The ratio of the number of dolls Jacky had to the number of dolls Peter had was 5:2 but, after Jacky gave 15 dolls to Peter, they have an equal number of dolls. How many dolls did they have altogether?​

Answer:

y=1/3x+2

Step-by-step explanation:

y=mx+b form is where m = the slop and b = the y interecept.

Y - Intercept

we can tell the y-intercept is 2 just by looking at the graph

Slope

For the slope, we can pick two points on the line, in this case, I will pick the points (0,2) and (3,3). Then, we can use the slope formula (y2-y1)/(x2-x1) to find the points, and after plugging the points in, we get 1/3, which is the slope

Plugging the numbers into slop intercept form

So we now know the slope is 1/3 and y-intercept is 2, so after plugging it into slope-intercept form (y=mx+b), we get y=1/3x+2

The length of the arc which subtends a [tex]\pi/3[/tex] radians angle on a circle with 6 ft radius is given by: Option C: 6.3 feet approximately.

[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]

The superscript 'c' shows angle measured is in radians.

If radius of the circle is of r units, then:

[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]

For this case, we have:

Thus, if we take:

Length of the arc = L feet, then:

[tex]L =r \times \theta = 6 \times \dfrac{\pi}{3} = 2\pi \: \rm ft \approx 6.28 \approx 6.3 \: ft[/tex]

Thus, the length of the arc which subtends a [tex]\pi/3[/tex] radians angle on a circle with 6 ft radius is given by: Option C: 6.3 feet approximately.

Learn more about arc length here:

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Answer:

c

Step-by-step explanation:

i did it and got it right

Answer:

A. is the answer because 1/2 x 20 will equal 40 gallons

Answer:

19

Step-by-step explanation:

(5x+37)+(3x-9)=180

8x= 152

x=19

Answer:

55.75

Step by step explain:

33.00 divided by 4 equals 8.25

then multiply 8.25 by 7 which equals 55.75

Answer:

B and B

Step-by-step explanation:

For the first problem, the range is simply the data set rearranged from smallest to largest.

For the second problem, you just have to cross multiply each variable in order to expand the equation and get an answer.

The answer for that one is [tex]12x^{3} -42x^{2} +8x+55[/tex]

Answer:

Step-by-step explanation:

the area of this rectangle is

(10 + 2x)(8 + 2x) = 168

80 + 20x + 16x + 4x² = 168

4x² + 36x = 88

Step-by-step explanation:

A quadratic equation is an equation whose leading coefficient is of the second degree. The correct option is A.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

Let the width of the frame be represented by x. Therefore, the length and the breadth of the photographer be represented by (10+2x) inches and (8+2x) inches. Therefore, the total area of the photograph can be written as,

Area = Length × Breadth

168 inches² = (10+2x) inches × (8+2x)inches

168 = (10+2x)(8+2x)

168 = 80 + 20x + 16x + 4x²

0 = 80 + 20x + 16x + 4x² - 168

0 = 4x² + 36x - 88

4x² + 36x - 88 = 0

4x² + 36x = 88

Hence, the following quadratic equations that would be used when solving the width of the frame is 4x² + 36x = 88.

Learn more about Quadratic Equations:

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#SPJ5

Step-by-step explanation:

Area =5m×11m=55m²

perimeter =(11m+5m)×2=52m

hope it helps!

Answer:

$4

Step-by-step explanation:

12÷4=3

20÷4=5

56÷4=14

Answer:

21.75

Step-by-step explanation:

Because 6.00+6.25=12.25+7.00=19.75+8.00=27.75

Answer:

See below ↓

Step-by-step explanation:

Measures of the angles are equal 360° (total degree measure) - [∠G + ∠E]

[tex]\frac{1}{2a}[/tex]

Simplify or expand

[tex](2a)^{-1}[/tex]

Simplify using negative exponent rule [tex]a^{-n}=\frac{1}{a^n}[/tex]

[tex]\frac{1}{2a}[/tex]

I hope this helps you

:)

Answer:

[tex]y=14x^2+x-3[/tex]

Step-by-step explanation:

If the zeros of the polynomial are -1/2 and 3/7 then:

[tex]\implies x=-\dfrac12[/tex]

Add 1/2 to both sides:

[tex]\implies x+\dfrac12=0[/tex]

Multiply both sides by 2:

[tex]\implies 2x+1=0[/tex]

[tex]\implies x=\dfrac37[/tex]

Subtract 3/7 from both sides:

[tex]\implies x-\dfrac37=0[/tex]

Multiply both sides by 7:

[tex]\implies 7x-3=0[/tex]

Therefore, the factored form of the polynomial is [tex]y=(2x+1)(7x-3)[/tex]

Expanding the brackets so that the polynomial is in standard form:

[tex]\implies y=14x^2-6x+7x-3[/tex]

[tex]\implies y=14x^2+x-3[/tex]

Answer:

2, 0.2, 0.02

The first number is 2000.  The term to term rule is 'divide by 10'.

