Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
a^2-2a-224=0

Answer:

48.50 dollars.

Step-by-step explanation:

The collector has a total of 224 coins but 74 of them are 25 cents coins. So, in order to find the number of 20-cent coins we're going to subtract the number of 25-cent coins from the total.

Number of 20-cent coins = 224 - 74 = 150.

Thus, the collector has 150 20-cent coins and 74 25-cent coins for a total of 224 coins.

Now, to know the total value of the collection we need to multiply the value of the coins by the number of coins there are of this value (we are going to do it with the 20-cent and the 25-cent coins) and then sum up our results.

Total value = 74(25) + 150 (20) = 1850 + 3000 = 4850 cents.

So the total value is 4850 cents, we know that each dollar has 100 cents so, to express this number in dollars we are going to divide it by 100 and thus we have that the total value of the collection is 48.50 dollars.

Answer:

D) 3/2(X-4)

Step-by-step explanation:

Invert and multiply to get:

3(x+4)/2(x²-16)

factor the bottom

3(x+4)/2(x+4)(x-4)

The (x+4)’s cancel out, and you’re left with

3/2(X-4)

[tex]\dfrac{{x+4\over2}}{{x^2-16\over3}}[/tex]

[tex]=\dfrac{3(x+4)}{2(x+4)(x-4)}=\frac{3}{2(x-4)} [/tex]

but in original fraction, denominator can't be zero so we have to exclude x=±4

do that answer is D

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find GV

To find GV we use cosine

cos∅ = adjacent / hypotenuse

From the question

GV is the adjacent

GC is the hypotenuse

So we have

GC = 55°

GV = 55 cos 37

GV = 43.92495

We have the final answer as

Hope this helps you

Answer:

See below.

Step-by-step explanation:

First, recall the meanings of the domain and range.

The domain is the span of x-values covered by the graph.

And the range is the span of y-values covered by the graph.

1)

So, we have here an absolute value function.

As we can see, the domain of the function is all real numbers because the graph stretches left and right infinitely. Therefore, the domain of the function is:

[tex]\{x|x\in\textbb{R}\}[/tex]

(You are correct!)

For the range, notice how the function stops at y=7. The highest point of the function is (-2,7). There graph doesn't and won't ever reach above y=7. Therefore, the range of the graph is all values less than or equal to 7. In set notation, this is:

[tex]\{y|y\leq 7\}[/tex]

2)

We have here an ellipse.

First, for the domain. We can see the the span of x-values covered by the ellipse is from x=-4 to x=6. In other words, the domain is all values in between these two numbers and including them. Therefore, we can write it as such:

[tex]-4\leq x\leq 6[/tex]

So x is all numbers greater than or equal to -4 but less than or equal to 6. This describes the span of x-values. In set notation, this is:

[tex]\{x|-4\leq x\leq 6\}[/tex]

For the range, we can see that the span of x values covered by the ellipse is from y=-5 to y=1. Just like the domain, we can write it like this:

[tex]-5\leq y\leq 1[/tex]

This represents all the y-values between -5 and 1, including -5 and 1.

In set notation, thi is:

[tex]\{y|-5\leq y\leq 1\}[/tex]

Hi there! :)

Answer:

x = -7.

Step-by-step explanation:

Starting with:

3(2x + 2) = 3x - 15

Begin by distributing '3' with the terms inside of the parenthesis:

3(2x) + 3(2) = 3x - 15

Simplify:

6x + 6 = 3x - 15

Isolate the variable by subtracting '3x' from both sides:

6x - 3x + 6 = 3x - 3x - 15

3x + 6 = -15

Subtract 6 from both sides:

3x + 6 - 6 = -15 - 6

3x = -21

Divide both sides by 3:

3x/3 = -21/3

x = -7.

Answer:

x = -7

Step-by-step explanation:

3(2x+2) = 3x - 15

First, we should simplify on the left side.

6x + 6 = 3x - 15 ; Now we subtract six from both sides.

      -6          -6

6x = 3x - 21 ; next we just subtract 3x from both sides.

-3x   -3x

3x = -21

Finally, we divide 3 from both sides to separate the three from the x.

x = -7

Hope this helps!! <3 :)

Answer:

Step-by-step explanation:

Given that:

[tex]\mathtt{f(x) = ax^2 + bx + c}[/tex]

The derivative of the function of x is  [tex]\mathtt{f'(x) = 2ax + b}[/tex]

Thus; f(x) is increasing when f'(x) > 0

f(x) is decreasing when f'(x) < 0

i.e

f'(x) > 0 , when  b > 0  and a < 0

∴

2ax + b < 0

2ax < - b

[tex]\mathtt{x < \dfrac{-b}{2a}}[/tex]

f'(x) < 0 , when  b < 0  and a > 0

2ax + b > 0

2ax > - b

[tex]\mathtt{x > \dfrac{-b}{2a}}[/tex]

Answer:

Around 217 pounds

Step-by-step explanation:

Let's convert the height into inches.

