A. Put the following values in order from least to greatest:
4²,-√4, √4²,-2√4, 6-47, √

The total number of free throws shots Jason made was 6 and the total number of two point shots Jason made was 7.

First, let us understand the variables:

Any number, vector, matrix, function, its argument, set, or one of its elements can be specifically represented by a variable.

Let x and y be the quantity of shorts.

x is the number of attempts at the free throw line.

y is the quantity of two-point attempts.

According to the question, we have;

x + 2y = 20 ............equation 1

x + y = 13    ............equation 2

From equation 2 we can take out the value of x;

x = 13 - y     ............equation 3

substituting the value of x in equation 1, we will get;

(13 - y) + 2y = 20

13 - y + 2y = 20

13 + y = 20

y = 20 - 13

y = 7

putting the value of y in equation 3, we will get

x = 13 - 7

x = 6

Thus, the total number of free throws shots Jason made was 6 and the total number of two point shots Jason made was 7.

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Torren will have $5169 in the account at the beginning of year 8. Option A is correct.

The following formula can be used to calculate the compound interest.

[tex]A(n) = P(1 + r)^{(t- 1)}[/tex]

where,

A(n) denotes the final sum.

P stands for the initial deposit.

r denotes the interest rate (in decimal).

t denotes the time (in year).

The compound interest will be C.I = A - P in this case.

We are given in the question;

The account's initial deposit is $4500, and the term is 8 years.

As a result,

A = 4500 and

t = 8

As we all know, interest is compounded once a year.

We shall divide the interest rate in percentage form by 100 to convert it to decimal form.

r = 2% = 2/100

⇒r = 0.02

The given equation is

[tex]A(n) = 4500(1 + 0.02)^{(n- 1)}[/tex]

Substituting the given values in the above equation, we will get,

[tex]A(n) = 4500(1 + 0.02)^{(8- 1)}[/tex]

[tex]A(n) = 4500(1 + 0.02)^{7}[/tex]

[tex]A(n) = 4500 \times 1.14868[/tex]

[tex]A(n) = 5169.06[/tex]

[tex]A(n) = 5169[/tex]

Thus, Torren will have $5169 in the account at the beginning of year 8. Option A is correct.

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Answer:

-3 < x

Step-by-step explanation:

first of all get the positive x on one side, so we have

12 < 18 + 2x ( positive x is easier to work with)

then, get only x on one side

-6 < 2x

simplify

-3 < x

From the graph, if the price increases to $25

The quantity demand will decrease

Quantity supply increases --------This is the reaction from the retailers

Using the concept of equations, 1552 people attended the festival last year.

Two algebraic expressions are combined to create an algebraic equation using the equals (=) sign. Algebraic equations are also known as polynomial equations since they contain polynomials on both sides of the equal sign. An algebraic equation consists of variables, coefficients, constants, and algebraic operations including addition, subtraction, multiplication, division, and exponentiation.

An integer or set of integers that satisfy the condition in the equation are the roots or solutions of an algebraic equation.

Let the number of people who attended the festival last year =x

Then, we can write an equation as

1785=1.15 × x

x = 1785/1.15

=1552 people

So, last year's attendance = 1552

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3/4x+10=4

Then solve for x

3/4x = 4 - 10

x = (4-10)/(3/4)

. = -6/3/4

. = -24/3

. = -8

In consecuence , answer IS

x= -8

Answer:

B is correct. The slope is -3/2.

Answer:D

Step-by-step explanation:

Answer: $456

Step-by-step explanation: They will both have the same amount of money at 7 months

The cost of battery is £0.43.

Given,

In the question:

Tim buys a torch and a battery

The torch costs eleven times as much as the battery and

Tim pays with a £10 note and gets £4.84 change.

To find the how much does the battery cost?

Now, According to the question:

Let cost of battery = £ x

So, Cost of torch = £ 11x

Based on the given conditions :

=> x + 11x = £ 10 - £ 4.84

=> 12x = £ 5.16

=> x = £ 5.16/ 12

=> x = £ 0.43

Hence, The cost of battery is £0.43.

