Question 3
Rearrange the formula 5√x + y = z to make x the subject

The inequality expression has a solution of (-oo, -5]

From the question, the inequality is given as

7 x plus 5 less than or equals minus 30

The above inequality can be re-written as follows

7x + 5 ≤ -30

There are constants to add or subtract in the expression

So, we start by subtracting both sides of the expression by the constant -5

This gives

7x ≤ -35

Divide both sides by 7

So, we have the following representation

x ≤ -5

Express as interval notation

(-oo, -5]

Hence, the solution to the expression is (-oo, -5]

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The population of California by the year 2020 is  41 million.

The term population has to do with the number of people that live in a place or a town. We have the following information from the question;

Initial population (Po) = 37 million

Population growth rate (r) = 1.0%

Time interval (t) = 10 years

P = The population of the city of California at the time t

Now using the formula;

P = Poe^rt

P = 37 * 10^6 e^0.01 * 10

P = 4.089 * 10^7 or 41 million

They would have a population of 41 million in ten years.

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Answer: 6 and 2

Step-by-step explanation:

to find your factors, you want to set the equation equal to 0 and find what adds up to your middle term and multiplies to your last term

[tex]x^{2} -8x+8=-4\\x^{2} -8x+12=0\\(x-6) (x-2) = 0\\x-6= 0\\x-2=0\\x=6\\x=2[/tex]

Answer:

1) The top angle = 128°

Right angle = 52°

Bottom angle = 128°

Left angle = 52°

2) The top angle = 159°

Right angle = 21°

Left angle = 21°

Step-by-step explanation:

The left problem would involve verticle angles being congruent to each other.

[tex]5x + 2 = x + 42\\\\6y + 8 = 7y - 12[/tex]

Solve each equation:

[tex]5x + 2 = x + 42\\4x = 40\\x = 10[/tex]

[tex]6y + 8 = 7y - 12\\20 = y[/tex]

Substitute:

The top angle = 128°

Right angle = 52°

Bottom angle = 128°

Left angle = 52°

The right problem would involve supplementary angles.

[tex]\frac{1}{4}y - 1 + 27x + 24 = 180\\\\27x + 24 + 4x + 1 = 180[/tex]

Solve for second equation (for simplicity) :

[tex]27x + 24 + 4x + 1 = 180\\31x + 25 = 180\\31 = 155\\x = 5[/tex]

Substitute x = 5 into other equation :

[tex]\frac{1}{4}y - 1 + 27x + 24 = 180\\\frac{1}{4}y - 1 + 27(5) + 24 = 180\\\frac{1}{4}y = 22\\y = 88[/tex]

Substitute :

The top angle = 159°

Right angle = 21°

Left angle = 21°

Answer:

yes because 4+8>11

Step-by-step explanation:

one you add the 2 smallest numbers and if it is greater then the larger number then it is a triangle but if it is equal or less than the biggest number it is not a triangle

Answer:yes because 4+8>11

Step-by-step explanation:

Answer:

The answer is -3n,10.1,11/10,19/2,-101 is the right answer form my side

When plate is rotated 720° about the origin in the counterclockwise direction they form parallel segments.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The coordinates of the figure EFGH are given as:

E = (-4,8)

F = (-7,5)

G = (-4,3)

H = (-2,5)

The rule of rotation 720 degrees counterclockwise about the origin in the

(x,y) -> (-y,x)

So, we have:

E' = (-8, -4)

F' = (-5, -7)

G'= (-3, -4)

H' = (-5, -2)

when plate is rotated 720° about the origin in the counterclockwise direction they form parallel segments.

Hence when plate is rotated 720° about the origin in the counterclockwise direction they form parallel segments.

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The real world description of the quantity two times x and quantity divided by 10 is the cost per pizza for 2 pizzas divided by 10 people.

According to the question,

We have the following information:

Two times x and the quantity is divided by 10.

So, we have the following expression for this word problem:

2x/10

Now, in option a, the expression will be:

(x/10)+2

Now, in option b, the expression will be:

(x+2)/10

Now, in third option, the expression for the word problem will be:

10x/2

Now, in option d, we have the following algebraic expression:

2x/10

Now, the last expression matches with the expression given in the question.

Hence, the correct option is d.

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Answer:

x=21/5, x=4.2, or x=4 1/5

Step-by-step explanation:

Three groups of cubes are shown with 4 groups of tens and 3 ones in each group is incorrect and 0.46is correct for 1.38 ÷ 3

A division is a process of splitting a specific amount into equal parts.

Rohan's model is represented as:

1.38 ÷ 3=0.43

The model is incorrect, and the correction is as follows:

Express 1.38 as 1.20 + 0.18

Now (1.20 + 0.18)÷ 3

(1.20÷ 3)+(0.18÷ 3)

0.4+0.06

0.46

Hence, the correct result of the model is 0.46

Hence Three groups of cubes are shown with 4 groups of tens and 3 ones in each group is incorrect and 0.46 is correct

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Answer:

Step-by-step explanation:

Make the subject of 6x = t

Solution of the given system of equations using Cramer's rule is given by : x = -96 / 190 , y = -17/19 .

