approximate
[tex] log_{3}14 + 1 [/tex]
​

The value of given expression is 341

Solution:

Given that we have to find the value of given expression

Given expression is:

[tex]4x^2 + 2x - 1[/tex]

Given value is x = 9

Substitute x = 9 in given expression

[tex]\rightarrow 4(9)^2+2(9) - 1[/tex]

Solve the above expression

[tex]\rightarrow 4 \times (9 \times 9) + 18 -1\\\\\rightarrow 4 \times 81 + 17\\\\\text{Multiply the terms 4 and 81 }\\\\\rightarrow 324 + 17\\\\\text{Add the numbers }\\\\\rightarrow 341[/tex]

Thus the value of given expression is 341

For this case we have that by definition, the perimeter of a rectangle is given by:

[tex]P = 2l + 2w[/tex]

Where:

l: It is the length of the rectangle

w: It is the width of the rectangle

According to the statement we have to:

[tex]l = w + 3 \frac {1} {6} = w + \frac {19} {6}\\P = 15 \frac {1} {3} = \frac {46} {3}[/tex]

The length and perimeter are expressed in centimeters.

Substituting we have:

[tex]\frac {46} {3} = 2 (w + \frac {19} {6}) + 2w\\\frac {46} {3} = 2w + \frac {38} {6} + 2w\\\frac {46} {3} = 2w + \frac {19} {3} + 2w\\\frac {46} {3} = 4w + \frac {19} {3}\\\frac {46} {3} - \frac {19} {3} = 4w\\\frac {27} {3} = 4w\\[/tex]

[tex]9 = 4w\\w = \frac {9} {4}[/tex]

Thus, the width of the rectangle is [tex]\frac {9} {4}[/tex] centimeters.

The length is:

[tex]l = w + \frac {19} {6} = \frac {9} {4} + \frac {19} {6} = \frac {54 + 76} {24} = \frac {130} {24} = \frac {65} {12}[/tex] centimeters.

Answer:

[tex]l=\frac{65}{12}[/tex] centimeters

[tex]w=\frac{9}{4}[/tex] centimeters

Answer:

The length of the triangle is [tex]\frac{65}{12} cm[/tex] and the width is [tex]\frac{9}{4} cm[/tex]

Step-by-step explanation:

Given

Length of the Rectangle = [tex]3\frac{1}{6}[/tex] longer than the width

Perimeter of the Rectangle = [tex]15\frac{1}{3}[/tex]

Required

What are the width and length of the rectangle.

Let L represent the length of the rectangle, W represent the width of the rectangle and P represent the Perimeter.

So, we have that

L = [tex]3\frac{1}{6}[/tex] + W

P = [tex]15\frac{1}{3}[/tex]

Perimeter of a rectangle is calculated by 2( L + W)

So,

P = 2( L + W) becomes

[tex]15\frac{1}{3} = 2(3\frac{1}{6} + W + W)[/tex]

[tex]15\frac{1}{3} = 2(3\frac{1}{6} + 2W)[/tex]

Convert fractions to improper fractions

[tex]\frac{46}{3} = 2(\frac{19}{6} + 2W)[/tex]

Open Bracket

[tex]\frac{46}{3} = 2 * \frac{19}{6} + 2 * 2W[/tex]

[tex]\frac{46}{3} = \frac{19}{3} + 4W[/tex]

Make 4W the subject of of formula

[tex]4W = \frac{46}{3} - \frac{19}{3}[/tex]

[tex]4W = \frac{46 - 19}{3}[/tex]

[tex]4W = \frac{27}{3}[/tex]

[tex]4W = 9[/tex]

Make W the subject of of formula

[tex]W = \frac{9}{4}[/tex]

Recall that

L = [tex]3\frac{1}{6}[/tex] + W

So, [tex]L = 3\frac{1}{6} + \frac{9}{4}[/tex]

[tex]L = \frac{19}{6} + \frac{9}{4}[/tex]

[tex]L = \frac{38 + 27}{12}[/tex]

