8th grade math
Subject in math: comparing ratios and graphs

Among the given numbers, [tex]\sqrt{17} > \frac{22}{7}[/tex]

We have two numbers, which are 22/7 and [tex]\sqrt{17}[/tex]

Both of the numbers are irrational numbers, they are nonrepeating and nonterminating.

A fraction written in a particular way is called decimal form.

Now, evaluating both the given numbers in decimal form, we get,

22/7 = 3.14

and [tex]\sqrt{17} = 4.12[/tex]

Now, Clearly, 4.12 > 3.14

Thus, [tex]\sqrt{17} > \frac{22}{7}[/tex]

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The cost of the sheet metal per square foot is $30.

The first step is to determine the square feet that the contractor used. This can be determined by subtracting the square feet of sheet she bought from the sheet metal she has used so far.

Sheet metal used = 8.2 - 2.1 = 6.1 square feet.

This means that 6.1 square feet costs $183.

The second step is to determine the cost of one square feet of sheet metal. This can be determined by dividing $183 by 6.1

$183 / 6.1 = $30

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a) Given the triangle ABC, you have to do a counterclockwise 90º rotation of the figure.

To make said rotation you have to invert the coordinates of each point of the figure and invert the sign of the x-coordinate of the image point.

In general:

Preimage point; Image point

P(x,y) → P'(-y,x)

The y-coordinate turns into the x-coordinate and the x-coordinate turns into the y-coordinate.

The x-coordinate of the image point must have the opposite sing as the original one.

So for triangle ABC:

A to A'

(3,-2) → (-(-2),3)= (2,3)

B to B'

(3,-6) → (-(-6),3)= (6,3)

C to C'

(9,-2) → (-(-2),9)= (2,9)

The coordinates for the 90º counterclockwise rotation are A'(2,3), B'(6,3) and C(2,9)

b) Triange A'B'C' was translated a certain number of units, its new position is given as triangle A''B''C'':

A''(-3,-4)

B''(1,-4)

C''(-3,2)

To determine what kind of translation was done, first step is to draw triangle A''B''C'' and compare it to triangle A'B'C':

As you can see in the graphic, triangle A'B'C' was translated horizontally to the left a k number of units and vertically downwards a m number of units.

Horizontal translation

These translations are made over the x-axis, the translation factor k is added (movement to the rigth) or subtracted (movement to the left) from the x-coordinate of each point:

In this case the translation was made to the left, so:

Preimage point; Image point

P(x,y) → P'(x-k,y)

Vertical translation

These translations are made over the y-axis, this means that the translation factor m will be added (↑up) or subtracted (↓down) from the y-coordinates of each point.

For the example, the movement was downwards so we can express it as:

Preimage point; Image point

P(x,y) → P'(x,y-m)

You can unite both movements in the same expression as:

Preimage point; Image point

P(x,y) → P'(x-k,y-m)

Going a little further you can determine the amount of units the figure was translated by comparing a set of points from the preimage and image:

Given A'(2,3) and A''(-3,-4)

For the horizontal movement compare the x-coordinates. We know that to determine the x-coordinate of A'', k units were subtacted from the x-coordinate of A', so:

2-k=-3

-k=-3-2

-k=-5

k=5

For the vertical movement, compare the y-coordinates of both point. We know that m units were subtracted from the y-coordinate of A' to determine the y-coordinate of A'', so:

3-m=-4

-m=-4-3

-m=-7

m=7

This means that the translation rule for A'B'C' → A''B''C'' is (x-5,y-7)

Explanation

Let the unknown pack of books x. Therefore;

Hence;

Answer: Mr Valentino can buy approximately 3 packs

Answer:

31.7 units²

Step-by-step explanation:

Since the two semicircles have the same radius, they have the same combined area as a full circle.