As given in the question,

Given system of equations are as follow:

-10x -10y = 14

-10x + 9y = -3

Solution of the given system of equations using Cramer's rule is given by :

D = [tex]\left|\begin{array}{ccc}-10&-10\\-10&9\\\end{array}\right|[/tex]

   = -90 -100

   = -190

Dₓ = [tex]\left|\begin{array}{ccc}14&-10\\-3&9\\\end{array}\right|[/tex]

    = 126 - 30

    = 96

[tex]D_{y}[/tex] = [tex]\left|\begin{array}{ccc}-10&14\\-10&-3\\\end{array}\right|[/tex]

     = 30 +140

     = 170

x = Dₓ/D

 = 96/ -190

 = -96/190

y = [tex]D_{y}[/tex]/ D

  = 170/-190

  = -17/19

Therefore, solution of the given system of equations using Cramer's rule is given by : x = -96 / 190 , y = -17/19 .

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The model motorcycle is 1/3 feet or 4 inches long.

Given:

A model motorcycle has a scale of 0.8 in : 1.4 ft.

If the real motorcycle is 7 ft long.

= 0.8 inches * 1 foot/12 inches

= 8/10 * 1/12 feet

= 8/120

= 1/15 feet

scale/actual = 0.8 in / 1.4 ft = 1/15/14/10 = 10/210 = 1/21

Let L be the model motorcycle length.

scale / actual = L/7

L/7 = 1/21

L = 7/21

L = 1/3 feet

L = 1/3 feet * 12 inches/1 feet

L = 4 inches

Therefore the model motorcycle is 1/3 feet or 4 inches long.

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Answer:

Acquisition cost refers to an amount paid for fixed assets, for expenses related to the acquisition of a new customer, or for the takeover of a competitor.

Answer:

[tex]x=\frac{37}{6} \\[/tex]

Step-by-step explanation:

Since A and b are complimentary angles There sum is equal to 90°

In other words:

We know A = (7x+18)  and b = (5x-12)

Next, insert these values into the equation (A+ b = 90°):

[tex](7x+18) + (5x-12)=90[/tex]

Drop the () since we are not multiplying anything

[tex]7x+18 + 5x-12=90[/tex]

Combine like terms: 7x and 5x, 18 and-12

[tex]7x +5x +18-12=90\\\\12x+ 16=90\\[/tex]

Subtract 16 from both sides of the equation

[tex]12x=74\\[/tex]

Divide by 12 and get:

[tex]x=\frac{37}{6} \\[/tex] or [tex]x=6.16666...[/tex]

Hope this helps :)

If the ratio of a basketball players completed free throws to attempted free throws is 9 to 12. If she attempted 20 free throws, the number of  free throws she completed is 27 free throws.

Given data:

Attempted free throws = 9 to 12

Free throws = 20

Formulate

9/12= 20/x

Cross-multiply

9x = 20× 12

9x = 240

Divide both side by 9x

x = 240/9

x = 26.6

x = 27 free throws (Approximately)

Therefore the free throws is 27.

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(4.25,6.5) is the solution of the equation.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The estimate is pretty close for both equations. For the first equation, the estimate results in a value that is only 0.2125 units away from the constant.

For the second equation, the estimate results in a value that is only 0.25 units away from the constant.

The solution lies at approximately (4.25,6.5).

Hence (4.25,6.5) is the solution of the equation.

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The correct notation of A is a subset of B is A⊆B( option B)

A set is a collection of objects or elements.Subsets are a part of one of the mathematical concepts called Sets, grouped in the curly braces, such as {a,b,c,d}.

The elements of sets could be anything such as a group of real numbers, variables, constants, whole numbers, etc. It consists of a null set as well.

If a set A is a collection of even number and set B consists of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B.

Therefore the correct notation of A is a subset of B is A⊆B.

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1. The bank discount on the note of $6,000, maturable in 160 days at 3.5%, is $93.33.

2. The original noteholder will receive total proceeds of $5,906.67 after the bank discount.

Bank discount is the difference between the below-par and par (face) values.

For example, if the bank discounts a note, the noteholder will receive an amount smaller than the face value they would have received if they had held the note till its maturity.

The discount represents the finance charge levied for cashing the note earlier than its due date.

Amount due at maturity = $6,000

Discount rate = 3.5%

Time (period) = 160 days

Days in the year for ordinary interest = 360 days

Bank discount = $93.33 ($6,000 x 3.5% x 160/360)

The proceeds = $5,906.67 ($6,000 - $93.33)

Thus, the bank discount is the difference between the face value and the net proceeds (discounted value) resulting from discounting a note before its maturity.

