If the right triangle's dimensions are enlarged by 3 units, the new area would be *blank* square units. Just write the numerical answer.
Your answer
15 points!!

Check the picture below.

[tex]\stackrel{parent}{y=x^2}\hspace{5em}y=\stackrel{A}{4}(\stackrel{B}{1}x\stackrel{C}{-2.5})^2\stackrel{D}{-3} \\\\\\ \hspace{7em} \begin{array}{llll} \textit{stretch by }4\cdot 1\implies 4\\\\ \textit{translated by }\frac{2.5}{1}\implies 2.5\textit{ to the right}\\\\ \textit{downwards shift by }3 \end{array}[/tex]

Step-by-step explanation:

you are "hiding" some more information (like how much they made together).

without that we cannot calculate the actual values.

all I can do is set up the equations expressing the given relations between the parts of the total :

a = amount Alberto made

b = amount Benjamin made

c = amount Carlota made

b = 3×a

c = 2×b = 2× 3×a = 6×a

that's it.

your see ? now we need something that "ties" all 3 together, an equation of all 3 variables, where we can use the first 2 equations (by substitution) and then solve for the remaining third variable.

and that is missing.

if it is something like "together they made x", then we would have

a + b + c = x

a + 3a + 6a = x

10a = x

a = x/10

b and c we get then from the first 2 equations by simply using the calculated value of a :

b = 3×(x/10) = 3x/10

c = 6×(x/10) = 6x/10 = 3x/5

Answer:

r 104.20

Step-by-step explanation:

87tickets x r 2.00 = 174

174 - 69.80 = r 104.20

The exponential function is P = 5.63(1.0145)ⁿ. And the population of the city in 2018 is 6.1379 million, the number of the years when the population of the city is 10 million is 40 years, and the doubling time will be 49 years.

The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

In​ 2012, the population of a city was 5.63 million. The exponential growth rate was 1.45​% per year.

Then the exponential function will be given as

P = 5.63 (1.0145)ⁿ

Where P is the population (in million) and n is the number of years.

Then the population of the city in 2018 will be

n = 2018 - 2012 = 6

Then we have

P = 5.63 (1.0145)⁶

P = 5.63 x 1.0902

P = 6.1379 million

The number of the years when the population of the city is 10 million.

    10 = 5.63 x (1.0145)ⁿ

1.776 = (1.0145)ⁿ

Taking log both sides, then we have

log 1.776 = n x log 1.0145

            n = 39.90

            n ≅ 40 years

Then the doubling time will be

2 = (1.0145)ⁿ

Taking log on both sides, then we have

log 2 = n x log1.0145

      n = 48.1489

      n ≅ 49 years

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x + 2x + 6 = 27

3x + 6 = 27

x + 2 = 9

x = 9 - 2

x = 7

2 × 7 = 14

14 + 6 = 20

Answer:

See below under "Explanation".

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle f(x) = 3.55x - 4[/tex]

[tex]\displaystyle x = \{ 17, 21, 24, 34 \}[/tex]

Step 2: Find Profit

To find the profit the store makes each day, we input the number of customers that visited the store each day into our given function:

For the day that had 17 customers:

[tex]\displaystyle\begin{aligned}f(17) & = 3.55(17) - 4 \\& = 60.35 - 4 \\& = \boxed{56.35} \\\end{aligned}[/tex]

∴ the butcher store made $56.35 when 17 customers visited the store.

For the day that had 21 customers:

[tex]\displaystyle\begin{aligned}f(21) & = 3.55(21) - 4 \\& = 74.55 - 4 \\& = \boxed{70.55} \\\end{aligned}[/tex]

∴ the butcher store made $70.55 when 21 customers visited the store.

For the day that had 24 customers:

[tex]\displaystyle\begin{aligned}f(24) & = 3.55(24) - 4 \\& = 85.2 - 4 \\& = \boxed{81.2} \\\end{aligned}[/tex]

∴ the butcher store made $81.20 when 24 customers visited the store.

For the day that had 34 customers:

[tex]\displaystyle\begin{aligned}f(34) & = 3.55(34) - 4 \\& = 120.7 - 4 \\& = \boxed{116.7} \\\end{aligned}[/tex]

∴ the butcher store made $116.70 when 34 customers visited the store.