Rectangle: length 10; width 6

Circle: diameter 6; radius 3

area = area of rectangle - area of circle

area = LW - πr²

area = 10 × 6 - 3.14159 × 3²

area = 60 - 28.27431

area = 31.72569

Answer: 31.7 units²

Given:

1. Arrange the expression, with the variables are written first

2. Distribute the "minus" operation

3. Expand by multiplying the first two expressions

*multiply the first terms

*multiply the outer terms

*multiply the inner terms

*multiply the last terms

This will give us:

*combine like terms

*Remove the parenthesis

4. Combine like terms

The final answer would be:

If Mr. Jones served 85 hot dogs to 50 people the proportion of hot dogs is:

If he expects 68 people at the fall picnic, the amount of hot dogs he will need is the number of people multiplied by this proportion:

Answer

The proportion that could be used to find how many hot dogs Mr. Jones will need for the fall picnic is 85/50

He will need 115.6 hot dogs (since the number of hot dogs is a whole number, He will have to buy 116 hot dogs)

Parallel lines will have the same slope.

Then we can calculate the slope for this line and it will be the same for all its parallel lines.

Given two points (x1,y1) = (6,2) and (x2,y2) = (-6,3) we can calculate the slope m as:

The slope for this line and all its parallels is m = -1/12.

Answer: -1/12

Answer:

Yes

Step-by-step explanation:

Answer: yes it is linear

Step-by-step explanation: linear line is a straight line and y=-4 is 1 line so it is linear

the Answer:is y=-3x+1 so it would b c:)

The depth of the diver after 4 minutes when a scuba diver descends below the surface of a lake at a rate of 12 feet per minute is 48 feet.

The concept that is used in the solution is the concept of rate in mathematics. A rate can be described as a special ratio having two terms that are in different units.

The rate that is been given is 12 feet per minute which implies that 12 feet will operate at the time of 1 minute. Then we were now given the depth of the diver after 4 minutes, using the given rate, then ;

12feet = 1mins

X feet = 4mins

where X is the depth of the diver after 4 minutes then we can cross multiply,

X= (4mins *12feet) / 1mins

= 48feets.

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Answer:

Step-by-step explanation:

decrese by 10

The expression that could represent how much flour Lena uses for baking cookies and bread is 2c + 2 1/2b + 1/2.

What is an algebraic expression?

An algebraic expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.

For example 2x + 4, 58m + 2n, 100p + 3q + r.

According to the given question:

(Question with options is attached below)

Let c be the number of cookie batches and b be the number of bread loaves Lena makes.

Lena makes 2 cups of flour for a batch of cookies

∴ Flour used to make cookie batches = 2c

She uses 2 1/2 cups for loaf of bread

∴ Flour used for bread loaves = 2 1/2 b

Ans 1/2 cup flour is used for dusting workbench

Hence expression for the amount of flour used is sum of flour used for making batches of cookies, bread loaves and for dusting.

The expression is 2c + 2 1/2b + 1/2

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Answer:

First you need to know how many feet are in a mile (5280 ft) and so you would multiply this by 3 and to show your work because teachers need that now sadly you do this

[tex]3x5280=[/tex]

15820

:)

The average force that the table applies to the cat is 40N, by using newton's law.

What is the meaning of acceleration?

Acceleration: the rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting.

Given that the mass of the cat is 4 kg. The gravity is 10 meters per second-squared.

Force is the product mass and acceleration.

Mass = 4 kg

Acceleration = 10 ms⁻².

The force that  the table applies to the cat  is (4 kg × 10 ms⁻²) = 40 N.

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If Alejandro has a computer support business. The number of customers he will need in order to break even is 38 customers.

Given data:

Cost of business = 48 x + 500

Income = R = 65 x - 145

Let x is the number of customers. He

Income equation  

R= 65x- 145

Substitute 48x + 500  for y

48x + 500 = 65x -145

Substract 48x from both side

500 = 17x - 145

Add 145 to each side

645 = 17x

Divide both side by 17x

x =645 /17

x = 37.9

x = 38 customers (Approximately)

Therefore the number or customers is 38 customers.

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Let's begin by listing out the information given to us:

Expanded notation is a form of writing in which the value of each digit; it arranges the digit in their values of tens, hundreds, tens etc.

Hence, option B is the correct answer

The value of x for which the perimeter of the rectangle is less than 128 is x < 30.

The perimeter of a rectangle is the sum of the whole sides of a rectangle. Recall a rectangle is a quadrilateral with opposite sides equal to each other and opposite side parallel to each other.

Therefore, the perimeter of the rectangle is less than 128.

