Find the numbers. A room is 12 feet longer than it is wide. Half the perimeter of the rectangular floor is 72 feet. Find the length and the width. Use elimination or substitution to solve this problem.

In order for a triangle to shrink in size but stay proportional to its original size, the scale factor, K, must be between zero and one.

What is scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

In order for a triangle to shrink in size but stay proportional to its original size, the scale factor, K, must be between zero and 1.

The image is contracted if the scale factor is less than 1 (0< k <1).

The image is enlarged if the scale factor is more than 1 (k > 1).

The image remains the same if the scale factor is 1 (k = 1).

Hence, the scale factor k should be between 0 and 1.

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Answer:

Can you please show the picture

Step-by-step explanation:

In 7th grade math, students learn basic algebra, ratios and proportions, geometry, graphing, probability, equation and statistics.

In 7th grade math, students typically learn basic algebraic principles, including linear equations, variables, and functions. They also learn about ratios, proportions, and percents. Geometry is typically introduced, with topics such as angles, lines, triangles, and circles. Additionally, students may be taught more advanced topics such as graphing, probability, and statistics.In 7th grade math, students learn basic algebra, ratios and proportions, geometry, graphing, probability, and statistics.

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Answer:

5.4

Step-by-step explanation:

"The 'Angle Bisector' Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle."

thus,

DB/AB = DC/AC

2.8/AB = 3/5.8

multiply both sides by AB to make it a numerator

2.8 = 3*AB/5.8

multiply both sides by 5.8/3 to isolate AB

2.8 * 5.8/3 = AB = 5.413 ≈ 5.4

Therefore , the solution of the given problem of triangle comes out to be

AB length = 5.4 units.

In a plane, any three points can be joined to form triangles, which have three sides and three angles. They were among the first geometrical forms to be investigated. Because each polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle, they are especially significant.

Here,

According to the "Angle Bisector Theorem," a triangle's opposing side will be divided into two segments that are proportional to the other two sides.

thus,

DC/AC = DB/AB.

2.8/AB = 3/5.8

By multiplying both sides by AB, the numerator is created.

2.8 = 3*AB/5.8

To distinguish AB, multiply both sides by 5.8/3.

2.8 * 5.8/3 = AB = 5.413 ≈ 5.4

Therefore , the solution of the given problem of triangle comes out to be

AB length = 5.4 units.

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Answer:

$302

Step-by-step explanation:

p(x) 3x^4 = x^4-3x^2+5

We put 3 in for x and solve

3(3)^4 = 3^4 -3(3)^2 + 5

3(81) = 81 -3(9) + 5

243 = 81 - 27 + 5

243 = 59

Then we add 243 with 59 and get

$243 + $59 = $302

So, they spend together $302

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3x-y=-9

Step-by-step explanation:

Answer: 3x - y = - 9

Step-by-step explanation:

Re-write the equation in the following form:

3x + 9 = y

Take the y to LHS:

3x + 9 - y = 0

Now, take the 9 to the RHS:

3x - y = -9. This is your answer.

Answer:

P = 12.50 + 1.25t

Step-by-step explanation:

To find an equation to represent the price of a pizza, we need to first figure out the original price of a pizze.
Since the price is 16.25 dollars, and there are 3 toppings, each of which cost 1.25, the original price would be:

16.25 - 3(1.25) = 12.50

Thus, we can represent the cost of a pizze with toppings as:
P = 12.50 + 1.25t, where P = Price and t = amount of toppings.

Hope this helps!

Answer:

6

Step-by-step explanation:

The growth factor is the number that is raised to an exponent.

Answer: 6

Because the sine and cosine ratios involve dividing a leg (one of the shorter two sides) by the hypotenuse (the longest side), the ratio values will never be greater than one, because (some number) / (a larger number) is always less than one.

Sine & cosine are trigonometric functions of an angle in mathematics. In the context of a right triangle, the sine and cosine of an acute angle are defined as follows: for the specified angle, the sine is the ratio of the length of the side opposite that angle to the length of the triangle's longest side (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse.

The sine and cosine functions for an angle θ are simply denoted as sin θ and cos θ. In general, the definitions of sine and cosine can be extended to any real value expressed in terms of the lengths of specific line segments in a unit circle.

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In 5 years the population will be fewer than 13000.

What is percentage ?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. Percentage, a relative value showing hundredth parts of any amount, is a relative measure that indicates how many questions on a test you correctly answered out of 100 (75/100). Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified percentage.

20000( 1 - 9% )^5

≈ 12481

12481 < 13000

ie 5 years

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Ai Mi have to pay $10.50 to buy 3 pounds of chicken.

An expression for the cost to buy pp pounds of chicken, assuming at least one pound is purchased.

Cost = (3.5 * pp) - 2.5

The cost to buy 3 pounds of chicken without the coupon would be 3 * $3.50 = $10.50

With the coupon, Ai Mi would have to pay $10.50 - $2.50 = $8.

The expression for the cost to buy pp pounds of chicken:

Cost = (3.5 * pp) - 2.5

Here, pp represents the number of pounds of chicken that Ai Mi wants to buy.

