Part A
STRUCTURE Find two consecutive even integers such that twice the lesser of the two integers is 4 less than two times
the greater integer.
a. Write and solve an equation to find the integers.

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!

61/100 is the equivalent fraction for the given decimal number.

A decimal number then has two components: a whole number part and a fractional part. The decimal place value system for the whole part of a decimal number is the same as the whole number value system. However, we get the fractional part of the decimal number as we move toward the right after the decimal point.

A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken.  The number below the line is called the denominator.  It shows the total number of equal parts the whole is divided into or the total number of the same objects in a collection.

for converting a decimal into a fraction we need to multiply and divide the decimal by the 10^n where n is the number of digits after the decimal.

61/100 is the equivalent fraction for the given decimal number.

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Answer:

Step-by-step explanation:

(4x+8)

4(x+2)

The line segment BC has a length of 13 units.

In this question we know the locations of the two ends of a line segment. The procedure consists in calculating the vector behind the line segment and later determing its magnitude by Pythagorean theorem. If we know that B(x, y) = (8, - 7) and C(x, y) = (- 4, - 2), then the length of the line segment BC is:

BC = (- 4, - 2) - (8, - 7)

BC = (- 12, 5)

BC = √[(- 12)² + 5²]

BC = 13

The line segment BC has a length of 13 units.

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Answer:

Step-by-step explanation:

The x-coordinates form the domain.

We know the x-coordinates of the end points of the line, the first numbers in pair of coordinates:

Also, since both points are closed circles, the endpoints are included.

So the domain is the interval between 0 and 4, both inclusive.

This is shown as:

The matching answer choice is A.

The domain of the function includes all x-values from 0 to 4, including both 0 and 4.

So, the correct answer is option A: {[tex]{x | 0 \leq x \leq 4}\\[/tex]}.

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. In this case, the function begins with a closed circle at (0, 2) and ends with a closed circle at (4, 6), which means that the function is defined at these specific points.

Since the function is a linear function, it represents a straight line.

A linear function is continuous, and it extends indefinitely in both directions.

Therefore, any x-value between 0 and 4 will also be defined by the linear function.

In mathematical notation, we can represent the domain as:

Domain: {x | 0 ≤ x ≤ 4}

This means that the domain of the function includes all x-values from 0 to 4, including both 0 and 4.

So, the correct answer is option A: {[tex]{x | 0 \leq x \leq 4}\\[/tex]}.

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complete question:

A linear function is shown on the graph.

a linear function that passes through the points (0, 2) and (4, 6)

What is the domain of the function?

[tex]{x | 0 \leq x \leq 4}\\{x | 0 < x < 4}\\{y | 2 \leq y \leq 6}\\{y | 2 < y < 6}[/tex]

graph is attached

The value of the inequality is a x ≥2 or x ≤ -2.

According to the statement

We have to find that the value in the inequality.

So, For this purpose, we know that the

Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

From the given information:

7x-14 ≥0 or 4x+5 ≤ -3​

The value of the inequality is a :

7x-14 ≥0 or 4x+5 ≤ -3​

x ≥14/7 or x ≤ -3​-5/4

x ≥2 or x ≤ -8/4

x ≥2 or x ≤ -2.

So, The value of the inequality is a x ≥2 or x ≤ -2.

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Answer:

9

Step-by-step explanation:

9 because 3x3=9

The area of the triangle is 6√3 square units.

A triangle with a right angle or two perpendicular sides is referred to as a right triangle, a right-angled triangle, or perhaps more formally as an orthogonal triangle (formerly known as a rectangle triangle). Trigonometry's foundation is the relationship between the right triangle's sides and other angles.

The ratios of a given object's sides 30°-60°-90° triangle are 1 : √3: 2.This information allows us to calculate the lengths of something like the triangle's orthogonal sides.

3(2/√3) = 2√3 . . . . side AB in the attached figure.

And also:

2·3 = 6 . . . . . . . . . . side AC in the attached figure.

Then the area of the triangle is:

A = 1/2bh

A = 1/2(6)(2√3) = 6√3 . . . . square units.

the area of the triangle 6√3 square units.

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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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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:

[tex]3^{4}[/tex]

Step-by-step explanation:

Because 3x3x3x3

3 multipily by 4 times as it's same number

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

Answer:68.48

Step-by-step explanation:a²+b²=c²  a=60 b=33 so 60²+33²=4689 and take the square root of that which equals 68.48

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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[tex]\fbox{x = - 4} \: \sf or \: \fbox{ x = 2}[/tex]

Step-by-step explanation:

[tex] \frac{x}{2} = \frac{4}{x} - 1[/tex]

multiply whole equation with 2x,

[tex] \hookrightarrow\frac{x}{2} \times 2x = ( \frac{4}{x} \times 2x) - (1 \times 2x)[/tex]

[tex]\hookrightarrow {x}^{2} = 8 - 2x[/tex]

