have the same scaling factor.

so,

RT × f = BD

and the same f must then apply to

ST × f = CD

21 × f = 98

f = 98/21 = 14/3 = 4.666666666...

33 × 14/3 = 15x - 11

11 × 14 = 15x - 11

154 = 15x - 11

15x = 165

x = 11

On solving the inequality we get that values 7 and 8 are solutions to the inequality, hence, option 3.

Here, we are given an inequality as follows-

9 < 3x + 4

Inequalities are solved in a similar manner as we solve equations.

Subtracting 4 from both sides of the inequality we get-

9 - 4 < 3x + 4 - 4

5 < 3x

dividing both sides by 3, we get-

5/3 < 3x/3

5/3 < x

x > 5/3

5/3 in decimal can be written as 1.66

Thus,

x > 1.66

From the given options only 7 and 8 are greater than 1.66.

Thus, on solving the inequality we get that values 7 and 8 are solutions to the inequality, hence, option 3.

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Answer:

12-month option is cheaper per month

Step-by-step explanation:

A gym offers a 12-month membership for $125 or an 8-month membership for $90. Which option has the lesser price per month?

12-month option:

125/12 = $10.42

8-month option:

90/8 = $11.25

12-month option is cheaper per month.

Answer:

4 = -27x^2+12x

5 = 2x^3+x^2

6 = -5x^2+4x-1

7 = x-y+2z

Step-by-step explanation:

Simple collecting like terms and distributive properties.

Answer:

go to gogle

Step-by-step explanation:

The consecutive age is 6 and 7 and Malik is 6 years old.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let their Consecutive age be x, x+1

So, x(x+ 1)= 42

x²+ x - 42 = 0

x² + 7x- 6x - 42=0

x( x+ 7)- 6 ( x+ 7)= 0

(x+ 7)( x-6)= 0

x = 6, -7

Hence, the consecutive age is 6 and 7.

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Exponential Model

Some phenomena can be modeled as an exponential function of the form:

Where Po is the initial value, r is the rate of change, and t is the time.

If the value of P decreases in time (decaying function), then r is negative. If the value of P increases in time (growth), then r is positive.

We know an investment of Po=$4500 has been losing value (decay) at a rate of r = -2.5% = -0.025 each year.

The value of the investment when t = 5 years is:

Calculating:

The investment will be worth $3964.93 in 5 years

Hello,

The temperature changes at rate of -1.5 degree celsius every hours and the reading of temperatures starts at 0 degree celsius which can be modeled into the linear equation of f(t) = -1.5t where f(t) is the temperature function and t is time.

The problem then asks, “what was the temperature 7 hours ago?” This question asks for the temperature 7 hours ago which means t = -7 in this case since we are solving for temperature 7 hours ago, not next 7 hours.

Time being negative in this scenario means in past or hours ago, generally time cannot be negative as it’s scalar quantity.

Substitute t = -7 in the temperature function, this’ll result in:

Therefore, 7 hours ago, the temperature was at 10.5 degree celsius. Please let me know if you have any questions!

Four siblings whose ages are consecutive integers. If the sum of their ages is 86 then The eldest sibling is 20, followed by siblings 21, 22, and 23.

Consecutive means in order.  Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.

Let x = the one sibling

Let x + 1 = the second sibling

Let x + 2 = the third sibling

Let x+4 = the fourth sibling.

If you add the four siblings together they equal 86

(x) + (x +1) + (x + 2) + (x+3) = 86  I put the parentheses in so that you can see each sibling, but it is not needed.

x + x+ 1 +x + 2 + x+ 3 = 86  Combine like terms

4x + 6 = 86 Subtract 6 from both sides

4x = 80

x = 20

The eldest sibling is 20, followed by siblings 21, 22, and 23.

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Answer:

all integers are rational numbers

Step-by-step explanation:

Answer:

a.3.95x^2+1

9999999999999999999999999

Answer:

204

Step-by-step explanation:

Hello!

If y varies directly with x, that means y is a result of multiplying a number by x.

When x is 5 and y is 60, x is being multiplied by 12 to get y. That means, the direct variation equation is y = 12x.

Replace 17 with x to find y.

The value of y when x is 17 is 204.

Answer:

Point-slope form: y - 6 = -1/3(x + 6)

Slope-intercept form: y = -1/3x + 4

Finding the numeric value of the regression equation, the best prediction of Riley's height is given by:

65.84 inches.

