Figure B is a dilated image of figure A. What is the scale factor?

The average time in two races must be less than 7 minutes.

Given,

Runner's times in three races = 6.9 minutes, 6.6 minutes, 6.5 minutes.

Runner will run two more races.

The average time of all five races = less than 6.8 minutes

We have to find the average time needed in the two races:

Now,

(6.9 + 6.6 + 6.5 + x + y) / 5 < 6.8

Here, x and y are the time in two races.

Let's assume the average as 6.5 which is less than 6.8.

Then,

(6.9 + 6.6 + 6.5 + x + y) / 5 = 6.5

(6.9 + 6.6 + 6.5 + x + y) = (6.5 × 5)

x + y = (6.5 × 5) - (6.9 + 6.6 + 6.5)

x + y = 32.5 - 20

x + y = 12.5

Now, we have to find the average of two races:

That is, (x + y) / 2 = 12.5 / 2 = 6.25.

Above is a solution required by an assumption. By this solution we came to know that the average of two races must be less than 7 minutes.

So, let's conclude like:

The average time in the two races must be less than 7 minutes.

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Answer:

d

Step-by-step explanation:

bc i think it is

To find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).

The correct answer choice option C

This is a method of writing or of displaying real numbers as a decimal number between 1 and 10 followed by an integer power of 10.

which number is one thousand times larger than 2.3 x 10²

1000 to scientific notation

= 10³

2.3 x 10² × 1000

= 2.3 x 10² × 10³

= 2.3 × 10^5

Furthermore, scientific notation helps us to express numbers in decimal number between 1 and 10 followed by an integer power of 10. It also help us to represent numbers in this pattern.

Therefore, to find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).

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The inequality will be -  {x ∈ R: x > x+2} that describes a set of all real numbers x more than 2 units from 0.

Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols <,>,=,etc.

The equation-like form of the formula 5x - 4 > 2x + 3 has an arrowhead in lieu of the equals sign. It is an illustration of inequity. This shows that the left half, 5x - 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.

Given,

all real numbers x more than 2 units from 0

So, the inequality representing the the information will be -

{x ∈ R: x > x+2}

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The condition for two line segments to be congruent is that they must have equal length.

What is a line segment?

A geometrical figure which is a part of a straight line having two unique endpoints is called a line segment. Each point on the line segment lies within the two given endpoints

Explanation of the fact that for the two given line segments to be congruent, they must have the same length

The given statement is False. Because two line segments are said to be congruent if and only if they have exactly the same length. If we construct a ray shorter than the line segment, then both will never be congruent according to the properties of congruence. So, for these two to become congruent, they must have the same length.

Hence, we obtain that the two line segments are congruent if they have exactly the same length.

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Quadratic equation which is x² + x - 272 = 0 can be used to find the product of two consecutive integers.

An algebraic equation of a second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

Let one number be x,

second number will be - (x+1)

so, the product of two numbers will be -

x(x+1) = 272

x² + x = 272

x² + x - 272 = 0

The quadratic equation, used to find the numbers is x² + x - 272 = 0.

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Answer:

Each side is 2 centimeters.

Hope this helps :)

Step-by-step explanation:

A square has sides that are all equal. So in this case the area is 4 square centimeters, and in order to find that we had to multiply 2 sides in which they are equal to each other. All the sides were 2 centimeters. We get 2 sides and multiply to get the area of the square chip.

2 cm × 2cm = 4 square centimeters

Considering the definition of an equation and the way to solve it, the equation is 901.5 + 46x= 1775.50  and the number of players the team can bring to the tournament is 19.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear.

The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.

The solution of a equation means determining the value that satisfies it and the equality must be true. To solve an equation, keep in mind:

Being "x" the number of players the team can bring to the tournament, and knowing that:

the equation in this case is:

901.5 + 46x= 1775.50

Solving:

46x= 1775.50 - 901.5

46x= 874

x= 874 ÷ 46

x=19

Finally, the equation is 901.5 + 46x= 1775.50  and the number of players the team can bring to the tournament is 19.

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Answer:

3

Step-by-step explanation:

the absolute value is distance of a number from 0 so +3 absolute value is 0

The cone has a volume of (D) 288in3.

