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The required, two expressions are not equivalent, and Pat's claim is false.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
a) To show that Pat is wrong, we can substitute p = 3 into both expressions and compare the results:

4 - (p + p + p) = 4 - (3 + 3 + 3) = 4 - 9 = -5

4 - p + p + p = 4 - 3 + 3 + 3 = 7

Since the two expressions have different values when p = 3, Pat's claim is false.

b) Simplifying each expression algebraically, we have:

4 - (p + p + p) = 4 - 3p

4 - p + p + p = 4 + p

Therefore, the two expressions are not equivalent, and Pat's claim is false.

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Answer: variable Y, coefficient 11, Constant 4.5

Step-by-step explanation:

variable: Y

coefficient: 11

Constant: 4.5

The price after the reduction is 0.72x

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

Original price = x

Reduction = 28%

Using the above as a guide, we have the following:

Reduced price = Original price * (1 - Reduction)

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

Reduced price = x * (1 - 28%)

Evaluate

Reduced price = 0.72x

Hence, the reduced price is 0.72x

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Answer:

9 ft

Step-by-step explanation:

63 divided by 7 is 9.

Hope this helped!

The answer is 6.03 did this help?

The value of x will be 12. For the given image.

The arc length formula for a circle is times the radius of a circle. Arc length ( Angle x radius ) is a way to express the arc length formula in radians.

By dividing the arc length by the circle's circumference and multiplying the result by 360 degrees, one can calculate the angle of an arc. 0

To calculate the value of x make the equation below,

x / 4 = 18 / 6

x = ( 18 x 4 ) / 6

x = 12

Therefore, the value of x will be 12.

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The  orientation and ratio of the sides of the similar right triangles are  presented as follows;

(a)  ΔZXY ` ΔZYW ~ ΔYXW

(b) ZX/YX =  XY/WX

ZW/ZY =  ZY/ZX

Similar triangles are triangles that have the same shape but may have different  size.

(a) Similar triangles are triangles that have congruent internal angles.

Making use if the angles of the triangle, we get;

∠x ≅ ∠x  (reflexive property of congruency)

∠YZW ≅  ∠YZWX (All 90 degrees angle are congruent)

Therefore; ΔZXY ~ ΔZYW by AA similarity postulate

Similarly; ΔZXY is similar to ΔYXW by AA similarity postulate

The similar triangles are therefore;

(b) The proportion of the corresponding sides of similar triangles are equivalent, and the cosine of an angle in a right  triangle is the ratio of the adjacent side to the hypotenuse side, therefore;

ZX/YX =  XY/WX

The tangent  of an interior angle of a right triangle is the ratio of the opposite side to the adjacent side of the right triangle, therefore;

ZW/ZY =  ZY/ZX

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Answer:

difference: -4 cubic inches

% change: -10%

Step-by-step explanation:

The difference between the new volume and the original volume is ...

 (new volume) - (original volume) = (36 in³) - (40 in³) = -4 in²

__

The percentage change is figured with respect to the original volume:

 % change = (difference)/(original volume) × 100% = (-4 in³)/(40 in³) × 100%

 = -1/10 × 100% = -10%

By answering the above question, we may state that So, 5333/10000 of linear equationthe cookies in the cookie jar are oatmeal cookies with nuts.

In algebra, a linear equation is one that of the form y=mx+b. The slope is B, and the y-intercept is m. As y and x are variables, the previous sentence is frequently referred to as a "linear equation with two variables". Bivariate linear equations are linear equations with two variables. Linear equations may be found in many places, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the structure y=mx+b, where m denotes the slope and b the y-intercept, it is referred to as being linear. A mathematical equation is said to be linear if its solution has the form y=mx+b, where m stands for the slope and b for the y-intercept.

For the sake of a simple computation, let's say that the cookie jar contains 100 cookies.

The issue states that 4/5 of the cookies in the jar are oatmeal cookies. So,

80 oatmeal cookies are equal to 4/5 * 100.

Two thirds of the oatmeal cookies have nuts in them. So,

2/3 times 80 equals 53.33 oatmeal cookies with nuts (approx)

As a result, the percentage of cookies in the cookie jar that are made with oats and nuts is:

53.33/100 = 0.5333

This is expressed as a fraction:

0.5333 = 5333/10000

So, 5333/10000 of the cookies in the cookie jar are oatmeal cookies with nuts.

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use the process of elimination, once you solve, it will give you one variable that will work for both equations, once you plug that in, it will give you the other variable.

