What is the point slope form of the line with slope −3/7 that passes through the point (5, 8)?

Each piece is approximately (2.67) yards long.

To find the length of each piece, we divide the total length of the ribbon (8 yards) by the number of pieces (3).

First, we set up the division:

[tex]\[ \frac{8 \text{ yards}}{3} \][/tex]

Now, let's perform the division:

[tex]\[ 8 \div 3 = 2 \, \text{with a remainder of } 2 \][/tex]

So, each piece is [tex]\(2 \frac{2}{3}\)[/tex] yards long.

To express the length in a mixed number (a whole number plus a fraction), we rewrite [tex]\(2 \frac{2}{3}\)[/tex] as:

[tex]\[ 2 + \frac{2}{3} \][/tex]

To convert the fraction into yards, we multiply the numerator (2) by the unit fraction [tex]\(\frac{1}{3}\)[/tex]:

[tex]\[ 2 \times \frac{1}{3} = \frac{2}{3} \][/tex]

So, each piece is [tex]\(2 \frac{2}{3}\)[/tex] yards long, or [tex]\(2\frac{2}{3}\)[/tex] yards.

Alternatively, in decimal form:

[tex]\[ 2 \frac{2}{3} \text{ yards} = 2.666... \text{ yards} \][/tex]

So, each piece is approximately (2.67) yards long.

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]

Name the corresponding part if RST WXY.

Answer:

RS = WX

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:

[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 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

The polynomial which is written in ascending order is:

           [tex]-11-6x+2x^2+8x^3[/tex]

To write the polynomial in ascending order means to write it in the increasing powers of x.

Here the polynomial which is written in ascending order is:

                 [tex]-11-6x+2x^2+8x^3[/tex]

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.

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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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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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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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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a. At least 108 tickets must be sold to cover the cost.

b. To make a $980.68 profit, 230 tickets must be sold.

To solve this problem, let's break it down step by step:

a. To cover the cost of $859.32, we need to find out how many tickets need to be sold at $8 each.

Let's denote:

C = total cost of the dance

T = number of tickets sold

P = price per ticket

Given:

C = $859.32

P = $8

We can use the formula: Cost = Number of tickets * Price per ticket

So, we have:

859.32 = T * 8

To find T, divide both sides by 8:

T = 859.32 / 8

T = 107.415

Since we can't sell a fraction of a ticket, we round up to the nearest whole number.

T = 108

Therefore, at least 108 tickets must be sold to cover the cost.

b. To make a $980.68 profit, we need to find out how many tickets must be sold.

Profit = Total Revenue - Total Cost

Profit = (Price per ticket * Number of tickets) - Total Cost

Given:

Profit = $980.68

Total Cost = $859.32

Price per ticket = $8

Let T represent the number of tickets to be sold.

So, we have:

Profit = (8 * T) - 859.32

We want to solve for T:

Profit + Total Cost = Price per ticket * Number of tickets

Profit + Total Cost = 8T

(Profit + Total Cost) / Price per ticket = T

(980.68 + 859.32) / 8 = T

1840 / 8 = T

T = 230

Therefore, to make a $980.68 profit, 230 tickets must be sold.

Complete Question:

It costs $859.32 to have a school dance. The dance is $8 per ticket.

a. How many tickets must sold to cover the cost?

b. How many tickets must be sold to make a $980.68 profit?

the answer to your question is g=3 1/2

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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LCM of 15 & 6 = 30

 then take the highest exponent for each variable

 answer is:

30x^4y^8z^9

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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