The area of a triangle is twice the area of a square. If the base of the triangle and a side of the square are equal, what is the ratio of the height of the triangle to the side of the square?

To find equivalent fractions for 1/12 and 3/8 using the least common denominator, multiply the numerator and denominator of each fraction by the appropriate factor to obtain fractions with a common denominator of 24.

To find an equivalent fraction for 1/12 and 3/8 using the least common denominator, we need to determine the smallest multiple that both denominators (12 and 8) have in common. The least common multiple of 12 and 8 is 24.

To convert 1/12 to a fraction with 24 as the denominator, we need to multiply the numerator and denominator by 2:

1/12 = (1 * 2) / (12 * 2) = 2/24.

To convert 3/8 to a fraction with 24 as the denominator, we need to multiply the numerator and denominator by 3:

3/8 = (3 * 3) / (8 * 3) = 9/24.

Final answer:

The equivalent fractions with the least common denominator of 24 for 1/12 and 3/8 are 2/24 and 9/24, respectively.

Explanation:

To find an equivalent fraction for each fraction with the least common denominator (LCD), you first need to determine the LCD for 1/12 and 3/8. In this case, the LCD for 12 and 8 is 24. Then, you adjust each fraction to have the denominator of 24.

For 1/12: Multiply both the numerator and the denominator by 2 to get 2/24.

For 3/8: Multiply both the numerator and the denominator by 3 to get 9/24.

Therefore, the equivalent fractions with a common denominator of 24 are 2/24 and 9/24.

To understand equivalency in general, when you multiply the numerator and the denominator of a fraction by the same number, you are creating a fraction that represents the same value as the original.

Answer:

1 plain = $0.75; 1 cheese = $0.95; 1 super = $1.25

Step-by-step explanation:

We have three conditions

(1) 5P = 3S

(2)  S = C + 0.30

(3)  P = C – 0.20                           Substitute (3) into (1)

=====

(4)   5(C – 0.20) = 3S                   Substitute (2) into (4)

      5(C – 0.20) = 3(C + 0.30)     Remove parentheses

         5C – 1.00 = 3C + 0.90       Add 1.00 to each side

                    5C = 3C + 1.90        Subtract 3C from each side

                    2C = 1.90                 Divide each side by 2

                      C = $0.95              Substitute C into Equation (2)

=====

                      S = 0.95 + 0.30

                      S = $1.25               Substitute C into Equation (3)

=====

                     P = 0.95 – 0.20

                    P = $0.75

1 plain = $0.75; 1 cheese = $0.95; 1 super = $1.25

Answer:

(a) [tex]\left\{\begin{array}{l}0.8m=2\\p+0.2m=3\end{array}\right.[/tex]

(b) correct choice is 2.5 lb peanuts and 2.5 lb mixture (2.5, 2.5);

Step-by-step explanation:

Let p represent the number of pounds of peanuts needed to make the new mixture, and let m represent the number of pounds of the 80% almond-20% peanut mixture.

1. In m pounds of the 80% almond-20% peanut mixture there are 0.8m pounds of almonds and 0.2m pounds of peanuts.

2. When added p pounds of peanuts to m pounds of mixture, you get (p+0.2m) pounds of peanuts and 0.8m pounds of almonds.

3. In 5 pounds of the 40% almond-60% peanut mixture there are [tex]0.6\cdot 5=3[/tex] pounds of peanut and [tex]0.4\cdot 5=2[/tex] pounds of almonds.

(a) Then you get a system of two equations:

[tex]\left\{\begin{array}{l}0.8m=2\\p+0.2m=3\end{array}\right.[/tex]

(b) Solve this system. From the first equation

[tex]m=\dfrac{2}{0.8}=2.5\ pounds,[/tex]

then

[tex]p+0.2\cdot 2.5=3,\\ \\p=3-0.5,\\ \\p=2.5\ pounds.[/tex]

Answer:

The correct answer is D

Step-by-step explanation:

Please see the attachment

Answer:d

Step-by-step explanation:

Answer:

11.7 Gallons

Step-by-step explanation:

First turn the percentage into a decimal then multiply it by the whole number which is 18 and you should get 11.7 and that is how many gallons are currently in the tank

Answer:

11.7

Step-by-step explanation:

To solve this problem, we need to find what is 65 percent of 18.

To do this, we can simply multiply 18 by .65. Don't forget the decimal!

The answer is 11.7

Hope this helps! (Brainliest Please!)

