An equilateral triangle has a perimeter of 15x3 + 33x5 feet. What is the length of each side?

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ANSWER

10.9

EXPLANATION

We use the Altitude Theorem to determine the value of h.

According to the Altitude Theorem, the height, h is equal to the geometric mean of the two segment created by the leg of the altitude on the hypotenuse.

This implies that:

[tex] h= \sqrt{MP \times PO} [/tex]

That's,

[tex]h= \sqrt{(24- 7)7} [/tex]

[tex]h= \sqrt{17 \times 7} [/tex]

[tex]h= \sqrt{119} [/tex]

[tex]h= 10.9[/tex]

to the nearest tenth.

Well, just looking at this problem we know 3 formulas that will help us. Firstly we have C (The Circumference) is Equal to 2π Times the Radius, r.

In Equation form that looks something like this:

C=2πr

We also know that the radius is half of the diameter, r=D/2  or D=2r

So, if C=62.8, then 62.8=2πr must also be true.

By doing some quick re arranging we get to the equation r=62.8/2π

This equation gives us 9.99, Which is essentially 10.

Now that we know that r=10, we can find that diameter, D=2r, is Equal to 20.

Therefore, your answers are

Radius = 10

Diameter = 20

Circumference = 62.8 (Given)

If there are any questions about anything I did please feel free to ask more questions and I will respond ASAP!

X^2+4x+4+12x+24-14=0

x^2+16x+14=0

x= -16 ± √(16)^2-4(1)(14) /2(1)

=-16± √200   /2

-16 ± 2√50    /2

-16 ± 10√2   /2

-8 ± 5√2  

Answer: A) x=-8±5[tex]\sqrt{2}[/tex]

Step-by-step explanation: to find the solutions of the given equation, we need to use the substitution u=x+2, so the equation would now be:

[tex]u^{2} +12u-14=0[/tex]

the quadratic formula is:

u=(-b±[tex]\sqrt{b^{2}-4ac }[/tex])/2a

in this case a=1;  b=12;  and c=-14

so replacing the values it remains:

u=(-12±[tex]\sqrt{12^{2}-4*1*(-14) }[/tex])/2*1

u=(-12±[tex]\sqrt{144+56}[/tex])/2

u=(-12±[tex]\sqrt{200}[/tex])/2              

we can write 200 as 100*2 and the square root of 100 is 10:

u=(-12±10[tex]\sqrt{2}[/tex])/2

u=-6±5[tex]\sqrt{2}[/tex]

and finally:

x=u-2

x=-6±5[tex]\sqrt{2}[/tex]-2

x=-8±5[tex]\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

[tex]5m=35\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup^1m}{5\!\!\!\!\diagup_1}=\dfrac{35\!\!\!\!\!\diagup^7}{5\!\!\!\!\diagup_1}\\\\\boxed{m=7}[/tex]

Answer:

4/10= 0.4

3 1/10= 3.1

7/10= 0.7

6 5/10= 6.5

9/10= 0.9

Step-by-step explanation:

Answer: Sasha has 20 bars to start of with. Let's assume Sasha keeps 6 bars for herself. The problem says Sasha has twice as many bars as Hanna, so Hanna HAS to have 3 bars. The problem says Kyle got 3 more bars than Hanna, so 3+3=6, and Hannah got 2 less bars than Noah.. Noah has to have bars because 5-3=2

Sasha 6, Kyle 6, Noah 5, Hanna 3= 6+6+5+3=20

Step-by-step explanation:

Final answer:

Using equations based on the relationship between the number of muesli bars each person has, we determine that Sasha ended up with 6 muesli bars.

Explanation:

The subject of this question is mathematics, specifically it involves solving a word problem by setting up equations based on the given relationships among the quantities. Let's find out how many muesli bars Sasha had in the end.

Let's denote the number of muesli bars Sasha, Hannah, Noah, and Kyle have as S, H, N, and K respectively. The problem gives us the following relationships:

H = N - 2 (Hannah has two fewer bars than Noah)

K = H + 3 (Kyle has three more bars than Hannah)

S = 2H (Sasha has twice as many bars as Hannah)

Since there are 20 muesli bars in total, we can write the equation:

S + H + N + K = 20

Substituting the relationships into the equation we get:

2H + H + (H + 2) + (H + 3) = 20

Combining like terms, we have:

5H + 5 = 20

Subtracting 5 from both sides, we get:

5H = 15

Dividing both sides by 5, we find H:

H = 3

Now, we can find S:

S = 2H = 2(3) = 6

So, Sasha had 6 muesli bars in the end.

The current value of a future sum of money. The Present Value allows us to calculate what is the value of today that has an amount of money that we will not receive right now but later, in the future.