Rearranging above equation and making a quadratic equation,

[tex]\hookrightarrow {x}^{2} + 2x - 8 = 0[/tex]

Comparing above equation with, ax²+bx+c,

a =1, b=2, c= -8

Using formula,

[tex]x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

Substituting the given values,

[tex]x = \frac{ - 2 ± \sqrt{ {2}^{2} - 4 \times 1 \times ( - 8)} }{2 \times 1}[/tex]

[tex]x = \frac{ - 2 ± \sqrt{ 4+32} }{2}[/tex]

[tex]x = \frac{ - 2 ± 6 }{2}[/tex]

[tex]x = \frac{ - 2 + 6}{2} = \frac{4}{2} = 2[/tex]

or

[tex]x = \frac{ - 2 - 6}{2} = \frac{ -8}{2} = - 4[/tex]

[tex] \fbox{x = -4} \: \sf or \: \fbox{ x = 2}[/tex]

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An elevator can carry 15 adults or 20 children at one time during the course of a day the elevator Carries a full passenger load 52 times if all the passengers were children 260 more people would the elevator carry than If all the passengers were adults.

52 trips[tex]\times[/tex]15 adults = 780 adults for the course of a day

52 trips[tex]\times[/tex] 20 children = 1,040 children for the course of a day

The elevator can carry 1040-780=260 more children than adults in a day

A vehicle that travels in a vertical shaft to transport people or cargo between floors of a multistory structure is an elevator, also known as a lift. The majority of contemporary elevators are moved by electric motors through a network of wires and sheaves with the help of a counterweight (pulleys).

Traction elevators come in two varieties: gearless traction and gearless traction. The most sophisticated option is a gearless traction elevator, which operates the hoisting mechanism using counterweights and has a wheel that is directly connected to the engine.

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Answer: $206

Step-by-step explanation:

n=packets of noodles.

c=packets of cookies.

d=packets of dry fruit.

2n+20c+50d=

2(3)+20(5)+50(2)=

6+100+100=

6+200=$206

Answer:

264 square ft

Step-by-step explanation:

8*33=264

Answer: 3 groups of 5 = 5 + 5 + 5 = 15. 5 groups of 3 = 3 + 3 + 3 + 3 + 3 = 15. 3 groups of 5 has the same answer as 5 groups of 3! So, 3 x 5 = 5 x 3. This means that when you multiply 2 numbers, the order of the numbers (which number is first and which is second) does not matter, the answer will still be the same. Multiplication Terms

Step-by-step explanation: I hopes this helps.

Answer:

13/20

Step-by-step explanation:

I hope this helps, have a great day :)

Answer:

96

Step-by-step explanation:

?

The surface area of the square pyramid with length of the base 6m and slant height of the pyramid 5m is 96 m².

A square pyramid is a 3-D geometrical figure with the base of the shape of square and four triangular faces from each side of the square joining together at the top to form vertex.

The surface area of a square pyramid is given as:

Base area of the square face + 1/2 (perimeter of base × slant height)

Since square base has side of length 6m and the slant height of the pyramid is 5m then surface area is given by;

Surface area = (6×6) + 1/2 (4×6×5)

=> 36 + 1/2 (120)

=> 36 + 60

=> 96 m²

Thus, surface area of square pyramid is 96 m².

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The average rate of given function F(x) = 7x -12 from -2 to 3 is equal to 7.

As given in the question,

Given function F(x) = 7x -12

x₁= -2

x₂ =3

Average rate of the function F(x) is

= {F(x₂) - F(x₁)}/ (x₂ - x₁)

= [7(3)-12 - {7(-2)-12}]/ [3-(-2)]

=(21-12+14+12)/ 5

=35/5

=7

Therefore, the average rate of given function F(x) = 7x -12 from -2 to 3 is equal to 7.

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Answer:

z = -4

Step-by-step explanation:

Let's solve the problem,

→ 3(z - 1) - 1/2 (4z + 10) = 4 (z - 3/2) + 10

→ 3z - 3 - 2z - 5 = 4z - 6 + 10

→ z - 8 = 4z + 4

→ 4z - z = -4 - 8

→ 3z = -12

→ z = -12/3

→ [ z = -4 ]

Hence, the value of z is -4.

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:

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]

Answer:

b

Step-by-step explanation:

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

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

chance of 3 is 1/6 and chance of 2 is 1/6 so finale answer is 1/36

The correct option is r < 0 for the given inequalities of  p < 0, q > 0, and p + q = r.

For the given inequalities;

p < 0, q > 0, and p + q = r;

As, we know that if p < 0; then it hold the negative value.

And for  q > 0, it have the positive values.

Because -negative(P) was closer to zero than Positive q, let's say p = -10 and q = 5.

p + q = r

Put the values;

r = -10 + 5 = -5,

r = -5

Therefore, r < 0 is the correct condition for the given inequalities.

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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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