7x + 3y = 13

2x -3y   = -4

add the "y"; 3y + (-3y) = 0

9x = 9

x = 1

plug in the "x" value into either question to solve for "y"

7(1) + 3y = 13

7 + 3y = 13

3y = 6

y = 2

Answer:

Step-by-step explanation:

7x + 3y = 13

2x -3y   = -4

add the "y"; 3y + (-3y) = 0

9x = 9

x = 1

plug in the "x" value into either question to solve for "y"

7(1) + 3y = 13

7 + 3y = 13

3y = 6

y = 2

Step-by-step explanation:

1) length of YZ:

[tex]YZ=\sqrt{XZ^2-XY^2} ;= > \ YZ=8.485=8.5;[/tex]

2) angle X:

[tex]m \angle X=arccos(\frac{XY}{XZ});= > \ m \angle X=arccos\frac{1}{3}=70.6 к;[/tex]

3) angle Z:

[tex]m \angle Z=arcsin(\frac{XY}{XZ});= > \ m \angle Z=arcsin\frac{1}{3}=19.4 к;[/tex]

The height of the water in the tank after 5 minutes is approximately 732.6 inches.

V = πr²h, where V is a cylinder's volume, r is its radius, and h is its height, is the formula for calculating a cylinder's volume. The formula is created by first determining the area of the cylinder's base, which equals r2, and then multiplying that area by the cylinder's height to determine the volume. The volume of tanks, pipelines, and other cylindrical objects may be calculated using this formula, among many other uses.

The volume of a cylinder, which is:

V = πr²h

Given that, diameter is 15 feet, so the radius is 7.5 feet.

Also,

2 feet per second = 2 * 12 * 60 inches per minute = 1440 inches per minute

V = πr²h

Substituting the values:

V = π(7.5)^2(14405)

Here, 14405 is the amount of water that flows into the tank in 5 minutes.

Divide the volume of water by the area of the base of the cylinder

V/A = h

2,044,123/(π(7.5)^2) ≈ 732.6 inches

Hence, the height of the water in the tank after 5 minutes is approximately 732.6 inches.

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Mr. Hamstra can travel about 70 miles when his tank is 1/4 full.

The distance a car can go on a given quantity of gasoline is measured as gas mileage, also known as fuel efficiency. By dividing the distance driven by the amount of gasoline used, one may determine gas mileage. For instance, a car's gas mileage is 25 mpg (300/12 = 25) if it can go 300 miles on 12 gallons of petrol. Many variables, including traffic, speed, weather, road gradient, and vehicle maintenance, can have an impact on gas mileage.

Given that, Mr. Hamstra’s car holds 14 2/5 gallons of gas and averages 20 miles per gallon.

Thus, when his tank is 1/4 full, it contains:

1/4 * 14 2/5 = 14 2/5 / 4 = 3 1/2 gallons.

Hence, Mr. Hamstra can travel about 70 miles when his tank is 1/4 full.

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All statements and reasons are shown below.

A triangle is a closed two-dimensional geometric shape that has three sides, three angles, and three vertices. Triangles are one of the basic shapes in geometry and can be classified according to the length of their sides (scalene, isosceles, or equilateral) or the size of their angles (acute, right, or obtuse). The sum of the angles of a triangle is always 180 degrees, and the Pythagorean theorem can be used to find the length of one side if the other two sides are known in a right triangle.

According to the given figure:

4. In ΔFGH and ΔFJH,

        Statement                                   Reason

5. In ΔTVY and ΔXWY,

        Statement                                   Reason

6. In ΔKML and ΔPMN,

        Statement                                   Reason

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Answer:

In business and economics, cost, revenue, and profit are key concepts that relate to the financial aspects of a business.

Cost refers to the expenses incurred by a business in order to produce, sell or distribute its products or services. This includes direct costs, such as the cost of raw materials, labor and overhead expenses, as well as indirect costs, such as marketing and administrative expenses.

Revenue, on the other hand, refers to the income generated by a business through the sale of its products or services. Revenue can be calculated by multiplying the price of a product or service by the number of units sold.

Profit is the difference between revenue and cost, and is a measure of how much money a business earns after all of its expenses are paid. A business earns a profit when its revenue exceeds its total costs, including both fixed and variable costs.

Profit can be further broken down into gross profit and net profit. Gross profit is the difference between revenue and the direct cost of producing or delivering a product or service. Net profit, on the other hand, is the profit that remains after all expenses, including indirect costs, taxes and interest payments, have been deducted from revenue.