To find the volume:

Given:

Formula:

The Pythagorean theorem is used to calculate height.

The volume of the cone:

Therefore, the volume of the cone is (D) 288in³.

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The complete question is given below:
Right triangle ABC, shown, has a vertical leg 6 inches long and a hypotenuse 10 inches long. If the triangle was rotated 360 degrees around the vertical leg to form a right circular cone, what would be the volume of this cone, in cubic inches?

A. 32

B. 96

C. 128

D. 288

E. 384

Answer:

b

Step-by-step explanation:

(x-8)(x+2)= x^2 - 6x - 16

Evaluate expression and Name the property used in each step.

              =   { [5/(3 times 1)] } 3/5

              =    {[5/(3.1)]} 3/5

We can write,

Multiplicate identity,      

              = [5/3] 3/5

Substitution,

            = (5/3) (3/5)

Cancel the numerator and denominator values,

So,

We can write,

            = 1 Multiplicative Inverse

Therefore,

3/5evaluate the expression and name the property used in each step. [5/(3times1)] 3/5 is = 1 Multiplicative Inverse.

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Answer: M(-3,1.5)

Step-by-step explanation:

A(-7,3)    B(1,0)

[tex]\displaystyle\\M(x,y)=(\frac{x_A+x_B}{2} ,\frac{y_A+y_B}{2} )\\\\M(x,y)=(\frac{-7+1}{2},\frac{3+0}{2} )\\\\M(x,y)=(\frac{-6}{2},\frac{3}{2} )\\\\M(x,y)=(-3,1.5)\\\\Thus,\\\\M(-3,1.5)[/tex]

All the above data were obtained by entering them in excel format and obtaining it using standard methods.

A low standard deviation shows that the values tend to be close to the mean (also known as the expected value) of the set, whereas a high standard deviation suggests that the values are spread out over a wider range. The standard deviation is a measure of variance or dispersion in statistics. Standard deviation, often known as SD, is most frequently represented in mathematical texts and equations by the lowercase Greek letter (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

For sample size 5, Mean = 117.6 and Standard Deviation = 9.2

For sample size 12, Mean = 103.5 and Standard Deviation = 8.6

For sample size 30, Mean =104.6 and Standard Deviation = 8.7

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a)

Solution,

According to fuel gauge,the petrol left is exactly between 1/2 and 3/4 part of the 40 litres.

i.e. Left fuel = (1/2 + 3/4)/2 litres

Here,

1/2 of 40l = 1/2×40l

= 20l

3/4 of 40l = 3/4×40l

= 30l

Then,

Left fuel = (20l + 30l)/2

= 50l/2

= 25l

Consumed fuel = 40l - 25l

= 15l

Therefore,15 litres of petrol is used to travel 240km

b)

Solution,

Consumed fuel = 15l

Distance covered = 240km

Then,

Fuel consumption rate = 240km/15 l

= 16km/l

Therefore,the rate of petrol consumption is 16km/l of his car for this journey

======================================================

Explanation:

The ratio 3:5 is equivalent to 3x:5x after multiplying both parts by x.

Jess has 3x dollars and Marie has 5x dollars

3x+5x = 64

8x = 64

x = 64/8

x = 8

Therefore,

The ratio 24:40 reduces to 3:5 after dividing both parts by the GCF 8.

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

Another way to solve:

m = amount Marie has

64-m = amount Jess has

3/5 = (64-m)/m

3m = 5(64-m)

3m = 320-5m

3m+5m = 320

8m = 320

m = 320/8

m = 40 dollars is the amount Marie has

Answer:

$8,758

I hope this helps!

Answer:

Step-by-step explanation:

a)

Peter now = x years old

John now = y years old

Five years ago

y-5 = 2(x-5)

y-5 = 2x-10

y = 2x-5

b)

x+y=28

y=28-x

Therefore

2x-5 = 28-x

3x = 33

x = 11

y = 28 - (11)

y = 17

Therefore

In three years time John will be:

17 + 3 = 20

c)

y-5 = 2x-10

Lefthand side:

(17)-5 = 12

Righthand side:

2(11)-10=22-10=12

Therefore 

Lefthand side =Righthand side

YAY!

From calculating the percentages we can say that 43 more students went on Friday than Saturday.

