Huilan is 11 years older than Thomas. The sum of their ages is 61. What is Thomas's age?

Answer:

6x^2-17x+12

Step-by-step explanation:

Distribute

2x^2-3x+1+x^2-2x+2(-2x+3)^2

Square (2x+3)

(-2x+3)(-2x+3)

FOIL

4x^2-6x-6x+9

Combine like terms

4x^2-12x+9

re-write equation

2x^2-3x+1+x^2-2x+2+4x^2-12x+9

Combine like terms

6x^2-17x+12

The length of BC is 50 miles (approx).

What is Trigonometry?

Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles.

Solution:

In the triangle ABC,

The perpendicular = BC

The Base = AB = 6 miles

by using the trigonometric ratio "tan"

tan (58) = BC / AB

8.33 = BC / 6

49.98 miles = BC

BC = 50 miles (approx)

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Josephine have £3882.9 amount after 2 years and £3994.9 amount after 3 years.

Using the formula of compound interest we can find the amount after t years compounded annually at the r per cent rate.

The formula of compound interest is as follows,

[tex]A=p(1+\frac{r}{100} )^t[/tex]

Where P is the principal value, A is the amount, r is the rate and t is the time.

Here we have a principal value of £3,500 and a rate is 4.5%.

Now, finding the amount after 2 years by putting the values in the formula of compound interest,

[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^2\\\\A=3500(1+0.045 )^2\\A=3500(1.045)^2\\A=3500\times1.092025\\A=3882.0875[/tex]

So, After 2 years Josephine will have £3882.9.

Now, finding the amount after 3 years,

[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^3\\\\A=3500(1+0.045 )^3\\A=3500(1.045)^3\\A=3500\times1.141166125\\A=3994.0814375[/tex]

So, After 3 years Josephine will have £3994.9.

Therefore, After 2 years Josephine will have £3882.9 and after 3 years Josephine will have £3994.9 when 4.5% interest is compounded annually.

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Answer: dont be rude

Step-by-step explanation:

Answer:

G LCM (least common multiple) of 3, 9, and 12. After doing that, find the number that is between 61 and 107.

Step-by-step explanation:

Least common multiple (lcm) is where g finds out the number that can be divided by all the numbers (3, 9, and 12 in this case) and still come out with a whole number.

The budget of KT's Restaurant for newspaper advertising for the coming year is $58,533,500

Given,

The length of advertisement of KT's Restaurant in Vidalia Times in week days = 5,000

The length of advertisement of KT's Restaurant in Vidalia Times in Saturdays = 10,000

The cost of daily column = $27.55 per column inch

The cost of Saturdays = $29.35 per column inch

We have to find the budget of KT's Restaurant for newspaper advertising for the coming year;

Here,

There are approximately 53 Saturdays in a year.

So,

365 - 53 = 312

Then,

The budget of advertisement on daily column = 312 × 5000 × 27.55 = $42,978,000

The budget of advertisement on Saturday column = 53 × 10,000 × 29.35 = $1,555,500

Therefore,

The total budget for advertisement = 42,978,000 + 1,555,500 = $58,533,500

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Based on the calculations, this equation 4f + 2(12f − 4) = 3(2f − 4) − f + 3 has one solution, which is equal to -1/23.

In Mathematics, no solution is also referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.

This ultimately implies that, an equation would have no solution or zero solution when both sides of the equal sign are not the same and the variables cancel out.

From the information provided, we have the following equation:

4f + 2(12f − 4) = 3(2f − 4) − f + 3

Opening the bracket, we have:

4f + 24f - 8 = 6f - 12 - f + 3

28f - 8 = 5f - 9

By collecting like terms, we have the following:

28f - 5f = -9 + 8

23f = -1

Dividing both sides by 23, we have:

f = -1/23

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Answer:

The answer is 55, you can figure this out as each number is increasing by 10

a_n=-5+10n

hope it helps

The values of x and y are -1 and 6 respectively, this forms an ordered pair of (-3,6) and (-1,2).

Given the equation and ordered pair in the question;

Find the y-value by substituting the x-value into the equation and solving for y.

y = 4x + 6

Plug in x = -3

y = 4( -3 ) + 6

y = -12 + 6

y = 6

Find the x-value by substituting the y-value into the equation and solving for x.

y = 4x + 6

Plug in y = 2

2 = 4x + 6

2 - 6 = 4x

-4 = 4x

x = -4/4

x = -1

Therefore, the ordered pair are (-3,6) and (-1,2).

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Answer:

-----------------------------------

Answer:

Perimeter = -3h + 24

Step-by-step explanation:

Forming the expression,

→ 7 + (14 - 6h) + (3h + 3)

Let's simplify the expression,

→ 7 + (14 - 6h) + (3h + 3)

→ 7 + 14 - 6h + 3h + 3

→ (-6h + 3h) + (7 + 14 + 3)

→ -3h + 24

Hence, answer is -3h + 24.

