1
Select the correct answer.
What are the zeros of this quadratic function?
fx)=(x-7)(x+8)
OA
x = 0 and x = 7
OB. x= 0 and x = -8
OC. x=-7 and x = 8
OD. x=7 and x = -8

The total number of coins Balu had in his collection was 216 coins, computed using the linear equation in one variable, x = x/2 + x/3 + 36.

Asian coins were 1/2 a fraction of this, that is, (1/2)*216 = 108 coins.

We assume the total coins with Balu to be x.

The fraction of coins from Asian countries = 1/2.

Thus, the number of coins from the Asian countries = 1/2 of x = x/2.

The fraction of coins from European countries = 1/3.

Thus, the number of coins from the European countries = 1/3 of x = x/3.

The number of coins from America = 36.

Thus, the total number of coins = x/2 + x/3 + 36.

But, we assumed that the total number of coins is x.

Thus, we get a linear equation in one variable as follows:

x = x/2 + x/3 + 36.

We solve this equation as follows:

x = x/2 + x/3 + 36,

or, x - x/2 - x/3 = 36,

or, (6x - 3x - 2x)/6 = 36,

or, x/6 = 36,

or, x = 36*6 = 216.

Thus, the total number of coins Balu had in his collection was 216 coins, computed using the linear equation in one variable, x = x/2 + x/3 + 36.

Asian coins were 1/2 a fraction of this, that is, (1/2)*216 = 108 coins.

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The probability that they win both contracts is 33% if there is a 45% probability of winning the first contract and the probability of winning the second contract after winning the first contract.

Probability is the rate of successful outcomes to the total outcomes of an event.

P(E) = n(E)/n(S)

Where E -event, n(E) - successful/favorable outcomes of event E, and n(S) - total outcomes of the event.

It is given that,

An aerospace company has submitted bids on two separate federal government defense contracts.

The probability of winning the first contract is - 45%

The probability of winning the second contract if they win the first contract is  - 73%

The probability of winning the second contract if they lose the first contact is - 45%

So, the probability that they win both contracts is

= (probability of winning the first contract) × (probability of winning the second contract)

= 0.45 × 0.73

= 0.3285 ≅ 0.33

⇒ 33%

Therefore, the probability that they win both contracts is 33%.

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The ship's horizontal distance from the lighthouse is 1930.59 feet. Using trigonometric ratio 'tanθ' the distance is calculated.

The trigonometric ratios are used for determining the lengths of the right-angled triangle. There are six basic trigonometric ratios. they are:

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

sec θ = hypotenuse/adjacent

cosec θ = hypotenuse/opposite

cot θ = adjacent/opposite

It is given that,

The height of the bacon-light is 135 feet above the water

Consider the horizontal distance between the boat and the lighthouse = x feet

The angle of elevation is given as 4°

Constructing a model as below in the figure.

From the trigonometric ratios, we have

tan θ = 135/x

⇒ tan 4° = 135/x

⇒ x = 135/tan 4°

∴ x = 1930.589 feet ≅ 1930.59 feet (rounding to the nearest hundredth of a foot)

Therefore, the ship's horizontal distance from the lighthouse is 1930.59 feet.

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4.6 moles in 187 grams of magnesium oxide (mgo).

To solve ,

             number of moles is equals to the mass in grams divided by RFM

                 RFM=16+24.3=40.3

                            =187/40.3

                             =4.6 moles of MgO

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BC is 3 across & CA is 3 up, but this creates a right-angle triangle. So, Pythagoras Theorem is used to find AB

AB = root 3^2 + 3^2

AB = 3 root 2

or 4.242640687

Thus, AB is 4.24 to 2d.p

(root means square root)

Hope this helps!

Answer:

Step-by-step explanation:

Comment

The first thing you ought to notice is that the original shape is a rectangle, with 2 of the y coordinates of the 4 points of 1. What that statement means is that two of the points (1,1) and (3,1) both sit on the line y = 1. they don't move. The other two points do move and they form a circular shape. So what you are going to get is a cylinder.

Answer: cylinder

Answer: 345

Step-by-step explanation: the alls

Answer: C.

