The axis of symmetry for a quadratic equation can be found using the formula x =-b/2a , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane. When the equation is solved for a, such that b is the numerator of the resulting fraction, what is the denominator of the fraction?

Answer:

it has no solution

Step-by-step explanation:

Answer:

2 no.be x and y

x+y=67

x-y=11

solving both eqx

x=39

y=28

small no=28

To find the length, divide the area by the width.

See the attached picture:

Answer:

The coordinates of A' are (-9,4)

Step-by-step explanation:

we know that

Each point of the original figure and its image are the same distance away from the line of reflection

so

step 1

reflected the point A(3,4) over the line x=2

The distance of the point to the line of reflection is 3-2=1 units

therefore

The coordinate of the reflected point is (2-1,4) ----> (1,4)

step 2

reflected the point (1,4) over the line x=-4

The distance of the point to the line of reflection is 1-(-4)=5 units

therefore

The coordinate of the reflected point is (-4-5,4) ----> (-9,4)

Answer: is c (-9,4) the guy had it right but wrong letter

Step-by-step explanation:

Answer:

3, 7, 12, 14, 21

Step-by-step explanation:

3 is the minimum value of the data set.

The median is 12. (it is in the middle of 3 and 12 if you look at the question)

The first quartile is 7 (if you count, it is equidistant from either end)

the third quartile is 14. (it is in the middle of 12 and 21 if you look at the question)

21 is the maximum value of the data set.

Answer: 3 is minimum, 7 is first quartile, 12 is median, 14 is third quartile, and 21 is maximum.

Answer:

(-1, -3)

Step-by-step explanation:

We suppose your notation means you want to reflect given point P across the horizontal line y=1.

The x-coordinate will remain the same.

The new y-coordinate will be such that y=1 is the midpoint between the original and its reflection:

(5 + y)/2 = 1

5 + y = 2 . . . . multiply by 2

y = 2 -5 = -3 . . . subtract 5

The reflected point is (-1, -3).

___

The same sort of math applies whenever you have a midpoint and want to find the other end point. Double the midpoint value and subtract the end point you have in order to find the other end point.

Here is the set up:

Use a^2 + b^2 = c^2

Let c = length of ladder

Let b = distance of ladder's base from the building.

We must find a.

(a)^2 + (8.2)^2 = (15.5)^2

a^2 = (15.5)^2 - (8.2)^2

a^2 = 173.01

Take the square root on both sides.

sqrt{a^2} = sqrt{173.01}

a = 13.1533265754

We now round off to the nearest tenth of a foot.

a = 13.2 feet

Did you follow?

The distance between the point of the base of the building to the point where the ladder touches it for this case is 13.14 ft approx.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Consider the diagram attached below.

We've got:

Usually buildings are vertical, so perpendicular to the ground.

Therefore, we can take ABC a right angled triangle, and therefore, use Pythagoras theorem here:

[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\15.5^2 = |AB|^2 + 8.2^2\\|AB|^2= 240 - 67.24\\\\|AB| = \sqrt{172.76} \approx 13.14 \: \rm ft[/tex]

(took only positive root as length cannot be negative).

Thus, the distance between the point of the base of the building to the point where the ladder touches it for this case is 13.14 ft approx.

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Answer:

B. 11%

Step-by-step explanation:

Using the formula

Real rate of return = nominal rate - inflation rate

Note that the nominal rate of a business is the return on investment in a particular year.

Therefore if Josephine earned a 15% return on her investments last year, her nominal rate is also 15%

Since the inflation rate is 4%

Rate of return = 15%-4%

Rate of return = 11%

Answer:

Step-by-step explanation:

The radius of the ball is ...

  r = C/(2π) = (16π cm)/(2π) = 8 cm

The formula for the area of a sphere is ...

  A = 4πr²

Filling in the value of the radius, we find the area of the ball to be ...

  A = 4π(8 cm)² = 256π cm² ≈ 804.25 cm²

Then 256π or 804.25 is the number of square centimeters needed to cover the given ball with one coat of latex.

