Students in Mrs.Whites class took their Chapter 1 math test on Monday

Given inequality:

To graph it first, consider line:

Find two points on the line.

Let them be x- and y-intercepts:

Now, plot the two points.

Next, draw a dashed line trough the two points. Dashed line because the line is not included into solution set, due to '<' sign.

The last step, shade the area below the line. Below the line because 'y <' means 'y-values less than' which appears below the line.

Answer:

See attachment.

Step-by-step explanation:

Given linear inequality:

[tex]y < \dfrac{1}{2}x+2[/tex]

When graphing inequalities, temporarily replace the inequality sign for the equals sign:

[tex]\implies y=\dfrac{1}{2}x+2[/tex]

Find two points on the line by substituting two values of x into the equation:

[tex]x=0 \implies y=\dfrac{1}{2}(0)+2 =2\implies (0, 2)[/tex]

[tex]x=4 \implies \dfrac{1}{2}(4)+2=4 \implies (4,4)[/tex]

When graphing inequalities:

Therefore, to graph the given linear inequality:

The width of the cake is 54 inches

from the question, we have the following parameters that can be used in our computation:

The above parameters mean that

Length = 18

Width = 3 * Length

So, we have

n = 3 * length

substitute the known values in the above equation, so, we have the following representation

n = 3 * 18

Evaluate

n = 54

Hence, the width is 54 inches

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Complete question

Gilda's sponge cake is three times as long as it is wide. The sponge cake is 18 inches long. Use n to represent the cake's width.

Determine the width of the cake

The width of the cake which is represented as n would be = 54 inches

The length of the sponge cake that is owned by Gilda = 18 in.

The width of the sponge cake owned by Gilda (n) = 3( length)

That is;

n = 3( 18)

n = 54 inches.

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The opportunity cost of Madeline based on the information would be 8 units of gizmos .

The benefit or gain that a person might have obtained or earned if he or she had not chosen the current alternative is known as opportunity cost.

Madeline has spent $24 ($2 x 12) on the widgets in this question since she purchased 12 of them at a cost of $2 each. In this case, her opportunity cost would be the gadgets she could have purchased, which works out to $24 / $3 = 8 units.

Therefore, the opportunity cost is 8 units.

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A. The interest Bianca earned for a period of 3 years is $382.50. The correct option is B. $382.50

B. The number of years Bianca kept the account open is 11 years

From the question, we are to calculate how much interest Bianca will earn for a period of 3 years

From the simple interest formula, we have that

S.I = PRT

Where S.I is the simple interest

P is the principal

R is the rate

and T is the time

From the given information

P = $3,000

R = 4.25% = 0.0425

T = 3

Therefore,

S.I = $3,000 × 0.0425 × 3

S.I = $382.50

B.

From the given information, Bianca receives $4,402.50 when she closes the account

Thus,

The simple interest = $4,402.50 - $3,000

Simple interest = $1402.5

We are to calculate how many years Bianca kept the account open. That is, T

Using the formula,

S.I = PRT

$1402.5 = $3000 × 0.0425 × T

$1402.5 = $127.5 × T

T = $1402.5/$127.5

T = 11

Hence, the time is 11 years

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The question is a word problem, where; the amount of money Alex has is the same as the amount Monte will have if he gives Alex $12, and the amount of money Monte will have will be twice the amount with Alex if he receives $6 from Alex, indicating that the amount of money Alex has is $30, while the amount of money with Monte is $54.

A word problem is a verbal presentation of a mathematical or science question, using words and sentences, rather than numbers and symbols, and for which the solution is found mathematically, or by using standard scientific steps.

Let x represent the amount of money Alex has, and let y represent the amount of money Monte has, we get;

x + 12 = y - 12...(1)

2·x = y + 6...(2)

Adding 12 to both sides of equation (1), we get;

x + 12 + 12 = y - 12 + 12

x + 24 = y - 0 = y

x + 24 = y

y = x + 24

Plugging in the value of y into equation (2), we get;

2·x = y + 6

2·x = x + 24 + 6 = x + 30

2·x = x + 30

Subtracting x from both sides of the above equation, we get;

2·x - x = x + 30 - x

x = x - x + 30 = 0 + 30

x = 30

The amount of money Alex has, x = $30

y = x + 24

Therefore; y = 30 + 24 = 54

The amount of money Monte has, y = $54

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Answer: $2.25

Step-by-step explanation:

We are required to find the cost per kilometer of Emmanuel.

