One solution to the problem below is 3.
What is the other solution?
b²-9=0

Answer:

20% increase

Step-by-step explanation:

To find the percent increase, use this formula

New value - original value

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

original value

114-95

-----------

95

19

---- = .2

95

.2 is 20%, so it is a20% increase

Answer:

2.603 degrees

Step-by-step explanation:

This word problem is talking about a triangle. 500 meters high would be the height and 11 Kilometers would be the base. We should convert kilometers to meters in order to make this easier. 11 kilometers = 11,000 meters.

Height = 500

Base = 11,000

The hypotenuse ends up being 11,011.35777

in order to find the angle of depression (assuming it is a constant rate) we would measure the angle where the hypotenuse meets the base. (11,000 & 11,011.35777) the angle comes out at 2.603 degrees. Hope this helped!

It is possible to arrange the total of mangoes by using 20 piles of 9 mangoes, 18 piles of 10 mangoes, or 15 piles of 12 mangoes.

The conditions for mangoes to be arranged are that the piles should have either 9, 10 or 12 mangoes and reminders are not allowed. This means you need to fit all the mangoes and no mangoes can be left.

Based on the conditions and the total number of mangoes (180 mangoes), here are the possibilities that you can determine using division:

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Answer:

C. 16 days

Step-by-step explanation:

Let´s say each worker does 1 ¨work¨, for each day, in order to complete the job in 15 days. That´s a total of 150 work.

If only 6 workers worked for the first 5 days, then we only do 30 by Day 5.

2 more workers join, so they do 8 work each day, 24 work in 3 days, 54 work by Day 8.

4 more workers join to complete the job, so we now do 12 work each day.

150 - 54 = 96

96 work is left to do, which would be done in 8 days by 12 workers.

8 days + 8 days = 16 days

The solution to the system of equation is (0, 1)

Given the following system of equation as shown below

2^(x)+3^(y)=5,

2^(x+2)+3^(y+1)=18

Rewrite

2^(x)+3^(y)=5,

2^x*2^2 + 3^y*3^1 = 18

___________

2^(x)+3^(y)=5,

4(2^x) + + 3(3^y) = 18

Let a = 2^x and b = 3^y

Substitute

a + b = 5

4a + 3b = 18

a = 5 - b

Substitute

4(5-b) + 3b = 18

20 - 4b + 3b = 18

-b = -2

b = 2

since a = 5 - b

a = 5 - 2

a = 3

Recall that a = 2^x and b = 3^y

2^x = 2

x = 0

Similarly

3^y = 3

y =1

Hence the solution to the system of equation is (0, 1)

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The transformation that occurred after the dilation of the parallelogram is a translation of 9 units to the right.

A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but it must have opposite sides that are parallel for it to be a parallelogram. If the opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is referred to as a parallelogram.

The initial parallelogram was dilated by a scale factor of 2 about point P.

The points of the initial parallelogram are: (-4, 0), (-2, 0), (-3, -3), (-5, -3).

The parallelogram obtained on dilation will have the points: (-6, 0), (-2, 0), (-4, -6), (-8, -6).

The points of the final parallelogram are: (3, 0), (7, 0), (5, -6), (1, -6).  

(-6,0) →(3,0)  ⇒ (x,y)→(x+h , y+k)

x = -6 , x+h = 3 ⇒ h=3-x = 3-(-6) = 9

y = 0 , y+k = 0 ⇒ k = 0

The transformation rule is (x,y)→( x+9 , y )

That is, a translation of 9 units to the right.

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Answer:

A. a translation of 9 units to the right

Step-by-step explanation:

Edge 2023

Answer:

BC = 18 cm

Step-by-step explanation:

As we can see from the diagram:

AB + BC + CD = AD

⇒ 10 cm + BC + 11 cm = 39 cm

⇒ BC + 21 cm = 39 cm

⇒ BC = 39 cm - 21 cm

⇒ BC = 18 cm

It's 4 buns & 5 cakes

Hope my explanation to the other one helps, if not, you can draw them; while following the steps & you may get it better.

E.g draw a box for the bun & a circle for the cake, then, adding them up to get the 95p. Also, you keep taking away from 435p

The measure of arc RT is 156 degree.

Given:

arc TRM=102°

Hence:

arc RST=2×1O2°

arc RST=204°

Measure of arc RT

arc RT= 2(180° - 102°)

arc RT = 2(78°)

arc RT = 156 degrees

Therefore the correct option is B.