[tex]L = \frac{65}{12}[/tex]

Hence, the length of the triangle is [tex]\frac{65}{12} cm[/tex] and the width is [tex]\frac{9}{4} cm[/tex]

Answer:

Solving Systems of Equations (Simultaneous Equations) If you have two different equations with the same two unknowns in each, you can solve for both unknowns. There are three common methods for solving: addition/subtraction, substitution, and graphing.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

If your on e2020 Then A is your answer

Answer:

A

Step-by-step explanation:

TOOK QUIZ MADE 100

Answer:

Yes opposite sides are parallel

Step-by-step explanation:

The 2 pairs of opposite triangles are congruent by (SAS).

Therefore alternate angles are congruent, so opposite sides are parallel.

Answer:

Step-by-step explanation:

Let the total cost for renting a car a day be X

: X = $22 + 20m cent

Answer:

we need the picture or answer choices

Step-by-step explanation:

Answer:

they are equal

Step-by-step explanation:

Both -4 4/25 and -4.16 are the same number. Neither is 'bigger' because they hold an equal value.

To determine which number is bigger between -4 4/25 and -4.16, we should understand that a larger negative number is the one closer to zero on the number line. First, let's convert -4 4/25 into a decimal format. This number is the same as -4.16 (as 4/25 is equal to 0.16).

Therefore, both -4 4/25 and -4.16 are exactly the same. In the context of negative numbers, 'bigger' means being closer to zero. Thus, neither is 'bigger' because they are equal.

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Three equivalent expressions to 24k + 12k are 36k, 12k(2 + 1), and 6k(4 + 2). To calculate Cammie's total spending on x pounds of plums and y pounds of oranges, the expression 3x + 2y is used.

Equivalent expressions for 24k + 12k can be found by combining like terms or using the distributive property. Here are three equivalent expressions:

For the second part of the question, an expression to determine the total amount Cammie will spend on x pounds of plums at $3 per pound and y pounds of oranges at $2 per pound is given by:

3x + 2y

This expression represents the total cost by multiplying the quantity of each fruit by its price and then adding the results together.

Answer:

12

Step-by-step explanation:

Answer:

Therefore, the resulting expression for the price Genevieve will pay

will be:  [tex]p-100-\frac{3}{20}p[/tex]

Step-by-step Explanation:

Let the original cost of a laptop = p dollars

So, subtract the $100 and 15% off coupon (15% off on original 'p' cost)

The resulting expression for the price Genevieve will pay can be computed as:

[tex]p-100-15\%\:p[/tex]

[tex]=p-100-15\frac{p}{100}[/tex]

[tex]=p-100-\frac{3}{20}p[/tex]        ∵ [tex]15\%\mathrm{\:in\:fractions}:\quad \frac{3}{20}[/tex]

Therefore, the resulting expression for the price Genevieve will pay

will be:  [tex]p-100-\frac{3}{20}p[/tex]

Keywords: price, algebraic expression

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For this case we must propose a rule of three:

20 people ----------------> 24 days

32 people ----------------> x

Where the variable "x" represents the number of days it takes 32 people to build the barn.

[tex]x = \frac {32 * 24} {20}\\x = \frac {768} {20}\\x = 38.4[/tex]

Thus, it takes 32 people approximately 39 days to build the barn.

Answer:

It takes 32 people about 39 days to build the barn.

To find how many days it will take 32 people to build the barn, calculate the total man-hours (20 × 24 = 480 man-hours) and divide that by the number of workers (480 \/ 32 = 15). Thus, it takes 32 people 15 days to build the barn.

The student's question involves solving a problem by understanding the concept of work rate and man-hours. To find out how many days it would take for 32 people to build a barn if it takes 20 people 24 days, we first need to calculate the total man-hours required to build the barn. The total man-hours is the product of the number of workers and the number of days they work, which in this case is 20 people × 24 days = 480 man-hours.

Once we have the total number of man-hours, we can then calculate how many days it will take for 32 people to complete the same amount of work. This is done by dividing the total man-hours by the number of workers, resulting in 480 man-hours / 32 people = 15 days.