If the ball is only considered to be covered when it has two coats of latex, then twice that amount, 512π or 1608.50 square centimeters of latex are required.

The amount of latex needed to cover a rubber ball with two coats, when the circumference of the ball is 16π cm, is 512π cm².

To calculate the amount of latex needed to paint a rubber ball, we first need to calculate the surface area of the ball. The formula for the surface area of a sphere is 4πr², where r is the radius of the sphere. Given that the circumference of the sphere (rubber ball) is 16π cm, we can substitute this into the formula 2πr to find the radius, which equals 8 cm.

Substituting the radius into the surface area formula, we get 4π(8 cm)² = 4π(64 cm²) = 256π cm². This is the surface area for one layer of latex. But as the toy factory paints their balls with two coats of latex, we need to double this surface area, which gives us 512π cm² as the total area to be covered with latex.

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Answer:

A. $1,056,000 ≤ x ≤ $1,344,000

Step-by-step explanation:

The average annual salary of each of the 48 employees is given as;

$25,000

The total salary that the company pays to its employees annually is thus;

$25,000 * 48 = $1,200,000

Now, the total annual maximum variance  of the employees salaries would be;

$3,000 * 48 = $144,000

The lower limit of the total salary that the company pays to its employees annually is calculated as;

$1,200,000 - $144,000 = $1056000

The upper limit of the total salary that the company pays to its employees annually is calculated as;

$1,200,000 + $144,000 = $1344000

Therefore, the range of the total salary that the company pays to its employees annually is;

$1,056,000 ≤ x ≤ $1,344,000

The total annual salary range for a company with 48 employees, where each earns an average of $25,000 with a maximum variance of $3,000, is calculated by multiplying the number of employees by the minimum and maximum salaries. The range is from $1,056,000 to $1,344,000 (Option A).

The goal is to find the range of the total annual salary that the company pays to its employees. The average annual salary for each of the 48 employees is $25,000, with a possible variance of $3,000 either way. This means that the lowest possible salary could be $22,000 ($25,000 - $3,000) and the highest possible salary could be $28,000 ($25,000 + $3,000).

To find the range of the total salary that the company pays annually, we multiply the number of employees by the minimum and maximum possible salaries.

Therefore, the range of the total salary that the company pays to its employees annually is from $1,056,000 to $1,344,000. The correct answer to the question is A. $1,056,000 ≤ x ≤ $1,344,000.

Answer:

D. poor reputation

Step-by-step explanation:

Answer:

The answer is C.

Step-by-step explanation:

[tex]{( {x}^{4} y)}^{3} = {x}^{4 \times 3} {y}^{3} = {x}^{12} {y}^{3} [/tex]

Answer with explanation:

In Δ ABC and ΔA DE

 AC=AD----------[Given]

BC=DE----------[Given]

∠BAC=∠DAE-------[Given]

Any of the two criteria which are →[SAS,SSS] can't be used to prove ⇒ΔABC≅  ΔA ED

Because, neither two sides and Included angle of two triangles ,nor three corresponding sides of two triangles, are congruent to each other.

Option A : Neither Apply

1. Angle BAC = angle EAD( given)

2. line BC = line DE ( given)

3. line AC = line AD( given)

4. Triangle ABC is congruent to AED by SAS or SSS postulate of congruency.

The Side-Angle-Side (SAS) postulate states that if two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

1. Angle BAC = angle EAD( given)

2. line BC = line DE ( given)

3. line AC = line AD( given)

4. Triangle ABC is congruent to AED by SAS or SSS postulate of congruency.

Answer:

  x ≈ 1.8 cm gives the greatest volume

Step-by-step explanation:

After cutting x cm from each corner in each direction, the cardboard can be folded up to make a box that is x cm deep and (12 -2x) by (10 -2x) in length and width. Clearly, values of x are limited to 5 or less, since cutting 5 cm from each side would leave a width of zero. Then the volume is given by ...

