One number is 3 more than 2 times the other, and their sum is 27. find the numbers. if x represents the smaller number, then the larger number is 3x + 2 2x + 3 2(x + 3)

The converse, inverse, and contrapositive of the given statement are provided. They are logically consistent with the original statement, pointing to the synonymous relationship between congruence and identical length in segments. The additional statement about angles is also factual, as one greater than an acute angle is, by definition, an obtuse.

1.) Converse: If two segments have the same length, then they are congruent.
2.) Inverse: If two segments are not congruent, then they do not have the same length.
3.) Contrapositive: If two segments do not have the same length, then they are not congruent.

The contrapositive is true because it is a logical inverse of the original statement, which is also true. In geometry, congruent means being of the same size and shape, which directly implies having the same length.

4.) The statement: 'If m∠A is greater than an acute ∠B, then ∠A must be obtuse' is true. An acute angle is one that is less than 90 degrees. If ∠A is greater than this, it must be between 91 and 180 degrees, which by definition, makes it an obtuse angle.

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The expression of the word problem can be written as M-99=299 where M is 398.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that 99 subtracted from m is 299. The expression for the word problem can be written as:-

M-99=299

M = 299 + 99

M = 398

Therefore, the expression of the word problem can be written as M-99=299 where M is 398.

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Rammy can buy 5 pounds or less of peaches that is x ≤ 5. Then the correct option is B.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Rammy has $9.60 to spend on some peaches and a gallon of milk. Peaches cost $1.20 per pound, and a gallon of milk costs $3.60.

The inequality 1.20x + 3.60 ≤ 9.60 models this situation, where x is the number of pounds of peaches.

Then the number of pounds of peaches can Rammy buy will be

1.20x + 3.60 ≤ 9.60

           1.20x ≤ 6

                  x ≤ 5

Rammy can buy 5 pounds or less of peaches that is x ≤ 5. Then the correct option is B.

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Final answer:

To find the cost of each slice of white chocolate torte, divide the total cost to produce two tortes ($11.90) by the total number of slices (16), resulting in approximately 74 cents per slice.

Explanation:

Cost of Each Slice of White Chocolate Torte

To calculate the cost of each slice of white chocolate torte, we start by determining the total cost of producing the tortes. The restaurant's cost is $11.90 for 2 tortes, and each torte is cut into 8 slices. This means there's a total of 2 tortes × 8 slices/torte = 16 slices. Dividing the total cost by the number of slices gives us the cost per slice:

Total cost for 2 tortes: $11.90

Number of slices per torte: 8

Total number of slices: 2 tortes × 8 slices/torte = 16 slices

Cost per slice: $11.90 / 16 slices = $0.74375 per slice

Therefore, each slice costs approximately 74 cents to make.

The value of the equation 3ab - 9ab + 7ab is [tex]\boxed{ab}[/tex].

Further explanation:

There are two properties.

1. The property of addition or property of sum.

2. The property of subtraction.

3. The property of division.

4. The property of multiplication.

Given:

The equation is 3ab - 9ab + 7ab.

Explanation:

Consider the equation S = 3ab - 9ab + 7ab.

The equation contains the two variables that are “a” and “b”.

In the equation we have two operations one is addition and another is subtraction.

Solve the above equation to obtain the value of the equation.

First add 3ab and 7ab.

[tex]\begin{aligned}X&=3ab+7ab\\&=10ab\\\end{aligned}[/tex]

Now subtract 9ab from 10ab.

[tex]\begin{aligned}S&=10ab-9ab\\&=1ab\\&=ab\\\end{aligned}[/tex]

The value of S is ab.

Hence, the value of the equation 3ab - 9ab + 7ab is [tex]\boxed{ab}[/tex].

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Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Number System

Keywords: property, zero, eight, sum, addition, identity, shows, subtraction, number sentence, division, multiplication, variables.

Answer: [tex] f(x)=54205(0.87)^t[/tex]

Step-by-step explanation:

Given: The initial value of cement mixer (A) = $54,205

After one year, the value of mixer = $47,158.35

The constant rate of depreciation (b)=[tex]\frac{47158.35}{54205}=8.7[/tex]

The exponential function represent the value after depreciation of t years is given by :-

[tex]f(t)=A(b)^t\\\\\Rightarrow\ f(x)=54205(0.87)^t[/tex]

Hence, the function best represents the value of the cement mixer after t years will be

[tex] f(x)=54205(0.87)^t[/tex]

The conjugate of the complex number -8 + 2i is -8 -2i. By multiplying the complex number by its conjugate we get the answer 68, which corresponds to option C.

To solve this question, we first need to know what a conjugate is. In complex numbers, if a number is represented as a + bi, its conjugate will be a - bi. The provided complex number in the question is -8 + 2i, so its conjugate would be -8 - 2i.

Next, we multiply the complex number by its conjugate. This would give us (-8 + 2i) × (-8 - 2i). Executing this multiplication based on the rule of multiplication of brackets (a+b)(a-b) = a2 - b2, we have (-8)2 - (2i)2, which results in 64 - (-4) = 68.

Therefore, the product of (-8 + 2i) and its conjugate is equal to 68, which is option C.

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Mr. Staley buy 20 binders for his mathematics class.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Mr. Staley has $62 to buy binders for his mathematics class.

And, The cost of each binders = $3

Now,

Since, The cost of each binders = $3

Hence, Number of binders = $62 / $3

                                          = 20.67

Since, We get the remainder 2 and the quotient is 20.

So, we get;

Mr. Staley buy 20 binders for his mathematics class.

Thus, Mr. Staley buy 20 binders for his mathematics class.