Therefore, it will take 32 people 15 days to build the barn.

Answer:596

Step-by-step explanation:

There are a total of  216 boys in the college.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  there is an introductory engineering course if 396 students are enrolled and there are 6 boys to every five girls.

Given that the ratio of boys to girls = 6/5

Since there are a total of 396 students in the college

so.

6x + 5x = 396

11x = 396

x = 36

Thus, the number of boys in College = 36 * 6

Number of boys in college = 216

therefore, There are a total of  216 boys in the college.

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Answer:

We just add numerators and rewrite denominator.

Adding unlike dominators:

We need to find the same denominators. You need to find the least common multiple (LCM) of the two denominators.

Step-by-step explanation:

You mean unlike denominators and like denominators.

Adding like dominators: We just add numerators and rewrite denominator :

Example : [tex]\frac{1}{4} +\frac{2}{4}=\frac{1+2}{4} =\frac{3}{4}[/tex]

Adding unlike dominators:

We need to find the same denominators. You need to find the least common multiple (LCM) of the two denominators.

For example :

[tex]\frac{1}{5}+\frac{3}{4}[/tex]

LCM for 5 and 4 is 20 : Now, divide by 5 and multiply by 1 for first fraction. 20 divide by 4 and multiply by 3 :

[tex]\frac{1*4}{20} +\frac{3*5}{20}=\frac{4}{20} +\frac{15}{20}=\frac{19}{20}[/tex]

Step-by-step explanation:

If you have a problem like 1 5/21 + 3 42/56 = ?

You have to find a common denominator. So you should of got 1 280/1176 and 3 882/1176. Then you add 1 280/1176 + 3 882/1176 = 4 1162/1176. Then you need to simplify the fraction. When you simplify the fraction you get 83/84. So your answer is 4 83/84.

If you have a common denominator you save your denominator and the numerator change. If you can then simplify it.

Answer: 22

Step-by-step explanation:

3x + 5y = 2 .......................... equation 1

2x - 6y = 20 ........................... equation 2

solving the system of linear equation by elimination method. Multiply equation 1 by 2 and equation 2 by 3 , then we have

6x + 10y = 4 ............................. equation 3

6x - 18y = 60 ........................... equation 4

subtract equation 3 from equation 4 , then we have

-28y = 56

divide through by -28

y = -2

substitute y = 2 into equation 1 to find the value of x , then we have

3x + 5 (-2) = 2

3x - 10    = 2

3x = 2 + 10

3x = 12

x = 4

Therefore :

5x - y = 5 (4) - (-2)

          = 20 + 2

          = 22

The equation for a circle with center (2,8) and radius 3 is written as (x - 2)^2 + (y - 8)^2 = 9.

The question provided describes the properties of a circle and is asking for its equation.

A circle with a center (2,8) and radius 3 can be represented by the equation (x - 2)^2 + (y - 8)^2 = 3^2.

This is derived from the general equation of a circle (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center and r is the radius.

Answer:

x=2 and y=−5

Step-by-step explanation:

Answer:

9x + 5y = 29 ........... (1) and

3x + y = 7 ........... (2)

Each game of ping pong requires 1 number of token and each game of pinball requires 4 number of tokens.

Step-by-step explanation:

Let, each game of ping pong requires x number of tokens and each game of pinball requires y number of tokens.

So, from the given conditions we can write

9x + 5y = 29 ........... (1) and

3x + y = 7 ........... (2)

Now, solving equations (1) and (2) we get,

9x + 5(7 - 3x) = 29

⇒ 35 - 6x = 29

⇒ 6x = 6

⇒ x = 1 token.

Now, putting x = 1 in equation (2) we get,

3 + y = 7

⇒ y = 4 tokens.

So, each game of ping pong requires 1 number of token and each game of pinball requires 4 number of tokens. (Answer)

Answer:

5

Step-by-step explanation:

Answer:

Part A) Circumference

Part B) [tex]C=\pi D[/tex]

Part C) The distance traveled in one rotation is 628.32 feet

Step-by-step explanation:

Part A) we know that

The distance around the circle is equal to the circumference.