   The cost per kilometre is $2.25 OR $2 and 25cents.

According to the question, the total cost of the journey = $32

The total distance covered during the journey =

14 2/9 km

Therefore, the cost per kilometre can be evaluated mathematically as follows;

Cost per kilometer = cost of the journey ÷ Distance of the journey

= 32 ÷ 14 2/9

By converting 14 2/9 to an improper fraction; we have;

   = 32 ÷ 128 / 9

   = 32 × 9/128

   = (32×9) / 128

   = 288 / 128

   = 2 32/128

   = 2.25 dollar per kilometer

Therefore, the cost per kilometer is $2.25

Answer:

-4

Step-by-step explanation:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-8)}{0-2}=\frac{8}{-2}=-4[/tex]

The slope of the line that passes through the points (2, -8) and the origin is calculated using the formula m = rise/run, which gives -4.

In this Mathematics problem, we are asked to find the slope of the line that passes through two points using the formula m = rise/run, where 'm' is the slope. The points provided are (2, -8) and the origin, which is (0, 0).

To find the slope (rise/run), we can subtract the y-values (rise) and the x-values (run) of the two points, respectively. So, the formula becomes: m = (-8 - 0) / (2 - 0) => m = -8/2 = -4.

Therefore, the slope of the line that passes through the points (2, -8) and the origin is -4.

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On solving the provided question we can say that to plot data - dread = $0.16; Turkey = $1.24; Cheese = $0.30

The most typical approach to display data using a chart is a graph that shows the relationship between two additional variables. Diagrams created by hand or on a computer are also acceptable. Move 2 units to the right after starting at the origin before going 3 units up. The coordinates for the points 2, 3, should be shown on the coordinate plane. Clearly state your points. The pink dot with the letter P thus stands for 2.3. Before creating a line chart, you need first generate a number line for each value in your data collection. Put an X (or dot) over each value of the data on the number line after that. For each instance when a value appears in a record, place an X over the corresponding number.

to plot data -

dread = $0.16

Turkey = $1.24

Cheese = $0.30

Lettuce = $0.06

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One of the common terms for exponential decay is half-life, which refers to the period of time it takes for a quantity to fall by an exponential rate and halve its initial value.

In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time. It can be written as [tex]y = a(1 - b)^x[/tex], where y represents the final amount, a represents the initial amount, b represents the decay factor, and x is the amount of time that has passed.

The exponential decay formula aids in determining the rapid decline over time, or exponential decline. The exponential decay formula is used to calculate various types of decay, including radioactivity decay, half-life, and population decay.

The time it takes for a quantity to drop by an exponential rate to halve its initial value is known as the half-life, which is one of the popular words used to describe exponential decay.

Each 20 minutes there is 1/2 as much    one hour is 3 half lives :

start 30      then    15     then    7.5     then   3.75  gm

30(1/2)3 = 3.75 gm

The complete question is;

Write an exponential decay function to model each situation. Then find the value of the function after the given amount of time. Bismuth-214 has a half-life of approximately 20 minutes. Find the amount of bismuth-214 left from a 30-gram sample after 1 hour.

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Answer:

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

Solve each equation.

1)

2)

3)

The final statement is: The square roots of 529 are [tex]529^{1/2}[/tex]  -23 and 23

The square root of a number is defined as the value, which gives the number when it is multiplied by itself. The radical symbol √ is used to indicate the square root. For example, √16 = 4. The radical symbol is also called a root symbol or surds.

Given here: The number 529 and to find its square root equivalent.

We know 529=23² and (-23)²=529

Also √529= [tex]529^{1/2}[/tex]

Thus these are the square root equivalent of the number 529

Hence, The square roots of 529 are -23,23 and [tex]529^{1/2}[/tex]

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Answer:

false

Step-by-step explanation:

I think it's false but I don't really remember, but I would go with someones else answer cause I'm not sure

When the bargain was 40% off the standard price, the cost of the kayak trip for one adult was $53.40.