Answer:

D.) 11

Step-by-step explanation:

-9=-k^2-7k+k Plugging in k for x

-9=k^2-6k Combine like terms

0=k^2-6k+9 Add 9 to both sides

0=(k-3)(k-3) Factor

k=3

The equation is now

f(x)=x^2-7x+3

so

f(-1)=(-1)^2-7(-1)+3

f(-1)=1+7+3

f(-1)=11

The correct option regarding the area of the figure is given as follows:

14+16.25π units².

The figure, given with no scale at the end of the answer, is composed by:

The sides of the right-triangle are given as follows:

The area of a right triangle is given by half the multiplication of the sides, hence:

At = 0.5 x 7 x 4 = 14 units.

The radius of the semicircle is half the hypotenuse of the right triangle, hence, applying the Pythagorean Theorem:

h² = 7² + 4²

h = sqrt(7² + 4²)

r = 0.5sqrt(7² + 4²)

r = 4.03 inches.

The area of a semicircle of radius r is:

As = πr².

Hence:

As = π(4.03)² = 16.25 π.

The total area is obtained as the sum of the areas of each separate part, hence:

A = At + As = 14+16.25π units².

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Answer:

Step-by-step explanation:

14+8.125

C

The amount of each semiannual interest payment is $7200.

Given that,
A company issues 9%, 4-year bonds with a par value of $160,000 on January 1 at a price of $165,386, when the market rate of interest was 8%. The bonds pay interest semiannually.

Simple interest is defined as the percentage of earnings on the lending for a period of time

Here,
Value of a single bond    =  $160,000
Issue price of bond         =  $165, 386
Rate of interest                =     9%
the market rate of interest =     8%
Interest payment             =      Semi-annually

Semi-annual interest payment      =  Value of the single bond × rate of interest/2
                                                       = $160,000 × 0.09/2
                                                       =  $7200

Thus, the amount of each semiannual interest payment is $7200.

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The ordered pairs that are solutions to the linear equation x + 2y = 4 are given as follows:

The linear function in this problem is defined as follows:

x + 2y = 4.

To complete the ordered pairs, we take the given coordinate and then solve for the missing coordinate .

For the first ordered pair, the given coordinate is of x = -3, hence we have to solve for y when x = -3, thus:

-3 + 2y = 4.

2y = 7.

y = 7/2

y = 3.5.

Hence the ordered pair is:

(-3, 3.5).

For the second ordered pair, the given coordinate is of y = -7, hence we have to solve for x when y = -7, thus:

x + 2y = 4.

x - 14 = 4

x = 18.

Hence the ordered pair is:

(18, -7).

The ordered pairs that we have to complete are given as follows:

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(I suggest using desmos graphing calculator for the future.)

(0,5) and (4,0) or the one in the left upper corner. Hope this helps.

The critical points of the given inequality are; x=-6 and x=2

1) When the denominator is equal to zero, at that point, we will have a critical point.

We are given the inequality;

(2x + 5)/(x - 2) ≥ (x - 1)/(x - 2)

Thus, x - 2 = 0

x = 2.

Thus, x = 2 is a critical point

2) Simplify the numerator to get the expression such that p(x) ≥ 0 or p(x) ≤ 0.

Thus, at p(x) = zero, we have other critical point(s)

Multiply both sides by (x - 2) to get;

2x + 5 = x - 1

2x - x = - 1 - 5

x = - 6

Then, the two critical points are x = 2 and x = - 6.

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The dimensions of the rectangle is 83 feet x 46 feet

What is the Perimeter of a Rectangle?

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

The perimeter P of the rectangle = 258 feet

Let the length of the rectangle be = L

Let the width of the rectangle be = W

And , The width is 37 feet less than the length. ,

So , W = L - 37

Perimeter P = 2 ( Length + Width )

Substituting the values of L and W in the equation , we get

Perimeter P = 2 ( L + L - 37 )

2 ( L + L - 37 ) = 258

( L + L - 37 ) = 129

2L - 37 = 129

Adding 37 on both sides , we get

2L = 166

Divide by 2 on both sides , we get

Length L of the rectangle = 83 feet

Substituting the value of L in equation ,we get

W = L - 37

Width W of the rectangle = 46 feet

Therefore , Length = 83 feet and Width = 46 feet

Hence , the dimensions of the rectangle is 83 feet x 46 feet

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Answer:

r = -8.6

Step-by-step explanation:

ooooo IXL, one of my fav programs from my school days

Anyway

Multiply by -3 to get rid of that awful fraction

[tex]-3*2.2=\frac{r+2}{-3} *-3[/tex]

Solve that:

[tex]-6.6=r+2\\aka: r+2=-6.6[/tex]

Subtract 2 from both sides to isolate the r variable:

[tex]r=-8.6[/tex]

And.... We have our answer!

r = -8.6

Using the percentage concept, it is found that 60.29% of the people surveyed were completely satisfied with the car.