In summary, cost refers to the expenses incurred by a business, revenue refers to the income generated by the sale of products or services, and profit is the difference between revenue and cost, indicating how much money a business earns after all expenses are paid.

Step-by-step explanation:

Horizontal cross-sections of the prisms at the same height have the same area.

Option D.

A right rectangular prism is a three-dimensional shape with six faces which are all rectangles. It has twelve edges and eight vertices.

An oblique triangular prism is a prism with 2 congruent triangular faces and 3 rectangular faces at an angle to the triangular faces.

This is the volume of solid figures concept.

The volume of a prism is obtained by multiplying the area of its base to its height. If the two given solid figures have the same volume and the same height then, the areas of their bases are also equal.

In this case, the height of the right rectangular prism and the oblique triangular prism are 12 cm and both prisms have the same volume, we can conclude that:

Horizontal cross-sections of the prisms at the same height have the same area.

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Answer:

Step-by-step explanation:

To solve the equation graphically, we need to first rearrange it into the form of y = f(x). So, let's simplify the given equation:

(x - 3)² - 2 = x + 1

Expanding the left side:

x² - 6x + 9 - 2 = x + 1

Simplifying:

x² - 7x + 6 = 0

Now we can graph the function y = f(x) = x² - 7x + 6 and the line y = x + 1 on the same coordinate axes and find their intersection points.

Here's a graph of the function and the line:

Graph of y=x^2-7x+6 and y=x+1

We can see that the two curves intersect at two points, which have x-coordinates of approximately 1.2 and 5.8. So, the solutions to the equation are x ≈ 1.2 and x ≈ 5.8.

Answer:

Yes he was correct in returning the 100

Step-by-step explanation:

Pen 68.75

Pencil 73.50

Paint box 112.35

Add all together, you get 254.60

If he paid 500 to the shopkeeper, he will collect (500.00-254.60) =245.40

If the shopkeeper gave him 345.40, then he had an excess and should give back the 100

10 3/8. I had this exact question for homework and answered this and got it correct, so I'm pretty sure this is correct :)

The total surface area of the given solid is 256 inch²

Surface area is the measure of the total area that the surface of an object occupies. It is usually expressed in square units, such as square meters, square centimeters, or square feet.

Here in this problem take the surface of the solid as the number of faces and calculate the area of each face as shown below.

Here we have

Solid box with dimensions 4 in, 5 in, and 8 in

The surface of the given solid can be divided as given in the picture

The surface area of the shape = Sum of areas of [ 1 to 12 faces ]

Area of (1, 2, 3, 7, 8, 9 faces ) = 6 (4 × 4 )= 96 inch²  

Area of (4, 5, 6, 10, 11, 12 faces ) = 6 (5 × 4) = 120 inch²    

Area of bottom = (8 × 5) = 40 inch²  

Total Surface area = [ 96 + 120 + 40 ] = 256 inch²

Therefore,

The total surface area of the given solid is 256 inch²

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Answer:19?

Step-by-step explanation:

b. The distance between points K and L is 10 units.

c. ΔJKL is not an equilateral triangle.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

Given points as:

J (-5,-3)

K (1,5),

L (7,-3)

b. To determine the distance between points K and L, we can use the distance formula:

distance = √(x₂ – x₁)² + (y₂ – y₁)²

Substituting the coordinates of K and L, we get:

distance = √((7 - 1)² + (-3 - 5)²)

distance = √(36 + 64)

distance = √(100)

distance = 10

Therefore, the distance between points K and L is 10 units.

c. To determine if JKL is an equilateral triangle, we need to check if all three sides have the same length.

We can find the lengths of each side using the distance formula:

JK = √((1 - (-5))² + (5 - (-3))²) = √(6^2 + 8²) = 10

KL = 10 (as we found in part b)

LJ = √((-5 - 7)² + (-3 - (-3))²) = √((-12)²) = 12

Since all three sides have different lengths (JK and KL are 10 units, while LJ is 12 units), JKL is not an equilateral triangle.

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Answer: m∠G = 41°

Step-by-step explanation:

      Opposite angles of parallelograms are congruent. This means that m∠G = m∠E, so we can write an equation using the given information.