5 feet 8 = [tex]5\cdot12 + 8 = 60 + 8 = 68[/tex]

6 feet [tex]= 6\cdot12 = 72[/tex].

We can set up a proportion

[tex]\frac{205}{68} = \frac{x}{72}[/tex]

We can use the cross products property to find x.

[tex]205\cdot72=14760\\\\\\14760\div68\approx217[/tex]

Hope this helped!

Answer:

217.0588235 lbs

Step-by-step explanation:

Convert ft inches to inches

5 ft = 5*12 = 60 inches

5 ft 8 inches = 68 inches

6 ft = 6*12 = 72 inches

We can use ratios to solve

205 lbs        x lbs

------------- = ----------------

68 inches     72 inches

Using cross products

205 * 72 = 68x

Divide by 68

205 *72/68 = x

217.0588235 lbs

Answer:

Hello,

The answer would be,

A union B = {3,6,9,12}

and A intersection B= {6,9}

Answer:

[tex]\huge\boxed{ A\ union \ B = \{3,6,8,9,12\}}[/tex]

[tex]\huge\boxed{A\ intersection \ B = \{6,9\}}[/tex]

Step-by-step explanation:

A = {3,6,9,12}

B = {6,8,9}

A∪B = {3,6,9,12} ∪ { 6,8,9}   [Union means all of the elements should be included in the set of A∪B]

=> A∪B = {3,6,8,9,12}

Now,

A∩B = {3,6,9,12} ∩ {6,8,9}  [Intersection means common elements of the set]

=> A∩B = {6,9}

Answer:

125π ft²

Step-by-step explanation:

1/4π(30)² - 1/4π(20)² = 125π

A(t) = 100t^2 + 500t + 625

3,025 square pixels

Answer:

A(t) equals 100t²+ 500t + 625.

The area of the square image after 3 seconds is 3,025 square pixels.

Answer and Step-by-Step explanation:

% increase = 100 x [(new price) - (original price)] / (original price)] = 100 (9.67 - 9.56) / 9.56

% increase ≅ 1.2% (to the nearest tenth)

Answer:

A) 1236 units²

Step-by-step explanation:

Cylinder = 2[tex]\pi[/tex]h+2[tex]\pi[/tex]r²

2(3.14)(7.5)(15)+2(3.14)(7.5x7.5)

706.5+353.25=1059.75

1/2 Sphere = 1/2(4)[tex]\pi[/tex]r²

2(3.14)(7.5)(7.5)

353.25

TOTAL: 1059.75+353.25=1413

HOWEVER...you need to subtract the top of the cylinder ([tex]\pi[/tex]r²) 176.625

1413-176.625=1236.375

So the answer would be A.  (Silo’s do have a bottom, or else the answer would be D)

Answer:

1,236 units²

Step-by-step explanation:

I got it correct on founders edtell and screenshot below as proof

Answer:

[tex]Probability = \frac{1}{3}[/tex]

Step-by-step explanation:

Given

[tex]Set:\ \{1, 2, 3, \ldots, 24\}[/tex]

[tex]n(Set) = 24[/tex]

Required

Determine the probability of selecting a factor of 4!

First, we have to calculate 4!

[tex]4! = 4 * 3 * 2 * 1[/tex]

[tex]4! = 24[/tex]

Then, we list set of all factors of 24

[tex]Factors:\ \{1, 2, 3, 4, 6, 8, 12, 24\}[/tex]

[tex]n(Factors) = 8[/tex]

The probability of selecting a factor if 24 is calculated as:

[tex]Probability = \frac{n(Factor)}{n(Set)}[/tex]

Substitute values for n(Set) and n(Factors)

[tex]Probability = \frac{8}{24}[/tex]

Simplify to lowest term

[tex]Probability = \frac{1}{3}[/tex]

Answer:

(- 1, 4 )

Step-by-step explanation:

The line x + 2 = 0 can be expressed as

x + 2 = 0 ( subtract 2 from both sides )

x = - 2

This is the equation of a vertical line parallel to the y- axis and passing through all points with an x- coordinate of - 2

Thus (- 3, 4 ) is 1 unit to the left of - 2

Under a reflection in the line x = - 2

The x- coordinate will be the same distance from x = - 2 but on the other side while the y- coordinate remains unchanged.

