Please help! My teacher didn't teach us this and idk what to do

Please Help! My Teacher Didn't Teach Us This And Idk What To Do

Answers

Answer 1

Answer:

A. 112 feet

B. 3 seconds

C. 256 feet

Step-by-step explanation:

The function [tex]d(t)=-16t^2+96t+112[/tex] describes the height of the quarter above the water.

When [tex]t=0,[/tex] then

[tex]d(0)=-16\cdot 0^2+96\cdot 0+112\\ \\d(0)=112\ feet[/tex]

Part A. The quarter was tossed from 112 feet.

Find the vertex of parabola represented by quadratic function d(t):

[tex]t_v=\dfrac{-b}{2a}=\dfrac{-96}{2\cdot (-16)}=3\\ \\d(t_v)=d(3)=-16\cdot 3^2+96\cdot 3+112\\ \\d(3)=-144+288+112\\ \\d(3)=256\ feet[/tex]

Hence,

Part B. It will take 3 seconds to reach the maximum height.

Part C. The maximum height is 256 feet


Related Questions

length of a rectangle is 4 more than its breadth.represent in the form equation​

Answers

Let length be x and breadth be y.
x=y+4

Answer:

L = B + 4

Step-by-step explanation:

Let the breadth be B

Let the length be L

But from the question, we were told that the length is 4 more than the breadth. This is expressed as

L = B + 4

Morse code is a way to transmit text using a series of dots or dashes. The Morse Code for "Add" is shown. What fraction of the shapes are dots in the Morse code for "Add"

Answers

Add in Morse code is :

.—..-..

There are 8 total symbols, 5 of them are dots.

The fraction would be 5/8 are dots.

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

The Morse Code for Add is:

.__.._..

There are 5 dots and 3 dashes, so there are 8 figures in total. The fraction is 5 divided by the total number of symbols, which is 8. So the answer is [tex]\frac{5}{8}[/tex]

A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. If fencing costs $ 4 divided by ft for the legs and $ 16 divided by ft for the​ hypotenuse, write the total cost C of construction as a function of h.

Answers

Answer:

[tex]\frac{8h}{\sqrt{2}} + 16h[/tex]

Step-by-step explanation:

First we need to compute the side length as a function of h

So x be the side length of the right isosceles triangle, in Pythagorean formula we have

[tex]x^2 + x^2 = h^2[/tex]

[tex]2x^2 = h^2[/tex]

[tex]x = \frac{h}{\sqrt{2}}[/tex]

The cost for the legs is

[tex]C_l = 4*2x = \frac{8h}{\sqrt{2}}[/tex]

The cost for the hypotenuse is

[tex]C_h = 16h[/tex]

So the total cost in term of h is

[tex]C = C_l + C_h = \frac{8h}{\sqrt{2}} + 16h[/tex]

The total cost C of construction as a function of h is C =  16 / h +  8√2 / h

The pen is in the shape of an isosceles right angle. This means one of the

angle is 90 degrees and 2 sides of the triangle are equal and the base angles

are equal too.

Using pythagora's theorem

Therefore,

x² + x² = h²

2x² = h²

x² = h² / 2

x = √h²/ √2 = h/√2

cost of the legs = 4 / h/√2 + 4 / h /√2 = 8√2 / h

cost of the hypotenuse = 16 / h

Total cost = 16 / h +  8√2 / h

C =  16 / h +  8√2 / h

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The following examples illustrate the inverse property of multiplication. Study the examples, then choose the statement that best describes the property.

1
5
• 5 = 1

√2 (
1
√2
) = 1

Inverse property of multiplication: For all real numbers except , a • = 1.

Answers

Answer:

[tex]\text{Inverse property of multiplication: For all real numbers except }0,\text{ }a\cdot 1/a=1[/tex]

Explanation:

These are the examples given to illustrate the inverse property of multiplication:

         [tex]1/5\cdot 5=1\\\\ \sqrt{2}\cdot (1/\sqrt{2})=1[/tex]

And you must complete the statement to describe the property.

