A painting measures 15 cm long by 24 cm high. You buy two posters, each showing an enlargement of the painting. The first poster measures 45 cm long by 72 cm high. The second poster measures 97.5 cm long by 156 cm high. Which of the following is true? (Hint: To be an accuarate representation of the painting, would the the poster be similar to the painting?)

Answer:

Step-by-step explanation:

tan∅ = opposite / adjacent

From the question

AC is the adjacent

BC is the opposite

So we have

tan (a) = BC / AC

tan (a) = 24/7

Hope this helps you

Answer:

The mean number of the children is 1.2

Step-by-step explanation:

Given

Children: 0, 1, 2, 1, 2

Required

Determine the Mean number

The mean of a set is calculated as follows;

[tex]Mean = \frac{\sum x}{n}[/tex]

Where x is the given set and n is the number of sets

In this case, n = 5 children

Hence;

[tex]Mean = \frac{0 + 1 + 2 + 1 + 2}{5}[/tex]

[tex]Mean = \frac{6}{5}[/tex]

[tex]Mean = 1.2[/tex]

Hence, the mean number of the children is 1.2

Answer:

30, 85, 95, 150

Step-by-step explanation:

The angles of a quadrilateral add to 360

Let x be the smallest angle

x+55

x+65

x+120 are the other three angles

Add the 4 angles together and they sum to 360

x+x+55 x+65+ x+120 = 360

Combine like terms

4x+240 = 360

Subtract 240 from each side

4x+240-240 = 360 -240

4x = 120

Divide by 4

4x/4 = 120/4

x = 30

x+55= 30+55 = 85

x+65 = 30+65 = 95

x+120 = 30+120 = 150

Answer:

{-0.5, 0.1}

Step-by-step explanation:

[tex]x = \frac{8 \pm \sqrt{(-8)^2 - 4 \cdot -20 \cdot 1}}{-40} = \frac{8 \pm 12}{-40}[/tex]

so x is 20/-40 = -0.5 or x = -4/-40 = 0.1

==================================================

Explanation:

We'll use the hinge theorem here. This says (more or less) that the larger an angle is, the side opposite of that will be longer.

Imagine that the segments with the single tickmarks represent a door swinging open/shut. The more open a door is, the further the distance it is from the handle to the frame. In terms of these triangles, the segment 25 is larger than 5x-10 because the angle 90 (opposite the 25) is larger than the angle 85 degrees (opposite the 5x-10)

In symbols we say

5x - 10 < 25

We also say 5x - 10 > 0 or 0 < 5x - 10 to ensure that the segment of length 5x-10 is not 0 or negative.

Put the two inequalities together and we get 0 < 5x - 10 < 25

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

Solve for x

0 < 5x - 10 < 25

0+10 < 5x - 10 < 25 + 10 .... adding 10 to all sides

10 < 5x < 35

10/5 < 5x/5 < 35/5 ... dividing all sides by 5

2 < x < 7

We have x between 2 and 7, and not equal to either endpoint.

Answer:

a) 3/1 that is 3

b) 8/7

c) the mixed fraction is converted into simple fraction: 3*2+2/3 = 8/3

therefore the reciprocal is 3/8

d) 1/5

e) the mixed fraction is converted into simple fraction: 6*6+1/6 = 37/6

therefore the reciprocal is 6/37.

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Answer:

a. [tex]3[/tex]

b. [tex] \frac{8}{7} [/tex]

c. [tex] \frac{3}{8} [/tex]

d. [tex] \frac{1}{5} [/tex]

e. [tex] \frac{6}{37} [/tex]

Step-by-step explanation:

a. [tex] \frac{1}{3} [/tex]

Just flip the fraction , you will get:

[tex] = \frac{3}{1} [/tex]

[tex] = 3[/tex]

b. [tex] \frac{7}{8} [/tex]

flip the fraction

[tex] = \frac{8}{7} [/tex]

c. [tex]2 \frac{2}{3} [/tex]

The first thing you have to do is that convert mixed fraction into improper fraction

[tex] \frac{8}{3} [/tex]

Flip the fraction

[tex] = \frac{3}{8} [/tex]

d. [tex]5[/tex]

flip the fraction

[tex] = \frac{1}{5} [/tex]

e. [tex]6 \frac{1}{6} [/tex]

Convert mixed fraction into improper fraction

[tex] = \frac{37}{6} [/tex]

Flip the fraction in order to get reciprocal

[tex] = \frac{6}{37} [/tex]

Hope this helps...

Best regards!!