Thus

(- 3, 4 ) → (- 1, 4 )

Answer:

Step-by-step explanation:

Hello, please consider the following.

For x > 1, we can apply Pythagoras theorem as below.

[tex]\text{Let's estimate this sum of two squares.} \\\\(2x)^2+(x^2-1)^2=4x^2+x^4-2x^2+1=x^4+2x^2+1\\\\\text{Let's estimate this square, now.} \\\\(x^2+1)^2=x^4+2x^2+1\\\\\text{The two expressions are equal, meaning.} \\\\(2x)^2+(x^2-1)^2=(x^2+1)^2\\\\\text{Using Pythagoras' theorem, we can say that this is a right triangle.}[/tex]

Thank you

Answer:

32 years old

Step-by-step explanation:

The husband is 32 years old as the wife is 3 years younger than the husband. The son is 3 years older than the daughter. Their family altogether total age today is 68 years while 4 years ago their age total was 54 years. The difference is 14 years. If we divide the difference into 4 then the age can not be whole number which means daughter is born after 2 years. She is now 2 years older. Son is 3 years older than the daughter which means he is 5 years old. The husband then must be 32 years old and wife is 3 years younger which means she is 29 years old now.

32 + 29 + 5 + 2 = 68 years.

Answer:

150

Step-by-step explanation:

70% of 500 people are adults and the remainder are children.

There are 150 children

Answer: Option D. will be the answer.

Explanation: The bowling scores for six persons have been given as 27, 142, 145, 146, 154, 162.

The most appropriate measure of the center of these scores will be the median.

Here median will be mean of 146 and 146 because number of persons are 6 which is an even number.

So there are two center scores those are 145 and 146 and median =  

Option D. will be the answer.

Answer:

d. 19

Step-by-step explanation:

Degrees of freedom is the number is the number of value which is used in the final calculation. It calculate as n-1, where n is the sample size. The degrees of freedom for the given scenario is 19. The sample size is 20 so the degrees of freedom is 1 less which will be 19.

Answer:

The number to be multiplied is the "multiplicand"

Step-by-step explanation:

a base when it is written in exponential notation

Answer:

P (x= 5) =  0.0001

P(x=3) =  0.008699

Step-by-step explanation:

This is a binomial distribution .

Here p = 0.8  q= 1-p = 1-0.8 = 0.2

n= 15

So we find the probability for x taking different values from 0 - 15.

The formula used will be

n Cx p^x q^n-x

Suppose we want  to find the value of x= 5

P (x= 5) = 15C5*(0.2)^10*(0.8)^5 = 0.0001

P(x=3) = 15C3*(0.2)^12*(0.8)^3 =  9.54 e ^-7= 0.008699

Similarly we can find the values for all the trials from 0 -15  by substituting the values of x =0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15.

The value for p(x = 5) is 0.0001 and the value for p(x = 3) is 0.008699.

It is given that the 80% of all brand A external hard drives work in a satisfactory manner throughout the warranty period.

It is required to find the sampling distribution if n =15 samples.

It is defined as the probability distribution for the definite sample size the sample is the random data.

We have p =80% = 0.8 and q = 1 - p ⇒ 1 -0.8 ⇒ 0.2

n = 15

We can find the probability for the given x by taking different values from 0 to 15

the formula can be used:

[tex]\rm _{n}^{}\textrm{C}_x p^xq^{n-x}[/tex]

If we find the value for p(x = 5)

[tex]\rm _{15}^{}\textrm{C}_5 p^5q^{15-5}\\\\\rm _{15}^{}\textrm{C}_5 0.8^50.2^{10}[/tex]⇒ 0.0001

If we find the value for p(x = 3)

[tex]\rm _{15}^{}\textrm{C}_3 0.8^30.2^{12}\\[/tex] ⇒  

Similarly, we can find the values for all the trials from 0 to 15 by putting the values of x = 0 to 15.

Thus, the value for p(x = 5) is 0.0001 and the value for p(x = 3) is 0.008699.

Learn more about the sampling distribution here:

https://brainly.com/question/10554762

Answer:

=6 units squared

Step-by-step explanation:

area=1/2h(a+b)

        =1/2×2(4+2)

        =6

Answer:

integer of course

Step-by-step explanation:

an integer can either be negative or positive.