Inverse property of multiplication: For all real numbers except __, a • __ = 1.

In the first example, 1/5 and 5 are reciprocal numbers of each other, also known as multiplicative inverses. And the example is showing that the product of 1/5 and its reciprocal is 1.

In the second example,    [tex]\sqrt{2}\text{ and }(1/\sqrt{2})[/tex]    are reciprocal of each other. Again, the example is showing that the product of those a number at its reciprocal is 1.

That is a general property, that can be written as:

             [tex]a\cdot 1/a=1[/tex]

That property is satisfied by any number except 0, because the reciprocal of    [tex]0[/tex]  , i.e.    [tex]1/0[/tex]    is not defined.

Then, the statemen is:

[tex]\text{For all real numbers except }0,\text{ }a\cdot 1/a=1[/tex]

The statement that best describes the inverse property of multiplication is: Inverse property of multiplication: For all real numbers except 0, a * a⁻¹ = 1.

This means that if you multiply a number by its reciprocal, you will always get 1.

The examples you provided illustrate this property nicely:

5 * 1/5 = 1

√2 * 1/√2 = 1

Note that the inverse property of multiplication does not hold for the number 0, because the reciprocal of 0 is undefined.

Here is another example of the inverse property of multiplication:

3 * 1/3 = 1

You can check any other real number and its reciprocal, and you will always find that the product is 1.

The inverse property of multiplication is a useful property in mathematics, and it is used in many different areas, such as algebra, calculus, and physics.

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What is 4x4 i need to know

Answers

Answer: 16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

4x4 is 4 groups of four.

You can visibly show this by doing four lines of four dots.

••••

••••

••••

••••

count those dots, you get 16

Identify the x intercept and y intercept of the line 2x-4y=-12

Answers

-12/2 = -6 = x
-12/-4 = 3 = y

The x intercept is -6 and the y intercept is 3

The x-Intercepts of the line 2x - 4y = -12 is -6 and the y-intercept is 3.

To identify the x and y intercepts of the line, we set one variable to zero and solve the equation for the other variable.

For the x-intercept, we set y=0 and solve for x in the equation: 2x - 4(0) = -12, hence x = -6.

For the y-intercept, set x=0 and solve for y in the equation: 2(0) - 4y = -12, hence y = 3.

Therefore, the x-intercept is -6 and the y-intercept is 3

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Polynomial equation when zeros are -4, -2, 1, 4

Answers

The required poynomial equation is [tex]x^{4}+x^{3}-18x^{2}-16x+32[/tex].

Step-by-step explanation:

Given,

The zeros of the polynomial are - 4, - 2, 1 and 4

To find, the polynomial equation = ?

We know that,

The polynomial equation = (x - A)(x - B)(x - C)(x - D)

= (x + 4)(x + 2)(x - 1)(x - 4)

= [(x + 4)(x - 4)] [(x + 2)(x - 1)]

= ([tex]x^{2}-16[/tex])([tex]x^2-x+2x-2[/tex])

=  ([tex]x^{2}-16[/tex])([tex]x^2+x-2[/tex])

= [tex]x^{4}+x^{3}-2x^{2}-16x^{2}-16x+32[/tex]

= [tex]x^{4}+x^{3}-18x^{2}-16x+32[/tex]

Thus, the required poynomial equation is [tex]x^{4}+x^{3}-18x^{2}-16x+32[/tex].

