A birthday cake was cut into equal pieces, and 10 pieces were eaten. The
fraction below shows how much cake was left over. According to the fraction,
into how many pieces was the cake cut?
1
11
A. 1
B. 10
C. 21
D. 11

say the numbers are "a" and "b", we know that they're in the ratio of 2:3, or namely that

[tex]\stackrel{\textit{in the ratio of 2 to 3}}{a~:~b\qquad \qquad 2:3}\qquad \qquad \implies \qquad \cfrac{a}{b}=\cfrac{2}{3}\implies \cfrac{3a}{2}=b \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{their sum is 55}}{a + b = 55}\implies a + \cfrac{3a}{2}=55\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( a + \cfrac{3a}{2} \right)=2(55)} \\\\\\ 2a+3a=110\implies 5a=110\implies a = \cfrac{110}{2}\implies \boxed{a = 22}[/tex]

[tex]\stackrel{\textit{we know that}}{\cfrac{3a}{2}=b}\implies \cfrac{3(22)}{2}=b\implies \boxed{33=b} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{their product is 384}}{ab=384}\implies a\left( \cfrac{3a}{2} \right)=384\implies \cfrac{3a^2}{2}=384\implies 3a^2=768 \\\\\\ a^2=\cfrac{768}{3}\implies a^2=256\implies a=\sqrt{256}\implies \boxed{a=16} \\\\\\ \stackrel{\textit{we know that}}{\cfrac{3a}{2}=b}\implies \cfrac{3(16)}{2}=b\implies \boxed{24=b}[/tex]

The positive numbers for both the parts are obtained as 22,33 and 16,24 respectively.

A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.

(a) As per the question, the numbers can be considered as 2x and 3x respectively.

Then, the equation for their sum can be written as follows,

3x + 2x = 55

⇒ 5x = 55

⇒ x = 11

The numbers are obtained as 2 × 11 = 22 and 3 × 11 = 33.

(b) Similarly, the equation for the product of numbers can be written as,

3x × 2x = 384

⇒ 6x² = 384

⇒ x² = 64

⇒ x = 8

The numbers are obtained as 2× 8 = 16 and 3 × 8 = 24.

The required number for both the cases are 22,33 and 16,24 respectively.

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Answer:

-6 is Y

Step-by-step explanation:

When ever the number is outside of the f(x) it is = y.

Answer:

0.80

Step-by-step explanation:

its the farthest away from 0.60

Answer:

It is 7 2/11 is less then 7 4/10

Step-by-step explanation:

You do not have to worry about the whole number because they are the same. You have to compare the fractions, so if comparing fractions 10 is less then 11 so 1/10 has a larger space then 1/11. That is how i got the answer. Hope this helps. Am I right?

Answer:

[tex]\huge\purple{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}[/tex]

[tex]7 \frac{2}{11} < 7 \frac{4}{10} [/tex]

Answer: B

Answer:

Try this on for size

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

[tex]7^{\tfrac 14} = \sqrt[4]{7}[/tex]

Answer:

Option D

Step-by-step explanation:

The expression is a=2b-3

Answer:

D. The wait time will be about 2 mins.

Step-by-step explanation:

You have to substitute the x into the equation as we know it is 10.

So, y = (-1.62 × 10) + 18.

Thus, y = -16.2 + 18.

Then, y would equal 1.8.

Therefore you would round to the nearest minute which would be 2.

Hope this helps :)

Answer:

70°

Step-by-step explanation:

Size of angle a = (180°-40°) ÷ 2 (angle sum of triangle; base angles of isos triangle)

                         = 140° ÷ 2

                         = 70°

Answer:

a + 40° = 180°

a t40°-40° =180°- 40°

a = 140°

Step-by-step explanation:

isosceles add up to 180°

Answer:

(8,-9)

Step-by-step explanation:

using the principle of vectors, you match each number to their coordinates and add them

so we have (7+1,-12+3)

which is equal to (8,-9)

Answer:

5/2

Step-by-step explanation:

Formula: y2-y1/x2-x1

Labeled:

(1,3)

1 = x2

3 = y2

(7,-12)

7= x1

-12 = x1

In order:

3+12 / 1-7

=15/6

which is simplified to 5/2

so when trying to find the slope of two points you want to use a certent formula which is y2 minus y1 over x2 minus x1 and if the x1 or y1 is negative it will be plus.

first you need to label them and then put them in the order you labeled them to the formula. After subtract or add and if you can simplify it then simplified it to get your answer.

this is the best way I can explain it, sorry

:(

Answer:

Step-by-step explanation:

Domain : [-9,-3]

Range: [2,6]

Answer:

um I think it's the range is 30

Answer:

x = 35

Step-by-step explanation:

First, set both equations equal to each other because it is the same angle (congruent)

6x - 20 = 4x + 50

-4x and +20 to both sides of the equation and you end up with:

2x = 70

divide both sides by 2 and:

x = 35

Answer:

  18

Step-by-step explanation:

Maybe you want to fill in the blank so this is true for all x:

  4(4x -14) -14x + ___ = -2(-x +19)

Simplifying, we get ...

  16x -14x -56 + ___ = 2x -38

Adding 56-2x to both sides leaves ...

  ___ = 18

The missing number is 18.

Answer:

9

Step-by-step explanation:

375 - 150 = 225

225 / 25 = 9

Answer:

I believe the answer would be 9 weeks

Answer:

0.25

Step-by-step explanation:

1/4 is equal to 1.00 split into 4 equal parts. 0.25*4 = 1.00 , meaning that each 1/4 is equal to 0.25

Answer:

0.25.