Answer: Choice A) 9/45 and 8/40

------------------------

If you divide both top and bottom of 9/45 by the GCF 9, you get 1/5

If you divide top and bottom of 8/40 by the GCF 8, you also get 1/5

So the original fractions must be the same

------------------------

Another way to check is to use a calculator and see that 9/45 = 0.2 and 8/40 = 0.2, so 9/45 = 8/40

Or you can subtract the fractions and you should end up with 0, so, 9/45 - 8/40 = 0

-------------------------

You can also set up a proportion and cross multiply

9/45 = 8/40

9*40 = 45*8

360 = 360

The last equation is true, so the first equation must be true

Answer:

The equation of the line is y=-x

Step-by-step explanation:

To find the equation for a line, we need to know 2 points.

One of the points is (0,0) because it goes through the origin.  Another point is (5,-5).  We can calculate the slope because we have 2 points using the formula.

m = (y2-y1)/(m2-m1)

m = (-5-0)/(5-0)

m = -5/5

m=-1

The slope is -1

We know the y intercept (where it crosses the y axis) is 0.  Using the slope intercept form of a line

y = mx+b

y =-1x+ 0

y = -x

The equation of the line is y=-x

Answer:

15%

17 kids are part of club A and B

Answer:

522

Step-by-step explanation:

We are given that the price of the motorcycle is 3238 and if we borrow it then the payment per month will be 165 for 24 months.

So the total amount that we are going to pay if we borrow the motorcycle will be 165 × 24  = 3960

While the actual price of the bike is 3438.

Difference in the payment and actual price = 3960 - 3438 = 522

Therefore, you can save 522 by paying cash.

Answer:

30/80 is the fraction of decrease. Converting this to a fraction with a denominator of 100, we get the fraction; 

37.5/100

Now we just take the numerator of the number to get the percent, which is the solution. 

37.5%

Answer:

36/25

Step-by-step explanation:

[tex](\frac{5}{6})^{-2}=(\frac{6}{5})^{2}\\(\frac{6}{5})^2=\frac{6}{5}\times\frac{6}{5}\\=\frac{36}{25}[/tex]

Steps:

Flip the fraction (negative exponent)

Square the fraction

Answer:

36/25 or 1 11/25

Step-by-step explanation:

(5/6)^-2

A negative exponent tells us to flip the fraction.  It only eliminates the negative part of the exponent.

(6/5) ^2

We can split it apart (a/b)^x = a^x/b^x

6^2/5^2

36/25

1 11/25

Answer:

slope = - [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

calculate the slope m using the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (2, 6) and (x₂, y₂ ) = (6, 5)

m = [tex]\frac{5-6}{6-2}[/tex] = - [tex]\frac{1}{4}[/tex]

Answer:

JP = MI

Step-by-step explanation:

JP = TI (right)

Angle B = Angle I (right)

Angle BJP = Angle IMT (right: Angle J = Angle M)

JP = MI (wrong: JP = IT)

I hope I helped you.

Answer:

JP = MI

Step-by-step explanation:

Answer:

the answer is C because the slope of the line is what you need to look for with these kinds of problems. it could be any point on the line, but answer C is the only one of its kind.

Step-by-step explanation:

The ordered pair is the solution to the system is (5,3).

A pair of numbers that are written in a particular order, enclosed in brackets are known as ordered pairs.

Malique solved the system of equations below;

[tex]\rm 2x+4y=22\\\\6x+2y=36[/tex]

Reduce the greatest common factor on both sides of the equation

[tex]\rm x+2y=11\\\\3x+y=18[/tex]

From equation 1

[tex]\rm x+2y=11\\\\x=11-2y[/tex]

Substitute the value of x in the equation 2

[tex]\rm 3x+y=18\\\\3(11-2y)+y=18\\\\33-6y+y=18\\\\-5y=18-33\\\\-5y=-15\\\\5y=15\\\\y=\dfrac{15}{5}\\\\y=3[/tex]

Substitute the value of y in the equation 1

[tex]\rm x+2y=11\\\\x + 2(3)=11\\\\x+6=11\\\\x=11-6\\\\x=5[/tex]

Hence, the ordered pair is the solution to the system is (5,3).

Learn more about ordered pair here;

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Answer:

x = 55

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

the sum of the 4 angles in a quadrilateral = 360°

the angles to the left and above 130° angle = 50°

Since 130° and 50° form a straight angle and are supplementary

the third angle in the left triangle = 180° - (50 + 30)° = 100°

thus the angle to the right = 180° - 100° = 80°  ( straight angle )

the third angle in the upper triangle = 180° - (50 + 45)° = 85°

the angle below it = 180° - 85° = 95° ( straight angle )

We now have 3 angles inside the quadrilateral of 130°, 80° and 95°

x = 360° - (130 + 80 + 95)° = 55

Answer:

if m1= 60° than m2 must= A. 30° Since perpendicular lines form a right

Answer:

905.26

Step-by-step explanation:

905.255

We are rounding to the hundredths place, so we need to look at the thousandths place.  That digit is also a 5. 5>= 5 so we need to round the 5 in the hundredths place up to a 6

905.255 rounds to 905.26

Answer:

905.26 is your answer

Step-by-step explanation:

The 5 you are solving for will be underlined and bolded.