QUESTION 4 of 10: Your restaurant purchases 1,625 bottles of Chablis per year. The annual increase of purchases has been 6%. If this
increase continues for 5 years, what will be your average increase in bottles purchased per year over that time?
a) 110 bottles
b) 190 bottles
c) 260 bottles
d) 400 bottles

Answers

Answer:

A - 110

Step-by-step explanation:

So if it is 6% increase you would times the number by 1.06. So you would do this like 5 times:

1,625 x 1.06 = 1722.5

1722.5 x 1.06 = 1825.85

1825.85 x 1.06 = 1935,401

1935.401 x 1.06 = 2051,52506

2051.52506 x 1.06 = 2174,6165636

Now you have the total number of bottles after 5 years, you would find the increase which is 2174.6165636 - 1,625 ≈ 550. 550 / 5 = 110

A

⭐ Answered by Foxzy0⭐

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The average increase in bottles purchased per year over that time is c) 110 bottles.

What is percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is generally denoted using the percent sign ''%''.

Now it is given that,

Number of bottles purchased per year, a = 1,625

Percentage increase per year, r = 6% = 0.06

Total time period, n = 5 years

Since, the equation of a exponential growth function is given as,

y = a(1 +r)ⁿ

⇒ y = 1625(1 +0.06)⁵

⇒ y = 1625(1.06)⁵

⇒ y = 1625*1.338

⇒ y = 2,175

Therefore, average increase in bottles purchased per year over that time   = (2175 - 1625) / 5

= 550 / 5

= 110 bottles

Thus, the average increase in bottles purchased per year over that time is c) 110 bottles.

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What number is halfway between .2 and .3

Answers

Final answer:

The number halfway between 0.2 and 0.3 is 0.25, which is found by adding the two numbers and dividing the total by 2.

Explanation:

The number halfway between 0.2 and 0.3 can be found by calculating the average of the two numbers. To find the average, you add the two numbers together and then divide by 2.

To show the steps:

Add 0.2 and 0.3 together: 0.2 + 0.3 = 0.5.Divide the sum by 2 to get the midpoint: 0.5 ÷ 2 = 0.25.

Therefore, the number that is halfway between 0.2 and 0.3 is 0.25.

The number halfway between 0.2 and 0.3 is 0.25.

To find the number halfway between 0.2 and 0.3, you calculate the average of the two numbers. Here's the step-by-step process:

Add the two numbers together: 0.2 + 0.3 = 0.5.Divide the sum by 2 to get the average: 0.5 / 2 = 0.25.

So, the number halfway between 0.2 and 0.3 is 0.25. This method ensures that you find the exact midpoint between two values.

56∙9÷14∙ 1/3
help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help

Answers

Answer:

Result = 12

Step-by-step explanation:

Fractions

Fractions are the general expression for rational numbers, defined as

[tex]\displaystyle \frac{a}{b}, \ b\neq 0[/tex]

Where a and b are integer numbers. Some operations with fractions have special rules than those with integers. The product of two or more fractions is

[tex]\displaystyle \frac{x}{y}\cdot \frac{w}{z}\cdot \frac{r}{s}=\frac{xwr}{yzs}[/tex]

We'll use that rule to operate the numbers given in the question:

[tex]\displaystyle 56\cdot \frac{9}{14}\cdot \frac{1}{3}=\frac{504}{42}[/tex]

The fraction can be simplified to an integer by dividing it

[tex]\displaystyle \frac{504}{42}=12[/tex]

Answer:The Answer is 12.

Step-by-step explanation:

When going through a step by step problem you always  wanna go from the left to right.(Unless you have parentheses)

56*9=504

504/14=36

36*1/3=12

There for, you answer is 12.

Hope this helped you. Remember Stay Positive!

72% of the students in Math 6th at AZVA are currently passing mastering their lessons. If 324 students are currently mastering their Math lessions, how many students are in Math 6th?

a) Use a percent equation OR set up a proportion that will use to solve the problem.

b) Solve the problem. Show your work.

Answers

Answer:

Step-by-step explanation:

72% of the students in math 6 = 324

let x represent the students in math 6

turn ur percent to a decimal

0.72x = 324

x = 324 / 0.72

x = 450 students <===

Answer:

its 233.28

Step-by-step explanation:

cuz i took a test and this was the right answer

A triangle with a height of 12
inches has an area of 42 square
inches. How long is the base of
the triangle? (need help) need it asap​

Answers

The area of a triangle is 1/2*base*height

So make your equation: 1/2*b*12=42

6*b=42

b=7

So the base is 7 inches long

Hope that helped!