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Answer:

56

Step-by-step explanation:

solution

Here

P=8a=8·7=56

Answer:

56 units

Step-by-step explanation:

the perimeter of a rectangular octagon  with sides of length a

is equal to:  8 × a

Then

the perimeter of a regular octagon with a side length of 7 units

is equal to:  8 × 7 = 56 units

The value of n given the form of the function is (b) positive odd number

The form of the graph is given as:

f(x) = a(x + k)^1/n + c

For the given graph, we have the following features:

a > 0 --- a is positive

k > 0 --- k is positive

c < 0 --- c is negative

If n is an even number, the function would be undefined because the even root of a number is undefined

However, the function is defined if n is an odd number,

Hence, the value of n given the form of the function is a positive odd number

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The sum of the first five terms is 11/2

The series is given as:

1/2, -1,2,-4…

Calculate the common ratio of the series using

r = -4/2

Evaluate

r = -2

The sum is then calculated as:

[tex]S_n = a\frac{1 - r^n}{1 - r}[/tex]

This gives

[tex]S_n = \frac{1}{2} * \frac{(1 - (-2)^5}{1 + 2}[/tex]

Evaluate

[tex]S_n = \frac{1}{2} * \frac{33)}{3}[/tex]

Evaluate

[tex]S_n =\frac{11}{2}[/tex]

Hence, the sum of the first five terms is 11/2

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308 gallons of 7% and 77 gallons of 2% are needed to obtain the desired 385 gallons.

Since a dairy needs 385 gallons of milk containing 6% butterfat, to determine how many gallons each of milk containing 7% butterfat and milk containing 2% butterfat must be used to obtain the desired 385 gallons, the following calculation must be performed:

Therefore, 308 gallons of 7% and 77 gallons of 2% are needed to obtain the desired 385 gallons.

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Step-by-step explanation:

1. if the number of pages in the 1st day is 'x', then the 2d day - 'x+10', the 3d day - 'x+20', the 4th day - 'x+30', the 5th day - 'x+40' and the last day - 'x+50' pages;

2. if the sum of all the pages is 300, then it is possible to make up the equation:

x+x+10+x+20+x+30+x+40+x+50=300;

3. x=25, it means:

1st day - 25;

2d day - 35;

3d day - 45;

4th day - 55;

5th day - 65;

6th day - 75 pages.

The solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1

The equation is given as:

[tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex]

Split the equation as follows:

[tex]y\ =\ \left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}[/tex]

[tex]y = 1 + x^2[/tex]

Next, we plot the graph of both equations (see attachment)

From the attached graph, the intersection point is (1, 2)

Remove the y value

x = 1

Hence, the solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1

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By applying trigonometric expression and direct comparison, we conclude that a = 2 such cos 255° - cos 195° = √a / 2

In this question we need to simplify a trigonometric expression in order to find the value of a. In this case, we need to use the following formula:

[tex]\cos \theta - \cos \xi = - 2\cdot \sin \left(\frac{\theta + \xi}{2} \right)\cdot \sin \left(\frac{\theta - \xi}{2} \right)[/tex]

Then,

cos 255° - cos 195° = - 2 · sin 225° · sin 30°

cos 255° - cos 195° = - 2 · sin (- 135°) · sin 30°

cos 255° - cos 195° = 2 · sin 135° · sin 30°

cos 255° - cos 195° = 2 · (√2 / 2) · (1/2)

cos 255° - cos 195° = √2 / 2

Then, by direct comparison we find that a = 2.

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The total cost to laminate the tabletop is $96.

The first step is to determine the area of the trapezoid.

Area of the trapezoid = 0.5 (sum of parallel sides) x height

0.5 x (6 + 10) x 3 = 24 feet²

The total cost of laminating = cost per square feet x area

$4 x 24 = $96

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Answer:

A) 39

Step-by-step explanation:

If you calculate the volume of the cube which is the V=a^3 you get 27, then calculating the pyramid, the Length is 3, and the Width is also 3. Then the height is 4. so you put that into the formula to calculate the volume which is V=L*W*H
    --------

        3

you get 12. Now its simple, you just add the 2 volumes, so you do 27+12 and its 39.