A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.

given

Shawn spent $267 on five persons,

$267 / five equals $53 (or 40%, or 40/100, or two out of five),

= $ 53.

When the bargain was 40% off the standard price, the cost of the kayak trip for one adult was $53.40.

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Answer:

The difference in elevation between the mountain and the valley is 13,158 feet.

12,790 feet (mountain elevation) - (-368 feet (valley elevation)) = 13,158 feet

Step-by-step explanation:

The Congruent Triangles figure are attached below.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.

The following the Congruent properties:

Given:

1. ΔFUN and ΔCAR

If the both triangles are congruent then

FU = CA

UN = AR

NF = RC

and, <FUN = <CAR, <UNF = <ARC and <NFU = <RCA.

This is because Congruent Triangles have Corresponding Side and angles equal in length.

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The solution of the inequality in set-builder notation is {d I d ≤ 7}.

The correct option is A.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality,

7 - 3d ≥ 28.

To solve the inequality:

Simplifying,

-3d ≥ 28 - 7

-3d  ≥ 21

-d  ≥ 7

d ≤ 7.

Therefore, the solution is {d I d ≤ 7}.

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We plotted the inequality given in question as a solid line in the graph.

In mathematics, graph of inequality means graphical representation of unequal comparison regarding an expression. Inequality having ≤ and ≥

sign is shown as a solid line. Other inequality while plotting is shown as a dotted line.

we are given an inequality x≤ - 3y

As per the rules of solving an inequality, we need to start with an isolated variable from the left side.

we notice, x is located on the left side.

the value of x must be less than or equal to -3 y. So, the graph of the inequality is located on the negative X coordinate, and it is a straight solid line. We know, the sign ≤ or ≥ indicates that inequality of the graph will be a solid line.

if we look at the graph given in question, we find that the line is drawn as a dotted line but we have less than or equal sign. So, the graph is needed to correct.

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2 is a common sample in the 2 events, therefore they are not mutually exclusive.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will discover the likelihood of outcomes for a random experiment using this fundamental probability theory, which is also applied to the probability distribution.

Two occurrences are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, provide a clear illustration.

If we roll a dice which is fair

Events that we get to shw even are = {2, 4, 6}

Events that we get when getting less that 3 = {1, 2}

So, 2 is a common sample in the 2 events, therefore they are not mutually exclusive.

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The required equation of the line is given as y = 5x -6.

Given that,
To determine the equation of a line passing through the point P(9, -8) and perpendicular to the line AB y = 3x + 6.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

The slope of the given line
y = 3x + 6.
m = 3

The equation of the perpendicular line is given as,

y - y₁ = -1/m (x - x₁)

Substitute the value in the above equation,

y + 8 = -1 / 3 (x - 9)
y = -x/3 + 3 - 8
y = -x/3 - 5

Thus, the required equation of the line is given as y = -x/3 - 5.

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Therefore , the solution to the given problem of composite number comes out to be Since Morgan's claim regarding Composite Numbers is true, we can infer that he is right.

Prime numbers can really be expressed as the sum of two different numbers. The sum of two or more numbers is what is referred to as a composite number. Examples of prime numbers include 2,3,5,71,11 since they only have two factors, one and itself. Examples of composite numbers include 4,6,8,10,12 since they contain more than two contributing variables.

Here,

we can see Morgan's claim that any numbers with a 2 in the place of a one are composite numbers.

We can conclude that Morgan is correct given the prior description of composite numbers by stating that all numbers with a 2 in the place of a one are composite numbers.

In actuality, any even integer—aside from 2—is a composite number.

Therefore , the solution to the given problem of composite number comes out to be Since Morgan's claim regarding Composite Numbers is true, we can infer that he is right.

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Answer:

true because i guessed and got it right trust me

Answer:

11x-10

Step-by-step explanation:

3x+8x-10............