Present value seeks to reflect that it is always better to have an amount of money today than to receive it in the future. In fact, if we have the money today we can do something to make it productive, such as investing in a company, buying shares or leaving it in the bank that pays us interest, among other options. In addition, even if we do not have a certain plan to invest the money we can simply spend it to satisfy our tastes and we do not have to wait to receive the money in the future.

Answer:

A) The current value of a future sum of money

Step-by-step explanation:

on plato

To solve this all you need to do is take the fraction 2/5 and multiply it by a number (this means you multiply BOTH the denominator and the numerator)

1. Multiply the original fraction by 2:

[tex]\frac{2*2}{5*2} = \frac{4}{10}[/tex]

2. Multiply the original fraction by 3:

[tex]\frac{2*3}{5*3} = \frac{6}{15}[/tex]

3. Multiply the original fraction by 4:

[tex]\frac{2*4}{5*4} = \frac{8}{20}[/tex]

4. Multiply the original fraction by 5:

[tex]\frac{2*5}{5*5} = \frac{10}{25}[/tex]

5. Multiply the original fraction by 6:

[tex]\frac{2*6}{5*6} = \frac{12}{30}[/tex]

All of the fractions above are equal to 2/5 and to each other. You can keep doing this with higher numbers if you wold like, but these are just a few examples.

Hope this helped!

Hello There!

Some equivalent fractions of 2/5 are:

2/5 = 4/10 = 6/15 = 8/20 = 10/25 = 12/30 = 14/35 = 16/40 = 18/45 = 20/50 = 22/55 = 24/60 = 26/65 = 28/70 = 30/75 = 32/80 = 34/85 = 36/90 = 38/95 = 40/100 = 42/105

Equivalent fractions are fractions that equal each other, but they look different from each other. These fractions are represented differently.

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=12\\ h=6 \end{cases}\implies V=\pi (12)^2(6)\implies \stackrel{\textit{volume of A}}{V=864\pi }[/tex]

so their difference is 864π - 648π = 216π.

if we take 864π to be the 100%, what is 216π off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 864\pi &100\\ 216\pi &x \end{array}\implies \cfrac{864\pi }{216\pi }=\cfrac{100}{x}\implies 4=\cfrac{100}{x} \\\\\\ 4x=100\implies x=\cfrac{100}{4}\implies x=25[/tex]

Answer:

$13,997.53

Step-by-step explanation:

The simplest, minimally acceptable answer would stem from multiplying by 5 the $247.43 monthly payment and subtracting the result from the amount initially owed:

$15,234.68

-$ 1,237.15

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

$13,997.53

To calculate the net change to the loan from Quiana's perspective over the past 5 months, subtract the total amount she has repaid from the initial loan amount. In this case, the net change is $13,997.53.

The amount owed to the lender = $15,234.68

Amount repaid = $247.43

Time = 5 months

To calculate the net change to the loan from Quiana's perspective over the past 5 months, we need to subtract the total amount she has repaid from the initial loan amount.

Since she repaid $247.43 each month for 5 months, the total amount repaid is $247.43 x 5 = $1237.15.

To find the net change to the loan, we subtract the total amount repaid from the initial loan amount:

= $15,234.68 - $1237.15

= $13,997.53.

The correct answers are:

A. P = 58 and Q = 78

C. P = -78 and Q = -52

D. P = 58 and Q = -78

To determine which values of P and Q result in the equation Px + 52 = Qx - 78 having exactly one solution, we need to ensure that the coefficients of x on both sides are not equal. This means P should not be equal to Q.

The given equation is:

Px + 52 = Qx - 78

First, let's rearrange the terms to isolate x:

Px - Qx = -78 - 52

(P - Q)x = -130

For this equation to have exactly one solution, P - Q must be non-zero. Therefore, P - Q.

Let's evaluate each option:

A. P = 58 and Q = 78

- P - Q = 58 - 78 = -20

- Since -20 is not zero, this pair results in exactly one solution.

B. P = 52 and Q = 52

- P - Q = 52 - 52 = 0

- Since 0 is zero, this pair does not result in exactly one solution.

C. P = -78 and Q = -52

- P - Q = -78 - (-52) = -78 + 52 = -26

- Since -26 is not zero, this pair results in exactly one solution.

D. P = 58 and Q = -78

- P - Q = 58 - (-78) = 58 + 78 = 136

- Since 136 is not zero, this pair results in exactly one solution.

To find out how many weeks Tameca needs to save to have at least $100, we create an inequality, 5w + 55 >= 100, where 'w' represents the number of weeks. Solving this inequality gives w >= 9. Therefore, Tameca needs to save for at least 9 weeks.

The subject of this problem is linear inequalities, which falls under Mathematics. To solve this problem, let's denote the number of weeks that Tameca needs to save money as 'w'. Since she already has $55 and is saving $5 each week, the inequality that represents this situation is 55 + 5w >= 100.

