What is the solution to the equation 1/4x +2= -5/8x - 5

Answer:

x = - [tex]\frac{2}{9}[/tex]

Step-by-step explanation:

Given

[tex]\frac{2}{5}[/tex] (x - 2) = 4x

Multiply both sides by 5 to clear the fraction

2(x - 2) = 20x ( divide both sides by 2 )

x - 2 = 10x ( subtract x from both sides )

- 2 = 9x ( divide both sides by 9 )

- [tex]\frac{2}{9}[/tex] = x

Answer:

451cm cubed

Step-by-step explanation:

The volume of any prism = Area of cross section times height.

So, we substitute area of Cross section with 41 cm squared and height with 11.

41 x 11 = 451

Answer:

Option B.

Step-by-step explanation:

We take a point D from the figure attached,

Coordinates for the point D → (-1.5, 3.5)

And coordinates of D' → (3.5, 1.5)

Coordinates of D when rotated about the origin,

Option A. Rotated by 270° clockwise.

Rule to be followed,

D(x, y) → D'(-y, x)

D(-1.5, 3.5) → D'(-3.5, -1.5)

Therefore, Option A. is incorrect

Option B. rotation by 90° clockwise

Rule to be followed

D(x, y) → D'(y, -x)

D(-1.5, 3.5) → D'(3.5, 1.5)

Therefore, Option B. is correct.

Option C. 90° counterclockwise

Rule to be followed,

D(x, y) → D'(-y, x)

D(-1.5, 3.5) → D'(-3.5, -1.5)

This option C is incorrect.

Option D. 180° counterclockwise

Rule to be followed,

D(x, y) → D'(-x, -y)

D(-1.5, 3.5) → D'(1.5, -3.5)

Therefore, option D is incorrect.

Answer:

B. 90 clockwise

Step-by-step explanation:

Answer:

132 degrees is the measure of angle ABC.

Step-by-step explanation:

ABD = 180 because it is a straight line.

BCD = 48

ABD - BCD = 180 - 48

180 - 48 = 132

Answer:

ABC =132

Step-by-step explanation:

The two angles form a straight line so they add to 180

ABC + 48 = 180

Subtract 48 from each side

ABC +48-48 = 180-48

ABC =132

Answer:

D

Step-by-step explanation:

3x-4y=6

-4y=-3x+6

y=(3/4)x-(3/2)

positive slope with y-intercept at -3/2 corresponds to D

Graph includes the points (0,-3/2) and (2,0). Therefore, option D is the correct answer.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

The given linear equation is 3x-4y=6

Graph the line using the slope and y-intercept, or two points.

Slope: 3/4

y-intercept:

(0,-3/2)

Plot the points (0,-3/2) and (2,0)

Therefore, option D is the correct answer.

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Answer:

60 possible sequences.

Step-by-step explanation:

That would be 6! / 3! 2!

   6*5*4*3*2*1

=  ------------------

     3*2*1*2*1

= 5*4*3

= 60.

Answer:

the difference would be 28 degrees.

Step-by-step explanation:

The question says difference so we subtract the two following temperatures 30 and -2 which would be 28 degreees.

Answer: The difference between the high and low temperature in the thermometer is 32°F.

Step-by-step explanation:

Given information: Highest temperature = 30°F and the lowest temperature = -2°F.

We need to find the difference between the high and low temperature in the thermometer.

Difference between the high and low temperature is

Difference = Highest temperature - Lowest temperature

Difference = 30°F - (-2°F)

Difference = 30°F + 2°F

Difference = 32°F

Answer:

the slope is zero because

Step-by-step explanation:

this is a perfect horizontal line passing through y=-3

I've been thought

hope it helps

Answer:

Slope = 0

This is because the line does not go up or down. And the line is horizontal leading to the factor of the slope being 0.

Answer:

C

Step-by-step explanation:

cuz

Answer:16.5

Step-by-step explanation:

15 times 10 percent=1.5, Add 1.5 to 15 =16.5

Answer: $150

Step-by-step explanation:

PRICE x 10% = $15

PRICE x .1 =$15

PRICE = $15 /.1

PRICE = $150

Answer:

44, 46, and 48

Step-by-step explanation:

add them and you should get 138.

Answer:

work is shown and pictured

Step-by-step explanation:

Explanation:

The formula for volume of a sphere is:

V=43πr3

Since we know the volume, and have to find the diameter (twice the radius), we need to determine the radius first.

Hence, using the given data:

2304π=43πr3

We can cancel π from each side.

2304=43r3

Multiply both sides by 34.

2304×34=34×43r3

2304×34=34×43r3

2304×34=r3

5762304×34=r3

576×3=r3

To find the cube root, we separate the factors of the number on the left.

3⋅3⋅3⋅4⋅4⋅4=r3

(3⋅4)(3⋅4)(3⋅4)=r3

12×12×12=r3

12=r

Since the radius (r) is 12, the diameter, which is 2r, will be:

2×12=24

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The Whispering Lakes  Neighborhood Association is  having a hamburger cookout.  Each family can choose whether  to order the hamburgers or  bring their own. Use the  information in the table to solve  the number stories. Use  drawings, tables, or equations  to show what you did.

