A princess has two pet dragons. The dragons can eat 300kg of chocolate in 12 days. How many DAYS will the same 300kg last if got 4 more dragons for her birthday?

The number of problems that were on the text was 240 problems.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the total number of problems that were on the text, y represent the time to be spent, hence:

y = x/8

Also:

y - 6 = x/10

x/8 - 6 = x/10

x = 240

The number of problems that were on the text was 240 problems.

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Hello!

Rate of income tax = Tax paid / Monthly income

⇒ Rate = 8,000 / 40,000

⇒ Rate = 0.2

⇒ Rate = 20%

∴ The rate of income tax is 20%.

Answer:

The side splitter theorem.

Step-by-step explanation:

You have a pair of parallel lines intersecting a triangle.

Answer:

12stickers

Step-by-step explanation:

that's all I could do.have a nice day.hope it helps.

If Jay spends 40 at the store, the number of points he will earn is; 10 points

Let the number of rewards points a customer earns be y

Let the amount of money, in dollars, that the customer spends at the store be x.

Since the number of rewards points a customer earns varies directly with the amount of money, in dollars, that the customer spends at the store, then we can say that;

y ∝ x

Thus;

y = kx

where k is the constant of proportionality.

We are given x = 15 when y = $60. Thus;

60 = 15k

k = 60/15

k = 4

If Jay spends $40, it means the number of points will be;

40 = 4x

40/4 = x

x = 10 points.

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Two points that lie on the graph of f^-1(x) are (7, -1) and (6,1)

The table of values is given as:

x       f(x)

-1       7

1        6

3       5

4      1

6    -1

Swap the points to determine the inverse function f^-1(x)

x       f^-1(x)

7       -1

6        1

5       3

1        4

-1      6

The points from the above table are (7, -1) and (6,1)

Hence, two points that lie on the graph of f^-1(x) are (7, -1) and (6,1)

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Answer:

Step-by-step explanation:

ΔABC ≅ ΔDEF

The length AB = 28 and the length of DE = 7. Since these are corresponding sides, we know that DEF= 1/4 (ΔABC)

So, since ΔABC = 160, we know that ΔDEF will be 1/4 of that, meaning that ΔDEF is 40.

ΔDEF = 40cm²

Answer:

10 cm2

Step-by-step explanation:

The ratio per side is 28/7 = 4

When two similar figures have a ratio of 4:1, the difference between their areas is:

[tex](4)^{2} :(1)^{2}[/tex]

[tex]16:1[/tex]

That is, the dimension of the area of the largest figure is 16 times larger than the smallest figure.

So for this case:

the area of the larger figure is

ΔABC = 160 sq.cm

Then the area of the minor figure is:

ΔDEF= 160/16 = 10 sq.cm

Hope this helps

Answer:

15

Step-by-step explanation:

→ Write the ratio of men to days to hours

30 : 12 : 8

→ Write the new proportion

24 : x : 8

→ Find the multiple between 30 and 24

1.25

→ Multiply by 12

12 × 1.25 = 15

The first quartile of the data set is 28.

From the question, we are to determine the first quartile of the given data set

The first quartile or lower quartile, (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.

The given data set is

14,28,33,42,53,81,97

In the given data set, the first quartile is 28.

Hence, the first quartile of the data set is 28

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Answer:

2

Step-by-step explanation:

By the triangle proportionality theorem,

[tex] \frac{12}{2y - 1} = \frac{4y - 4}{1} \\ \\ 12 = (2y - 1)(4y - 4) \\ \\ 12 = 8 {y}^{2} - 12y + 4 \\ \\ 8 {y}^{2} - 12y - 8 =0 \\ \\2 {y}^{2} - 3 y - 2 = 0 \\ \\ (2y + 1)(y - 2) = 0[/tex]

From this, we know that y = -1/2 or 2.

However, as distance must be positive, we disregard the negative case, giving us y = 2.

The second transformation is a rotation about point H.

It should be noted that a congruent triangle simply means when two triangles have the same sides and the same angles.

As two rigid transformations, to map ΔHJK to ΔLMN.

The first is a translation of vertex H to vertex L, and the second transformation is a rotation about point H.

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Answer:

B. a rotation about point H

Step-by-step explanation:

got it correct on my quiz

The height of the wall from the question is 13.27ft

The theorem states that the square of the longest side is equal to the sum of square of other two sides.

From the given question

Hypotenuse (ladder length) = 15ft

Adjacent = 7feet

Required

Height of the wall H

According to the theorem

15² = 7² + H²

H² = 225 - 49

H² = 176

H = 13.27feet

Hence the height of the wall from the question is 13.27ft

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The additional information needed to prove both triangles are similar are:

A. ∠B ≅ ∠M

C. △ABC was rotated and dilated by a scale factor between 0 and 1

E. ∠C ≅ ∠L

When a triangle is rotated and dilated by a scale factor, the new triangle formed has the same shape but different size of the original triangle. However, all its corresponding angles remains congruent.

Thus, for triangles ABC and NML to be similar to each other, since we already known each have one congruent right angles, the additional information needed are:

A. ∠B ≅ ∠M

C. △ABC was rotated and dilated by a scale factor between 0 and 1

E. ∠C ≅ ∠L

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What's the equation with a slope of -4 that goes through (-1,1)? find it

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The equation used, here is [tex]\bf{y-y1=m(x-x1)}[/tex].