A percentage is the number of desired outcomes, multiplied by 100%, and divided by the number of total outcomes.

In this problem, researching in the internet, it is found that:

A total of 1260 + 650 + 180 = 2090 people were surveyed.

Of those, 1260 were completely satisfied.

Hence:

60.29% of the people surveyed were completely satisfied with the car.

The angle x will be 34°.

From the properties of circles we get to know that the angle at the center and the angle between two tangents are always supplementary.

Supplementary angles are those which always sum to to 180°.

For example ∠HJK is supplementary to ∠HIK the their sum will come out to be 180°.

similarly ∠ROP + ∠RQP = 180°

∠RQP = 180° - ∠ROP

∠ROP is given to us 146°

After putting it in the equation above we get ∠RQP = 34°

Therefore x comes out to be 34°.

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The Greatest Common Factor is [tex]b^{2}[/tex] Option B

The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers

Find the common factors of each term in order to find the greatest common factor (GCF).

The Prime Factors of:

[tex]b^{5}[/tex] = [tex]b^{5}[/tex]

2[tex]b^{4}[/tex] = 2[tex]b^{4}[/tex]

[tex]3b^{3}[/tex] = [tex]3b^{3}[/tex]

[tex]b^{2}[/tex] = [tex]b^{2}[/tex]

From the common factors, the greatest common factors is [tex]b^{2}[/tex]

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Answer:

  4/3

Step-by-step explanation:

You want the limit as t→1 of (t³+t²-5t+3)/(t³-3t+2).

The fact that each polynomial evaluates to 0 at t=1 tells you that (t-1) is a factor of each. Factoring that out gives ...

  [tex]\dfrac{t^3+t^2-5t+3}{t^3-3t+2}=\dfrac{(t-1)(t^2+2t-3)}{(t-1)(t^2+t-2)}=\dfrac{(t-1)(t-1)(t+3)}{(t-1)(t-1)(t+2)}\\\\=\dfrac{t+3}{t+2}[/tex]

The limit at t = 1 is found by direct substitution:

  lim = (1 +3)/(1 +2) = 4/3

Answer:

Step-by-step explanation:

The rule for dilation of a quadrilaterial is Do.0.08 (z,y) (0.08z, 0.08y). What is the Y coordinate of a new point if the new coordinate is (3-9)? Round to the nearest

hundredth if necessary

The integers that would make the inequality true is the set of integers less than 20.

From the question we are to determine the integer that would make the given inequality true

The given inequality is

x - 4 < 16

To determine the integer that would make the inequality true, we will solve the inequality for the variable x

Solving the inequality

x - 4 < 16

Add 4 to both sides of the inequality

x - 4 + 4 < 16 + 4

x < 20

Hence, the solution to the given inequality is x < 20. All integers less than 20 will make the inequality true.

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The rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.

The surface area of a sphere with radius r is given by4π[tex]r^{2}[/tex]

Given;

S = surface area at time t,  and r = radius at time t

radius of a spherical ball is increasing at a rate of 2 cm/min

radius: 6cm

Area of a sphere is A = 4π[tex]r^{2}[/tex]

Step 1: Differentiate area of a spherical ball

A = 4π[tex]r^{2}[/tex]

[tex]\frac{dA}{dt}[/tex] =[tex]\frac{d}{dt}[/tex](4π[tex]r^{2}[/tex])

=4π [tex]\frac{d}{dt}[/tex]([tex]r^{2}[/tex])

=4π2r [tex]\frac{dr}{dt}[/tex]

[tex]\frac{dA}{dt}[/tex] = 8πr

since we have that dr/dt = 2 cm/min. Thus, the radius of the ball is 6cm, we have;

[tex]\frac{dA}{dt}[/tex]= 8π(6)(2) =96π

So, the rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.

Note that measuring area unit is cm2/min

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The distribution that is needed for the problem that we have here is the t distribution.

With its bell-shaped structure and heavier tails, the t-distribution, commonly referred to as the Student's t-distribution, is a kind of probability distribution that resembles the normal distribution.

When there are insufficient samples or unknown variances, it is used to estimate population parameters. T-distributions have broader tails than normal distributions because they are more likely to contain extreme values.

We have tn-1

where n = 70

so that we would have

t70 - 1

= t69

Therefore we would have to use the t distribution here.

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