905.255

Note the place value to the right of the value you are solving for. It is a 5. Because it is a 5, round up.

905.255 rounded to the nearest hundredth is 905.26

905.26 is your answer

~

By definition, BF = 1/2 * CE;

So, BF = 1/2 * 90 = 45.

BF = 45

(Midsegment Length Theorem)

Answer:

BF=45

Step-by-step explanation:

Here the given point B and point [tex]F[/tex] are the midpoint of the sides AC and AE respectively in triangle ACE .

According to converse of Thales theorem -if a line divides any two sides of a triangle in equal parts then that line will be parallel to the third side of the triangle.

Also ,

In the above said condition, that line will be half of the third side

On applying this concept in the given triangle ACE

[tex]BF= \frac{1}{2} *CE\\BF=\frac{1}{2} *90\\BF=45[/tex]

Hence BF=45

Answer:

First man rate is 115

Second man rate is 50

Step-by-step explanation:

Let's assume rate of charge of first men is x

rate of charge of second  men is y

we are given

the sum of the two rates was 165. per hour

so, we get

[tex]x+y=165[/tex]

Two men worked on a car. the first man worked 20 hours and the second man worked 15 hours. Together they charged 3050

so, we get

[tex]20x+15y=3050[/tex]

we can simplify it

[tex]5(4x+3y)=3050[/tex]

[tex](4x+3y)=610[/tex]

so, we got system of equations as

[tex]x+y=165[/tex]

[tex]4x+3y=610[/tex]

We can solve for y from first equation and plug into second equation

[tex]y=165-x[/tex]

[tex]4x+3(165-x)=610[/tex]

[tex]x+495=610[/tex]

[tex]x=115[/tex]

now, we can solve for y

[tex]y=165-115[/tex]

[tex]y=50[/tex]

Answer:

10mph

Step-by-step explanation:

it's a ratio

6.2 miles divided by .62=10

Given : Molly bought a pair of Gloves which cost £4

Given : Molly sold the Gloves and Skirt for a Total of £48

Given : Molly made 100% Profit on the Cost of the Gloves

⇒ Molly sold the Gloves at a Cost of £8

Selling Price of Gloves + Selling Price of Skirt = £48

⇒ £8 + Selling Price of Skirt = £48

⇒ Selling Price of Skirt = £40

Given : Molly made 20% Profit on the Total Cost

[tex]\mathsf{\implies (\frac{Selling\;Price\;of\;Skirt\;and\;Gloves - Cost\;Price\;of\;Skirt\;and\;Gloves }{Cost\;Price\;of\;Skirt\;and\;Gloves}) \times 100 = 20}[/tex]

[tex]\mathsf{\implies (\frac{48 - 4 - Cost\;Price\;of\;Skirt}{4 + Cost\;Price\;of\;Skirt}) \times 100 = 20}[/tex]

[tex]\mathsf{\implies (\frac{44 - Cost\;Price\;of\;Skirt}{4 + Cost\;Price\;of\;Skirt}) \times 5 = 1}[/tex]

[tex]\mathsf{\implies 5(44 - Cost\;Price\;of\;Skirt) = 4 + Cost\;Price\;of\;Skirt}[/tex]

[tex]\mathsf{\implies 220 - 5(Cost\;Price\;of\;Skirt) = 4 + Cost\;Price\;of\;Skirt}[/tex]

[tex]\mathsf{\implies 6(Cost\;Price\;of\;Skirt) = 216}[/tex]

[tex]\mathsf{\implies (Cost\;Price\;of\;Skirt) = 36}[/tex]

Profit Percentage on the Cost of the Skirt :

[tex]\mathsf{\implies (\frac{Selling\;Price\;of\;Skirt - Cost\;Price\;of\;Skirt}{Cost\;Price\;of\;Skirt}) \times 100}[/tex]

[tex]\mathsf{\implies (\frac{40 - 36}{36}) \times 100}[/tex]

[tex]\mathsf{\implies (\frac{4}{36}) \times 100}[/tex]

[tex]\mathsf{\implies (\frac{1}{9}) \times 100}[/tex]

[tex]\mathsf{\implies 11.11\%}[/tex]

A linear equation is any equation that results in a straight line, as each value is a fixed number from the previous.

In a non-linear equation, a variable is being raised to a power, which results in a curved line.

Answer:

b. y^2 = x^2 + 3   not a linear equation

Step-by-step explanation:

Linear equations are equations in which the variable is in the first degree, or only to the first power.

a. y = x + 6    Nothing above the first power

b. y^2 = x^2 + 3   X and y are to the second power

c. x = 5   Only to the first power

d. 2x = 3y  Only to the first power

The answer is:  " 7:45 a.m. "  .