[tex]\bf{y-1=-4(x-(-1)}[/tex] | simplify after putting in the information given

[tex]\bf{y-1=-4(x+1)}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

                          [tex]\bf{=y-1=-4(x+1)}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

The equation in point slope form is y-1 = 1/4(x - 12)

The formula for calculating the equation of a line is expressed as;

y = mx + b

m is the slope

b is the intercept

Slope = 1+3/12+4

Slope = 4/16

Slope = 1/4

For the intercept

1 = 1/4(12) + b

b = 1 - 3

b = -2

Hence the equation in point slope form is y-1 = 1/4(x - 12)

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The standard form is:

4y - x = -8

We know that the point-slope equation of the line is:

y - 1 = (1/4)*(x - 12)

Expanding the right side, we get:

y - 1 = (1/4)*x - 3

Now we can move the term with x to the left side:

y - (1/4)*x = +1 - 3

y - (1/4)*x = -2

Now we can multiply both sides by 4:

4y - x = -8

This is the standard form of the linear equation.

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The compound inequality that represents the given graph is x < -2 or x ≥ 4. The correct option is B. x < -2 or x ≥ 4

From the question, we are to write the compound inequality that represents the given graph

In the graph, we have

x < -2

or

x ≥ 4

Hence, the compound inequality that represents the given graph is x < -2 or x ≥ 4. The correct option is B. x < -2 or x ≥ 4

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Answer:

36

Step-by-step explanation:

MC : BC : MB = 1 : √3 : 2

MC : BC = 1 : √3

12 : BC = 1 : √3

BC = 12 : 1/√3

BC = 12 × √3/1

BC = 12 × √3

BC = 12√3

MC : MB = 1 : 2

12 : MB = 1/2

MB = 12 : 1/2

MB = 12 × 2/1

MB = 12 × 2

MB = 24

AB = 2BD

AB = 2CD√3

AB = 2(½BC)√3

AB = 2(½ × 12√3) √3

AB = 2 × 6√3 × √3

AB = 12 × √9

AB = 12 × 3

AB = 36

The setup boxes in the synthetic division are (b)

The dividend is given as:

x^3 + 4x^2 + x - 6

The divisor is given as:

x - 2

Set the divisor to 0

x - 2 = 0

Solve for x

x = 2

Remove the variables in the dividend

1 + 4 + 1 - 6

Remove the arithmetic signs

1  4  1 - 6

So, the setup is:

2 | 1  4  1 - 6

Hence, the setup boxes are (b)

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Answer:

I think it's C

Step-by-step explanation:

Hope it helps

Because we can't divide by zero, csc(θ) is undefined when θ = 0°, so the correct option is A.

First, remember that:

[tex]csc(\theta) = 1/sin(\theta)[/tex]

And also remember that we can't divide by zero.

Then the function csc(θ) is undefined for the values of θ such that sin(θ) = 0.

We know that sin(0°) = 0.

Then csc(0°) is undefined. This means that the correct option is the first one.

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Answer:

2

Step-by-step explanation:

3/4=6/8

(6/8)/(3/8)=2

At the end of week 3, plant 1 is 0.6 inches taller than plant 2.

For plant 1, the height (in inches) equation as a function of the number of weeks is:

[tex]h_1(w) = 2.5 + \frac{4}{10}*w[/tex]

The height for w = 3 is:

[tex]h_1(3) = 2.5 + \frac{4}{10}*3 = 3.7[/tex]

So the height at the end of week 3 is 3.7 inches.

For plant 2 the equation is:

[tex]h_2(w) = 2.5 + \frac{1}{5}*w[/tex]

The height for w = 3.

[tex]h_2(3) = 2.5 + \frac{1}{5}*3 = 3.1[/tex]

So the height at the end of week 3 is 3.1 inches.

The difference is:

3.7 in - 3.1 in = 0.6 in

At the end of week 3, plant 1 is 0.6 inches taller than plant 2.

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Answer:

-b

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

Answer:1\6

Step-by-step explanation:

The area of the enlarged picture on the wall is gotten as; D: 486 in²

The formula for Linear scale factor is;

L.S = Image distance/object distance

Thus, from the attached image, we can find the Linear scale factor as;

L.S = OL'/OL

L.S = 54/ 12

L.S = 9/2

Area scale factor is equal to the square of linear scale factor. Thus;

Area scale factor = (9/2)²

Area scale factor = 81/4

Now,

81/4 = Area of larger rectangle/Area of smaller rectangle

Area of the smaller rectangle = 4 ×6 = 24 in²

Thus;

Area of enlarged picture on wall = (81/4) × 24

Area of enlarged picture on wall = 486 in²

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Answer:

Step-by-step explanation:

its D

Answer:

Distance on the graph is representing the distance from Michelle's home. On her morning jog, Michelle ran to the end of her street, turned around and jogged at a slower pace back home.

Answer:

[tex]\frac{(20x+12)}{2}[/tex] and [tex]\sqrt{100x^2+36}[/tex]

Step-by-step explanation:

The expression 2(5x + 3) equals 10x + 6

One other way to get 10x + 6

[tex]\frac{(20x+12)}{2}[/tex]

finally, you could do:

[tex]\sqrt{100x^2+36}[/tex]

Answer:

= ax + b ln x - c/x + C

Step-by-step explanation:

Recall:

integral a dx = ax + C

integral 1/x dx = ln x + C

integral x^(n) = [x^(n +1)]/(n + 1) + C

Also:

c = variable in this problem

C = constant you add when you integrate

Separate each term of the numerator and set it over the denominator.

integral (ax^2 + bx + c)/x^2 dx =

integral [(ax^2)/x^2 + (bx)/x^2 + c/x^2] dx

Simplify each term and separate into the sum of 3 integrals.

= integral (a dx) + integral (b/x dx) + integral (c/x^-2) dx

= ax + b ln x + (cx^-1)/(-1) + C

= ax + b ln x - c/x + C