39 is the answer by calculating the volume using formula!

well, we know the suits are all reduced by 20%, so the man saved 20% of 231.20

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 231.20}}{\left( \cfrac{20}{100} \right)231.20}\implies 46.24[/tex]

The sum accumulated by 31st December 2018 is Rs 4,163,060.00

What is future value?

Future value is the accumulated amount that investments would yield in future period when the amounts invested are added with the total interest earned.

Note in this case that Rs500,000  would be invested subsequently for 4 years( 2015-2018 , January 1st of each year)

We can determine the future value of each investment using the future value formula shown below:

FV=PV*(1+r)^N

PV=amount invested

r=interest=10%

N=number of years that an amount is invested(for instance, the amount invested on 1st January 2014 will earn interest in 2014,2015,2016, 2017 and 2018 i.e. for 4 years)

Total FV=1,000,000*(1+10%)^5+500,000*(1+10%)^4+500,000*(1+10%)^3+500,000*(1+10%)^2+500,000*(1+10%)^1

Total FV=Rs 4,163,060.00

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The monthly payments for each add-on interest loan will be $29.71.

Given Information and Formula Used

Principal Amount, P = $1150

Rate of Interest, R = 6%

Duration of loan in years, T = 4

The formula for simple interest is given as,

I = (P × R × T)/100

Calculating the Add-On Interest For Each Month

Interest, I = (P × R × T)/100

Substituting the values of P, R, and T in the above formula, we get,

I = $ (1150 × 6 × 4)/100

I = $ 27600/100

I = $276

Calculating the Total Monthly Payment With Interest

Amount of add-on interest loan, A = P + I

A = $1150 + $276

A = $1,426

Monthly payment with interest = A/(4×12)

= $ 1426/48

= $29.71

Hence, the monthly payments for each add-on interest loan would be $29.71.

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Using proportions, it is found that the total percentage increase in the investor's stock account was of 6.2%.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The values of the stocks of Company A and Company B, after the increase are given, respectively, by:

The total values are given as follows:

The percent increase is given by the increase divided by the initial value and multiplied by 100%, hence:

P = (8668 - 8160)/8160 x 100% = 6.2%.

The total percentage increase in the investor's stock account was of 6.2%.

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Answer:

[tex]r=\sqrt{\frac{V}{\pi h}}[/tex]

Step-by-step explanation:

[tex]V = \pi r^{2} h \\ \\ r^{2} =\frac{V}{\pi h} \\ \\ r=\sqrt{\frac{V}{\pi h}}[/tex]

Answer:

The answer is circle.

Step-by-step explanation:

For all the rest of the shapes, we use certain base x height formulas.  Square uses base x height along with parallelograms and trapezoids. For a triangle, we use [tex]\frac{base x height}{2}[/tex]. Though, for a circle, we use the formula  [tex]\pi r^{2}[/tex] where r= radius.

The probability of pulling a blue or yellow card, written as a reduced fraction is 7/50

From the question, we have the following probabilities:

P(Pink) = 1/5

P(Blue) = 1/25

P(Yellow) = 1/10

P(Black) = 1/15

The probability of pulling a blue or yellow card, written as a reduced fraction is the calculated as:

P(Blue or yellow card) = P(Blue card) + P(Yellow card)

Substitute the known values in the above equation

P(Blue or yellow card) = 1/25 + 1/10

Express 1/25 as 2/50 and 1/10 as 5/10

P(Blue or yellow card) = 2/50 + 5/50

Take the LCM

P(Blue or yellow card) = (2+ 5)/50

Evaluate the sum

P(Blue or yellow card) = 7/50

Hence, the probability of pulling a blue or yellow card, written as a reduced fraction is 7/50

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Answer:

rjdjdj shiejd shsuisis shusisos

Answer:

108°

Step-by-step explanation:

We know for a theorem that A = B, so:

4x + 28 = 2x + 68

Isolating the x:

2x = 40

x = 20

Now let's plug in the equation for A:

4(20) + 28 = 108°

The answer is: 2(m+1)

First combine like terms.
we do 6m-4m which is 2m
2m+2=?

Second we factor. We notice that both terms have 2.
2(m+1)

by distributive law, the 2 is distributed to m and 1.

The return on the investment is 3%

The given parameters are:

Buying rate = 7%

Selling rate = 10%

The return on the investment is

ROI = Selling - Buying

So, we have:

ROI = 10% - 7%

Evaluate

ROI = 3%

Hence, the return on the investment is 3%

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