On solving the provided question, we can say that the linear function is  f(x) = -2x +3 and by the graph y = f(x) = -1

Two distinct but related concepts are referred to as linear functions in mathematics. A polynomial function of degree 0 or 1 is a linear function in calculus and related subjects if its graph is a straight line. Any function that depicts a straight line on a coordinate plane is said to be linear. For instance, y = 3x - 2 is a linear function since it depicts a straight line on the coordinate plane. f(x) = 3x - 2 can be used to represent the function since f(x) can be linked to y.

here,

the linear function is  f(x) = -2x +3

and by the graph y = f(x) = -2x +3 = -2(2) + 3 = -4+3 = -1

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The points on the number line are opposite numbers, so that the required answer is as attached.

A number line is a straight line which extends from negative infinity to positive infinity on which the position of all directed numbers can be located.

Directed number are numbers with sign, which shows its direction i.e negative or positive.

In the given question since the points are opposite numbers, then we have single number but opposite in directions. Therefore there must be at equal distance to point 0 on the number line.

Considering the given conditions in the question, the opposite numbers are; -5 and +5. While the point 0 is the midpoint between -5 and +5.

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The "net asset value" is used to compute both entry load as well as exit load as a percentage.

Entry load is the sum of money or fee that an investor must pay to join a scheme or a company as an investment.

Exit loads are fees or amounts collected from investors for quitting a plan or a corporation as a shareholder.

Thus, the "net asset value" is used to compute both entry load as well as exit load as a percentage.

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Answer:

y = 5

Step-by-step explanation:

2(y + 4) = 3(2y - 4)

2y + 8 = 6y - 12

-4y = -20

y = 5

Based on the equation that models the company's profit as P = 4x - 10,000, if 5,000 units are sold, the company's profit is $10,000.

The profit equation shows the difference between the revenue and the costs during a financial period.

The revenue is a product of the units sold and the number of units.

Profit, P = 4x - 10,000

Number of units sold = x

If 5,000 units are sold:

The profit = $10,000 (4 x 5,000 - 10,000)

Check:

Total revenue = $20,000 (4 x 5,000)

Unit selling price = $4

Number of units sold = 5,000

Total costs = $10,000

Thus, using the profit equation, the company generated a profit of $10,000 from selling 5,000 floats for children.

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Resolving F2 into components along the u and v axes, the magnitudes of the components are determined as 150 N and 77.6 N.

According to the sine law, the side length of a triangle should be divided by the sine of the opposite angle. That is, when we divide side a by the sine of angle A, we get the same result as side b divided by angle B and side c divided by angle C.

For the given diagram, first, draw the vector components. Then, by sine law, we get,

[tex]\begin{aligned}\frac{F_u}{\sin 75^{\circ}}=\frac{F_2}{\sin 75^{\circ}}=\frac{F_v}{\sin 30^{\circ}}\end{aligned}[/tex]

Now, substitute the value of F₂, and we get,

[tex]F_u=F_2=\mathrm{150\;N}[/tex]

Now, solve for [tex]F_v[/tex], we get,

[tex]\begin{aligned}F_v&=\frac{F_2\sin 30^{\circ}}{\sin75^{\circ}}\\&=\mathrm{\frac{150\;N\times 0.5}{0.966}}\\&=\mathrm{77.64\;N}\end{aligned}[/tex]

The required answers are 150 N and 77.64 N.

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After 1 year Charles will earn $187 more kelvin

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

The interest rate of Kelvin's investment is 2.6% anually.

The interest rate of Charles' investment is 4.3% anually

The amount received by kelvin = 11000 + 11000× 2.6/100

= 11000+ 286 = $11286

The amount received by Charles = 11000 + 11000× 4.3/100

= 11000+ 473 = $11473

The difference in what Charles earn and kelvin earn is = 11473 - 11286 = $187

Therefore Charles will earn $187 more than kelvin

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The value of the given fraction is -1.33.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Any number can be expressed as fractions.

Given is an expression in fractions of the form,

(1 - 5) / (6 - 3) = (-4) / 3

Actually we got an improper fraction here.

Improper fractions have larger value on the numerator than the denominator.

If we need the answer in decimal form, just divide the number 4 by 3 and give negative sign for the answer.

So here the given answer is -1.33.

Hence the decimal form of the fraction (-4)/3 is -1.33.

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