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Answer: I think A? not fully sure

Step-by-step explanation:

Answer: 224 student ride the bus to school each day.

Step-by-step explanation:

In megan random sample of 60 students number of students preferred riding bus is found out to be 42 student.

Student riding the bus if the total number of students in the bus is 320

ratio of the student surveyed  to the student ride bus =

                                                                      =

Assuming the total number of   student riding bus = x

now,

                                           x =  224

hence, 224 student ride the bus to school each day.

Step-by-step explanation:

Answer:

5/48

Step-by-step explanation:

[tex]\frac{5/8}{6}=\frac{5}{8(6)}=\frac{5}{48}[/tex]

Answer:

5/48 or 0.104

Step-by-step explanation:

⅝ ÷ 6

changer division sign to multiplication sign

⅝ × ⅙ = 5/48 or 0.104

Answer:

b) associative

Step-by-step explanation:

The associative property of multiplication was used to change the position of the parentheses

Answer:

3.73 (m)

Step-by-step explanation:

b = 8 * tan (25)

b = 8 * 0.466308

b = 3.730461

Answer:

Step-by-step explanation:

the anser is 3 + 5 =8

The values for the stated domain of the function are-

F(-4) = 10; F(2) = 4; F(0) = 0.

As per the stated function.

F(x) = 6-x

The domain for the function are-

-4,2,6

The value of the function are, put each value in the place of x in the function.

F(-4) = 6 - (-4)

F(-4) = 6 + 4

F(-4) = 10

F(2) = 6 - 2

F(2) = 4

F(6) = 6 - 6

F(0) = 0

Thus, the values for the stated domain of the function are- 10, 4 and 0 respectively.

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Answer:

f) Line l.

g) ∠1 and ∠3,  ∠2 and ∠4,  ∠5 and ∠7,  ∠6 and ∠8.

h) ∠3 and ∠6,  ∠2 and ∠7.

i) ∠4 and ∠5,  ∠1 and ∠8.

j) ∠2 and ∠3,  ∠6 and ∠7.

Step-by-step explanation:

The transversal is a line that crosses two other lines in the same plane at two distinct points.

Therefore, the transversal line of the given diagram is line l as it crosses lines j and k.

Corresponding angles are pairs of angles that are in the same position relative to both lines crossed by the transversal.

Alternate interior angles are pairs of angles on the inner side of the two lines that the transversal crosses, but on opposite sides of the transversal.

Alternate exterior angles are pairs of angles on the outer side of the two lines that the transversal crosses, but on opposite sides of the transversal.

Consecutive interior angles are pairs of angles on the inner side of the two lines that the transversal crosses, and are on the same side of the transversal.

The quadratic equation has no real roots. The roots are x = -1 +√5/2 i or x = -1 - √5/2 i

To determine the number of roots of a quadratic equation ax²+bx+c=0 you need to compute the discriminant (b²-4ac)

If the discrimant is less than 0, then the quadratic has no real roots.

If the discriminant is equal to zero then the quadratic has equal roosts.

If the discriminant is more than zero then it has 2 distinct roots.

Given: 2x² + 4x + 7

a = 2, b = 4, c = 7

b² - 4ac = (4)² -4(2×7) = 16-56 = -40

Since the discriminant is less than 0, thus 2x² + 4x + 7 has no real roots i.e. it has two imaginary roots

To find the roots, you can use the completing the square method:

2x² + 4x + 7 = 0

Divide through by 2:

x² + 2x + 7/2 = 0

x² + 2x = -7/2

Add the the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (1)² = -7/2 + (1)²

Factorise:

(x+1)² = -7/2 +1

(x+1)² = -5/2

x+1 = ± √-5/2

x = -1 ±√5/2 i                   (Note: √-1 = i)

x = -1 +√5/2 i or x = -1 - √5/2 i

Therefore, the roots are x = -1 +√5/2 i or x = -1 - √5/2 i

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The length, in centimeters of the rectangle if the width is:

1. 10 centimeters

2. 3.6 centimeters

The perimeter of a rectangle is given by the formula

P = 2( Length, L + width, w)

P/2 = L + w

L = P/2 - w

Perimeter is given to be 48, L is solved below

at w = 10 centimeters

L = 48/2 - 10 = 14 cm

at w = 3.6 centimeters

L = 48/2 - 3.6 = 20.4 cm

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Polynomial identities apply beyond just polynomials by replacing the variables with numbers to create a numerical expression.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

A polynomial identity is an equation that helps us to easily solve expressions involving larger exponents and numbers. Generally, polynomial identities are used for the expansion of the expression, by breaking down the expression into simpler units.

Polynomial identities apply beyond just polynomials by replacing the variables with numbers to create a numerical expression.

Hence, Polynomial identities apply beyond just polynomials by replacing the variables with numbers to create a numerical expression.

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