Answer:

c is 35

d is 13

Step-by-step explanation:

I multiplied both sides, and then simplified the equation.

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Answer:   simplified algebraic expression  : x

Step-by-step explanation:

The given phrase : 100 % of x

We can write 100 as 1 because 100% means complete or entire part.

Also, replace 'of' by '×' (Multiply sign).

So, the given phrase will become

1 × x   [Algebraic expression]

= x         [Simplified]

hence, the simplified algebraic expression is 'x'.

Answer:

see below

Step-by-step explanation:

-3.55 g≤ -28.4

Divide each side by -3.55, remembering to flip the inequality

-3.55 g/-3.55≥ -28.4/-3.55

g≥8

Closed circle at 8 and the line goes to the right

Answer:

See Below.

Step-by-step explanation:

We have the expression:

[tex]3pf^2-21p^2f+6pf-42p^2[/tex]

Part A:

Find the GCF. Notice that we have a three in every term and a p in every term. Thus, the GCF will be 3p. Factor:

[tex]3p(f^2-7pf+2f-14p)[/tex]

This is the most we can do.

Part B:

Continuing from where we left off, we can factor the entire expression by grouping:

[tex]\displaystyle \begin{aligned} &= 3p(f^2-7pf+2f-14p) \\ \\ &= 3p(f(f-7p)+2(f-7p)) \\ \\ &=3p((f+2)(f-7p))\end{aligned}[/tex]

Answer:

B

Step-by-step explanation:

Just reduce your x's and y's. The x^-1 cancels with the x^5, and the y^-9 and y^-3 get simplified. After some basic simplifying, you get answer B.

Answer:

4x^3+8x^2

Step-by-step explanation:

Multiply each term:

4x^3+8x^2

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Answer:

Colin has 8 sheets left for his third class.

Step-by-step explanation:

Given that:

Total Number of pieces of papers = [tex]x[/tex]

Number of pieces of papers used for 1st class = 5 fewer than half of the pieces in the pad

Writing the equation:

[tex]\text{Number of pieces of papers used for 1st class =} \dfrac{x}{2} -5 ...... (1)[/tex]

Also, Given that number of pieces of papers used for the 2nd class are 2 more than that of papers used in the 1st class.

[tex]\text{Number of pieces of papers used for 2nd class =} \dfrac{x}{2} -5+2 = \dfrac{x}2 -3 ...... (2)[/tex]

Now, number of pieces of papers left for the third class = Total number of pieces of papers in the pad - Number of pieces of papers used in the first class - Number of pieces of papers used in the first class

[tex]\text{number of pieces of papers left for the third class = }x-(\dfrac{x}{2}-5)-(\dfrac{x}{2}-3)\\\Rightarrow x-\dfrac{x}2-\dfrac{x}2+5+3\\\Rightarrow x-x+5+3\\\Rightarrow 8[/tex]

So, the answer is:

Colin has 8 sheets left for his third class.

Answer:

x = 2

Step-by-step explanation:

3(2x+1) = 15

6x +3 = 15

6x = 12

x - 2

Answer:

67 - p = 52

Step-by-step explanation:

the train starts with 47 people:      47

it picks up 20 more:      47 + 20 = 67

p people get off:                            67 - p

52 people are left on train:           67 - p = 52

Answer:

2√2

Step-by-step explanation:

By simplifying we get the value is [tex]2\sqrt{2}[/tex]

The combination in which numbers, variables, functions are present, is called expression.

Example : 6y-3x+2, 2y-3 etc.

The given expression is [tex]\frac{1}{\sqrt{2}+1 } +\frac{1}{\sqrt{2}-1 }[/tex]

Simplifying,

First we take the LCM of [tex]\sqrt{2}+1[/tex] & [tex]\sqrt{2}-1[/tex]

Then expression becomes, [tex]\frac{(\sqrt{2}-1)-(\sqrt{2}+1) }{(\sqrt{2}+1)(\sqrt{2}-1)}[/tex]

Now, using [tex](a+b)(a-b)=a^{2}- b^{2}[/tex] we get, [tex]\frac{\sqrt{2}-1+\sqrt{2}+1 }{(\sqrt{2}) ^{2} - 1^{2} }[/tex]

Now, simplifying, we get,  [tex]\frac{2\sqrt{2} }{2-1}[/tex] = [tex]2\sqrt{2}[/tex]

Learn more about expression here :

https://brainly.com/question/4344214

#SPJ2

Answer:

0.9

Step-by-step explanation:

This is a sine triangle. We have the hypotenuse (7) and an angle opposite of x (6). The formula for sine is opposite/hypotenuse; 6/7 = 0.8571428571428571. This, rounded to the nearest tenth, is 0.9.