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The number of hours that Julius can spend online this week is 1 1/3 hours.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Julius is allowed to surf the internet for only 3 hours a week. He has already been online for 1 2/3 hours this week.

This will be Illustrated as x.

x + 1 2/3 ≤ 3.

x ≤ 3 - 1 2/3

x ≤ 1 1/3.

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Answer:

9 ft

Step-by-step explanation:

assuming the 3 was a mistake T'T volume is l x w x h so if the base is l x w then 12 x 14 (168) is the base then divide the volume from the base (1512 / 168) the answer is 9 ft

The bake sale sign has a 6 ft2 space.

An object's area is how much space it takes up in two dimensions.

It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The word "area" refers to a free space.

A shape's length and width are used to compute its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc.

But a shape's area is a two-dimensional measurement. In order to measure something in a square, it is done so using measurements like square inches (in2), square feet (ft 2), square yards (yd2), etc.

The majority of forms and things have corners and edges. 

According to our question-

The opposite sides of a rectangle's quadrilateral (it has four sides and four angles) are equal and parallel.

Area of a rectangle equals length times width.

The area of the bake sale sign = length * breadth

Hence, The bake sale sign has a 6 ft2 space.

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Answer:

-3 (x - 4) (x - 1)

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 6.5 when x = 1.3

6.5 = 1.3k ( divide both sides by 1.3 )

5 = k

y = 5x ← equation of variation

expression h-9 is represented as statement 'h decreased by 9'.

Subtraction is an operation used to find the difference between numbers. When you have a group of objects and you take away a few objects from it, the group becomes smaller. For example, you bought 9 cupcakes for your birthday party and your friends ate 7 cupcakes. Now you are left with 2 cupcakes. This can be written in the form of a subtraction expression: 9 - 7 = 2 and is read as "nine minus seven equals two".

Given expression

h-9

Here h is a variable, 9 is constant and - is the symbol of subtraction.

the phrase "decreased by" tells us to use subtraction.

Statement for the above expression

h decreased by 9.

Hence, the statement 'h decreased by 9' represents expression h - 9.

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The amount of mold after n days is 3 × (1.5)ⁿ⁻¹.

Geometric progression is a sequence of numbers such that the ratio of two consecutive numbers is the same for whole sequence.

This ratio is common ratio.

At first, mold was 3 cm², then 4.5 cm², and it was increasing each day by 50%.

a₁ = 3

a₂ = 4.5

a₃ = 4.5 + (4.5 × 50%) = 6.75

.............

Here the common ratio, r = a₂/a₁ = a₃/a₂ = ..... = 1.5

n th term of a GP = a rⁿ⁻¹, where a is the first term and r is the common ratio.

Area of mold after n days = 3 × (1.5)ⁿ⁻¹

Hence the mold at any time can be calculated by the formula 3 × (1.5)ⁿ⁻¹.

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We can use the Z-score formula to determine what percent of patients have a score equal to or lower than the patient's score of 45 on the cognitive abilities test.

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

The Z-score formula is:

Z = (X - M) / SD

Where:

X = Patient's score (45)

M = Mean score (52)

SD = Standard deviation (5)

Plugging in the given values:

Z = (45 - 52) / 5

Z = -7 / 5

Z = -1.4

This Z-score of -1.4 corresponds to a percentage of approximately 9.1% of patients who have a score equal to or lower than the patient's score of 45 on the cognitive abilities test.

It is important to note that this percentage is approximate, as it's calculated based on the standard normal distribution table which provides approximate values, and it assumes the scores of the test are normally distributed, in case this assumption is not met the result may not be accurate.

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2 is not a polynomial root of  [tex]x^{3} + 4x^{2} + 3x[/tex] . A polynomial is an equation that employs addition, subtraction .

A polynomial is a mathematical statement made up of variables (also known as indeterminates) and coefficients that uses solely the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that employs addition, subtraction, multiplication, and division of numbers to combine variables, constants, and exponents (No division operation by a variable).

given

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

= [tex]2^{3} + 2^{2} + 3(2) = 0\\8 + 4 + 6 = 0 \\18= 0[/tex]

Consequently, 2 is not a polynomial root of  [tex]x^{3} + 4x^{2} + 3x[/tex] .

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The probability that 3 or more copies will be demanded in a particular day is 0.64.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The probability for 3 or more copies to be demanded is the sum of all the probability distributions for 3 or more copies demanded per day.

This can be written in an equational form -

P(x) = 0.14 + 0.12 + 0.10 + 0.08 + 0.07 + 0.06 + 0.04 +0.03

P(x) = 0.64

Therefore, the probability is 0.64.

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We have P(A ∩ B) is 2/5  and P(A ∪ B) is 5/5.
Lincoln and West Pine high schools offer both hockey and golf.

P(A ∩ B) is the probability that a randomly chosen high school has both a hockey team and a golf team. The probability that a school picked at random offers both hockey and golf is 2/5 (Lincoln and West Pine are the only schools that offer both out of 5 total schools.)

East Valley, Lincoln, West Pine, Adams and North River high schools offer hockey or golf or both.

