1. In a 30-60-90 triangle, the length of the hypotenuse is 6. What is the length of the shortest
side?
a. 2
b. 3
c. 3.12
d. 31/3
e, 6-3

Answer:

Step-by-step explanation:

From the picture we have:

4w = 3l

If w = 12 ft, then

3l = 4(12)

3l = 48             divide both sides by 3

l = 16 ft

The dimensions of rectangular floor are 4w × (l + w).

Substitute the values of w and l:

4w = 4(12) = 48 ft

l + w = 16 + 12 = 28 ft

The formula of an area of a rectangle:

A = width × length

Substitute:

A = (48)(28) = 1344 ft²

Answer:

-15

Step-by-step explanation:

the y-intercept would be -15

Answer:

x = - 5, x = 3

Step-by-step explanation:

To find the x- intercepts let y = 0, that is

x² + 2x - 15 = 0

Consider the factors of the constant term (- 15) which sum to give the coefficient of the x- term (+ 2)

The factors are + 5 and - 3, since

5 × - 3 = - 15 and 5 - 3 = + 2, hence

(x + 5)(x - 3) = 0

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 3 = 0 ⇒ x = 3

x- intercepts at (- 5, 0) and (3, 0)

Answer:

x = ±√ 24.500 = ± 4.94975

Step-by-step explanation:

:  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =  

        A2 - B2

Step-by-step explanation:

4x² + 98 = 0

2x² + 49 = 0

2x² = -49

x² = -49/2

x = ±√(-49/2)

x = ±7i√(1/2)

x = (±7i√2) / 2

Answer:

16 : 25

Step-by-step explanation:

The ratio of girls : boys = 320 : 500

To simplify divide both parts by 10

320 : 500 = 32 : 50 ← now divide both parts by 2

32 : 50 = 16 : 25 ← in simplest form

Final answer:

To calculate the simplified ratio of the number of girls to the number of boys in the school, we divide the numbers 320 (girls) and 500 (boys) by their greatest common divisor, which is 80, resulting in the simplest form of 4:6.25 or 16:25.

Explanation:

The question is asking us to find the ratio of the number of girls to the number of boys in a school, and then to simplify this ratio to its simplest form. There are 320 girls and 500 boys in the school. To find the ratio, we compare the number of girls to the number of boys, which gives us 320 to 500.

To simplify the ratio, we look for the greatest common divisor (GCD) that both numbers share. Both 320 and 500 are divisible by 10 for certain, and further simplification can be found by dividing by the GCD of 80. So, if we divide both numbers by 80, we get 4 to 6.25, which simplifies further to a ratio of 4:6.25 or 16:25 when both sides are multiplied by 4. Therefore, the simplified ratio of the number of girls to the number of boys is 16:25.

Answer:

D. 754 m

Step-by-step explanation:

When calculating the circumference of the circle it ends up as 753.98 but rounded it's 754.

Answer: It’s 754!

Explanation: I also got this one on a test lol

Answer:

(–2.2, –3)

Step-by-step explanation:

y = – 3

y = x – 0.8

Substitute the value of y into the second equation

-3 = x-.8

Add .8 to each side

-3 +.8 = x-.8+.8

-2.2 = x

-3 =y

Answer:

The solution for the system of equations is (–2.2, –3)

Step-by-step explanation:

The solution of the system of equations can be expressed with its components in x and y in the form (x,y) where x is the value of x and y is the value of y. The values of x and y can be found solving the system of equations given.

1. Write the system of equations and name each equation:

[tex]y=-3[/tex] (Eq.1)

[tex]y=x-0.8[/tex] (Eq.2)

2. Replacing Eq. 1 in Eq. 2 and solving for x, we have:

[tex]y=x-0.8[/tex]

[tex]-3=x-0.8[/tex]

[tex]-3+0.8=x[/tex]

[tex]-2.2=x[/tex]

3. Express the answer as the solution tho the system of equations:

(x,y)=(-2.2,-3)

Answer:

8y=-6 or 4y=-3

Step-by-step explanation:

We are given two equations

[tex]x+6y=9\\and\\-x+2y=-15[/tex]

In order to add the equations, the left hand side of one equation will be added to the left hand side of second equation. similarly, the right hand side of first equation will be added to the right hand side of the equation so,

[tex]x+6y+(-x+2y)=9+(-15)\\Combining\ alike\ terms\\x+6y-x+2y=9-15\\6y+2y=-6\\8y=-6\\Can\ also\ be\ written \ as\\4y=-3[/tex]

Answer:

The resultant equation is 8y = -6

Step-by-step explanation:

To get the system of equation that will results from adding the statement, we will follow the steps below;

x+6y=9 -------------------------------------------------------------------------------(1)

-x+2y=-15-------------------------------------------------------------------------------(2)

Adding equation (1) and equation(2), we will have;

(1-1)x + (6+2)y =(9-15)

x variable will go away

8y =-6

The resultant equation is 8y = -6

Answer:

73 m is equal to 730 dm

Step-by-step explanation:

We Need to convert 73 m into dm

We know that 1 meter is equal to 10 decimeter

We are given 73 m. Multiply it with 10 and we will get value in decimeter

73*10

= 730 decimeter

So, 73 m is equal to 730 dm

Answer:

The correct answer would be 730 dm.

Step-by-step explanation:

M is the abbreviation of Meter and dm is an abbreviation of Decimeter. A meter is a unit of length as prescribed by the international system of units. This unit is used to measure the length. Decimeter is the smaller unit of meter. 10 Decimeter makes one meter, which means 1M equals 10DM. So where there are 73 meters, there would be 73 * 10 Decimeters in it. This is shown as below.

73 m = 73 * 10 = 730 DM

Answer:

The number is -8

Step-by-step explanation:

Let

x ---> the number

we know that

The algebraic expression is equal to

[tex]7x-x=-48[/tex]

Solve for x

[tex]6x=-48[/tex]

divide by 6 both sides

[tex]x=-48/6=-8[/tex]

-8 y e s -8 is the answer doods

Final answer:

To convert 27 feet to inches, multiply 27 by the conversion factor of 12 inches per foot, resulting in 324 inches.

Explanation:

To convert 27 feet to inches, we use the unit equivalence that 1 foot = 12 inches. We multiply the number of feet by the conversion factor to get the measurement in inches.

27 feet × 12 inches/foot = 324 inches.

Therefore, 27 feet is equivalent to 324 inches. This is a straightforward application of unit conversion, which is a fundamental skill in mathematics, especially useful for various applications in science, engineering, and everyday calculations.

Answer:

Top Right

Step-by-step explanation:

First things first, you can eliminate the bottom left option. The domain 3≤x≤6 means that the graph will only show points greater than or equal to 3 and less than or equal to 6. That option shows x = 2, which is not in this domain.

The symbols on either side of the x are known as ceiling functions. It means that y equals whatever whole number is greater than or equal to than x.

Basically, whatever y is, round it up to the nearest whole number to get x.

So, let's do a table from x = 3 to x = 6

   x ║ y               Now, see which graph best matches these

2.5 ║ 3               coordinates. Keep in mind that to be a function,

  3 ║ 3                the points cannot overlap (they have to pass the

3.5 ║ 4                vertical line test). It looks like the best answer is

  4 ║ 4                going to be the top right.

4.5 ║ 5

  5 ║ 5

5.5 ║ 6

  6 ║ 6

Answer:

Top Right Corner

Step-by-step explanation:

The swiftest way to know this is that on each end is a closed circle from 3 [open] to 6 [close]. Bottom left is close, but has an extra line signaling that x is equal to 2, and it is not included, so do not pick this one.

I am joyous to assist you anytime.

to get the slope of it, we simply need two points off the table, say (-4,-114) and (2,48).  Recall that the y-intercept, where the graph intercepts the y-axis, when that happens x = 0, so is right there on the table already.

[tex]\bf \begin{array}{rrll} x&y\\ \cline{1-2} -4&-114\\ -2&-60\\ 0&-6&\leftarrow y-intercept\\ 2&48\\ 4&102 \end{array}~\hfill (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-114})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{48})[/tex]

[tex]\bf slope\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{48-(-114)}{2-(-4)}\implies \cfrac{48+114}{2+4}\implies \cfrac{162}{6}\implies 27 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(\stackrel{slope}{27}~~,~~\stackrel{y-intercept}{-6} \right)~\hfill[/tex]

Answer:

a) Current Interest is $75.8

b) the final payment will be $11,830

Step-by-step explanation:

Principal Amount = $9,100

Interest rate = 10% or 0.1

Time = 36 months = 3 yeras

Balance after 27 payments = $2,526.85

a) What is the CURRENT month's interest?

The formula to find interest is:

Interest = P*r*t

P= Principal

r = Interest rate

t = time in years

Interest = 9100*0.1*3

Total Interest = 2730

As total period is 36 months so, divide total interest by 36

Current Month Interest = 2730/36

Current Month Interest = 75.8

So, current month interest is $75.8

b) What is the final payment?

The formula used will be

A = P(1+r*t)

A = Final amount

r = interest rate

t = time

Putting values:

A = P(1+r*t)

A = 9100*(1+0.1*3)

A = 9100*(1.3)

A = 11,830

So, the final payment will be $11,830

Answer:

c

Step-by-step explanation:

Divide using synthetic division, remembering to place a zero to denote the terms x³, x² and x

Since division by (x - 3) then evaluate using h = 3

3 | 1  0  0  0  7

    ↓

    1    3  9  27 81

   ----------------------

    1  3  9  27  88 ← degree 3 polynomial

quotient = x³ + 3x² + 9x + 27 , remainder = 88 → c

Follow below steps:

To divide x^4 + 7 by x - 3, we will use polynomial long division. This process is similar to the long division we use with numbers. Let's perform the division step by step:

Divide the term with the highest power in the dividend (x^4) by the highest power in the divisor (x) to get x^3.

Multiply the entire divisor by x^3 and subtract the result from the dividend.

The subtraction will give a new polynomial. Repeat the process until the degree of the remainder is less than the degree of the divisor, or until no further division can be carried out.

The correct result for the division of x^4 + 7 by x - 3 is option (a): x^3 - 3x^2 - 9x - 27 R 88.

Answer: Third Option

[tex]V = 200.96\ in^3[/tex]

Step-by-step explanation:

By definition, the volume of a cone is:

[tex]V = \frac{1}{3}\pi r^2h[/tex]

V is the volume of the cone

h is the height of the cone

r is the radius of the cone

In this case we know that:

[tex]r= 4\ in\\h= 1\ ft[/tex]

We know that in 1 ft there are 12 inches

So

[tex]h=12\ in[/tex]

Now substitute the values of h and r in the formula to obtain the volume of the cone

[tex]V = \frac{1}{3}\pi (4)^2(12)[/tex]

[tex]V = 16*4\pi[/tex]

[tex]V = 200.96\ in^3[/tex]

Answer:

16π

Step-by-step explanation:

The surface area of a sphere is:

A = 4πr²

where r is the radius, or half the diameter.

If the diameter is 4 units, then the radius is 2 units:

A = 4π (2)²

A = 16π

The surface area is 16π square units.

Answer:

j=2

Step-by-step explanation:

First, subtract by 5 from both sides of equation.

5-j-5=3-5

Simplify.

3-5=-2

-j=-2

Divide by -1 from both sides of equation.

-j/-1=-2/-1

Simplify, to find the answer.

-2/-1=2

It change negative to positive.

j=2 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

2

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1st step: again, reverse the equation (by flipping the equation around)

2nd step: do the equation ; 5 - 3  = 2

3rd step: (check your answer) ; 3 plus 2 equals 5

therefore, the answer 2 is correct.

Answer:

Step-by-step explanation:

[tex](4k^7)^3\ \text{it's equal to}\ 64k^{21}\\\\(4k^7)^3\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=4^3(k^7)^3=64k^{7\cdot3}=64k^{21}\\\\4^3(k^7)^3=4^n(k^7)^3\Rightarrow n=3[/tex]

The value of n in the simplified expression is 3.

To simplify an expression approach write an equivalent expression that includes no comparable terms. This means that we will rewrite the expression with the fewest phrases feasible.

Simplifying means to make it less complicated, clearer, or easier. maths to reduce (an equation, fraction, and many others) to a less difficult form by means of cancellation of commonplace factors, regrouping of phrases in the identical variable, etc.

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Answer:

The corresponding point is (3,-8)

Step-by-step explanation:

we know that

When you add a constant value (k), to the argument of a function, the graph is shifted  k units to the left.

so

In this problem

The rule of the transformation is equal to

f(x) ------> f(x+2)

(x,y) ------> (x-2,y)

(5,-8) -----> (5-2,-8)

(5,-8) -----> (3,-8)

Answer:

[tex]-439[/tex]

Step-by-step explanation:

we have

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

[tex]t(x)=3x[/tex]

we know that

[tex](sot)(x)=2-(3x)^{2}[/tex]

[tex](sot)(x)=2-9x^{2}[/tex]

For x=-7

substitute

[tex](sot)(-7)=2-9(-7)^{2}[/tex]

[tex](sot)(-7)=2-441[/tex]

[tex](sot)(-7)=-439[/tex]

[tex]\bf \begin{cases} x+2y=12\\ \cline{1-1} -x=-y-6\\ \boxed{x}=y+6 \end{cases}\qquad \qquad \stackrel{\textit{doing some substitution in the 1st equation}}{\boxed{y+6}+2y=12\implies 3y+6=12} \\\\\\ 3y=6\implies y=\cfrac{6}{3}\implies \blacktriangleright y=2 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that }}{x=y+6\implies }x=(2)+6\implies \blacktriangleright x=8 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (8,2)~\hfill[/tex]

Answer:

[tex]56wx - 15yz - \frac{29}{3} [/tex]

Step-by-step explanation:

[tex]1. \: 56wx - 5y \times 3z - 9 - \frac{2}{3} \\ 2. \: 56wx - 15yz - 9 - \frac{2}{3} \\ 3. \: 56wx - 15yz + ( - 9 - \frac{2}{3} )[/tex]

The expression equivalent to given condition is 56wx - 15yz - 29/3.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given expression,

(8w.7x - 5y.3z - 9) - 2/3

since variables are in the product, so their constants are multiplied,

8w.7x  = 56wx

5y.3z  = 15yz

the equation can be written as,

56wx - 15yz - 9 - 2/3

and   - 9 - 2/3 = (-27 - 2)/3 = -29/3

=> 56wx - 15yz - 29/3

Therefore, the equivalent form of the equation is  56wx - 15yz - 29/3.

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Answer:

C

Step-by-step explanation:

Total delivery orders is 97

The number of those placed by phone is 28

So you find the percentage of delivery orders placed by phone by doing 28 divided by 97.

.289 approximately so 28.9%  ( I rounded on my answer)

Choice C is the right answer

Step-by-step explanation:

problem answer in picture

The value of the expression after factorization is (x² + 2)(x² - 6)

'In math, factorization is when you break a number down into smaller numbers that, multiplied together, give you that original number.'

According to the given problem,

[tex]x^{4} - 4x^{2} - 12\\[/tex]

⇒ [tex]x^{4} + 2x^{2} - 6x^{2} - 12\\[/tex]

⇒ [tex]x^{2} (x^{2} +2) -6(x^{2} +2)[/tex]

⇒ [tex](x^{2} +2)(x^{2} -6)[/tex]

Hence, we can conclude the value of the given expression after factorization is [tex](x^{2} +2)(x^{2} -6)[/tex].

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Answer:

[tex]36xy^2 + 8x^2 + 27y^2 + 6x[/tex]

Step-by-step explanation:

Use the FOIL method of multiplying binomials.

First term in each binomial: [tex]-2x * -4x = 8x^2[/tex]

Outside terms: [tex]-2x * -3 = 6x[/tex]

Inside terms: [tex]-9y^2 * -4x = 36xy^2[/tex]

Last term in each binomial: [tex]-9y^2 * -3 = 27y^2[/tex]

Now, rearrange the terms correctly. [tex]36xy^2 + 8x^2 + 27y^2 + 6x[/tex]

This is our final answer, since it can not be simplified any more.

Answer:

C

Step-by-step explanation:

Edge 2020

Hello There!

Amount Saved = Original Price x Discount % / 100. So,

Amount Saved = 35 x 60 / 100

Amount Saved = 2100 / 100

Amount Saved = $21 (answer)

35 - 21 = 14

60% Off of $35.00 Is $14.00

Answer:

x = 19°

Step-by-step explanation:

Let The angle be "a"

Now according to the question,

⇒ 3 × a = (90° - a) - 14° (Then remove the brackets)

⇒ 3a =  90° - a - 14°

⇒ 3 + a = 76°

⇒ 40° = 76°

⇒ a = 76/4

Now since you got 76/4 you have to make it into simplest form so it'll be :

19/1

Your answer is : a = 19°

Answer:

A on edg.

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

We need to identify the equation in point slope form.

The standard equation of point slope form is:

(y-y₁) = m (x-x₁)

where m is the slope and x₁ and y₁ are the points

We are given point(4,-1) so,

x₁=4 and y₁=-1

And a perpendicular line: y =3x+5

Which is equal to y = mx+b

where m is slope so, slope m = 3

Since the line is perpendicular, so the slope in negative inverse of actual slope that m = -1/m

i.e, m = -1/3

So, the equation in point slope form is:

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

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

Answer:

The equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1) is y = -⅓x + ⅓

Step-by-step explanation:

Given

Let P represent the lind

Equation of P; y = 3x + 5

Let Q represent the other point.

Coordinates of Q; Q(4,-1)

It is said that the line P is perpendicular to point Q.

So, the first thing to do is to calculate the slope of Q;

Since both lines are perpendicular, then we make use of formula for calculating the condition of perpendicularity

This is given as m1m2 = -1

Where m1 = slope of P

m2 = slope of Q

To get m1;

m1 is the coefficient of x in equation of line P.

So, m1 = 3.

Now we can solve for m2

m1.m2 = -1. ---- make m2 the subject of formula

m2 = -1/m1

Substitute 3 for m1

m2 = -1/3

m2 = -⅓

Recall that the coordinates of Q is 4 and -1.

To calculate the equation of Q; we make use of the following

m = (y - y1)/(x - x1)

Where m = m2 = -⅓

x1 = 4 and y1 = -1

By substituton, we have

-⅓ = (y - (-1))/(x - 4)

-⅓ = (y + 1)/(x - 4) --- multiply both sides by 3(x - 4)

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

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

-x + 4 = 3y + 3 --- make y the subject of formula

3y = -x + 4 - 3

3y = -x + 1 --- divide through by 3

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

y = -x/3 + 1/3

y = -⅓x + ⅓

Hence, the equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1) is y = -⅓x + ⅓

Answer:

20 students

Step-by-step explanation:

It says 80% of 25 students got 83%+.

This means the number of students that got 83%+ is 80% of 25, or 25*0.8.

25*0.8 is 20, so 20 students got 83%+.

Answer:

20 students earned 83% or better in last maths test.

Step-by-step explanation:

We are given that on Ms. Smith's last math test, 80% of her 25 students earned an 83% or better.

We are to find the number of students who earned 83% or better on the test.

Number of students who earned 83% or more = 80% × 25 = [tex] \frac { 8 0 }{ 1 0 0 } \times 2 5[/tex] = 20