Answer:

59 degrees

Step-by-step explanation:

Sin = opposite / hypotenuse

In this case sin is 6/7

To find the angle of this we need to use the arcsin, or sin^-1 function

Arcsin(6/7) = 58.9972809 degrees

This gets rounded to 59 degrees

Answer:

The correct option is;

Simpson Paradox

Step-by-step explanation:

The phenomenon whereby particular trends are prevalent in small data portions but are not evident or an inverse trend is observe when the portions are joined together is known as Simpson's paradox.

Whereby the data for calculating the bating averages as found online are given as follows;

Season,                       Derek Jeter                           David Justice

1995,                           12/48 = 0.250                         104/411 ≈ 0.253

1996,                           183/582 ≈ 0.314                      45/140 ≈ 0.321

The overall hits to the overall bats ratio are;

,         (183 + 12)/(582 + 48) ≈0.310   (104+45)/(411+140) = 0.27

Which shows that  Derek Jeter's overall average was better than Justice's average  

Answer:

If the question is saying that length is 7x, then the answer (width) is x-2

Answer:

q = 4 mi

Step-by-step explanation:

Using the sine or cosine ratio in the right triangle and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{q}{4\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

[tex]\sqrt{2}[/tex] × q = 4[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )

q = 4

Answer:

[tex]y > \frac{2x}{3} + 1[/tex]

Step-by-step explanation:

Given:

The graph in the attachment where the coordinates are (3,3) and (-3,-1)

Required:

Which inequality represent the graph

The first step is to determine the slope of the graph

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where m represents the slope, [tex](x_1, y_1) = (3,3)[/tex] and [tex](x_2, y_2) = (-3,-1)[/tex]

[tex]m = \frac{-1 - 3}{-3 - 3}[/tex]

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

Simplify to lowest term

[tex]m = \frac{2}{3}[/tex]

Next is to determine the equation of the line using the slope formula

[tex]m = \frac{y - y_1}{x - x_1}[/tex], [tex](x_1, y_1) = (3,3)[/tex]  and [tex]m = \frac{2}{3}[/tex]

[tex]\frac{2}{3} = \frac{y - 3}{x - 3}[/tex]

Cross multiply

[tex]2 * (x - 3) = 3 * (y - 3)[/tex]

Open both brackets

[tex]2 x - 6 = 3y -9[/tex]

Collect like terms

[tex]2 x - 6 +9= 3y[/tex]

[tex]2 x+3= 3y[/tex]

Divide through by 3

[tex]\frac{2x}{3} + \frac{3}{3} = \frac{3y}{3}[/tex]

[tex]\frac{2x}{3} + 1 = y[/tex]

Reorder

[tex]y = \frac{2x}{3} + 1[/tex]

Next is to determine the inequality sign

The inequality becomes

[tex]y > \frac{2x}{3} + 1[/tex]

Answer:

The logarithmic parent function is the only one with negative numbers in the range

Step-by-step explanation:

Hello,

These functions have been very well known, I remind you their graphs below

The logarithmic parent function is the only one with negative numbers in the range

range for square root is [tex]\mathbb{R^{+}}[/tex]

range for logarithmic is [tex]\mathbb{R}[/tex]

range for exponential is [tex]\mathbb{R^{+}}[/tex]

THAT S TRUE

The square root and logarithmic parent functions have the same domain

domain for square root is [tex]\mathbb{R^{+}}[/tex]

domain for logarithmic is [tex]\mathbb{R}[/tex]

THAT S WRONG

The square root parent function domain is the most restricted

domain for square root is [tex]\mathbb{R^{+}}[/tex]

domain for exponential is [tex]\mathbb{R^{+}}[/tex]

THAT S WRONG

All three parent functions have the same domain

domain for square root is [tex]\mathbb{R^{+}}[/tex]

domain for exponential is [tex]\mathbb{R^{+}}[/tex]

domain for logarithmic is [tex]\mathbb{R}[/tex]

THAT S WRONG

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

$5.70

Step-by-step explanation:

1. 25.00 - 2.20 = $22.80

2. 22.80 divided by 4 = $5.70

Answer:

$5.70

Step-by-step explanation:

let the price for each canvas be $x

hence the price of 4 canvases will be $4x

It is given that after she paid for 4 canvases, she had a balance of $2.20 on her orginally $25 gift card.