The Ferris Wheel have a circular shape

so

To find out the distance around the Ferris Wheel you should use the circumference

Part B) What is the formula needed to solve this problem?

we know that

The circumference is equal to multiply the number π by the diameter of the circle

so

[tex]C=\pi D[/tex]

Part C) What is the distance traveled in one rotation?

we know that

One rotation subtends a central angle of 360 degrees

The distance traveled in one rotation is the same that the circumference of the Ferris wheel

we have

[tex]D=200\ ft[/tex] ----> diameter of the Ferris wheel

substitute in the formula of circumference

[tex]C=\pi (200)\\C=200\pi\ ft[/tex]

assume

[tex]\pi=3.1416[/tex]

[tex]C=200(3.1416)=628.32\ ft[/tex]

therefore

The distance traveled in one rotation is 628.32 feet

Step-by-step explanation:

Let:

x=length

(x/4)+1=width

P=2l+2w

62=2x + 2[(x/4)+1]

62=2x + 1/2x + 2

multiply both sides by 2

124=4x+x+4

5×=120

x=24

length: 24 inches

width: 7 inches

hope this helps!!

Answer: 68%

Step-by-step explanation: Since Tim made 85 free throws out of 125 free throws in total, we have the fraction 85/125 where 85 represents the number of free throws Tim made out of all of the free throws he shot last season.

To write the fraction 85/125 as a percent, remember that a percent is a ratio that compares a number to 100. So we need to find a fraction equivalent to 85/125 that has a 100 in the denominator. We can do this by setting up a proportion.

So we have [tex]\frac{85}{125} = \frac{n}{100}[/tex] where n is our variable.

Now using cross products to find the missing value in the proportion, we have 85 x 100 which is 8,500 = 125 x n or 125n

Now just divide both sides by 125 and we find that 68 = n.

This means that Tim made 68% of his free throws.

Answer:

∠ C < ∠ B < ∠ A.

Step-by-step explanation:

The length of the sides of a triangle are proportional to the measurement of its opposite side and vice-versa.

Now, in a triangle Δ ABC the opposite angle of side AB is ∠ C, the opposite angle of the side BC is ∠ A and the opposite angle of the side CA is ∠ B.

So, if it is given that AB < AC < BC, then we can say that ∠ C < ∠ B < ∠ A. (Answer)

Answer:

the melting point of water is 0

Answer:

Part A)

The unit price for the 12-cupcake option is $

2.42

The unit price for the 24-cupcake option is $

2.33

The unit price for the 50-cupcake option is $2.58

Part B) The 24-cupcake option has the lowest unit price

Part C) see the explanation

Part D) see the explanation

Step-by-step explanation:

Part A) Find each unit price to the nearest cent

we know that

To find out the unit rate divide the cost by the number of cupcakes

so

Part 1) 12 cupcakes for $29

[tex]\frac{29}{12}=\$2.42\ per\ cupcake[/tex]

Part 2) 24 cupcakes for $56

[tex]\frac{56}{24}=\$2.33\ per\ cupcake[/tex]

Part 3) 50 cupcakes for $129

[tex]\frac{129}{50}=\$2.58\ per\ cupcake[/tex]

Par B) Which option gives the lowest unit price?

The 24-cupcake option has the lowest unit price

Part C) One way to convert from inches to centimeters is to multiply the number of inches by 2.54. How many centimeters are in 1/4 inch?

Multiply 1/4 inches by 2.54

(1/4)(2.54)=0.635 cm

Part D) A stack of 500 pieces of paper is 1.875 inches tall.

Find the thick of each piece of paper

Divide 1.875 inches tall. by 500 pieces

[tex]\frac{1.875}{500}=0.00375\ in/piece[/tex]

therefore

Diego is incorrect

The unit price for the 12-cupcake is $2.42.

The unit price for the 24-cupcake is $2.32.

The unit price for the 50-cupcake is $2.58.