Step-by-step explanation:

The first number is a positive 4, which is your a1. Then the geometric sequence goes to a negative implying that it is multiplied by a negative. So the a1 = 4 and it is being multiplied by a negative 3.

Answer: C

[tex]\left \{ {{a_{1}=4 } \atop {a_{n}=a_{n-1}*(-3) }} \right.[/tex]

Step-by-step explanation:

The starting amount (a1) = 4

The rate is -3 because 4 * -3 = 12 and -12 and -12 * -3 = 36 etc.

The graph that represents Lola's Purchase is as shown in the attached file.

Lola bought x pencils that cost $0.25 and Y erasers that cost $0.50.

Total expenditure is less than $3.

Representing expense in the equation form gives us;

Expense on pencils + expense on erasers < 3

Thus;

0.25X + 0.50Y < 3

Dividing through by 0.25, we have;

X + 2Y < 12

This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.

From the standard equation of line in slope intercept form, we can deduce that; Slope of this line is = (-1/2)

The correct graph is attached below.

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Answer:

10 points

Step-by-step explanation:

From the passage, we know:

1. Jay earned 15 points after spending $60

2. We want to know the number of points he can earn if he spends $40

We can set this up into proportions.

60:15 = 40:x

The x is the number of points he will get after spending $40.

15(40) = 60x

600 = 60x

x = 10

Jay will earn 10 points if he uses $40.

There can be 36 combinations.

The total number of combinations of the dial can be found by using permutations without any number repeating.

There are four integers on the dial. They are 0, 1, 2, and 3.

It is also given that the numbers shouldn't repeat on the adjacent dial.

Therefore, we can say that there are 4 possible numbers on the first.

Similarly, on the second dial, only 3 numbers are possible since no two adjacent dials can have the same.

This is also the case for the third dial. It can also have 3 possible numbers.

Therefore, the total number of combinations is given by 4*3*3 = 36 combinations.

Therefore, we have found that there can be 36 combinations.

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The planning value for the population standard deviation is 4330.

Given the confidence interval 20000 and 35000.

We have to find the planning value of standard deviation.

Standard deviation is measuring dispersion of data. Uniform probability distribution has two bounds a and b. The standard deviation is given by :

s=[tex]\sqrt{(b-a)^{2}/12 }[/tex].

Annual starting salaries for college graduates be between 20000 and 35000.

It is uniform in the interval so, a=20000, b=35000.

Now we have to just put the values of a and b in the above formula to get the value of standard deviation.

s=[tex]\sqrt{(35000-20000)^{2} /12}[/tex]

=[tex]\sqrt{(15000)^{2} /12}[/tex]

=[tex]\sqrt{225000000/12}[/tex]

=[tex]\sqrt{18750000}[/tex]

=4330

Hence the planning values for the population standard deviation is 4330.

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Question is incomplete as it should includes the confidence interval of $20000 and $35000.

Answer:

85 grams

Step-by-step explanation:

Marble:  5 g/marble

17 marbles in a bag:  (17 marbles)*(5 g/marble) = 85 grams/bag of 17 marbles

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path. This can be obtained by considering this as a right angled triangle.

Let x be the length between man and the pole, y be the distance between the tip of the shadow and the pole.

Then y - x will be the length between the man and the tip of the shadow.

Since two triangles are similar, we can write

[tex]\frac{y-x}{y} =\frac{6}{15}[/tex]

⇒15(y-x) = 6y

15 y - 15 x = 6y

9y = 15x

y = 15/9 x

y = 5/3 x

Differentiate both sides

dy/dt = 5/3 dx/dt

dy/dt is the speed of the tip of the shadow, dx/dt is the speed of the man.

Given that dx/dt = 5 ft/s

Thus dy/dt = (5/3)×5 ft/s

dy/dt = 25/3 ft/s

Hence 25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path.