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Topic: Algebra I

Answer:

x = 6 [tex]\frac{8}{9}[/tex]

Step-by-step explanation:

From what I think the equation is, I got x = 6 [tex]\frac{8}{9}[/tex]

Answer:

C) 10,000,000

Step-by-step explanation:

Data provided in the question:  

- The phone number is of 7 digits

- we have choices from 0-9

meaning 10 number of choices, 0 1 2 3 4 5 6 7 8 9

we have 10 choices out of 10 for each of the 7 blanks

Therefore,

The total number of different phone numbers can there be in one area code that can be formed

= 10 × 10 × 10 × 10 × 10 × 10 × 10

= 10^7

= 10,000,000

Answer:

3/20

Step-by-step explanation:

Take the miles that Maria walked and subtract the miles that Cody walked

3/4 - 6/10

Simplify 6/10 by dividing the top and bottom by2

3/4 - 3/5

Get a common denominator of 20

3/4 *5/5 = 15/20

3/5 *4/4 =12/20

15/20 - 12/20

3/20

Answer:

0.15(3/20) miles more than Cody

3/4 = 0.75

6/10 = 0.6

Therefore, Maria walked 0.15(3/20) miles greater than Cody.

The number of students that took ENG but neither BIO nor P.E is 43.

A set is a collection of well-defined objects called elements of the given set.

Analysis:

see diagram below

In conclusion, the number of students that took ENG but neither BIO nor P.E is 43

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Answer:

[tex](\frac{2}{3})^{3} (\frac{1}{5}.\frac{2}{3} )^{-3} (\frac{1}{5})^{4} =(\frac{2^{3} }{3^{3} }) (\frac{2}{8} )^{-3} (\frac{1^{4}} {5^{4} })[/tex]

                          [tex]=(\frac{2^{3} }{3^{3} }) (\frac{2^{-3} }{8^{-3} } ) (\frac{1^{4}} {5^{4} })[/tex]

                          [tex]=\frac{2^{3} .2^{-3}.8^{3}. 1 }{3^{3} .5^{4} }[/tex]

                          [tex]=\frac{1.8^{3} }{3^{3} .5^{4} }[/tex]

                          [tex]=\frac{(2^{3}) ^{3} }{3^{3} .5^{4} }[/tex]

                          [tex]=\frac{2^{9} }{3^{3} .5^{4} }[/tex]

                          [tex]=\frac{512}{27.625}[/tex]

                          [tex]=\frac{512}{16875}[/tex]

Answer:

GCF is less than 3:

- 12 and 13

GCF is equal to 3:

- 6 and 27

- 12 and 21

- 3 and 6

GCF is greater than 3:

- 4 and 12

- 6 and 18

Step-by-step explanation:

6 and 27 GCF: 3

12 and 13 GCF: 1

4 and 12 GCF: 4

3 and 6 GCF: 3

12 and 21 GCF: 3

6 and 18 GCF: 6

Answer: c= -8

Step-by-step explanation:

c/2=-4  

-8/2=-4

-4 +5=1

Answer:

(f•g)(x) = (x)(2) = 2x

Step-by-step explanation:

(f•g)(x) is the "product" of functions f and g:  

(f•g)(x) = (x)(2) = 2x

Answer:

√25

= √( 5 x 5 )

= 5

√25 = 5

5 is an rational number, not an irrational number.

                 [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Given question:-}}}\rule{50}{1}[/tex]

              Jillian said, "√25 is irrational because it's a square root!" Why is

she incorrect?

    [tex]\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

    First let's see if we can simplify √25.

     We can, by using either our calculator or our brains.

       Anyway, √25=5 (5×5=25)

Now, let's take a look at what irrational numbers are.

            [tex]\dagger[/tex] Irrational numbers. This set includes numbers with an infinite

           number of digits after the decimal point. Irrational numbers

           cannot be expressed as fractions (p/q form)

Can [tex]\LARGE\textbf{5}[/tex] be expressed as a fraction? Sure!

This is how it's done:-

[tex]\Large\text{$\displaystyle\frac{5}{1}$}[/tex]

As you can see, 5 is not irrational.

            [tex]\rule{50}{1}\smile\smile\smile\smile\smile\rule{50}{1}[/tex]

Step-by-step explanation:

we don't see all answer options.

but I am sure it must be b.

simply because the right graph shows that the curve goes through

(4, 0) and (-4, 0)

and

(0, 3) and (0, -3)

but if I am mistaken about b showing that, please pick the graph that shows this.

the reason is to think when is the x term being 1, when y = 0, and when is the y term being 1, when x = 0.

these are some "cornerstones" for the graph based on the functional definition.

and the answers are the points listed above.

Answer:

Sine: 0.94

Cosine: -0.31

Cotangent: -0.3(infinite)

Cosecant: 1.05

Tangent: -3

Secant: -3.16

Formula for finding the 6 trigonometry functions

Finding opposite and adjacent angles

Hope this helps!