Step-by-step explanation:

sin∠M = cos∠N

sin∠M = cos(30°)

sin∠M = √3 / 2

m∠M = 60° or 120°

If ∠M is acute, m∠M = 60°.

Answer: The measure of ∠M is 60°

Step-by-step explanation:

The complement of 30° is 60°

sin∠M =cos∠N

sin∠60°=cos∠30°

the measure of ∠M is 60°

Answer:

4.25, 4.5, 4.75, 5.00, 5.25, 5.5, 5.75, 6.00

Step-by-step explanation:

it is an arithmetic sequence with common difference 0.25

Answer:

B

Step-by-step explanation:

11q + 5 ≤ 49

Subtract 5 from each side

11q + 5-5 ≤ 49-5

11q ≤44

Divide each side by 11

q ≤44/11

q≤4

There is a close circle at 4 because of the equals sign and the lines goes to the left

Answer:

B

Step 1:

To solve this, we need to isolate the variable q. To do so, we will subtract 5 from both sides of the inequality.

[tex]11q+5(-5)\leq 49(-5)\\11q\leq 44[/tex]

Step 2:

We divide both sides by 11 to get our q.

[tex]\frac{11q}{11}\leq \frac{44}{11} \\q\leq 4[/tex]

q ≤ 4

Step 3:

To find the correct graph, we need to know that a close circle means a ≤ or ≥ and an open one means a < or >. Here, we are using a ≤ so C and D are not our answers. Also remember that if the "arrow" is pointing left (<), then the arrow on the graph should be facing the left side. If the arrow is facing the right side, then that means we are using > or ≥. Here, we are using ≤ (left), so that means the arrow on the graph should be on a 4, facing left, with a closed circle.

Our answer is B.

Answer:B the amount of money in a bank account never changes.

Step-by-step explanation:

Answer:

B. The amount of money in a bank account never changes.

Step-by-step explanation:

Equilibrium is achieved when the state of a reversible reaction of opposing forces cancel each other out. While in a state of equilibrium, the competing influences are balanced out. Imagine a cup with a hole in it being filled with water from a tap. The level of water in this cup would stay the same if the rate at which the water that flows inside is the same as the water that flows outside. Option B will be the correct answer because the amount of money going into the account is at the same rate of money coming out of the account.

Answer:

[tex]\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}[/tex]

Step-by-step explanation:

Given that:

[tex]cosA=-\dfrac{1}3[/tex]

and

[tex]tanA > 0[/tex]

To find:

[tex]cos\dfrac{A}{2} = ?[/tex]

Solution:

First of all,we have cos value as negative and tan value as positive.

It is possible in the 3rd quadrant only.

[tex]\dfrac{A}{2}[/tex] will lie in the 2nd quadrant so [tex]cos\dfrac{A}{2}[/tex] will be negative again.

Because Cosine is positive in 1st and 4th quadrant.

Formula:

[tex]cos2\theta =2cos^2(\theta) - 1[/tex]

Here [tex]\theta = \frac{A}{2}[/tex]

[tex]cosA =2cos^2(\dfrac{A}{2}) - 1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =cosA+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =-\dfrac{1}3+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =\dfrac{2}3\\\Rightarrow cos(\dfrac{A}{2}) = \pm \dfrac{1}{\sqrt3}[/tex]

But as we have discussed, [tex]cos\dfrac{A}{2}[/tex] will be negative.

So, answer is:

[tex]\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}[/tex]

Answer:

[tex]\boxed{x \geq 353}[/tex]

Step-by-step explanation:

Hey there!

Info Given

- Dot is solid

- Line goes to the right

- Dot is at 353

So by using the given info we can conclude that the inequality is,

x ≥ 353

Hope this helps :)

Answer:

Inequality: 100 + 50w ≥ 18000

What to put on graph: w ≥ 358

Answer:

6

Step-by-step explanation:

Given, 3sin2x−7sinx+2=03sin2⁡x-7sin⁡x+2=0

⇒(3sinx−1)(sinx−2)=0⇒3sin⁡x-1sin⁡x-2=0

⇒sinx=13 or 2⇒sin⁡x=13 or 2

⇒sinx=13    [∵sinx≠2]⇒sin⁡x=13    [∵sin⁡x≠2]

Let  sinα=13,0<α<π2,sinα=13,0<α<π2, then sinx=sinαsinx=sinα

now x=nπ+(−1)nα(n∈I)x=nπ+(−1)nα(n∈I)

⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α Are the solution in [0,5π][0,5π]

Hence, required number of solutions are 6