__________________________________________

Step-by-step explanation:

__________________________________________

Start at:

____________________

6:00 a.m.

____________________

Add 1  1/4 hours ; which is

1 + (1/4) hours:

Note:  " 1 hr = 60 min." .

_____________________

So:

 (1/4 hr) *  ([tex]\frac{60 min }{ 1 h}[/tex]) ;

                                       =  (1/4) * 60 min;

                                       = (60/4) min.

                                       = 15 min.

______________________

So:  1  1/4 hr =  1 hr. 15 min.;

______________________

So:  Start at:  6:00 a.m .

Add  " 1  1/4 hrs."  ;  i.e. add 1 hr 15 min.

_______________________

6:00 a.m + 1 hr = 7:00 a.m.  ;

 7:00 a.m.  +  15 min. =  7: 15 a.m. ;

_______________________

Now, we are at:

_______________________

7:15 a.m.  ;

Now add:  "1/2 hour" to "7:15 a.m." to this time.

Note:  " 1 hr = 60 min.

So;

"1/2 hr = (1/2) * (60 min) = (60 / 2) min. = 30 min.

________________________

So: we have 7:15 a.m. ;

we add "30 min." to this time.

and we have:  7:45 a.m.

___________________________________________________

The answer is:  " 7:45 a.m. "  .

__________________________________________________

Answer:

it's 8:15

Step-by-step explanation:

start at 6:00+1:15 (aka 1 1/4 an hour) =7:45+30 min=8:15

Answer:

The answer is 55

Step-by-step explanation:

6 + 11 + 8 + 14 + 16 = 55

f(x) + n - move the graph n units up

f(x) - n - move the graph n units down

f(x + n) - move the graph n units to the left

f(x - n) - move the graph n units to the right

---------------------------------------------------------------------------------------

[tex]f(x)=-\dfrac{1}{5}x^2\\\\f(x+5)=-\dfrac{1}{5}(x+5)^2\\\\f(x+5)+2=-\dfrac{1}{5}(x+5)^2+2[/tex]

The equation y = -1/5 (x + 5)^2 + 2 is translated from the standard position by moving up and to the left.

In the equation y = -1/5 (x + 5)^2 + 2, the transformation of the graph from its standard position is determined by the constants within the equation. The -5 inside the parentheses causes a shift to the left by 5 units and +2 outside the parentheses represents an upward shift by 2 units. Therefore, the graph of the equation is moved up and to the left from its standard position where the vertex is at the origin.

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Answer:

[tex]\sqrt{2}[/tex]

Step-by-step explanation:

We plug in [tex]i[/tex] into [tex]f(x)[/tex] to get:

[tex]f(i)=1-i[/tex]

Here, [tex]i[/tex] is the imaginary number [tex]i=\sqrt{-1}[/tex]

To get absolute value of an imaginary number, we use the following formula:

[tex]a+bi=\sqrt{a^2+b^2}[/tex]

So absolute value of [tex]f(i)[/tex] is:

[tex]|f(i)|=\sqrt{(1)^2+(1)^2} \\=\sqrt{1+1} \\=\sqrt{2}[/tex]

a. The percentage of students who prefer strawberries is 33.33%.

b. The percentage of students who prefer the least favorite fruit is 8.33%.

c. The percentage of students who prefer apples or pears is 45.83%.

A) To find the percentage of students who prefer strawberries:

Add up the total number of students surveyed: 30 (apples) + 15 (oranges) + 40 (strawberries) + 25 (pears) + 10 (peaches) = 120 students.

Determine the number of students who prefer strawberries: 40.

Calculate the percentage: (Number of students who prefer strawberries / Total number of students surveyed) * 100 = (40 / 120) * 100 = 33.33%.

B) To find the percentage of students who prefer the least favorite fruit:

Identify the least favorite fruit, which is peaches with 10 preferences.

Calculate the percentage: (Number of students who prefer peaches / Total number of students surveyed) * 100 = (10 / 120) * 100 = 8.33%.

C) To find the percentage of students who prefer apples or pears:

Add up the number of students who prefer apples and pears: 30 (apples) + 25 (pears) = 55.

Calculate the percentage: (Number of students who prefer apples or pears / Total number of students surveyed) * 100 = (55 / 120) * 100 = 45.83%.

So, the answers are:

A) 33.33%

B) 8.33%

C) 45.83%

The detailed answer provides percentages for students preferring specific fruits from a survey.

A) What percent of students surveyed prefer strawberries?

B) What percent of students surveyed prefer the least favorite fruit?

C) What percent of students surveyed prefered apples or pears?