  V = x(12 -2x)(10 -2x)

The plot below shows the value of this cubic equation for volume, and identifies the peak as (x, V) ≈ (1.8, 96.8). That is, a cut of 1.8 cm will result in a box of approximate volume 96.8 cm³.

Answer:

3/1.5

x=3

y=1.5

x÷y= 2

I hope this helps. Question was worded odd.

If x equals a increased by 50% of a and y equals b decreased by 50% of b, the value of x/y is:

[tex]\frac{x}{y} =2[/tex]

Concept of Ratio

The ratio of a to b is 2 to 3

This can be written as:

[tex]a:b=2:3[/tex]

This can also be re-written as:

[tex]\frac{a}{b}=\frac{2}{3}[/tex]

x equals a increased by 50% of a

x  =  1.5a

x  =  1.5(2)

x  =  3

y equals b decreased by 50% of b

y  =  0.5b

y  =  0.5(3)

y  =  1.5

Therefore, the ratio x/y will be:

[tex]\frac{x}{y} =\frac{3}{1.5} \\\\\\\frac{x}{y} =2[/tex]

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Answer:

The quotient is 4x- 3.

Step-by-step explanation:

Answer:

5.97 cm  to 3 significant figures.

Step-by-step explanation:

The diameter of the circle will be equal to the length of the diagonal of the square.

Area = 56 = πr^2

r^2 = 56 / π

r = √(56 / π) =  4.222 cm

So the diameter = 8.444 cm.

This  is  = diagonal of the square so, by The Pythagoras Theorem:

x^2 + x^2 = 8.444^2     where x  is the side of the square.

x^2 = (8.444)^2 / 2

x^2 = 35.651

x =  5.971 cm

Answer:

Explanation:

1) What is the smallest possible area of the tabletop that will fit on Timothy’s table base?

The statement that the base can support a tabletop with a radius of at least 6 inches means that the radius has to be 6 inches or more, i.e. the smallest possible radius is 6 inches.

a) Area of a circle: A = π r²

The smallest area is given by the smallest radius, which we have just stated that is 6 in.

b) Calculations:

With that A = π (6 in)² = 36π in² ≈ 113.10 in².

Round the answer to the nearest whole square inch: 113 in²

2) What is the largest possible area of the tabletop that will fit on Timothy’s table base?

The statement that the base can support a tabletop with a radius no more than 23 inches means that the radius has to be 23 inches or less, i.e. the largest possible radius is 23 inches.

a) Area of a circle: A = π r²

The largest area is given by the largest radius, which we have just stated that is 23 in.

b) Calculations:

With that A = π (23 in)² = 529 π in² ≈ 1,661.9 in².

Round the answer to the nearest whole square inch: 1,662 in².

Answer is 113 for the first then 1662 for the second

Step-by-step explanation:

Answer:

B.  6Fx + 6Gy = 6H

    Qx + Ry = S

Step-by-step explanation:

Equivalent equations can be created many ways. One of the simplest is to multiply both sides of the equation by the same number. In the answer above, the first equation has been multiplied by 6. Nothing has been done to the second equation.

_____

Comments on other choices

A: some terms have been multiplied by 6. This changes the equation(s) so they are no longer equivalent to the ones you started with.

B: the correct choice

C: see A.

D: the first equation has been multiplied by 6, so that is equivalent to the original. The second equation has the sign of one of the terms changed, so it is now a different equation.

Answer: B.  6Fx + 6Gy = 6H

                     Qx + Ry = S

Step-by-step explanation:

Let's say S is the number of small boxes and L is the number of large boxes.

There were 6 more small boxes than large boxes, so:

S = L + 6

Each small box weighs 45 pounds, and each large box weighs 70 pounds.  The total weight was 1305 pounds, so:

45S + 70L = 1305

We can now solve the system of equations.  Using substitution:

45(L + 6) + 70L = 1305

45L + 270 + 70L = 1305

115L = 1035

L = 9

S = 9 + 6

S = 15

There are 15 small boxes and 9 large boxes.