The 24-cupcake option has the lowest unit price.

It is 0.636cm centimeters are in 1/4 inch.

The thick of each piece of paper is 0.00375cm per paper.

Given that,

A sign in a bakery gives these options:

12 cupcakes for $29

24 cupcakes for $56

50 cupcakes for $129

We have to determine,

Find each unit price to the nearest cent.

According to the question,

Price for 12 cupcakes for $29.

Unit price of 12-cupcakes = [tex]\rm\frac{29}{12} = 2.42[/tex]

The unit price for the 12-cupcake is $2.42.

Price for 24 cupcakes for $56.

Unit price of 24-cupcakes = [tex]\rm\frac{56}{24} = 2.33[/tex]

The unit price for the 24-cupcake is $2.32.

Price for 50 cupcakes for $129.

Unit price of 50-cupcakes = [tex]\rm\frac{129}{50} = 2.58[/tex]

The unit price for the 50-cupcake is $2.58.

To centimeters are in 1/4 inch.

Multiply 1/4 inches by 2.54,

[tex](\frac{1}{4} )(2.54)=0.635 cm[/tex]

It is 0.636cm centimeters are in 1/4 inch.

The thick of each piece of paper,

Divide 1.875 inches tall. by 500 pieces for thick of each piece of paper,

[tex]= \frac{1.875}{500} \\\\= 0.00375cm[/tex]

The thick of each piece of paper is 0.00375cm per paper.

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ANSWER: y= 3x - 6

STEP-BY-STEP EXPLANATION:

(1,-3) and (3,3)

X1=1           X2=3

Y1= - 3       Y2=3

1) Find the slope of the line.

To find the slope of the line passing through these two points we need to use the slope  formula:

m = [tex]\frac{Y2-Y1}{X2-X1}[/tex]

m= [tex]\frac{3-(-3)}{3-1}[/tex]   m=[tex]\frac{6}{2}[/tex] = 3

2)Use the slope to find the y-intercept.

Now that we know the slope of the line is 3 we can plug the slope into the equation and  we get:

y= 3x+b

Next choose one of the two point to plug in for the values of x and y. It does not matter  which one of the two points you choose because you should get the same answer in either  case. I generally just choose the first point listed so I don’t have to worry about which  one I should choose.

y= 3x+b       point (1,-3)

-3= 3(1) + b

-3-3=b

-6=b

3)Write the answer.

Using the slope of 3 and the y-intercept of -6 the answer is:

y = 3x - 6

Missing term = –2xy

Solution:

Let us first find the quotient of [tex]-8x^2y^3 \div xy[/tex].

[tex]-8x^2y^3 \div xy=\frac{-8x^2y^3 }{xy}[/tex]

                    [tex]=\frac{-8\times x\times x\times y\times y\times y}{xy}[/tex]

Taking common term xy outside in the numerator.

                    [tex]=\frac{xy(-8\times x\times y\times y)}{xy}[/tex]

Both xy in the numerator and denominator are cancelled.

                    [tex]=-8xy^2[/tex]

Thus, the quotient of [tex]-8x^2y^3 \div xy[/tex] is [tex]-8xy^2[/tex].

Given the quotient of [tex]-8x^2y^3 \div xy[/tex] is same as the product  of 4xy and ____.

[tex]-8xy^2=4xy[/tex] × missing term

Divide both sides by 4xy, we get

⇒ missing term = [tex]\frac{-8xy^2}{4xy}[/tex]

Cancel the common terms in both numerator and denominator.

⇒ missing term = –2xy

Hence the missing term of the product is –2xy.

Answer:

y = 9/10

Step-by-step explanation:

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1 - 2/3y = 6/15   Isolate/get y by itself, first subtract 1 on both sides

-2/3y = 6/15 - 1       [to combine fractions, they need to have the same denominator]

-2/3y = 6/15 - 15/15

-2/3y = -9/15        Multiply the inverse of -2/3, which is -3/2 on both sides to get y by itself

y = 27/30      Simplify

y = 9/10