Percentage is defined as quantity per hundred. Percentage is calculated by dividing the given number by the total number and multiplying it by 100.

From the survey we can see that 550 students were supposed to go on Friday. But it is given that 18 percent students did not go to the festival.

Number of students who went = 550 - (18% of 550 )

Therefore students = 550 - 99 =451 students

Again from the survey we can see that 480 students were supposed to go on Saturday . But it is given that 15 percent students did not go to the festival.

Number of students who went =480 - (15% of 480 )

Therefore students = 480 - 72 = 408 students

Therefore the number of more students who went on Friday than Saturday is 451-408 = 43 students

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The value of sin S is = 5/13

Given a right triangle with hypotenuse BD = 13 & BC = 12, Find CD,

By, Pythagoras theorem

BD2 = BC2 + CD2

132 = 122 + CD2

CD2 = 132 - 122

CD2 = 169 – 144

CD2 = 25

CD =  

CD = 5

We know that,

Sin   = opposite side/hypotenuse

Sin S = 5/13

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Hence, these triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

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Answer:

the approximate value should be 2.83

Answer:

[tex]xy^2+2x-4y^2[/tex][tex];-58[/tex]

Step-by-step explanation:

First, align the same terms next to each other so that combining like terms will be easier.

Remember like terms have the same variables and powers. To combine like terms, all you have to do is add/subtract the coefficients (the numbers in from of the variables).

[tex]2xy^{2} +2xy^{2} -3xy^{2} +3x-x-4y^{2}[/tex]

[tex]2xy^{2} +2xy^{2} -3xy^{2} =xy^{2}[/tex]

[tex]3x-x=2x[/tex]

And [tex]-4y^{2}[/tex] stays the same because there is no term that has [tex]y^{2}[/tex].

So, we have [tex]xy^{2} +2x-4y^{2}[/tex].

Now to evaluate for x= -2 and y= -3 you have to plug them into the simplified expression.

[tex](-2)(-3)^{2} +2(-2)-4(-3)^{2}[/tex]

According to PEMDAS we first solve the exponents: [tex](-2)(9) +2(-2)-4(9)[/tex]

Then we multiply:

[tex](-18) +(-4)-36[/tex]

Add/subtract:

-58

Answer: h=3V/a^2

Step-by-step explanation:

V=1/3a^2h

V=1/3 * a^2 * h

V*3=3*1/3 * a^2 * h

3V=a^2 * h

h=3V/a^2

To solve the equation, multiply both sides by 5/3. The solution is b = -10/3.

A linear equation is an equation of which the highest degree of its variables is 1.

Steps to solve linear equations:

The given problem:

Solve 3/5 b = -2

Notice that the variable, b, is already isolated on the left side.

Multiply both sides by 5/3:

3/5 b . 5/3 = -2 . 5/3

b = -10/3 (solved)

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Answer:

I don't know the exact question you're asking, but the solution for x would be x16.

Answer: 801.2

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

From the above diagram, we can deduce that:

5x + (x + 54) = 90 (Sum of Acute Angles)

Now, we can solve for x using this equation.

[tex]5x + (x + 54) = 90 \\ 6x + 54 = 90 \\ 6x + 54 - 54 = 90 - 54 \\ 6x = 36 \\ x = \frac{36}{6} \\ x = 6[/tex]

The distance between points  J(-3,2) and K(9,2) is 12 units.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

The given points are

J(-3,2) and K(9,2)

[tex]x_{1} =-3\\\\x_{2} =9\\\\y_{1} =2\\\\y_{2} =2[/tex]

According to given question we have

By the use of distance formula we have

[tex]\sqrt{(x_{2} -x_{1} )^{2}+ (y_{2} -y_{1} )^{2}} \\\\=\sqrt{(9 -(-3) )^{2}+ (2 -2 )^{2}}\\\\=\sqrt{(12 )^{2}}\\\\=12[/tex]

Therefore, the distance between points  J(-3,2) and K(9,2) is 12 units.

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Distance between is missing in question

Answer:

Explanation ↓

Step-by-step explanation:

The origin is the rotation’s set point unless expressed otherwise. In a coordinate plane, when the point (x, y) is revolved in a 90-degree clockwise directive, the projected vision will have a coordinate of (y, -x).