Lisa purchased a concert ticket on a website. The original price of the ticket was $85. She used a coupon code to receive a 20% discount. The website applied a 10% service fee to the discounted price. Lisa's ticket was less than the original price by what percent?

Answers

Answer:

10%

Step-by-step explanation:

The original price of the ticket was $85 and she had a discount of 20%. Since the website applied a 10% service fee to her discount price, then Lisa'a ticket would be 10% less than the original price.

The 5th power of what number is equal to 3^15?

Answers

3^15 = 14,348,907

Which means...

x^5 = 14,348,907

If we execute [tex]\sqrt[5]{14348907}[/tex] and do the same with x^5 we get...

x = 27

So the 5th power of 27 is equal to 3^15.

⭐ Answered by Hyperrspace (Ace) ⭐

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The fifth power of the number 27 is equal to 3¹⁵.

To find the fifth power of a number that is equal to 3¹⁵, we need to determine what number raised to the power of 5 gives us 3¹⁵.

Let's call the number we are looking for "x." So, we need to solve the equation:

x⁵ = 3¹⁵

To find x, we can take the fifth root of both sides of the equation:

x = (3¹⁵[tex])^{(1/5)[/tex]

x = 3³

x = 27

This means that if we raise 27 to the power of 5 (27⁵), we will get 3¹⁵ (3 raised to the power of 15).

In conclusion, the number we are looking for is 27, as 27^5 is equal to 3¹⁵.

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Write an expression to represent:
"15 times a number w"

Answers

Answer:

15×w

Step-by-step explanation:

15 times w is a number bigger 15 times or added up again and again 15 times:

w+w+w+w+w+w+w+w+w+w+w+w+w+w+w or 15×w

Final answer:

The expression to represent "15 times a number w" is written as 15w. Substituting ½ for w would lead to the multiplication 15 × ½, resulting in 7.5.

Explanation:

To represent the phrase "15 times a number w," you would write the algebraic expression 15w. This is accomplished by using the coefficient 15 to indicate that the number w is being multiplied by 15. So, if you were to substitute the value ½ for w into this expression, you would perform the multiplication 15 × ½ to get the result, which simplifies to 7.5.

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Assume that y varies directly with x. If y = -15 when x = -5, find y when x = 3.
Write and solve a direct variation equation to find the answer.
y=

Answers

Answer: Y = 9

Step-by-step explanation:

Y & X

Y = KX

K = Y / X = - 15 / - 5 = 3

X = 3

K= 3

Y=?

Y = KX = 3 x 3 = 9

Therefore, when X = 3, Y = 9

I need help on this please can someone help me with this

Answers

Answer:

C. 11

Step-by-step explanation:

First, find the value of "x" by solving the first equation. You need to move every other number to the other side of "x". When you move a number, you have to do the opposite operation to both sides.

5x + 6 = 10     The opposite of +6 is -6.

5x + 6 - 6 = 10 - 6     Subtract 6 from both sides

5x = 10 - 6       The "6" on the left cancelled out. Simplify the right side

5x = 4          The opposite of multiply by 5 is divide by 5

5x/5 = 4/5           Divide both sides by 5

x = 4/5           Value of "x"

Substitute the value of "x", which is 4/5, in the "x" for the second equation.

10x + 3

= 10(4/5) + 3             Multiply 10 and 4/5

= [tex]\frac{10*4}{5}[/tex] + 3        Combine into the numerator

= [tex]\frac{40}{5}[/tex] + 3         Divide the top by the bottom

= 8 + 3             Add

= 11                  Value of second equation

Therefore the value of 10x + 3 is 11.