We are required to determine the number of small boxes shipped and the number of large boxes shipped.

let

x = number of small boxes shipped

y = number of large boxes shipped

Weight of small boxes = 45 pounds

Weight of large boxes = 70 pounds

Total weight of boxes = 1305 pounds

There were 6 more small boxes shipped than large boxes

x = y + 6 (1)

x = y + 6 (1)45x + 70y = 1305 (2)

substitute x = y + 6 into (2)

45x + 70y = 1305

45(y + 6) + 70y = 1305

45y + 270 + 70y = 1305

45y + 70y = 1305 - 270

115y = 1035

divide both sides by 115

y = 1035 / 115

y = 9

Recall,

x = y + 6

x = 9 + 6

x = 15

Therefore,

the number of small boxes shipped is 15 and the number of large boxes shipped is 9

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ANSWER

The correct answer is C.

EXPLANATION

The correct answer is C.

Answer:

The measure of angle x is [tex]m\angle x=84\°[/tex]

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises.

so

[tex]m\angle x=\frac{1}{2}(168\°)=84\°[/tex]

Answer: LAST OPTION.

Step-by-step explanation:

The Pythagorean Theorem states the following relationship between the three sides of a triangle that has an angle of 90 degrees, known as "Right triangle":

[tex]a^2=b^2+c^2[/tex]

Where "a"is the hypotenuse and "b" and "c" are the legs of the right triangle.

If the triangle ABC is a right triangle then AB must be equal to [tex]BC^2+AC^2[/tex], then, you need to substitute the values into  [tex]a^2=b^2+c^2[/tex] to check this:

[tex]12^2=5^2+10^2\\144\neq 125[/tex]

Then the triangle ABC is not a right triangle.

Therefore, the statement that justifies why this triangle is not a right triangle is:

[tex]5^2+10^2\neq 12^2[/tex]

Answer:

Step-by-step explanation:

In the equation given, y = 51.20x + 32.96, x is the number of hours worked.  The number of hours worked is multiplied by the rate the plumber charges per hour.  So the choice in the left hand column is "the amount the charges increase for each additional hour off work".  In other words, if he works only 1 hour, x = 1, then the charge for his labor is 51.20(1) = 51.20.  If he works 2 hours, the charge for his labor is 51.20(2) = 102.40.

The 32.96 is fixed as the average cost of the parts.  The choice in the right-hand column is "average cost of parts for each visit".

[tex]\bf \textit{surface area of a rectangular prism}\\\\ SA=2(Lh+Lw+wh)~~ \begin{cases} L=length\\ w=width\\ h=height\\ \cline{1-1} L=55\\ w=35\\ h=20 \end{cases} \\\\\\ SA=2[(55\cdot 20)+(55\cdot 35)+(35\cdot 20)]\implies SA=2[1100+1925+700] \\\\\\ SA=2(3725)\implies SA=7450[/tex]

Answer: They earned $720 from the T-shirts.

Step-by-step explanation:

Given : The number of T-shirts sold was 3 times the number of hats.

The profit was $5 for each T-shirt sold and $2.50 for each hat sold.

The students raised $840 for the charity.

Let x denotes the number of T-shirts sold and y denotes the number of hats sold.

then, we will have the given system :-

[tex]5x+2.50y=840\\x=3y[/tex]

It is also given that they used the system below to analyze their success and found the solution to be (144, 48).

It means x= 144

It means the number of t-shirt sold = 144

The amount they earn from t-shirt = [tex]144\times5=\$720[/tex]

Hence, they earn $720 from the T-shirts.

Answer:

this is just proof of verification if you don't believe the guy above me

Step-by-step explanation:

Answer:

t = 1.55 sec

Step-by-step explanation:

Because we are asked to find the time it will take for the rocket to travel horizontally, we are only concerned with the x-dimension here.  