In order to solve this inequality, we need to isolate 'w'. You can do this by subtracting 55 from both sides of the inequality to get 5w >= 45. Then, divide both sides by 5 to get w >= 9.

Therefore, Tameca must save for at least 9 weeks in order to have a minimum of $100 in her savings account.

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Yes it is. 5\7 is a fraction, therefore it is rational; it can be written as a decimal, 0.714285...... [bar notation indication].

Answer: The quotient of (-5)÷(-7) is a rational number

Step-by-step explanation:

It is asked that the quotient of (-5) / (-7) is a rational number ?

Rational Number : A rational number  is a number which can be expressed in the form p/q  

We multiply the numerator and denominator  of the fraction by -1

[tex]\frac{(-5)(-1)}{(-7)(-1)}[/tex]

=[tex]\frac{5}{7}[/tex]

i.e. the number can be expressed in the form p/q where p=5 and q=7

So the quotient is a rational number

Answer:

24 in²

Step-by-step explanation:

The easy way:

The two legs, or shorter sides, of a right triangle form that triangle's base and height. Knowing that the area of a triangle is [tex]\frac{bh}{2}[/tex] (where b is the base and h is the height), we can use the 6 inch leg for the base and the 8 inch leg for the height to find an area of [tex]\frac{6(8)}{2}=\frac{48}{2}=24[/tex] in².

The harder but more general way

There's a nice formula for calculating the area of any triangle given its side lengths found by this Greek guy named Heron, and it's appropriately called Heron's formula:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)[/tex]

a, b, and c are the lengths of triangle, and s here is half the triangle's perimeter (also called the semi-perimeter), or mathematically:

[tex]s=\frac{a+b+c}{2}[/tex]

For our problem, let's pick a = 6, b = 8, and c = 10. This would give us

[tex]s=\frac{6+8+10}{2} =\frac{24}{2}=12[/tex]

Substituting that s back into Heron's formula, we get

[tex]A=\sqrt{12(12-6)(12-8)(12-10)}=\sqrt{12(6)(4)(2)}\\=\sqrt{72(8)}=\sqrt{576}=24[/tex]

So our area is 24 in²

Let, that number = x

It would be: x * 0.65 = 52

x = 52 / 0.65

x = 80

So, that number and your answer is 80

18 is 45% of 40

45%/100 = 0.45

0.45*40=18

Answer:

64

Step-by-step explanation:

115 - 51 = 64

Answer:

66

Step-by-step explanation:

put them in order from least to greatest.

51, 51, 56, 58, 68, 72, 90, 101, 101, 111, 114, 115, 117

Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is...

117-51=

66

Answer:

The second one.

Step-by-step explanation:

The slope of the graph, -1/3, is going down from left to right because it is negative, so it is decreasing. Slope is the rise over run, so because the slope is -1/3 look for lines that go down 1 unit and across 3 at the same time (from one corner of a square to the other). Then, because your y-intercept is a 5, just look for your line to cross the y-axis at 5. And that's it.

The second graph is the graph of the linear equation y = - 1/3x + 5.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The given linear equation is  y = - 1/3x + 5

We need to select the graph of the equation.

The slope of the line is -1/3

y intercept is 5.

Let us find few points to determine the graph.

if x=0, then y=-1/3(0)+5=5

So (0, 5) is one of the point

if x=1, then y=-1/3(1)+5

=14/3

(1, 14/3)

if x=2, then y=-1/3(2)+5

=13/3

(2, 13/3)

if x=3, then y=-1/3(3)+5

(3, 4) is point.

Now let us check these points which satisfy the graph.

Hence, the second graph is the graph of the linear equation y = - 1/3x + 5.

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The length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is simply 1.

The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle, with a radius of 1, can be found using the Pythagorean theorem. In a unit circle, the hypotenuse of any right triangle formed by a radius will always have a length of 1, because the radius of a unit circle is 1 by definition. So, the expression you are looking for is simply 1, since the hypotenuse in this case is the radius of the circle.

Answer:

Dependent variable is a response variable

Step-by-step explanation:

Search up definition for response variable and it literally saids it's another word for dependent variable haha

Answer: Y

Step-by-step explanation:

A p e x

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]2x-5 < 15[/tex]

Solve for the inequality

Adds 5 both sides

[tex]2x < 15+5[/tex]

[tex]2x < 20[/tex]

Divide by 2 both sides

[tex]x < 20/2[/tex]

[tex]x < 10[/tex]

The solution is the interval ------> (-∞,10)

All real numbers less than 10

In a number line , the solution is the shaded area at left of x=10 (open circle)

The graph in the attached figure

Answer:

252 cm²

Step-by-step explanation:

Area of a rectangle is width times length:

A = WL

If the width and length increase by a factor of 1.5:

A = (1.5 W) (1.5 L)

A = 2.25 WL

So the area increases by a factor of 2.25.