Help please I really need it

Answers

Answer:

X-Intercept is -45. (Answer would be (-45,0))

Step-by-step explanation:

You can use Desmos which is a graphing calculator to figure out the answer. Plug the equation into Desmos and it will show you a line and where the x-intercept is. And boom, you got your answer.

Find the output, yyy, when the input, xxx, is 555.

y = 5x-3y=5x−3

Answers

The output y is [tex]y=22[/tex]

Explanation:

The expression is [tex]y=5 x-3[/tex]

We need to determine the output y, when the value of input is x is 5.

That is, substituting [tex]x=5[/tex] in [tex]y=5 x-3[/tex], we get,

[tex]y=5(5)-3[/tex]

Multiplying the value within the bracket, we have,

[tex]y=25-3[/tex]

Subtracting the terms, we get,

[tex]y=22[/tex]

Thus, the value of output y is [tex]y=22[/tex]

Number 24 only please help me please

Answers

Check the picture below.

the idea being, that if we run an altitude segment from a right-angle in a triangle, and parallel to the opposite side, like in thise case, we end up with 3 similar triangles, a Large one, containing the other smaller ones, a Medium and a Small.

now, let's simply use proportions for those similar triangles.

[tex]\bf \stackrel{Large}{\cfrac{12}{4+x}}=\stackrel{Small}{\cfrac{4}{12}}\implies \cfrac{12}{4+x}=\cfrac{1}{3}\implies 36=4+x\implies \boxed{32=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Small}{\cfrac{4}{y}}=\stackrel{Medium}{\cfrac{y}{x}}\implies 4x=y^2\implies 4(32)=y^2\implies 128=y^2\implies \sqrt{128}=y \\\\\\ \sqrt{64\cdot 2}=y\implies \sqrt{8^2\cdot 2}=y\implies \boxed{8\sqrt{2}=y} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{Large}{\cfrac{z}{4+x}}=\stackrel{Medium}{\cfrac{x}{z}}\implies z^2=(4+x)x\implies z^2=4x+x^2\implies z = \sqrt{4x+x^2} \\\\\\ z = \sqrt{4(32)+32^2}\implies z = \sqrt{128+1024}\implies z = \sqrt{1152} \\\\\\ z = \sqrt{576\cdot 2}\implies z = \sqrt{24^2\cdot 2}\implies \boxed{z = 24\sqrt{2}}[/tex]

The graph of which function has a minimum located at (4, –3)?

f(x) = one-halfx2 + 4x – 11
f(x) = –2x2 + 16x – 35
f(x) = one-halfx2 – 4x + 5
f(x) = 2x2 – 16x + 35

Answers

Answer:

f(x) = 1/2x^2 – 4x + 5  (the third option)

Step-by-step explanation:

I looked it up on a graphing calculator.

The quadratic function that has a minimum located at (4, -3) is:

[tex]f(x) = (1/2)*x^2 - 4x + 5[/tex]

Which function has a minimum located at (4, -3)?

All the options are quadratic functions, so we need to find the one with a leading coefficient positive, which also has a vertex at (4, -3).

The 3 ones with positive leading coefficients are:

[tex]f(x) = (1/2)*x^2 + 4x -11[/tex]

[tex]f(x) = (1/2)*x^2 - 4x + 5[/tex]

[tex]f(x) = 2x^2 - 16x + 35[/tex]

The vertex of the first one is at:

[tex]x = -4/(2*1/2) = -4[/tex]

The x-value of the vertex must be x = 4, so we can discard this.

For the second quadratic function the x-value of the vertex is:

[tex]x = -(-4)/(2*1/2) = 4[/tex]

Then the y-value of the vertex is:

[tex]f(4) = (1/2)*4^2 - 4*4 + 5 = -3[/tex]

Then the vertex is at (4, -3), so this is the correct option.