We are told that the initial velocity is 50 ft/s and the angle is 75 degrees.  

The equation we are going to need to solve this involves the displacement, the initial velocity, the acceleration, and the time...all in the x dimension:

Δx = V₀t + 1/2at²

We have the displacement, we can solve for the initial velocity, we know acceleration, and time is what we are solving for.

Let's work to fill in these values:

Δx = 20 feet

V₀x = V₀ cos Ф (that's the closest thing I could find to theta)

a = 0 (acceleration is always 0 in the horizontal dimension)

t = ?

From the information we can determine the initial velocity in the x dimension using the formula

[tex]V_{0x}=V_{0}cos(\theta)[/tex]

Solving for the initial velocity in the x-dimension:

[tex]V_{0x}=50cos(75)[/tex], which gives us from our calculators that initial velocity in the x-dimension is 12.941 (I am not paying attention to significant digits here since 50 has only 1).

Now we can fill in our equation with the info:

[tex]20=12.941t+\frac{1}{2}(0)t^2[/tex]

Because a = 0, the whole portion of the equation after the plus sign equals 0, so we can disregard and simply solve:

20 = 12.941t so

t = 1.55 seconds

The time it will take for the rocket to travel 20 feet horizontally is 1.545 seconds.

There are three equations of motion, v= u +at, s = ut +(1/2)at²and v² = u²+2as.

The initial velocity is 50 ft/s

The angle is 75 degrees.  

s = ut +(1/2)at²

v= u cos [tex]\rm \theta[/tex]

v = 50 cos 75

v = 12.94 ft/s

a = 0  in horizontal direction

s = 20

20 = 12.94 *t

t = 20/12.94

t = 1.545 seconds.

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Answer:

Step-by-step explanation:

Answer:

The two numbers are .8*160=128 and .85*240=204

Step-by-step explanation:

First sentence:                 x+y=400

Second sentence           .8x+.85y=400-68

Solve y in the first sentence:  y=400-x

Plug first into second:     .8x+.85(400-x)=332

Distribute:                        .8x+.85(400)-.85x=332

Combine like terms:        -.05x+.85(400)=332

Simplify(multiply):              -.05x+      340=332

Subtract 340 on both sides:    -.05x       =332-340

Simplify(subtract):                     -.05x        =-8

Divide both sides by -.05:              x        =-8/-.05

Simplify (division):                           x        = 160

So y=400-x=400-160=240

Answer:

128 and 204. your welcome.

Step-by-step explanation:

Let x = the first number

Let y = the second number

So we can set up two equations:

x+y = 400

.8x + .85y = 400-68

Use substitution:

y = 400 - x

.8x + (.85)*(400-x) = 332

.8x + 340 -.85x = 332

8 = .05x

x = 160

So that makes y = 240

We want the decreased values so:

160*.8 = 128

240*.85 = 204

So the answers are 128 and 204

Final answer:

To find the solution of the system of equations -7x+y=-20 and 9x-3y=36, we can use the method of substitution. The solution is x = 2 and y = 6.

Explanation:

To find the solution of the system of equations -7x+y=-20 and 9x-3y=36, we can use the method of substitution or elimination. Let's use the method of substitution:

Step 1: Solve one equation for one variable in terms of the other variable. From the first equation, we have y = 7x - 20.

Step 2: Substitute this expression for y in the second equation. Substitute the value of y from Step 1 into the second equation: 9x - 3(7x - 20) = 36.

Step 3: Simplify and solve for x. Distribute the -3 to both terms inside the parentheses: 9x - 21x + 60 = 36.

Step 4: Combine like terms: -12x + 60 = 36.

Step 5: Subtract 60 from both sides of the equation: -12x = -24.

Step 6: Divide both sides of the equation by -12: x = 2.

Step 7: Substitute the value of x back into one of the original equations to find y. Using the first equation, we have -7(2) + y = -20. Simplifying, we get y =  6.

Therefore, the solution to the system of equations is x = 2 and y = 6.