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Answer:

[tex]m\angle WYX=20^{\circ}[/tex]

[tex]m\angle WYZ=70^{\circ}[/tex]

Step-by-step explanation:

We have been given that [tex]m\angle WYX=(4x-8)^{\circ}[/tex] and [tex]m\angle WYZ=(10x)^{\circ}[/tex].

Since ∠WYX and ∠WYZ are complementary, so they will add up-to 90 degrees.

[tex]m\angle WYZ+m\angle WYX=90^{\circ}[/tex]

Substitute the given values:

[tex]4x-8+10x=90[/tex]

Combine like terms:

[tex]14x-8=90[/tex]

[tex]14x-8+8=90+8[/tex]

[tex]14x=98[/tex]

[tex]\frac{14x}{14}=\frac{98}{14}[/tex]

[tex]x=7[/tex]

Let us substitute [tex]x=7[/tex] in measure of each angle as:

[tex]m\angle WYX=(4(7)-8)^{\circ}[/tex]

[tex]m\angle WYX=(28-8)^{\circ}[/tex]

[tex]m\angle WYX=20^{\circ}[/tex]

Therefore, the measure of angle WYX is 20 degrees.

[tex]m\angle WYZ=(10x)^{\circ}[/tex]

[tex]m\angle WYZ=(10(7))^{\circ}[/tex]

[tex]m\angle WYZ=70^{\circ}[/tex]

Therefore, the measure of angle WYZ is 70 degrees.

Answer:

the top tier is 64 cubic centimeters

the middle tier is 576 cubic centimeters

the bottom tier is 1728 cubic centimeters

the entire cake is 2368 cubic centimeters

The answer is Standard.

The same old shape for linear equations in variables is Ax+with the aid of=C. as an example, 2x+3y=five is a linear equation in popular shape. whilst an equation is given on this form, it is pretty clean to discover each intercept (x and y). This form is likewise very beneficial while fixing structures of two linear equations.

There are three major types of linear equations: point-slope shape, well-known shape, and slope-intercept shape.

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Answer:

[tex]AC=25[/tex]

Step-by-step explanation:

From the given figure, it can be seen that [tex]{\angle}A={\angle}C[/tex], thus ΔABC is an isosceles triangle.

Therefore,[tex]AB=BC[/tex]

⇒[tex]5x+5=7x-1[/tex]

Solving the above equation, we get

⇒[tex]5x-7x=-1-5[/tex]

⇒[tex]-2x=-6[/tex]

⇒[tex]x=3[/tex]

Now, substituting the value of x in AC, we have

⇒[tex]AC=6x+7[/tex]

⇒[tex]AC=6(3)+7[/tex]

⇒[tex]AC=18+7[/tex]

⇒[tex]AC=25[/tex]

Thus, the length of the side AC of the given triangle is 25 units.

The width of the porch is 5 feet.

Let's denote the width of the porch as x. The length of the porch is then x + 4. The area of a rectangle is given by length x width. So, we can set up the equation x(x + 4) = 75 to find the width of the porch. Expanding the equation, we get x² + 4x = 75. Rearranging the equation, we have x² + 4x - 75 = 0. This quadratic equation can be factored as (x - 5)(x + 15) = 0. Since the width of the porch cannot be negative, we discard the x + 15 = 0 solution. Therefore, the width of the porch is 5 feet.

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The distributive property demonstrated.

4(3 + 5) = 4 • 3 + 4 • 5

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

Given:

Expression,

4(3 + 5) = 4 • 3 + 4 • 5

Here,

we take LHS,

4(3 + 5)

= 4 x 3 + 4 x 5

= 12 + 20

= 32

We take RHS,

4 • 3 + 4 • 5

= 12 + 20

32.

So, this property is distributive property.

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There are 48639 ways for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard

The probability of an event is defined as the possibility of an event occurring against sample space.

[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]

Permutation is the number of ways to arrange objects.

[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]

Combination is the number of ways to select objects.

[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]

Let us tackle the problem.

This problem is similar to Pascal Triangle.

The Lord can move to the right or up in one way only.

We can put "1" in each box on the bottom and left to represent 1 possible movement.

To get the possibility of movement to another box, we will add the possibility of movement to the left, right, and diagonal squares as shown in Figure 1.

This process is repeated for the next box as shown in Figure 2.

Finally, after this process is repeated until the top right box, we get the results as shown in Figure 3.

There are 48639 ways for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard.

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation

Rewrite the given equation in slope intercept form:

5 y = 10 – 2 x

y = - 0.4 x + 2

Since the two lines are parallel, therefore they have similar slope which is – 0.4, so the equation is:

y = - 0.4 x + b

Given that x = 5, y = -4, find for b:

-4 = - 0.4 (5) + b

b = -2

So the answer is:

y = - 0.4 x – 2

or

2 x + 5 y = - 10

The interest for each loan is $40.32, $4, $175 and $468 respectively.

The formula to find the simple interest is S.I=P×T×R/100.

Where, P=Principal, T=Time period and R=Rate of interest.

With P=$252, T=2 years and R=8%.

Now, SP=252×2×8/100=$40.32

With P=$400, T=6 months (0.5 years) and R=2%.

Now, SP=400×0.5×2/100=$4

With P=$5000, T=1 year and R=3.5%.

Now, SP=5000×1×3.5/100=$175

With P=$6,240, T=9 months (0.75 years) and R=10%.

Now, SP=6,240×0.75×10/100=$468

Therefore, the interest for each loan is $40.32, $4, $175 and $468 respectively.

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Answer:

The dog  is rather running towards the trainer to receive a treat. So it is the second answer.

Name the corresponding part if RST WXY.

Answer:

RS = WX