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The product of t and three is 13.5

Answers

Answer: t = 4.5

Step-by-step explanation: 13.5/3 = 4.5

Answer:

T = 4.5

Step-by-step explanation:

The way to solve this is simple.

You just have to divide 13.5 by 3

and then you get the answer of 4.5!

Hope this helped!

~Oreo!!

Help please! these questions are really confusing me

Answers

Answer:

Figure 1: Option A :   [tex]$ \sqrt{\frac{\textbf{3}}{\textbf{2}}} $[/tex] ;   [tex]$ \frac{\textbf{1}}{\textbf{2}} $[/tex] ;  [tex]$ \sqrt{\textbf{3}}} $[/tex]

Figure 2: Option B: [tex]$ \frac{\sqrt{\textbf{19}}}{\textbf{10}} $[/tex] ;     [tex]$ \frac{\textbf{9}}{\textbf{10}} $[/tex] ;  [tex]$ \frac{\sqrt{\textbf{19}}}{\textbf{9}} $[/tex]

Figure 3: Option C:  [tex]$ \frac{\textbf{4}}{\textbf{5}} $[/tex]  ;  [tex]$ \frac{\textbf{3}}{\textbf{5}} $[/tex] ;  [tex]$ \frac{\textbf{4}}{\textbf{3}} $[/tex]

Step-by-step explanation:

[tex]$ \textbf{Sin A} \hspace{1mm} \textbf{= } \hspace{1mm} \frac{\textbf{opp}}{\textbf{hyp}} $[/tex]

[tex]$ \textbf{Cos A} \hspace{1mm} {\textbf{=} \hspace{1mm} \frac{\textbf{adj}}{\textbf{hyp}} $[/tex]

[tex]$ \textbf{Tan A} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{Sin A}}{\textbf{Cos A}} $[/tex]

We can simply follow these three formulas to solve the problem.

Figure 1:

Sin A = [tex]$ \frac{6\sqrt{3}}{12} $[/tex]  = [tex]$ \frac{\sqrt{3}}{2} $[/tex]

Cos A = [tex]$ \frac{6}{12} = \frac{1}{2} $[/tex]

Tan A = [tex]$ \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}} $[/tex]  = [tex]$ \sqrt{3} $[/tex]

Figure 2:

Sin A = [tex]$ \frac{2\sqrt{19}}{20} $[/tex]  = [tex]$ \frac{\sqrt{19}}{10} $[/tex]

Cos A = [tex]$ \frac{18}{20} = \frac{9}{10} $[/tex]

Tan A = [tex]$ \frac{\frac{\sqrt{19}}{10}}{\frac{10}{9}} $[/tex] = [tex]$ \frac{\sqrt{19}}{9} $[/tex]

Figure 3:

Sin A =   [tex]$ \frac{16}{20} $[/tex]   = [tex]$ \frac{4}{5} $[/tex]

Cos A = [tex]$ \frac{12}{20} = \frac{3}{5} $[/tex]

Tan A = [tex]$ \frac{\frac{4}{5}}{\frac{3}{5}} $[/tex]  = [tex]$ \frac{4}{3} $[/tex]

Hence, the answer.

Zoe had x dollars on Monday. 

Her sister took $4.50 from Zoe on Tuesday.

Zoe's mother gave her $20 on Wednesday.

Zoe spent half of her money on Thursday.

She had $17.80 left in her pocket.

how much did Zoe have on Monday​

Answers

13.00 I think I don’t know if that correct but that’s what I got
It’s $25.55 as if she took 4.50 from 20 it makes 15.50 and half of that it’s 7.75 plus $17.80 is $25.50

What is 15x when x=4

Answers

Answer:

60

Step-by-step explanation:

15*4=60

The 15x when x = 5 will be 60.

What is the arithmetic operator?

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given,

x = 4

Now,

15x is nothing but we need to multiply 15 with x

So,

15x = 15 × 4

15x = 60

Hence,The 15x when x = 5 will be 60.