To find the numeric value of a function, we replace each instance of the variable in the function or in the expression by the desired value.

The regression equation in this problem gives the armspan of a person, represented by y, as a function of the height x as follows:

y = 1.123x - 6.443.

Riley has an armspan of 67.5 inches, hence y = 67.5, and we can find the best prediction for his height replacing the lone instance of y in the equation by 67.5 and solving for x, as follows:

67.5 = 1.123x - 6.443.

1.123x = 67.5 + 6.443

x = (67.5 + 6.443)/1.123

x = 65.84 inches, which is the best prediction.

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Answer:

It’s B

Step-by-step explanation:I did it on edge 2022 got it right!

The simplified expression for this problem is given as follows:

(3²)^(1/3) = 3^(2/3) = [tex]\sqrt[3]{9}[/tex]

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

The exponents for this problem are given as follows:

2 and 1/3.

Hence the product is of:

2 x 1/3 = 2/3.

Converting the fractional exponent to a rational expression, we have that:

3^(2/3) = [tex]\sqrt[3]{3^2} = \sqrt[3]{9}[/tex]

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Answer:

D

Step-by-step explanation:

first find the zeros on the graph and their multiplicity.

zeros: -1, 2

mult: 3, 2

the equation that fits is f(x)=(x+1)^3(x-2)^2

Answer: you have to add 60 mL of the 70% solution.

Step-by-step explanation:

If you have 180 mL of a 30% alcohol mixture, then (180mL)(0.30) = 54mL of that solution is alcohol.

Similarly, if you have x mL of a 70% alcohol mixture, then (x mL)(0.70) = 0.70x mL of that solution is alcohol.

When you combine these two liquids, you will have (180 + x) mL of liquid and you want it to be 40% alcohol.

So, you simply need to solve the equation:

180(0.30) + x(0.70) = (180 + x)(0.40)

54 + 0.70x = 72 + 0.40x     (distribute the 0.40)

0.30x = 18        (subtract 54 from both sides and subtract 0.40x from both sides)

x = 60

So, you have to add 60 mL of the 70% solution.

Hope this helps!  :)

False. Exponent can be as big as it wants

The Cost of 68 shirts is 841. The total cost formula is used to calculate a total by combining the variable and fixed costs of providing goods.

How to find Cost :

Substitute x=68 in the above equation

so ,  f(x) = 12 (68)+25

       f(x) = 841

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Answer:

it is a. hope it helps

Step-by-step i think

Answer:

x=0.3

Step-by-step explanation:

-0.4x-4.15=x-1.6-2.97

-0.4x-x=-(1.6-2.97)+4.15

-1.4x=0.42

x=0.3

Answer:

x=0.3

Step-by-step explanation:

Answer: infinitely many solutions

Step-by-step explanation:

21 + 21 < 63

Calculate

42 < 63

infinitely many solutions

The coordinates of the mid- point are (5, 16)

Given,

The midpoint of the line,  given any points A (x₁, y₁) and B(x₂, y₂) .

In the question, we are given that the midpoint  is (3, 11) and (7, 21).

and, to find the co- ordinates of the line.

Now, We know that the Formula of mid point

M = ({(x₁ + x₂)/2},{(y₁ + y₂)/2}).

Here, the points are (3, 11) and (7, 21)

Therefore,

(x, y)  =  ({(x₁ + x₂)/2},{(y₁ + y₂)/2}).

=> (x, y) = [( [tex]\frac{3+7}{2}[/tex]) , ([tex]\frac{11 + 21}{2}[/tex]) ]

=> (x , y) = (10/2 , 32/ 2)

=> (x ,y) = (5 , 16)

Hence, The coordinates of the mid- point are (5, 16)

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Answer:

EC and CB

DC and AC

Angle DCB and Angle ECA

Step-by-step explanation:

Line EC and Line CB both have the same measure of 32ft.

Line DC and Line AC both have the same measure of 28ft.

The angles are the sum of the same measures.

When multiplying matrices, we have the following rule:

If the first matrix dimensions are 'a' and 'b' (that is, it has 'a' rows and 'b' columns) and the second matrix dimensions are 'c' and 'd', the product is only possible if we have b = c. Also, the resulting matrix dimensions will be 'a' and 'd'.