Given:

      m∠G = m∠E

Substitue:

      5x - 9 = 3x + 11

Add 9 to both sides of the equation:

      5x = 3x + 20

Subtract 3x from both sides of the equation:

      2x = 20

Divide both sides of the equation by 2:

      x = 10

      Then, we will substitute this value of x back into the expression for m∠G.

5x - 9 = 5(10) - 9 = 50 - 9 = 41°

2 times the square root of 48 minus the square root of 3 simplified is 7√3.

what is square root?

The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, it is the inverse operation of squaring a number. For example, the square root of 16 is 4 because 4 multiplied by itself (4 x 4) equals 16.

The symbol used to represent the square root is √. So, the square root of 16 is written as √16.

To simplify this expression, we can first simplify the square root of 48.

We know that 48 can be written as 16 x 3, and since 16 is a perfect square, we can simplify the square root of 48 as follows:

√48 = √(16 x 3) = √16 x √3 = 4√3

Now we can substitute this value into the expression:

2(4√3) - √3 = 8√3 - √3 = 7√3

Therefore, 2 times the square root of 48 minus the square root of 3 simplified is 7√3.

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Because the denominators of both fraction have been changed to 7/8=21/24 and 5/6=20/24, respectively,

In mathematics, a denominator is the lowest number in such a fraction that indicates how many equal parts are split into a whole. It is a fraction's divisor.

Divisor is another synonym for denominator. In a common fraction, the integer under the line is described by both of these terms. Similar to this, when discussing statistical values, the term "denominator" refers to the entire population or number out of which samples are selected.

Common denominator is going to be [tex]24[/tex]

[tex]8=2*2*2\\6=2*3\\24=2*2*2*3[/tex]

[tex]8[/tex] should be multiplied by [tex]3[/tex]

[tex]6[/tex] should be multiplied by [tex]4[/tex]

[tex]7/8=(7*3)/(8*3)=21/3\\5/6=(5*4)/(6*4)=20/24\\7/8=21/24\\5/6=20/24[/tex]

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Answer:

4=20

3=?

so 20×3 divide by 4 = 15

Step-by-step explanation:

Answer:25

Step-by-step explanation: 25 25 25

Answer:

26

Step-by-step explanation:

(6x + 4) + (4x + 6) = 90

180 - (4x + 6) = (6x + 4) + 90

Rearrange the equation.

180 - (-90) = (6x + 4) + (4x + 6)

270 = 6x + 4 + 4x + 6

270 = 10x + 10

260 = 10x

26 = x

I don't know if this is correct, so I apologize if its wrong.

Answer:

x = 8

Step-by-step explanation:

According to the picture,

These given two angles are complementary. That is, those two angles are added up to 90°.

Therefore,

( 6x + 4 ) + ( 4x + 6 ) = 90

Combine like terms.

6x + 4 + 4x + 6 = 90

10x + 10 = 90

Subtract 10 from both sides.

10x = 90 - 10

10x = 80

Divide both sides by 10.

x = 8

The area of the part that is painted blue is 679 ft.

What are the basic arithmetic operations?

The four basic arithmetic operations are addition, subtraction, multiplication, and division.

Arithmetic operations are the building blocks for all mathematical processes and methods. (Yeah, they’re kind of a big deal!) These types of operations are part of the “arithmetic” branch of math.

Arithmetic operations strip math down to the basics that we use every day, whether we realize it or not. Those basics are addition, subtraction, multiplication, and division.

The area

= 20×30+(1/2)×20×(40-30) -3x5 - 2×3

= boot 10x10- 15-6

= 700-21

= 679

Hence, The area of the part that is painted blue is 679 ft.

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The decay of Element X can be modeled by the equation:

N = N0 * (1/2)^(t/t1/2)

where N is the amount of Element X remaining after time t, N0 is the initial amount of Element X, t1/2 is the half-life of Element X, and ^(t/t1/2) denotes exponentiation with base 1/2.

We know that the initial amount of Element X is 470 grams, the half-life is 8 minutes, and we want to find the time it takes for Element X to decay to 10 grams. Let t be the time in minutes.

Then, we can set up the following equation:

10 = 470 * (1/2)^(t/8)

Dividing both sides by 470, we get:

(1/47) = (1/2)^(t/8)

Taking the natural logarithm of both sides, we get:

ln(1/47) = (t/8) * ln(1/2)

Solving for t, we get:

t = -8 * ln(47)/ln(2)

t ≈ 59.3

Therefore, it would take about 59.3 minutes, to the nearest tenth of a minute, for Element X to decay to 10 grams.