Step-by-step explanation:

To calculate the next term, divide the previous term by 10:

2000 ÷ 10 = 200

200 ÷ 10 = 20

Therefore, the next three terms will be:

20 ÷ 10 = 2

2 ÷ 10 = 0.2

2 ÷ 10 = 0.02

Term to term rule

To work out the term to term rule, give the initial number of the sequence and then describe the pattern:

The first number is 2000.  The term to term rule is 'divide by 10'.

Answer:

B

Step-by-step explanation:

The amount of change Zelma should receive is 20-0.40p, or 20 dollars minus the total amount of the bananas (each pound multiplied by 40 cents).

Answer: Simple the answer is c.

Step-by-step explanation:

First start out with 20 witch is a full number and subtract .40 p from 20

.40 is the cost of each banana and p is the amount of bananas that will be purchased.

Answer:

The correct answers are:

A.) 110 - 16 = 10h

B.) 110 = 16h + 10

Step-by-step explanation:

Sylvie needs $110 for a concert ticket and already has $16 in her pocket. She can make up the difference by working an additional 10 hours at her job.

To earn the $110 required for the concert ticket, she'll need to work 10 hours in addition to the $16 she already has.

As a result, the following calculation can be used to calculate her hourly rate:

110 = 16 + 10h

110 - 16 = 10h

I hope this helps! ^-^

Answer:

It is 1.1

Step-by-step explanation:

-hope this helps.

Answer:

craig had played approx 5 games..

Step-by-step explanation:

25 is the amount which craig have. 25-5.2=19.9 and when we divide 19.9 with 4 ie. 19.9÷4 = 4.9

Answer:

x = 5

Step-by-step explanation:

5x+17=42

5x + 17 - 17 = 42 - 17

Answer:

8p+5p

=13p

=6a-5b procesa

Answer:

( - y - 3 , - x - 1 )

Step-by-step explanation:

( x , y ) ----> ( - y , x ) ----> ( - y - 3 , x + 1 ) ----> ( - y - 3 , - x - 1 )

Their sum of ages is 45

So

Therefore

Step-by-step explanation:

let the tala's age be x and nabil's be y

x+y=45(equation 1)

x=y+27

x-y=27(equation 2)

solving 1 and 2 equation

x+y=45

x-y=27

______

2x=18

x=9

therefore the talas age is 9

putting the value of x in equarion 1

9+y=45

y=45-9

y=36

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

Volume of Barrel : [pi x h(r² + 2R²)] / 3

Barrel A : 2pi(r² + 2R²)]/ 3

Barrel B : 5pi(r² + 2R²)]/ 3

Barrel A + Barrel B = 532

5pi(r² + 2R²)/3 + 2pi(r² + 2R²)/3 = 532

5pi(r² + 2R²) + 2pi(r² + 2R²) = 1596

7pi(r² + 2R²) = 1596

pi(r² + 2R²) = 228

Barrel A = 2 x 228/3 = 76 ft³ SMALLER

Barrel B = 5 x 228/3 = 380 ft³

hope it's helpful, I'm not sure if (r) and (R) are the same if the two barrels has a similar shape. but if they're the same, then the answer is correct

Answer:

L: (15+6x) W: 2

L: (10+4x) W: 3

L: (5+2x) W: 6

Step-by-step explanation:

We don't have any numbers here to do calculations, so probably this is just an exercise in FACTORING. Also to practice that area is length times width.

The area given,

30 + 12x

can be factored several ways to be able to fill in the table.

This kind of factoring is like "un-distributive property" where a common factor can be factored out of the expression. Usually its helpful to factor out the greatest common factor (GCF) but in this case any common factor will do.

Also, unless there are more directions, either factor may be the length or the width.

2(15+6x)

3(10+4x)

6(5+2x)

Answer:

the answer is 56

Step-by-step explanation:

first off you need to add every number up which adds to be 336,

then you divide by the number of pieces in the data which in this case is 6,

366 divided by 6 is 56

I HOPE THIS HELPED!

Using the t-distribution, as we have the standard deviation for the sample, it is found that it can be concluded that the holes are being punched an average of 1. 84 cm.

At the null hypotheses, it is tested if the mean is of 1.84 cm, that is:

[tex]H_0: \mu = 1.84[/tex]

At the alternative hypothesis, it is tested if the mean is different of 1.84 cm, that is:

[tex]H_1: \mu \neq 1.84[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

Considering the hypothesis and the given sample, it is found that the parameters are as follows:

[tex]\overline{x} = 1.85, \mu = 1.84, s = 0.0235, n = 12[/tex].

Hence, the test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{1.85 - 1.84}{\frac{0.0235}{\sqrt{12}}}[/tex]

[tex]t = 1.47[/tex]

Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.1 and 12 - 1 = 11 df, the critical value is of [tex]|t^{\ast}| = 1.7959[/tex]

Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis and it can be concluded that the holes are being punched an average of 1. 84 cm.

More can be learned about the t-distribution at https://brainly.com/question/16313918