Knowing that rule, we have that:

For given[tex]$\mathrm{n}$[/tex] and [tex]$\mathrm{X}_{(1)}$[/tex], we can obtain the confidence interval [tex]$(\mathrm{a}, \mathrm{b})$[/tex].

Let[tex]$\mathrm{X}_1, \mathrm{X}_2, \ldots, \mathrm{X}_{\mathrm{n}}$[/tex] be a sequence of size [tex]$\mathrm{n}$[/tex] from the exponential distribution with rate[tex]$\lambda$.[/tex] Then the probability density function of the random is a given [tex]$\mathrm{f}\left(\mathrm{x}_{\mathrm{i}}, \lambda\right)=\lambda \exp (-\lambda \mathrm{x}) ; \quad 0 \leq \mathrm{x} < \infty$[/tex]

Let us consider a ordered random sample of size [tex]$\mathrm{n}$[/tex] as [tex]$\mathrm{X}_{(1)}, \mathrm{X}_{(2)}, \ldots, \mathrm{X}_{(\mathrm{n})}$[/tex]. Then [tex]$\mathrm{X}_{(1)}$[/tex] is the smallest of the sample. The density function of the smallest sample [tex]$\mathrm{X}_{(1)}$[/tex] is give by

[tex]$$\mathrm{f}\left(\mathrm{X}_{(1)}, \lambda\right)=\mathrm{n}\left[1-\mathrm{F}_{\mathrm{x}}(\mathrm{x}, \lambda)\right]^{\mathrm{n}-1} \times \mathrm{f}(\mathrm{x}, \lambda)$$[/tex]

As the cumulative density  is given by

[tex]=\int_0^{\mathrm{x}} \mathrm{f}(\mathrm{x}, \lambda) \mathrm{dx} \\&=\int_0^{\mathrm{x}} \lambda \times \exp (-\lambda \mathrm{x}) \mathrm{dx} \\&=1-\exp (-\lambda \mathrm{x})\end{aligned}$$[/tex]

The density of the minimum of the sample is given by

[tex]=\mathrm{n} \times[1-(1-\exp (-\lambda \mathrm{x}))]^{\mathrm{n}-1} \times \lambda \times \exp (-\lambda \mathrm{x})$[/tex]

[tex]$$\begin{aligned}&=\mathrm{n} \times[\exp (-\lambda \mathrm{x})]^{\mathrm{n}-1} \times \lambda \times \exp (-\lambda \mathrm{x}) . \\&=\mathrm{n} \lambda \times \exp (-\mathrm{n} \lambda \mathrm{x})\end{aligned}$$[/tex]

Thus, here [tex]$\mathrm{X}_{(1)}$[/tex] follows gamma distribution with parameter [tex]$\alpha=1 \quad$[/tex] and [tex]$\beta=\frac{1}{n \lambda}$[/tex].

We make use of the condition that if Y follows Gamma distribution with parameter with parameter [tex]$\alpha$[/tex]and [tex]$\beta$[/tex]. Then, we have

[tex]$\frac{2 \mathrm{Y}}{\beta} \sim \chi^2(2 \alpha, \mathrm{n}-1)$[/tex]

Thus we have that

[tex]\mathrm{T}=\frac{2 \mathrm{X}_{(1)}}{\frac{1}{\mathrm{n} \lambda}} \sim \chi^2(2, \mathrm{n}-1)$$[/tex]

[tex]$$\begin{aligned}\mathrm{b} &=\frac{\chi^2\left(1-\frac{\alpha}{2}, \mathrm{n}-1\right)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\&=\frac{\chi^2\left(1-\frac{0.03}{2}, \mathrm{n}-1\right)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\&=\frac{\chi^2(0.985, \mathrm{n}-1)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\\mathrm{a} &=\frac{\chi^2\left(\frac{0.03}{2}, \mathrm{n}-1\right)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\&=\frac{\chi^2(0.015, \mathrm{n}-1)}{2 \mathrm{X}_{(1)} \times \mathrm{n}}\end{aligned}$$[/tex]

Therefore for given[tex]$\mathrm{n}$[/tex] and [tex]$\mathrm{X}_{(1)}$[/tex], we can obtain the confidence interval [tex]$(\mathrm{a}, \mathrm{b})$[/tex].

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