2.25 × 112 cm² = 252 cm²

Answer:

A firm determines its profit by subtracting "Total Cost" from "Total Revenue".

Step-by-step explanation:

Given statement is "A firm determines its profit by subtracting _____ from ______. Now we need to fill the blanks with suitable words.

We know that there are some initial costs associated with production of any product. So to get the profit, we need to subtract the cost that that is spent during production of the product from total sales.

Hence final answer can be written as:

A firm determines its profit by subtracting "Total Cost" from "Total Revenue".

Answer:

d). 22

Step-by-step explanation:

add the -1 for x then solve

Answer:

To have an infinite number of solutions, the equations must graph the same line. That means the equations must be equivalent. To form an equivalent equation, use the properties of equality to rewrite the given equation in a different form. Add, subtract, multiply, or divide both sides of the equation by the same amount.

A system of two linear equations in two variables has an infinite number of solutions if the slope and y-intercept of the two lines is same.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line. If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that the equation is,

y = 2/3 x - 5

If the slope and y-intercept of the two lines are the same, a system of two linear equations in two variables has an infinite number of solutions.

The equations must graph the same line if there are infinitely many solutions. Therefore, the equations must be equal. The above equation may be rewritten in a different way using the equality principles to create an equivalent equation. Both sides of the equation should be increased, decreased, multiplied, or divided by the same quantity.

Thus, system of two linear equations in two variables has an infinite number of solutions if the slope and y-intercept of the two lines is same.

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The line perp. With this equation is y=-5/3+4x

Answer:

Step-by-step explanation:

f(x) + n - move the graph n units up

f(x) - n - move the graph n units down

f(x + n) - move the graph n units to the left

f(x - n) - move the graph n units to the right

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

G(x) = 1/x shifted 4 units up → G(x) + 4 = 1/x + 4

Answer: G(x)= 1/(x+4) +4

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

The circumference is always x2 of the radius

Answer:

9

Step-by-step explanation:

The coefficient is the number directly next to the variable, in this case, the variable being y, and the number being 9.

In the question:

9y + 5,

9 is the coefficient

y is the variable

5 is a constant (does not change).

Note that the coefficient and constant cannot change, but the value of the variable (y) can vary (hence the name).

~

The coefficient in the expression is 9.

The coefficient of a term in an algebraic expression is the number that is multiplied by the variable in the term.

To find the coefficient of a term, you can follow these steps:

1. Identify the variable in the term.

2. Look for the number that is multiplied by the variable.

3. That number is the coefficient of the term.

In the expression 5+ 9y, the variable is y. The number that is multiplied by y is 9.

Therefore, the coefficient in the expression is 9.

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Answer:

E,F and G

Step-by-step explanation:

we have

2x+y < 10 ---> inequality A

The solution of the inequality A is the shaded area below the dashed line

2x+y=10

Find the intercepts of the dashed line to plot the inequality A in the graph

The x-intercept is the point (5,0)

The y-intercept is the point (0,10)

2x-4y >8 ----> inequality B  

The solution of the inequality B is the shaded area below the dashed line 2x-4y=8

Find the intercepts of the dashed line to plot the inequality B in the graph

The x-intercept is the point (4,0)

The y-intercept is the point (0,-2)

The solution of the system of inequalities the shaded area

see the attached figure

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area of the solution of the system

In this problem the solutions are E,F and G

Answer:

See below

Step-by-step explanation:

(1) Create a table containing a few values of x and y

I chose x = -5, 0, and 5.

[tex]\begin{array}{rcc}& \mathbf{y = x + 6} & \mathbf{y = 3x - 2}\\\mathbf{x} & \mathbf{y} & \mathbf{y}\\-5 & 1 & -17\\0 & 6 & -2\\5 & 11 & 13\\\end{array}[/tex]

(2) Plot your points

Draw dots at the coordinates of each point ( Fig. 1).

(3) Draw the graph

Draw smooth lines through the points for each function.

Extend the lines in both directions to the edges of the plot area.

Your graphs should look like Fig. 2.

(4) Plot the solution

Note where the lines cross.

They appear to intersect at (4, 10).

Plot the point, and the finished graph should look like Fig. 3.

Answer:

(2, 4)

Step-by-step explanation:

Both equations have been solved for y, so to find x we need only set the equations = to each other:    y=-x+6   =  y=3x-2

Combining like terms, we get 4x = 8, and x = 2.  Substituting 2 for x in y = 3x -2, we get y = 3(2) - 2 = 4.

The solution is (2, 4).  If you were to graph these two lines, you'd find that they intersect at (2, 4).