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Answer:

6x+3=5x-8

6x-5x= -8-3(match the like terms)

x= -11

According to the rules of significant figures:



1.25 × 200 = 300

the answer is

TRue

The value of the expression is equal to 6.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is [3(6-14)]/(-4). The value of the expression will be calculated below,

E = [3(6-14)]/(-4).

Simply the expression by using mathematical operations,

E = [3( -8)]/(-4).

E = 3 x 2

E = 6

Therefore, the value of the expression is equal to 6.

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The equation that represents the table, in slope-intercept form, is: y = -2x + 11.

The slope-intercept form of an equation that represents a line is expressed as y = mx + b, where:

Using two pairs of values from the table, (6, -1) and (9, -7):

Slope (m) = (-7 -(-1)) / (9 - 6)

Slope (m) = -6/3

Slope (m) = -2.

Find the y-intercept, b, by substituting m = -2 and (x, y) = (6, -1) into y = mx + b:

-1 = -2(6) + b

-1 = -12 + b

-1 + 12 = b

b = 11

To write the equation, substitute m = -2 and b = 11 into y = mx + b:

y = -2x + 11

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The fraction form of 8 1/6 is 49/8 as the definition of fraction says, "An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided".

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction merely informs us of the number of parts that make up the whole. The slash that is written between the two numbers identifies a fraction. The numerator is the highest number, and the denominator is the lowest number. 1/2, for instance, is a fraction.

Here,

8 1/6=(6*8+1)/8

=49/8

According to the definition of a fraction, which states that it is "a number represented mathematically as a quotient, where the numerator and denominator are divided," the fraction form of 8 1/6 is 49/8.

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Answer:

3x+20

Step-by-step explanation:

trianglesPairs of congruent triangles

Triangles A is congruent since UV = WX

Triangle Δ KLJ = Δ MNO and are congruents

Triangle Δ UGI ≠ Δ MNO ≠ ΔKLJ is congruent

The last table shows the function that is decreasing only over the interval [tex](-1, \infty)[/tex].

From given tables we clearly see that in below table, the functions are decreasing as 'x' increases

x f(x)

-3 -5

-1 -1

-1 -1

0 0

1 -4

2 -8

We need to find interval [tex](-1, \infty)[/tex].

In first table,f(x)=-5,-2,-1,2. Here the functions are in increasing order

In second table, f(x)=-7,-6,1,-1. Here the functions does not follow a specific order

in third table, f(x)=-1,2,1,-6, Here also the functions does not follow a specific order.

In fourth table, f(x)=1,0,-4,-8. Here the functions are in decreasing order.

Hence, the fourth table shows the function that deceases over interval [tex](-1, \infty)[/tex].

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The value of x = x = 1 - [tex]\frac{2\sqrt{2i} }{4}[/tex] and x = 1 + [tex]\frac{2\sqrt{2i} }{4}[/tex] by using quadratic formula

Given,

In the question:

The equation is :

2x^2-4x+3=0

To solve by using the quadratic formula :

Now, According to the question;

[tex]2x^2 -4x+3=0[/tex]

Identify the coefficients

a = 2, b = -4 , c = 3

Use the quadratic Formula :

x = (-b±√(b²-4ac))/(2a)

Substitute into values above formula :

x = -(-4) +√(-4)²-4x 2 x 3))/(2x2)  or

x = -(-4) -√(-4)²-4x 2 x 3))/(2x2)

Determine the sign for exponential or radical expressions

x = -(-4) -√(-4)²-4x 2 x 3))/(2x2)

x =  4 -√16-4x 2 x 3))/(2x2)

Calculate the product or quotient

x = 4 -√16-24/4

x =  4 -√-8/4

x = 4 - √-8 x √-1/ 4

x = [tex]\frac{4\sqrt{2^2.2 } }{4}[/tex] x [tex]\sqrt{-1}[/tex]

Simplify the radical expression:

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

Rewrite by definition i = [tex]\sqrt{-1}[/tex]

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

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

Hence, The value of x = x = 1 - [tex]\frac{2\sqrt{2i} }{4}[/tex] and x = 1 + [tex]\frac{2\sqrt{2i} }{4}[/tex] by using quadratic formula .