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Answer:

The answer is the first option; 6^1/12

Step-by-step explanation:

We can simplify the question by using the radical rule to rewrite it as
6^1/3 ÷ 6^1/4

Then we use exponent rule which states that when we are dividing exponents of the same base, we have to subtract them. We see that the exponents are 1/3 and 1/4. So we use basic fractional division, here's the subtraction:

= 1/3 - 1/4
= 4/3 - 3/4 (we criss-crossed)
= 1/12 (we subtracted the denominators and multiplied the denominators)

Now that we have subtracted the exponents, we can write the answer as 6^1/12

Answer:

Option #1: [tex]6\frac{1}{2}[/tex]

Step-by-step explanation:

#1: Multiply [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] and [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex]:

[tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}} * \frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex]

#2: Combine and simplify the denominator:

- Multiply [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] by [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] = [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^{3} }{\sqrt[4]{6} \sqrt[4]{6}^3}[/tex]

- Raise [tex]\sqrt[4]{6}[/tex] to the power of 1

- Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents: [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^{3} }{\sqrt[4]{6}^{1+3}}[/tex]

- Add 1 and 3

- Rewrite [tex]\sqrt[4]{6}^4[/tex] as 6: [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^3}{6}[/tex]

#3: Simplify the numerator:

- Rewrite the expression using the least common index of 12: [tex]\frac{\sqrt[12]{6^4} \sqrt[12]{216^3}}{6}[/tex]

- Combine using the product rule for radicals: [tex]\frac{\sqrt[3]{6^4 *216^3}}{6}[/tex]

- Rewrite 216 as [tex]6^3[/tex]: [tex]\frac{\sqrt[3]{6^{4}*(6^{3})^{3}}}{6}[/tex]

- Multiply the exponents in [tex](6^{3})^3[/tex]: [tex]\frac{\sqrt[12]{6^{4}*6^{9}}}{6}[/tex]

- Use the power rule [tex]a^{m}a^{n}=a^{m+n}[/tex] to combine exponents and add [tex]4+9[/tex]:

[tex]\frac{\sqrt[12]{6^{13}}}{6}[/tex]

- Raise 6 to the power of 16: [tex]\frac{\sqrt[12]{13060694016}}{6}[/tex]

- Rewrite 13060694016 as [tex]6^{12}*6[/tex]: [tex]\frac{\sqrt[12]{6^{12}*6}}{6}[/tex]

- Pull terms out from under the radical: [tex]\frac{6\sqrt[12]{6}}{6}[/tex]

#4: Cancel the common factor of 6:

[tex]\frac{\sqrt[12]{6}}{6}=6\frac{1}{2}[/tex]

The correct simplified answer for [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] is Option #1: [tex]6\frac{1}{2}[/tex].

Answer:

D) f(x) = (1/2)^x

Step-by-step explanation:

at least that is what I think answer D is supposed to be.

I guess the other answer options are actually

A) f(x) = -2^x

B) f(x) = 2^x

C) f(x) = (1/2)^-x

let's look at the most interesting point here : (1, 1/2).

when x=1, then y = 1/2

A fails. because for x = 1 we get y = -2.

B fails. because for x = 1 we get y = 2.

C fails. because for x = 1 we get (1/2)^-1

and that is 1 / 1/2 = 2

so, the only function giving us (1, 1/2) is D, as

(1/2)¹ = 1/2

The true statement regarding the graphed function is that f(-2) = g(-2).

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given is a graphed function.

The graph contains two functions f(x) and g(x).

From the graph, it is clear that,

The two graphs intersect at a certain point, where the both functions passes through.

The intersecting point is (-2, 4).

This point can be written as (-2, f(-2)) and (-2, g(-2)).

This implies that,

f(-2) = g(-2)

Hence the true statement is f(-2) = g(-2).

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Your question is incomplete. The complete question is as given below.

Answer:

69%

Step-by-step explanation:

Overall grade = 0.35*minor grade + 0.65*major grade

major grade: 0.65*61 = 39.65

minor grade: 0.35*84 = 29.4

total: 39.65+29.4 = 69.05

Rounded = 69%

The total cost in 5 hours is $225

Given that the charges of a supply fee of an artist is $50

The charges per hour classes is $35

The total cost is expressed by c

The number of hours expressed by h

We need to calculate the total cost in 5 hour lesson

As per the given statement ,

C= 50 +35h

Where h is the number of hours

h = 5 hours

C = 50 + 35h

C = 50 + 35(5)

C = 50 +175

C = $225

The total cost in 5 hours is $225

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Answer:

34 miles from A

Step-by-step explanation:

Find time to cover 200 miles at ( 17 + 83 mph) = 200/100 = 2hours

 cyclist will be at   2 * 17 = 34 miles from A

Total Saving of Ethan is = $4600

Saving after donating 20% = $4600-$920

                                              =$3680

What is Percentage ?