Step-by-step explanation:

We divide 1 by 4:

4)  1. 00

    0.25

The term variable implies that the rate is bound to change over time, in this context variable interest rate may double as an Advantage and also as a disadvantage.

D. increases when the market rate increases

Variable interest rate is advantageous because as the market rate increases, the rate at which the customer will receive his/her interest will increase too

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Answer: a

Step-by-step explanation:

Answer:

B should be the answer because it did rotate and the origin is in the middle 0,0 which it look like to me it is on.

Answer:

cost of 5 story book=800

cost of 1 story book=800/5

=160

how many. book can be bought on rs.1400

=1400/160

=8.75

Step-by-step explanation:

=

Answer:

LQ = 5

Median = 6

Step-by-step explanation:

[tex]\frac{n+1}{2}[/tex] gives us 5.5, so we do the average of position 5 and 6. This gives us 6, so the median is 6.

Now we find the median of the bottom half of the numbers, which is 5, so the LQ is 5.

Now we find the median of the upper half of the numbers, which is 7, so the UQ is 7.

Answer:

There are 24 different combinations.

Step-by-step explanation:

2x4x3= 24

Answer:

Step-by-step explanation:

3| -2 =6

4| -5| =20

= -6+20

Simplify -

14

Thank You! I hope I could make your day just a little bit better!

Answer:

mario lost the race and luigi won

Step-by-step explanation:

all triangles are similar but B and D may be the answer

Answer:

He is correct

Step-by-step explanation:

72 girls and 84 boys

Divide both numbers by 12

6 : 7

He is correct

Jerod says that the ratio of girls to boys is 6:7 is correct.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that in the sixth grade there are 84 boys and 72 girls

Jerod says that the ratio of girls to boys is 6:7

We need to check whether Jerod statement is correct or incorrect

Now the number of boys=84

The number of girls=72

Now divide the number of girls by number of boys

72/84

6/7

So Jerod statement is true

Hence, Jerod says that the ratio of girls to boys is 6:7 is correct.

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Answer: D

Step-by-step explanation:

this is in y=Mx+ b form. M stands for the slope and b stands for the y intercept, or where the line intersects with the y-axis.

Going left to right, the line slopes downwards, therefore it is a negative Slope. This narrows down your answer to either a or d. the slope is -1 because you can only ever write x by itself if it means 1x. In this case it is negative so it would look like this: -x

for the y-intercept, simply look at where the line passes through the y-axis. In this case, it is positive 2.

your finished equation would be: y=-x+2

i hope this is helpful

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{4(x + 3) - 10 = 6(x -2)}\\\large\textsf{4(x) + 4(3) - 10 = 6(x) + 6(-2)}\\\large\textsf{4x + 12 - 10 = 6x - 12}\\\large\textsf{4x + 2 = 6x - 12}\\\large\text{SUBTRACT 6x to BOTH SIDES}\\\large\textsf{4x + 2 - 6x = 6x - 12 - 6x}\\\large\text{SIMPLIFY IT!}\\\large\text{NEW EQUATION: \textsf{-2x + 2 = -12}}\\\large\text{SUBTRACT 2 to BOTH SIDES}\\\large\textsf{-2x + 2 - 2 = 6x - 12 - 6x}\\\large\text{SIMPLIFY IT!}\\\large\textsf{-2x = -14}\\\large\text{DIVIDE -2 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{-2x}{-2}= \dfrac{-14}{-2}}\\\large\text{CANCEL out: }\rm{\dfrac{-2}{-2}}\large\text{ because it gives you 1}\\\large\text{KEEP: }\rm{\dfrac{-14}{-2}}\large\text{ because it helps solve for the x-value}\\\large\text{NEW EQUATION: }\mathsf{x = \dfrac{-14}{-2}}\\\large\text{SIMPLIFY IT!}\\\large\textsf{x = 7}\\\\\\\huge\boxed{\text{Therefore, your answer is: \boxed{\textsf{x = 7}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

4/3 or 1 1/3

Step-by-step explanation:

To find slope, we subtract the y-values (9 - 5), then divide the difference we find from that by the difference of the x-values (6 - 3). So, let's go ahead and do that now. First, what's 9 - 5? Well, the answer is 4. Next, we have to divide this value by 6 - 3, which is equivalent to 3. Then, we divide the two numbers - what is 4 ÷ 3? Well, we can represent this as 4/3, or 1 1/3. Hopefully that's helpful - if you have any questions on that, let me know! :)

Answer:

Slope is 4/3

Step-by-step explanation:

Slope or gradient can be found by using several formulas. For this situation, we can use rate of changes between two points also known as rise over run or changes in y over change so in x.

The formula of slope between two points can be expressed as several equations, expressions, etc such as:

[tex]\displaystyle \large{m=\frac{dy}{dx}=\frac{y_2-y_1}{x_2-x_1} =\frac{\Delta y}{\Delta x}[/tex] where m is a variable representing the slope.

Since we are given two points, we are going to use the y2-y1 over x2-x1 formula.

Let (3,5) be (x1,y1,) and (6,9) be (x2,y2) thus the slope is [tex]\displaystyle \large{m=\frac{y_2-y_1}{x_2-x_1} =\frac{9-5}{6-3} =\frac{4}{3}[/tex]

Therefore the slope of two points is 4/3.

__________________

Let me know in comment if you have any questions.

Answer:

114.59155

Step-by-step explanation:

Answer:

Sorry i didn't know that