Mrs. Ward found 80-ounce packages of hamburger on sale. If she needs to make  2 of each size hamburger, how many packages of meat will she need to buy?

Answer:

The number of meat packages is

100/80 = 1.25 = 5/4

Assuming that the number of packages cannot be in fraction, then she would need at least 2 packages of meat.

Number of meat packages = 2

Step-by-step explanation:

Please refer to the attached table where we are given size of hamburgers and the weight of corresponding hamburger patty in pounds.

small = 1/8 lb

medium = 1/4 lb

large = 1/2 lb

jumbo = 3/4 lb

king of burgers = 1 1/2 lb = 3/2 lb

To make 1 of each hamburger we need

Total weight of patty = 1/8 + 1/4 + 1/2 + 3/4 + 3/2

Total weight of patty = 25/8 = 3.125 lb

But she needs to make  2 of each size hamburger so,

Total weight of patty = (25/8)×2 = 25/4 = 6.25 lb

Mrs. Ward found 80-ounce packages of hamburger on sale

first we have to convert pounds into ounces

We know that 1 pound has 16 ounces

6.25×16 = 100 ounces

So the number of meat packages required is

100/80 = 1.25 = 5/4

Assuming that the number of packages cannot be in fraction, then she would need at least 2 packages of meat.

Number of meat packages = 2

Answer:

110

Step-by-step explanation:

Answer:

3.61 sec

Step-by-step explanation:

Set the given d= 3t + 3t ^2 equal to 50 and solve for t:

3t^2 + 3t - 50 = 0

This is a quadratic equation with coefficients 3, 3 and -50.  The discriminant is b^2 - 4ac, or 3^2 - 4(3)(-50), or 9 + 600 = 609

The roots of this quadratic are therefore:

     -(3) ± √609           -3 ± 24.68           21.68

t = --------------------  =  -------------------  =  ----------- = 3.61 sec

           2(3)                           6                     6

Answer:

1) 250°, 2) 44°

Step-by-step explanation:

1) See attached

If we add a line ⊥ to both AB and DE, we can find x as a sum of 2 internal angles of right triangles and 180°

∠D internal = 360°-312°=48°

x=180°+(90°-62°)+(90°-48°)= 180°+28°+42°= 250°

x=250°

2)

∠ADC= ∠ABC= 180°- ∠ADE= 180°- 110°= 70°

∠DBC= ∠ABC- ∠ABD= 70°-26°= 44°

∠DBC= 44°

Answer:

1. (-1/4,0)(1.5,0)

2.(-1/2,2)(6/4,2)

Step-by-step explanation:

just locate the numbers on the graph

Answer:

no

Step-by-step explanation:

25 minutes for $3 ends up being $7.20 for 1 hour which is greater than 6.

Answer:

no

Step-by-step explanation:

We can use ratios to see if they are equivalent

25 minutes        60 minutes

---------------- = -------------------

3 dollars           6 dollars

Using cross products

25*6 = 3 * 60

150 = 180

This is not true so they are not equivalent

Answer:

10 and 8

Step-by-step explanation:

Case 1:

20 and 2

20 = 2^2 x 5

2   = 2^1

=> LCM = 2^2 x 5 = 20 (not 40)

=> Incorrect pair of numbers

Case 2:

10 and 8

10 = 2 x 5

8  = 2^3

=> LCM = 2^3 x 5 = 40

=> GCF = 2

=> Correct pair of numbers

Case 3:

10 and 4

10 = 2 x 5

4  = 2^2

=> LCM = 2^2 x 5 = 20 (not 40)

=> Incorrect pair of numbers

Case 4:

8 and 5

8 = 2^3

5 = 5 x 1

=> GCF = 1 (not 2)

=> Incorrect pair of numbers

Hope this helps!

:)

The numbers which have the least common multiple (LCM) of 40 and greatest common factor (GCF) of the two numbers is 2 are 8 and 10.

The LCM (Lowest Common Multiple) of two or more numbers is the smallest number among all common multiples of the provided numbers. In contrast, the greatest common factor (GCF) is the highest number among all the common factors of the given numbers.

Given that, two whole numbers have the least common multiple (LCM) of 40. and greatest common factor (GCF) of the two numbers is 2.

Let the two numbers be x and y

Now, we know that,

LCM (a, b) × HCF (a, b) = a × b.

40 ×  2 = xy

xy = 80

Therefore, the product of two number is 80.

Now, from the given options, the only pair having product 80 is 8 and 10.

Therefore, the numbers are 8 and 10.

Hence, the numbers which have the least common multiple (LCM) of 40 and greatest common factor (GCF) of the two numbers is 2 are 8 and 10.

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Answer: 13

Step-by-step explanation: 15-2=13

Answer:

if the solution to the system is  1.5 and 2

Then the mistake was in line 2 the student should have subtracted the eqations instead of adding them.