As a fraction of 100, a percentage is a number or ratio. Although the abbreviations "pct.", and occasionally "pc" are also used, the percent sign ("percent") is frequently used to indicate it. A % has no dimensions and no associated unit of measurement.

How to calculate percentage?

Calculating a percentage involves dividing an item by its sum and multiplying the result by 100. The formula for percentage calculation is (value/total value)100%

Solution :

Let the Saving be 100%

Donated salary 20% = $920

finding 80% of the saving

Formula for percentage:

                                        [tex]\frac{value}{total value} *100[/tex]

                                        =[tex]\frac{20}{100} *920[/tex]

                                        = [tex]5*920[/tex]

                                        = [tex]4600[/tex]

Then the Total saving =$4600

The Total saving after donating 20% = $3680

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Based on the speed of the plane, the number of hours it will take to fly 3,008 miles is 5.47 hours.

The speed of the plane is given as 550 miles per hour

In order to reach 3,008 miles, the plane should travel for:

= Distance / Speed

= 3,008 / 550

= 5.47 hours

Rest of the question is:

how many hours will it take a plane to go 3 008 miles if it travels at 550 mph

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Discriminant for the quadratic equation  [tex]2x^2+x-3=0[/tex] is [tex]d=25[/tex]

How to find the d Discriminant of the quadratic equation ?

We know that the standard quadratic equation

[tex]ax^2+bx+c=0[/tex]

Discriminant of the equation is [tex]d=b^2-4ac[/tex]

Equation given in the question is

[tex]2x^2+x-3=0[/tex]

So we can find the values of [tex]a,b,c[/tex]

[tex]a=2\\b=1\\c=-3[/tex]

Substitute the values

[tex]d=1^2-4*2*(-3)\\d=1+24\\d=25[/tex]

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Answer:

~87.33 in³

Step-by-step explanation:

All you have to to is pkug the numbers in the formula. You start by doing 3.75 as the r² and you get around 14.06. Then you multiply that by the height (6.21) which gets you around 87.33. I hope this helps!

Answer:

Below in bold.

Step-by-step explanation:

Using the Pythagoras theorem:

Distance from the origin after  1 move = √(1^2 + 2^2) = √5.

So after 2016 distance is 2016√5 units.

This = 4507.9 units to the nearest tenth,

Answer:

(4)(2)(1)=

4+2+1=

explanation:

The area of the pool that needs to be covered is 960.42 square feet.

According to the question:

Let us find the perimeter of our given pentagon by multiplying each side length by 5.

[tex]Perimeter of community pool $=5 \times 23.62\\Perimeter of community pool $=118.1$[/tex]

Now let us find apothem of our pentagon by using Pythagoras theorem.  

[tex]a^{2}=20.10^{2}-11.81^{2}\\$a^{2}=404.01-139.4761\\$a^{2}=264.5339\\$a=\sqrt{264.5339}\\$a=16.2645$[/tex]

Upon substituting our given values in above formula we will get,

[tex]Area of community pool =\frac{1}{2} \times 16.2645 \times 118.1\\Area of community pool $=8.13224907 \times 118.1\\Area of community pool $=960.418615627971 \approx 960.42$[/tex]

Therefore, the area of the pool that needs to be covered is 960.42 square feet.

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Answer: B). 960 ft2

Step-by-step explanation:

The correct answer is 7.

A linear equation only has one or two variables. In a linear equation, no variable can be multiplied by a value greater than one or used as the denominator of a fraction. When you find the values that collectively make a linear equation true and plot those values on a coordinate grid, all the points fall on the same line.

I am aware that this query's equation is,

6b + 6 = 48

subtract 6 from both side in the equation.

6b + 6 - 6 = 48- 6

6b = 42

now, divide by 6 from both side in the equation.

6b/6 = 42/6

b = 7.

Therefore, the correct answer is 7.

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I understand this is the question.

Oksana wrote the equation below on the whiteboard.

6 b + 6 = 48

What is the value of b?

(a)4

(b)7

(c)8

(d)9