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The data that represent a population is helpful when we have to find the information only about one field.

In the given question we have decide how well data represent a population.

The total group you want to make judgments about is referred to as a population. Data is a set of quantitive data which refers the population only in numbers. So the data is only helpful when we have to find the only in small amount and only one field.

Data collection from a large population is typically only simple when the population is small, approachable, and cooperative.

Example: Gathering information from a population

A high school administrator is looking for trends in the final exam results of all graduating seniors. They use the entire population dataset since they are only interested in applying their findings to the graduating seniors in this high school. So the data is useful.

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Area of irregular shape is 41.13m².

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat.

Given,

Area of irregular shape = Area of rectangle + Area of semicircle

Area of rectangle = Length × Breadth

Area of rectangle = 9 × 3

Area of rectangle = 27 m²

Area of semicircle:

1/2πr²

1/2 × 3.14 × 3²

14.13 m²

Area of irregular shape = 27 + 14.13

Area of irregular shape = 41.13

Area of irregular shape is 41.13m².

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Answer:

(a.):  Company A:  3x + 30; Company B:  2x+85

(b.) Company B is cheaper as it would cost $245 for Mia to drive 80 miles

Step-by-step explanation:

The equations we need are linear and we can think of them as such.  x represents the slope (cost per mile) and the initial fee represents our y-intercept or constant (amount paid before Mia ever drives)

(a.):  Thus, for company A, we have y = 3x + 30 and for company B we have y = 2x + 85.

(b.) Since we know that Mia needs to drive 80 miles, we plug this into x for both companies and find which one is lower

Company A:  3(80) + 30 = $270

Company B: 2(80) + 85 = $245

Company B's price would be lower for Mia's needs.

Let's start by calculating the value for f(-1).

For this we go to the graph and count the number of squares to the left of the axis to be at -1. In this case f(-1) would be 5.

Now let's calculate f(4)

For this case the value of f(4) would be 0.

Similarly we calculate f(-3). As you can see in the graph it would be 6.

The last scenario would be for when f(x) = 9, we look for that value on the curve and realize that it corresponds to x = 1.

Answer:

0.8 repeated

Step-by-step explanation:

Because it is

The original statement is same as third statment and value of y is 27.

Writing the equation form for each statement -

Let the variable be represented as y.

1/3(30 - y) = 3/4

1/3×30 - y = 3/4

1/3×y - 30 = 3/4

1/3(30 - y) = 3/4

1/3(y - 30) = 3/4

Based on the interpretation of all the sentences in equation form, we find the statement 3 to be same as original statement. Solving the equation to get the value of y.

1/3(30 - y) = 3/4

10 - y/3 = 3/4

10 = 3/4 + y/3

10 = (3×4 + y×4)/12

10×12 = 12 + 4y

4y + 12 = 120

4y = 120 - 12

4y = 108

y = 27

Hence, the value of y is 27.

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Answer:

the answer is A.

1 over 3 (30 - y) = 3 over 4

Answer:

sin 30 = 7 *3^1/2 / c

sin 60 = x / c           definition of  30-60-90 -

sin 30 / sin 60 = 7 * 3^1/2 / x = .5 / .866 = .577

x = 7 * 3^1/2 / .577 = 21

Check:       tan 30 = 7 * 3^1/2 / 21 = .577 = tan 30

In general, given

b is related to the period of the function, such that, in the case of the tangent function,

Remember that the period of tan(x) is equal to pi.

Therefore, in our case,

The period of the function is 2pi, which means that it repeats every 2pi units.

To determine the next step, we need to slove the expression.

divide both sides by -1:

Square both sides of the equation: