Felix scored an 80% on his last test. He missed five problems. How many problems were on the test?

Answer:

Cos 2x = Cos (5x-3x)

Cos(5x)Cos(3x) + Sin(5x)Sin(3x)

Cos 8x = Cos (5x + 3x)

Cos(5x)Cos(3x) - Sin(5x)Sin(3x)

Cos 2x - Cos 8x

= Cos(5x)Cos(3x) + Sin(5x)Sin(3x) -

[Cos(5x)Cos(3x) - Sin(5x)Sin(3x)]

= 2Sin(5x)Sin(3x)

Cos 2x + Cos 8x

= Cos(5x)Cos(3x) + Sin(5x)Sin(3x) +

[Cos(5x)Cos(3x) - Sin(5x)Sin(3x)]

= 2Cos(5x)Cos(3x)

= 2Sin(5x)Sin(3x) ÷ 2Cos(5x)Cos(3x)

2 gets cancelled out

Sin(5x)/Cos(5x) is Tan(5x)

Sin(3x)/Cos(3x) is Tan(3x)

Hence the fraction is identical to

Tan(5x)Tan(3x)

Answer:

pentagon

Step-by-step explanation:

In this problem we have a pentagonal prism

so

The solid has two pentagonal bases and five lateral rectangular faces

we know that

A plane parallel to the base of a pentagonal prism will intersect a cross section that is the same shape as its bases

so

The shape of the horizontal cross section of the given prism, is a pentagon

Answer: Pentagon

Step-by-step explanation:

Complete Question:

Option 1: $30 an hour plus a non-refundable deposit of $50.

Option 2: $20 an hour plus a non-refundable deposit of $75.

Kyle is renting a jetski for the day. If he can rent the jetski in 1-hour increments, what is the minimum number of hours must he rent the jetski for option 2 to be a better deal than option 1?

Answer:

Kyle must rent the jetski for three hours for option 2 to be a better deal than option 1

Solution:

Let "x" be the number of hours

Therefore,

Charge for option 1: 50 + 30x

For 1 hour,

Charge = 50 + 30(1) = 80

For 2 hours,

Charge = 30(2) + 50 = 110

For 3 hours,

Charge = 30(3) + 50 = 140

For 4 hours,

Charge =  30(4) + 50 = 160

Charge for option 2 : 75 + 20x

For 1 hour,

Charge = 20(1) + 75 = 95

For 2 hours ,

Charge = 20(2) + 75 = 115

For 3 hours,

Charge =  20(3) + 75 = 135

For 4 hours,

Charge =  20(4) + 75 = 155

For the first two hours , the charge of option 2 is more than the rent of option 1

From 3 hours, option 2 will be better deal than option 1

The discount is $43.50, making the price of the discounted TV $246.50.

15% = .15

.15 x 290 = 43.5

$290 - $43.50 = $246.50

Answer:

C.  12x³ + 6x²

Step-by-step explanation:

I'm an FLVS kid and got the question right, so I wanted to explain my answer:

You just have to use the distributive property for this one. Multiply 2x² by each term in the brackets.

2x²(6x + 3) ← original question for ref.

2x²(6x) = 12x³

2x²(3) = 6x²

So the new terms are 12x³ +  6x²

The answer is C.

Answer:

39.69 degrees

Step-by-step explanation:

Let

x ----> the measure of the angle

we have that

[tex]tan(X)=0.83[/tex]

using a calculator

[tex]m\angle X=tan^{-1}(0.83)=39.69^o[/tex]

Answer:

Step-by-step explanation:

x - 10 = 0

x = 10

f(10) = 2*10² + 5 = 2*100 + 5 = 200 + 5

      = 205

Remainder = 205

Answer:

195 is the right answer

Step-by-step explanation:

195

Answer:

5 in

Step-by-step explanation:

I don't actually the ans

Answer:

C - 2/5

Step-by-step explanation:

Using the formula for slope

m = (y_2 - y_1) / (x_2 - x_1)

Given two points

( 4 , 5) (-1 , 3)

x_1 = 4

y_1 = 5

x_2 = -1

y_2 = 3

Insert the values into the equation

m = (y_2 - y_1) / (x_2 - x_1)

m = ( 3 - 5) / ( -1 - 4)

= -2 / -5

- $ - cancels out

m = 2/5

Slope = m = 2/5

The complex number from the table are

[tex]1+\sqrt{-3}, \ 4-3 \sqrt{-16}, \ \frac{3+2 \sqrt{-9}}{7}, \ 9 \sqrt{-\frac{7}{5}}[/tex]

Solution:

Let us solve and identify the complex number.

(A) [tex]5-\sqrt{\frac{9}{4}}[/tex]

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

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

           = 3.5

This is not a complex number.

(B) [tex]1+\sqrt{-3}[/tex]

[tex]1+\sqrt{-3}=1+\sqrt{-1\times 3}[/tex]

We know that [tex]\sqrt{-1} =i[/tex].

[tex]1+\sqrt{-3}=1+\sqrt{3}i[/tex]

This is a complex number.

(C) [tex]4-3 \sqrt{-16}[/tex]

[tex]4-3 \sqrt{-16}=4-3 \sqrt{-1\times 4^2}[/tex]

[tex]4-3 \sqrt{-16}=4-3\times4 \sqrt{-1}[/tex]

We know that [tex]\sqrt{-1} =i[/tex].

[tex]4-3 \sqrt{-16}=4-12i[/tex]

This is a complex number.

(D) [tex]\frac{2-\sqrt{12}}{5}[/tex]

[tex]\frac{2-\sqrt{12}}{5}=\frac{2-2\sqrt{3}}{5}[/tex]

There is no –1 in the root.

This is not a complex number.

(E) [tex]\frac{3+2 \sqrt{-9}}{7}[/tex]

[tex]\frac{3+2 \sqrt{-9}}{7}=\frac{3+2 \sqrt{-1\times 3^2}}{7}[/tex]    

We know that [tex]\sqrt{-1} =i[/tex].  

             [tex]=\frac{3+6i}{7}[/tex]

This is a complex number.

(F) [tex]9 \sqrt{-\frac{7}{5}}[/tex]

[tex]9 \sqrt{-\frac{7}{5}}=9 \sqrt{-1 \times \frac{7}{5}}[/tex]

We know that [tex]\sqrt{-1} =i[/tex].  

[tex]9 \sqrt{-\frac{7}{5}}=9 \sqrt{ \frac{7}{5}}i[/tex]

This is a complex number.

Hence the complex number from the table are

[tex]1+\sqrt{-3}, \ 4-3 \sqrt{-16}, \ \frac{3+2 \sqrt{-9}}{7}, \ 9 \sqrt{-\frac{7}{5}}[/tex]

Answer:

$339.25

Step-by-step explanation:

Since the credit card customer owes $523.85 and is only able to make a payment of $184.50

Amount still owed

= $523.85 - $184.60

= $339.25

The customer still owes $339.25

The product of a rational number multiplied by itself is called as a perfect square.,we can easily find out the square root for a number which is a imperfect square

Step-by-step explanation:

using the following formula we can find a square root for a number which is a imperfect square

X = Non perfect square

√x = (square root of nearest lower perfect square +(x - perfect square)÷2×(√perfect square )

[tex]√x = (square root of nearest lower perfect square +(x - perfect square)÷2×(√perfect square )[/tex]Example

√38

the nearest perfect root is 36

36 (√36=6)

so √38 = √36 + (38-36)/2√36

= 6 + 2/12

=6 + 1/6 = 6.166 (answer)

[tex]√38 the nearest perfect root is 36 36 (√36=6)so √38 = √36 + (38-36)/2√36 = 6 + 2/12=6 + 1/6 = 6.166 (answer)[/tex]

To find the square root of a non-perfect square, use estimation techniques or the quadratic formula if in relation to an equation. Use the imaginary unit i for square roots of negative numbers, and simplify by removing perfect squares when adding or subtracting radicals.

Finding the square root of a number that is not a perfect square can be done using a few different methods. One simple non-calculator method is to use estimation and refinement; start with an approximate guess and improve it. When dealing with negative numbers, remember that we use the imaginary unit i to denote the square roots of negative numbers. For example, a₂ can be written as 2i. Adding and subtracting radicals involves simplifying each radical by removing perfect squares and combining like terms.

For equations where the square root is part of a quadratic equation, ax²+bx+c = 0, if a, b, and c are non-zero, we should use the quadratic formula to find solutions. Estimation also applies when dealing with cube roots or higher, where we can start with an initial guess and use methods like calculus to refine it.

To estimate a surd like a₃ without a calculator, consider its place on the number line between two integers, knowing that a₃ is about 1.732. This helps get an approximate value which is often sufficient for many applications.

We see here that $1 will buy 5 ounces of ground turkey.

To find out how much $1 will buy, we can set up a proportion using the given information.

We know that $8 buys 40 ounces of ground turkey. Let's set up the proportion:

$8/40 ounces = $1/x ounces

To solve the proportion, we can cross-multiply:

$8 × x ounces = 40 ounces * $1

Simplifying further:

$8x = $40

To isolate x (the number of ounces that $1 will buy), we can divide both sides of the equation by $8:

x = $40 / $8

x = 5 ounces

Therefore, $1 will buy 5 ounces of ground turkey.

Alternatively, we can set up a ratio using the given information:

$8 for 40 ounces

To find out how much $1 will buy, we can find the unit price:

Unit price = Total cost / Total quantity

Unit price = $8 / 40 ounce

Unit price = $0.20 per ounce

Since $1 is equal to 100 cents, we can divide $1 by the unit price:

$1 / $0.20 per ounce = 5 ounces

Therefore, $1 will buy 5 ounces of ground turkey.

Complete question:

$8 buys 40 ounces of ground turkey, how much will $1 buy?

Answer:

y = -2x - 2

Plug the x- and y-values into the appropriate spaces in the slope-intercept form and see which value for b would make the equation true:

4 = -2(-3) +/- ?

4 = 6 - 2

4 = 4

I don't know if this makes sense, I'm sorry if it doesn't but the answer is correct because it goes through the point (-3,4)

The answer is y = -2x - 2

You have to first plug the x- and y-values into the correct spots in the slope-intercept form and see which value for b would make the equation true.

4 = -2(-3) +/- ?

4 = 6 - 2

4 = 4

Hope to help.

Answer:

[tex]-\frac{41}{4}[/tex]

Step-by-step explanation:

-4(8+y)=9

Distribute:

-32-4y=9

Add 32 on both sides:

-4y=41

Divide -4 with 41:

y=-41/4

Answer:

[tex]y = - \frac{41}{4} = - 10 \frac{1}{4} \\ [/tex]

Step-by-step explanation:

[tex]-4(8+y)=9 \\ - 32 - 4y = 9 \\ - 4y = 9 + 32 \\ - 4y = 41 \\ \\ y = - \frac{41}{4} = - 10 \frac{1}{4} [/tex]

Answer: The slope of BC is -2.

Step-by-step explanation:

We know that a rectangle has all opposite sides equal and parallel.

Each interior angle is a right angle.

Therefore , if rectangle ABCD is a rectangle then , AB should perpendicular to  BC.   [ ∵ Angle between AB and BC is 90° .]   (1)

Also , slope of line passing through (a,b) and (c,d) :  [tex]\dfrac{d-b}{c-a}[/tex]

If A is located at (3, 4) and B is located at (7,6) .

Then , The slope of AB = [tex]\dfrac{6-4}{7-3}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]

Also, the product of slopes of two perpendicular lines is -1.

Then , (Slope of AB) x  (Slope of BC) = -1     [From (1)]

[tex]\Rightarrow\ \dfrac{1}{2}\times (\text{Slope of BC})= -1\\\\\Rightarrow\ \text{Slope of BC}=-2[/tex]

Hence, the slope of BC is -2.

Answer:

7x=3x+24

4x=24

x=6

Answer:

[tex]x=6\\[/tex]

Step-by-step explanation:

[tex]7x=3x+24[/tex]

[tex]7x-3x=3x-3x+24[/tex]

[tex]4x=24[/tex]

[tex]\frac{4x}{4} =\frac{24}{4}[/tex]

[tex]x=6[/tex]

Answer:

Distance = 63 km

Step-by-step explanation:

Speed = 90 km/h

Time = 42 mins

Time = 42 / 60 = 0.7 hrs

Distance = Speed × time

Distance = 90 km/h × 0.7 hr

Distance = 63 km

Answer:   -√6 + 1

Step-by-step explanation:

[tex]\dfrac{\tan\bigg(-\dfrac{2\pi}{3}\bigg)}{\sin\bigg(\dfrac{7\pi}{4}\bigg)}-\sec(-\pi)\\\\\\=\dfrac{\tan(240^o)}{\sin(315^o)}-\sec(180^o)\\\\\\=\dfrac{\sqrt3}{-\dfrac{\sqrt2}{2}}-(-1)\\\\\\=\dfrac{-2\sqrt3}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)+1\\\\\\=\large\boxed{-\sqrt6+1}[/tex]

Answer:

3^4 and 81^1

Step-by-step explanation:

Answer:

240 minutes or 4 hours

Step-by-step explanation:

Step 1:  Multiply

8 * 30

240 min

If you want hours:

240 / 60

4 hours

Answer:  240 minutes or 4 hours

Observe that [tex]16r^4[/tex] is the square of [tex]4r^2[/tex], and 625 is the square of 25.

So, your expression is a difference of squares, and as such we can rewrite it as

[tex]16r^4-625=(4r^2+25)(4r^2-25)[/tex]

Now again, [tex]4r^2[/tex] is the square of [tex]2r[/tex], and 25 is the square of 5. So, we have a sum and a difference of squares.

But if we think of 25 as [tex]-(5i)^2[/tex], we have again the difference of two squares, so we have

[tex]4r^2+25=(2r+5i)(2r-5i)[/tex]

[tex]4r^2-25=(2r+5)(2r-5)[/tex]

Option A is the correct expression equivalent to 16r⁴-625.

The options in the question must have r in place of x.

The imaginary number 'i' is the solution of the algebraic equation x²+1.

Thus, x²+1=(x+i)(x-i).

We can observe that (a+bi)(a-bi)=(a²+b²)+i(-ab+ba)=a²+b².

Hence the factorization of a²+b² is (a+bi)(a-bi)

16r⁴-625

=(4r²-25)(4r²+25)

=(2r-5)(2r+5)(2r+5i)(2r-5i)

So, option A is the correct expression equivalent to 16r⁴-625.

To learn more about factorization visit- https://brainly.com/question/20293447?referrer=searchResults

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Answer:

29?

Step-by-step explanation:

Answer:it might be 29

Step-by-step explanation:

Answer:

2/3 ≥ 3/6

Step-by-step explanation:

Cross Multiply  

f/g=h/i

f×i=g×h

2×6> 3×3

12> 9

Answer:

The cost of 7 journals is less than the cost of 4 journals plus a $5 novel.

Step-by-step explanation:

Let

x -----> the cost of a journal

Verify each case

case 1) The cost of 7 journals is $5 greater than the cost of 4 journals

In this case the equation would be

[tex]7x=4x+5[/tex]

case 2) The cost of 7 journals is less than the cost of 4 journals plus a $5 novel.

so

[tex]7x<4x+5[/tex]

solve for x

subtract 4x both sides

[tex]3x<5[/tex]

divide by 3 both sides

[tex]x<\$1.67[/tex]

so

The cost of one journal must be less than $1.67

case 3) The cost of 7 journals is less than the cost of 4 journals with a $5 off coupon.

so

The inequality would be

[tex]7x<4x-5[/tex]

case 4) The cost of 7 journals is greater than the cost of 4 journals plus a $5 novel.

so

The inequality would be

[tex]7x>4x-5[/tex]

Value of h(1.5) is 33

Step-by-step explanation:

⇒ h(1.5) = 22 × 1.5 = 33

Final answer:

To find h(2) when x = 1.5, you first determine the constant of variation (k) using the given information h(x) = 44 when x = 2. This leads to k = 22. Plugging x = 1.5 into the direct variation equation h(x) = k*x, we get h(1.5) = (option D) 33.

Explanation:

If h(x) varies directly with x, then we can express this relationship as h(x) = k*x, where k is the constant of variation. We're given that h(2) = 44, so we can solve for k by plugging in the values:

44 = k*2 => k = 22.

Now that we have the value of k, we can find h(1.5) by multiplying k by 1.5:

h(1.5) = 22 * 1.5 = 33.

Therefore, the value of h(2) when x = 1.5 is (option D) 33.

Answer: c

Step-by-step explanation:

Answer:

C y = −4.6 and y = 4.6

Step-by-step explanation:

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