Step-by-step explanation:

The six trig functions are

[tex] \sin( \alpha ) = \frac{y}{r} [/tex]

[tex] \cos( \alpha ) = \frac{x}{r} [/tex]

[tex] \tan( \alpha ) = \frac{y}{x} [/tex]

[tex] \csc( \alpha ) = \frac{r}{y} [/tex]

[tex] \sec( \alpha ) = \frac{r}{x} [/tex]

[tex] \cot( \alpha ) = \frac{x}{y} [/tex]

Where

[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

[tex]r = \sqrt{ - 2 {}^{2} + {6}^{2} } [/tex]

[tex]r = \sqrt{40} [/tex]

[tex]r = 2 \sqrt{10} [/tex]

So we just plug in -2 for x, 6 for y, and our r value into these functions.

[tex] \sin( \alpha ) = \frac{6}{2 \sqrt{10} } = \frac{3}{ \sqrt{10} } = \frac{3 \sqrt{10} }{10} [/tex]

[tex] \cos( \alpha ) = \frac{ - 2}{2 \sqrt{10} } = \frac{ - 1}{ \sqrt{10} } = \frac{ - \sqrt{10} }{10} [/tex]

[tex] \tan( \alpha ) = \frac{6}{ - 2} = - 3[/tex]

Csc is the reciprocal of sine.

[tex] \csc( \alpha ) = \frac{ \sqrt{10} }{3} [/tex]

Sec is the reciprocal of cosine

[tex] \sec( \alpha ) = - \sqrt{10} [/tex]

Cot is the reciprocal of tan

[tex] \cot( \alpha ) = - \frac{1}{3} [/tex]

Answer:

x = 2, y = 13, z = 1

Step-by-step explanation:

2 * 2 * 13 * 13 * 17 is equal to 2x * 13y * 17z.

knowing that 2x = 2 * x

therefore

2 * 2 * 13 * 13 * 17 * 1

2 * x * 13 * y * 17 * z

meaning that

x = 2, y = 13, z = 1

Answer:

74

Step-by-step explanation:

(23-3)+(6×9)

(20) +(54)

=74

[tex]\text{Given that,}\\\\P(x) = 2x^4 -5x^2 +3x -9\\\\P(6) = 2\cdot 6^4 -5 \cdot 6^2 +3 \cdot 6 -9 \\\\~~~~~~~=2592-180+18-9\\\\~~~~~~~=2421\\\\\text{Hence the answer is option D.}[/tex]

The limit of f (x) as x approaches negative 1 is negative 1

The function is given as:

f(x) = x

The limit is represented as:

[tex]\lim_{x \to -1} f(x)[/tex]

Rewrite as:

[tex]\lim_{x \to -1} f(x)=x[/tex]

Substitute -1 for x

[tex]\lim_{x \to -1} f(-1)=-1[/tex]

So, we have:

As x approaches negative 1,f(x) approaches negative 1

Hence, t

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Answer:

[tex]P=0.71[/tex] or 71%

Explanation:

[tex]P=\frac{3.63*10^2}{1.48*10^8+3.63*10^8}[/tex]

[tex]=\frac{3.63}{5.11} =0.71[/tex] or 71%

The probability that exactly 1 doesn't grow will be 0.07

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

We can use Bernoulli estimation to solve this. P(g) = 0.85, probability of not growing into healthy plant P(n) = 1-P(g) = 1 - 0.85 = 0.15

Using the Bernoulli approximation:

P(n=1)=⁹C₁xP(n)¹.⁵xP(g)⁸.⁵

P(n=1)=9x0.15¹.⁵x0.8⁸.⁵

P(n=1)=0.07

Hence the probability that exactly 1 doesn't grow will be 0.07

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The value of d at the point of equilibrium, to the nearest whole number is 54

The equations are given as:

[tex]d = \frac{-5}{9}p + 94[/tex]

[tex]s = 3p - 160[/tex]

At the point of equilibrium, d = s.

So, we have:

[tex]\frac{-5}{9}p + 94 = 3p - 160[/tex]

Multiply through by 9

-5p + 846 = 27p - 1440

Collect like terms

27p + 5p = 1440 + 846

Evaluate the sum

32p = 2286

Divide through by 32

p = 71.4375

Substitute p = 71.4375 in [tex]d = \frac{-5}{9}p + 94[/tex]

[tex]d = \frac{-5}{9} * 71.4375 + 94[/tex]

Evaluate

d = 54.3125

Approximate

d = 54

Hence, the value of d at the point of equilibrium, to the nearest whole number is 54

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Answer:

its d :)

Step-by-step explanation:

Answer:

3/10 or 30%

Step-by-step explanation:

Add all of the marbles: 5+2+3=10

Then use a fraction to represent the three purple marbles: 3/10

That porportion is your answer

The number of blocks of clay needed by Hyla is 30 blocks

Area is the region bounded by a plane shape.

To calculate the number of blocks of clay needed by Hyla, we find the area of the bottom of the box and divide it by the area of the block.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, The number of blocks of clay needed by Hyla is 30 blocks

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