Hence we can assemble an equation:

$4x + $2.20 = $25

4x + 2.2 = 25   (subtract 2.2 from both sides)

4x = 25 - 2.2

4x =22.8  (divide both sides by 4)

x = 22.8 / 4

x = 5.7

Hence each canvas cost $5.70

Answer:

y = 3/4( x+5)( x+4) ( x-1)

Step-by-step explanation:

The formula for the polynomial is

y = c( x- a1)( x- a2) ( x-a3)  where c is a constant and a1,a2,a3 are the zeros

We have zeros -5,-4 and 1

y = c( x- -5)( x- -4) ( x-1)

y = c( x+5)( x+4) ( x-1)

We have a y intercept of -15

That means x=0 and y = -15

-15 = c ( 0+5)( 0+4) ( 0-1)

-15 = c( 5) ( 4) (-1)

-15 = c( -20)

Divide each side by -20

-15/-20 = c

3/4 =c

The equation is

y = 3/4( x+5)( x+4) ( x-1)

Answer:

10) [tex]10v^2-19v+6[/tex]

11) [tex]15x^3-7x^2-29x+20[/tex]

Step-by-step explanation:

Well first let's make the box.

10)

Look at the image below ↓

[tex]10v^2-19v+6[/tex]

11)

Look at the image below ↓

[tex]15x^3-7x^2-29x+20[/tex]

Thus,

number 10 is [tex]10v^2-19v+6[/tex] and number 11 is [tex]15x^3-7x^2-29x+20[/tex].

Hope this helps :)

Answer:

x=-15/2 and x=1

x=6 and x=3/4

Step-by-step explanation:

You have the following equations:

[tex]\frac{4x-3}{x+2}=\frac{2x}{x+5}[/tex]

[tex]\frac{2}{x-2}+\frac{3}{x}-\frac{9}{x+3}[/tex]

To solve both equations you can first multiply by the m.c.m of the denominators, and then solve for x, just as follow:

first equation:

[tex][\frac{4x-3}{x+2}=\frac{2x}{x+5}](x+2)(x+5)\\\\(4x-3)(x+5)=2x(x+2)\\\\4x(x)+4x(5)-3(x)-3(5)=2x(x)+2x(2)\\\\4x^2+20x-3x-15=2x^2+4x\\\\4x^2-2x^2+20x-3x-4x-15=0\\\\2x^2+13x-15=0[/tex]

In this case you use the quadratic formula:

[tex]x_{1,2}=\frac{-13\pm \sqrt{(13)^2-4(2)(-15)}}{2(2)}\\\\x_{1,2}=\frac{-13 \pm 17}{4}\\\\x_1=-\frac{15}{2}\\\\x_2=1[/tex]

Then, for the first equation the solutions are x=-15/2 and x=1

second equation:

[tex][\frac{2}{x-2}+\frac{3}{x}=\frac{9}{x+3}]x(x-2)(x+3)\\\\2x(x+3)+3(x-2)(x+3)=9x(x-2)\\\\2x^2+6x+3(x^2+3x-2x-6)=9x^2-18x\\\\2x^2+6x+3(x^2+x-6)=9x^2-18x\\\\2x^2+6x+3x^2+3x-18-9x^2+18x=0\\\\-4x^2+27x-18=0[/tex]

Again, you use the quadratic formula:

[tex]x_{1,2}=\frac{-27\pm \sqrt{(27)^2-4(-4)(-18)}}{2(-4)}\\\\x_{1,2}=\frac{-27\pm 21}{-8}\\\\x_1=6\\\\x_2=\frac{3}{4}[/tex]

Then, the solutions for the second equation are x=6 and x=3/4

Answer:

x = E/(p - y)

Step-by-step explanation:

p - y = e/x

x(p-y) = e

x = e/(p-y)

Answer:

Hey there!

p=e/x+y

p-y=e/x

x(p-y)=e

x=e/(p-y)

Hope this helps :)

Answer:

5.6

Step-by-step explanation:

(3÷3/4)÷5/7

[tex] \frac{3 \times 4}{3} \div \frac{5}{7} [/tex]

[tex]4 \div \frac{5}{7} [/tex]

[tex]4 \times \frac{7}{5} [/tex]

[tex] \frac{28}{5} [/tex]

=5.6

use "keep, change, flip " when dividing a number by a fraction.

keep the whole number

flip the divide sign to multiply

change the placement of number e.g. 5/7 becomes 7/8

then solve

Answer:

y+0

As y=0 represent x-axis whose slope is 0 and intersects y-axis at the origin.