P(A ∪ B) is the probability that a randomly chosen high school has either a hockey team or a golf team or both. The probability that a school picked at random offers either hockey or golf or both is 5/5 (All 5 high schools in the district offer at least one of the sports.)

Therefore, the correct answers of the problem statement are P(A ∩ B) is 2/5  and P(A ∪ B) is 5/5.

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Therefore, the fraction 5/4 in this equation represents the growth factor of the height of the item over time.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

The total number of equally sized components chosen is shown in the numerator. The denominator, however, shows the total number of equal pieces.

The fraction 5/4 in this equation represents the growth factor of the height of the item over time. The value of 3 in front of the fraction is the initial height and the exponent x represents the number of days that have passed, so the height of the item increases by a factor of 5/4 for every additional day. The height equation represents exponential growth.

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Answer:

To find the sale price of the suit, we need to first calculate the discount. The discount is equal to the original price multiplied by the discount rate, which in this case is $280 * 30% = $84.

Then we subtract the discount from the original price to find the sale price: $280 - $84 = $196.

So the sale price of the suit is $196.

Step-by-step explanation:

Sandra needs to score at least 87.67% to get an average score of 85%.

Let's look at the average formula in more detail in this part and use some examples to illustrate how it may be used. The following is an example of the average formula for a specific set of data or observations: Average = (Sum of Observations) ÷ (Total Numbers of Observations).

Given, Sandra has taken 3 Test this Quarter. She has scored an 78%, 76%, and a 93%.

Now as per the question she needs 85%.

The average of the 1st three tests is 78+76+93/3 = 247/3 = 82.33

Now to get 85%, we have to average out as 82.33+x/2 = 85

x+82.33 = 85*2 = 170

x = 170-82.33 = 87.67

Hence, Sandra needs to score at least 87.67% to get an average score of 85%.

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Answer:

3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18.

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The values of x and y, given the angles, can be found to be :

The parallel line is drawn such that ( 7 y - 12 ) degrees and ( 6 y + 8 ) degrees are equal to each other.

In the same vein, 4x degrees and 6x - 26 degrees are the same as well. This is because they are vertical angles.

The value of x is:

4x = 6x - 26

6x - 4 x = 26

2x = 26

x = 26 / 2

x = 13

The value of y is :
7 y - 12 = 6 y + 8

7y - 6 y = 8 + 12

y = 20

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Answer:

1.Given points are:-

(1,2)=(x1/,y1)

(3,4)=(x2,y2)

Now,from two point formula,

y-y1=(y2-y1)/(X2-X1)×(X-X1)

or,y-2=(4-2)/(3-1)×(X-1)

or,y-2=2/2×(X-1)

or,y-2=1(X-1)

or,y-2=X-1

or, X -1-y+2=0

or,X-y+1=0 is the req. eqn in standard form

2.Given points are:-

(2,5)=(x1, y1)

(3,7)=(x2,y2)

Now, from two point formula,

y-5=(7-5)/(3-2)×(X-2)

or,y-5=2/1×(X-2)

or,y-5=2(X-2)

or,y-5=2X-4

or,2X-y-4+5=0

or,2x-y+1=0 is the req. eqn in standard form.

c.do similarly

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Answer:

see explanation

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

First obtain the equations in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

(1)

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 2 ) and (x₂, y₂ ) = (3, 4 )

m = [tex]\frac{4-2}{3-1}[/tex] = [tex]\frac{2}{2}[/tex] = 1 , then

y = x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 4 ) , then

4 = 3 + c ⇒ c = 4 - 3 = 1

y = x + 1 ( subtract y from both sides )

0 = x - y + 1 ( subtract 1 from both sides

- 1 = x - y , that is

x - y = - 1 ← in standard form

Use the same procedure for the next 2 questions

(2)

(x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (3, 7 )

m = [tex]\frac{7-5}{3-2}[/tex] = [tex]\frac{2}{1}[/tex] = 2 , then

y = 2x + c ← is the partial equation

using the point (2, 5 ) to find c

5 = 2(2) + c = 4 + c ( subtract 4 from both sides )

1 = c

y = 2x + 1 ( subtract y from both sides )

0 = 2x - y + 1 ( subtract 1 from both sides )

- 1 = 2x - y , that is

2x - y = - 1 ← in standard form

(3)

(x₁, y₁ ) = (5, 2 ) and (x₂, y₂ ) = (3, 12 )

m = [tex]\frac{12-2}{3-5}[/tex] = [tex]\frac{10}{-2}[/tex] = - 5 , then

y = - 5x + c

using the point (5, 2 ) to find c

2 = - 5(5) + c = - 25 + c ( add 25 to both sides )

27 = c

y = - 5x + 27 ( add 5x to both sides )

5x + y = 27 ← in standard form

As you can see, 5y is an external angle of triangle ABC

we know that 5y=180-x

since angle B is 40, and angle A=x and C=x, we have

x%2Bx%2B40=180

2x=180-40

x=140%2F2

x=70

so, angle A=70 and C=70

then

5y=180-70

5y=110

y=110%2F5

y=22

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