Hence,

perimeter of a rectangle = 2(l + w)

perimeter of a rectangle = 2l + 2w

where

Therefore,

2(x + 4) + 2x < 128

2x + 8 + 2x < 128

4x + 8 < 128

4x < 128 - 8

4x < 120

Therefore,

x < 30

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80.64% probability that a component is at least 10 centimeters long.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean  and standard deviation , the z-score of a measure X is given by:

Z = x - μ / σ

Z-scores are used to measure how far a measure is from the mean. We find the p-value associated with this Z-score by looking at the z-score table after finding the Z-score. The p-value represents the probability that the measure is smaller than X, which is the percentile of X. The probability of the measure being greater than X is calculated by subtracting 1 from the pvalue.

μ = 14

Variance is 9.

The standard deviation is the square root of the variance.

So,

σ = √9 = 3

This is the pvalue of Z when X = 10

z = 10 - 14/3

z = -1.3

z = -1.3 has a p value of0.1936

1-0.1936 = 0.8064

80.64% probability that a component is at least 10 centimeters long.

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Answer:

0.7475

Step-by-step explanation:

The mean is μ=14, and the standard deviation is σ=9‾√=3.Open Excel.  Click on an empty cell.  Type =NORMDIST(12,14,3,1) and press ENTER.The probability, rounded to four decimal places, is P(X<12)≈0.2525.The desired probability is P(X≥12), so subtract from 1 to get P(X≥12)=1−0.2525=0.7475

Answer

The equation of the line is

y = (-x/7)

We can cross multiply and write it in the form of

7y = -x

OR

x + 7y = 0

Explanation

The slope and y-intercept form of the equation of a straight line is given as

y = mx + b

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

b = y-intercept of the line.

The relationship between the slopes of two lines that are perpendicular to each other is

m₁m₂ = -1

m₁ = Slope of line 1

m₂ = Slope of line 2

For the given equation, if we compare its equation with y = mx + b,

y = 7x - 3

y = mx + b

m = 7, b = -3

We can now find the slope of the line we want.

m₁m₂ = -1

m₁ = 7

m₂ = ?

m₁m₂ = -1

(7)m₂ = -1

7m₂ = -1

Divide both sides by 7

(7m₂/7) = (-1/7)

m₂ = (-1/7)

Then we can find the equation of the line we want.

For that line,

m = slope = (-1/7)

b = y-intercept (where the line crosses the y-axis) = 0

This is obtained from the point given that the line passes through the origin, (0, 0)

So, we can write y = mx + b

y = (-1/7)x + 0

y = (-x/7)

We can cross multiply and write it in the form of

7y = -x

OR

x + 7y = 0

Hope this Helps!!!

We can find the orthogonal vector when we use the dot product.

Then, the result must be equal to zero.

The vector u is given by coordinates <-7,-4>

Then, we need to find a vector in which their dor product will be equal to zero:

<-7,-4>*<1/7,-1/4> =-7*1/7 +(-4)*-1/4 = -1+1 =0

Therefore, the orthogonal vector is <1/7,-1/4>

The correct answer is option B

Answer:

Step-by-step explanation:

1.c

2.c

3.a

4.d

5.d

6.c

7. they are equal

8 A.a

8 B.d

9 A. c

9 B. b

10 A.c

10 B. b

11.b

12.d

13.b

14.b

15. a

16.d

17.c

18. 26.56 degrees

Answer: The answer is 64-18 so its 46 hope i helped

Step-by-step explanation:

64-18

Explanation

we can easily solve this by checking the equation

It is writen in slope- y intercept fom

hence

I hope this helps you

we have

y = - 3/5x - 3

To graph the line we need at least two points

so

Find the intercepts

step 1

Find the y-intercept (value of y when the value of x is zero)

For x=0

y=-(3/5)*(0)-3

y=-3

the y intercept is the point (0,-3)

step 2

Find the x-intercept (value of x when the value of y is zero)

For y=0

0=-(3/5)x-3

(3/5)x=-3

x=-5

so

the x-intercept is the point (-5,0)

step 3

Graph the line

Plot the intercepts and join them to draw the line

using a graphing tool

see the attached figure

please wait a minute

Answer:

Step-by-step explanation:

y=−

5

3x

​

−3

2 Add 33 to both sides.

y+3=-\frac{3x}{5}

y+3=−

5

3x

​

3 Multiply both sides by 55.

(y+3)\times 5=-3x

(y+3)×5=−3x

4 Regroup terms.

5(y+3)=-3x

5(y+3)=−3x

5 Divide both sides by -3−3.

-\frac{5(y+3)}{3}=x

−

3

5(y+3)

​

=x

6 Switch sides.

x=-\frac{5(y+3)}{3}

x=−

3

5(y+3)

​

Answer:

23,207/210

Step-by-step explanation:

[tex]\int\limits^7_4 {x^{2}+\frac{1}{x} } \, dx \\[/tex]

Right endpoints start at 7

It doesn't say how many so I will assume there are 3.

7, 6, 5

Plug in those values into the integrand:

7^2+ 1/7=

49+1/7

6^2+1/6=

36+1/6

5^2+1/5=

25+1/5

1(49+1/7+36+1/6+25+1/5)

110+1/7+1/6+1/5 The least common factor of 7,6,5 is 210

[tex]110 + \frac{30+35+42}{210} \\110 + \frac{107}{210} \\\frac{23,100+107}{210} \\\\\frac{23,207}{210} \\[/tex]

Answer:the real answer is (-2,1), (-1,4), (1,2)

Step-by-step explanation:

pls mark brainliest

Answer:

A. 0.5x² - 6x + 10

hope you get a point

ok

Could you send me all the options?

A function is a relationship between two magnitudes (x, y). In which, each value of the first corresponds to a single value of the second

Answer:

Shorter leg = 2.5 ft

Longer leg = 6.5 ft

Step-by-step explanation:

          Let the shorter leg = x ft

                       Longer leg =  (x + 4) ft

                     Hypotenuse = 7 ft

                   [tex]\sf x^2 + (x +4)^2 = 7^2[/tex]

     x² + x² + 2*x*4 + 4²   = 49

        x² + x²+ 8x + 16      = 49

         2x² + 8x + 16 - 49 = 0

           2x² + 8x - 33       = 0  

This is a quadratic equation. We can use the below mentioned formula to find the value of x.

a = 2 ; b = 8 ; c = -33

b² - 4ac = 8² - 4 * 2 * (-33)

             = 64 + 264

             =328

[tex]\sf x = \dfrac{-b \± \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\sf x = \dfrac{-8 \±\sqrt{328}}{2*2}\\\\\\x= \dfrac{-8 \±18.11}{4}\\\\\\x =\dfrac{-8+18.11}{4} ; \ x=\dfrac{-8-18.11}{4} > > \text{this is rejected because sides of } \\\\ \text{a triangle cannot be measured in negative value}[/tex]

[tex]\sf x = \dfrac{-8+18.11}{4}[/tex]

[tex]\sf x = \dfrac{10.11}{4}\\\\x =2.5275[/tex]

x+ 4 = 2.5275 + 4 = 6.5275

Shorter leg = 2.5 ft

Longer leg = 6.5 ft

Answer: the length of the shoter leg is 2,5 feet

               the length of the longer leg is 6.5 feet

Step-by-step explanation:

Let the length of the shoter leg is x feet

Than the length of the longer leg is (x+4) feet

We use Pythagoras' theorem:

[tex]\displaystyle\\x^2+(x+4)^2=7^2\\\\x^2+x^2+2(x)(4)+4^2=7(7)\\\\2x^2+8x+4(4)=49\\\\2x^2+8x+16-49=49-49\\\\2x^2+8x-33=0\\\\D=b^2-4ac\\\\Hence,\\\\D=8^2-4(2)(-33)\\\\D=8(8)+8(33)\\\\D=64+264\\\\D=328\\\\\sqrt{D}=\sqrt{328} \\\\x=\frac{-bб\sqrt{D} }{2(a)} \\\\x=\frac{-8б\sqrt{328} }{2(2)} \\\\x=-6.5277\notin (x > 0)\\\\x=2.5277\ feet\\\\x+4=2.5277+4\\\\x+4=6.5277\ feet[/tex]