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please help REAL ANSWERS ONLY

Answers

Use the distance formula: sqrt((x2-x1)^2+(y2-y1)^2)

Plug in variables:

sqrt((-3-2)^2+(5-8)^2)

sqrt((-5)^2+(-3)^2)

sqrt(25+9)

sqrt(34)

Rounded to the nearest tenth is 5.8 units

Hope this helped.

Consider the enlargement of a triangle that has a scale factor of 7.5.
A small triangle has a base of 5 centimeters and height of 2 centimeters. A larger triangle has a base of b and height of a.
Area Original = 1
2
(5)(2) = 5 cm2
What is the area of the enlarged triangle? cm2

Answers

Answer:    ✔ 281.25

Step-by-step explanation:

Answer:

281.25

Step-by-step explanation:

It is correct E d g e n u i t y

Suppose that receiving stations​ X, Y, and Z are located on a coordinate plane at the points ​(4​,5​), ​(-6​,-6​), and ​(-14​,2​), respectively. The epicenter of an earthquake is determined to be 10 units from X​, 5 units from​ Y, and 13 units from Z. Where on the coordinate plane is the epicenter​ located?
Find the coordinates of the epicenter.

Answers

Answer:

  (-2, -3)

Step-by-step explanation:

A careful graph shows the point (-2, -3) is at the intersection of the circles whose radii are the given distances from the receiving stations.

_____

The simultaneous equations for the circles can be solved algebraically.

The epicenter is 10 units from X, so lies on the circle ...

  (x -4)^2 +(y -5)^2 = 10^2

  x^2 -8x +16 +y^2 -10y +25 = 100

  x^2 +y^2 -8x -10y = 59

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The epicenter is 5 units from Y, so lies on the circle ...

  (x +6)^2 +(y +6)^2 = 5^2

  x^2 +12x +36 +y^2 +12y +36 = 25

  x^2 +y^2 +12x +12y = -47

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The epicenter is 13 units from Z, so lies on the circle ...

  (x +14)^2 +(y -2)^2 = 13^2

  x^2 +28x +196 +y^2 -4y +4 = 169

  x^2 +y^2 +28x -4y = -31

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Subtracting the second equation from each of the other two, we get ...

  (x^2 +y^2 -8x -10y) -(x^2 +y^2 +12x +12y) = (59) -(-47)

  -20x -22y = 106 . . . . eq1 -eq2

  (x^2 +y^2 +28x -4y) -(x^2 +y^2 +12x +12y) = (-31) -(-47)

  16x -16y = 16 . . . . . . . .eq3 -eq2

These simultaneous linear equations can be solved a variety of ways. We might use substitution:

  x = y+1 . . . . . from eq3 -eq2 divided by 16

  10(y +1) +11y = -53 . . . . . from eq1 -eq2 divided by -2

  21y = -63 . . . . . . . . . . . . simplify, subtract 10

  y = -3

  x = y+1 = -2

The epicenter is located at (x, y) = (-2, -3).

6v+13b=377
4v+9b=259

Answers

Answer:

v = 13

b = 23

Step-by-step explanation:

To solve this system of equations, we can negate one equation and add it to other to cancel out one variable.

Looking at v and b, the coefficients are 6, 4 and 13, 9, respectively.

It would be easier to use the LCM of 6 and 4

[tex]E_1 : 6v + 13b = 377\\E_2: 4v + 9b = 259\\\\4E_1 + (- 6)E_2:\\24v + 52b = 1508\\-24v - 54b=-1554\\\\0v -2b = -46\\-2b = -46\\b = 23\\\\4v + 9(23) = 259\\4v + 207 = 259\\4v = 52\\v = 13\\\\6(13) + 13(23)\\78 + 299\\377[/tex]

What is 22,119 rounded on o the nearest hundred

Answers

The hundreds numbers are 119.
119 rounded to the nearest hundred is 100.
That means that the answer is 22,100.
Answer is 22,100.
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