Step-by-step explanation:

if y = 2

Then 8y -5y = 3y

4x -x = (4 = 1.5 x 2 2/3) =4   if x = 1.5

3y = 2 2/3 = 3   if y = 2

The ratio stays the same.

The student mistake was in line 2, the student forgot to multiply the

right side of the equation by 2.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Given:

2x + 5y = 13

-x + 4y = 13

The first steps are correct.

In second step the LHS and RHS both should be multiplied by 2.

So,

-2x + 8y = 26

But, the student only multiply 2 on the LHS side.

Hence, the student mistake was in line 2, the student forgot to multiply the right side of the equation by 2.

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Answer: 27 miles in 1 gallon

Step-by-step explanation:

297/11

The unit rate of 297 miles in 11 gallons will be 27 miles/gallons.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b, will be the denominator.

We will be used when division is not possible wholly

For example 4/2 is divisible so we write 2 instant of 4/2 while 1/3 is not divisible so we write 1/3 instant of 0.33.

Proportion is the relation of a variable with another. It could be direct or inverse.

The ratio is very useful to determine complex calculation where decimal number become tough to solve.

Given,

297 miles in 11 gallons

297 miles ⇔ 11 gallons

Divide by 11 on both sides

297/11 miles ⇔ 11/11 gallons

27 miles ⇔ 1 gallon

So, 27 miles in 1 gallon.

Hence unit rate is 27 miles/gallon will be correct.

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Answer:

The image of the circle is 9·x² + 9·y² - 42·x + 33·y = 22

Step-by-step explanation:

We convert the equation to the form (x - h)² + (y - k)² = r²

Where:

(h, k) = Coordinates of the center of the circle

We therefore have;

x² + y² - 2·x + 3·y = 8 which gives;

x² - 2·x + 1 - 1 + y² + 3·y + (3/2)² - (3/2)² = 8

(x - 1)² + (y + 3/2)² - 1 - (3/2)² = 8

(x - 1)² + (y + 3/2)²  = 8 +  1 + (3/2)² = 45/4

Therefore, the center = (1, -3/2) and the radius = √5 × 3/2

The line joining the centers of the actual (1, -3/2) and reflected circle (h, k) is bisected by the line of reflection, therefore the midpoint of the line is on the line of reflection with coordinates;

Midpoint between (1, -3/2) and  (h, k) = [tex]\left (\dfrac{{h - 1}}{2}, \, \dfrac{k - 3/2}{2} \right )[/tex]

Which gives;

y = 2·x - 3 being equivalent to [tex]\dfrac{k - 3/2}{2} = 2\times\dfrac{{h - 1}}{2} - 3[/tex]

Which gives;

4·h -2·k -13 = 0.......(1)

Similarly the slope of the reflecting line is perpendicular to the line joining the centers of the actual and reflected circles

Therefore;

The slope of the line, y = 2·x - 3 = 2, hence we have;

[tex]\dfrac{\left ( \dfrac{k - 3/2}{2} \right ) + 3/2}{\left (\dfrac{{h - 1}}{2}-1 \right )} = \dfrac{1}{2}[/tex]

Which gives;

2·h -4·k -12 = 0.......(2)

Multiplying equation (2) and subtracting from equation (1) gives

4·h -2·k -13 - 2×(2·h -4·k -12) = 0

6·k + 11 = 0

k = -11/6

From which we have;

2·h -4×(-11/6) -12 = 0

Hence;

h = 7/3

Therefore, the center of the reflected circle = (7/3, -11/6)

The equation of the reflected circle is therefore;

(x - 7/3)² + (y + 11/6)² = 45/4

Which gives;

9·x² + 9·y² - 42·x + 33·y - 22 = 0

or x² + y² - 42/9·x + 33/9·y = 22/9.

Answer:

Jason has 75 pencils.

Step-by-step explanation:

In order to get from 4 to 100, you must multiply by 25 (100/4 = 25). And in order to find the amount of pencils Jason has, you must have an equivalent ratio. So you have to also multiply 3 by 25, 3 * 25 = 75. Jason has 75 pencils.

Answer:

15.94490514

Step-by-step explanation:

First, work out the average, or arithmetic mean, of the numbers:

Count: 5(How many numbers)

Sum: 357(All the numbers added up)

Mean: 71.4(Arithmetic mean = Sum / Count)

Then, take each number, subtract the mean and square the result:

Differences:

4.6, -26.4, -7.4, 8.6, 20.6

(Every Number minus Mean)

Differences^2:

21.16, 696.96, 54.76, 73.96, 424.36

(Square of each difference)

Now calculate the Variance:

Sum of Differences2:1271.2(Add up the Squared Differences)

Variance:254.24(Sum of Differences2 / Count)

Lastly, take the square root of the Variance:

Standard Deviation:15.94490514 (The square root of the Variance)

The volume is 15/16 cubic meters.

please see the attached picture for full solution

hope it helps