Matthew earned $75 in interest on
his savings account in one year.
The bank paid a simple interest
rate of 5%. What was the initial
amount of money Matthew put
into his savings account?​

Answer:

[tex]x=-2\sqrt5\ and\ x=2\sqrt5[/tex]

Step-by-step explanation:

Given:

The given equation to solve is:

[tex]x^2=20[/tex]

In order to solve the above equation, we take square root on both the sides.

While taking square root on both sides, we must consider both positive and negative values. So, this gives:

[tex]\sqrt{x^2}=\pm\sqrt{20}[/tex]

From the definition of square root function, we have

[tex]\sqrt{a^2}=a[/tex]

Therefore,

[tex]x=\pm\sqrt{20}[/tex]

Now, writing 20 into the product of its prime factors, we have

[tex]20=2^2\times 5[/tex]

Therefore, [tex]x=\pm\sqrt{2^2\times 5}[/tex]

We also know, [tex]\sqrt{a\times b}=\sqrt{a}\times\sqrt{b}[/tex]

So, [tex]\sqrt{2^2\times 5}=\sqrt{2^2}\times \sqrt{5}=2\sqrt5[/tex]

Therefore, [tex]x=\pm2\sqrt5[/tex]

So, there are two values of 'x'. They are:

[tex]x=-2\sqrt5\ and\ x=2\sqrt5[/tex]

Answer:

line c

Step-by-step explanation:

Answer:

The value of x is 22.

Step-by-step explanation:

We are given that,

12 less triple the difference of x and 10 is 24.

So, according to question :

  3(x - 10) - 12 = 24

Adding '12' on both sides of the above equation, we get

  3(x -10) - 12 + 12 = 24 + 12

⇒3(x - 10) = 36

Dividing the above equation by '3', we get

  3(x - 10) ÷ 3 = 36 ÷ 3

⇒x - 10 = 12

Now, adding '10' on both sides of the above equation, we get

  x - 10 + 10 = 12 + 10

⇒x = 22

So, the value of x is 22.

Answer:

Please see pic

Step-by-step explanation:

Go two places to the right (on x axis), then four places down (on y axis)

Sorry it would not let me attach a pic

Answer:

[tex]Rs\ 4,296[/tex]

Step-by-step explanation:

step 1

Find out the lateral area of the pillars

we know that

The lateral area of a rectangular prism is equal to

[tex]LA=PH[/tex]

where

P is the perimeter of the base

H is the height of the prism

Determine the perimeter of the base

[tex]P=4(1)=4\ ft[/tex] ----> is a square base

[tex]H=6\ ft[/tex]

The lateral area is equal to

[tex]LA=4(6)=24\ ft^2[/tex]

Remember that the number of pillars is 2

so

[tex]LA=2(24)=48\ ft^2[/tex]

step 2

Find the cost of tiling the pillars at the rate of  Rs 52 per square feet

Multiply the lateral area of the two pillars by the rate

so

[tex]48(52)=Rs\ 4,296[/tex]

Answer: 26.5 mph, or miles per hour

265/10 = 26.5

Answer: 26.5 mph

Step-by-step explanation: We need to divided 265 miles by 10 hours

265/10

Answer: 26.5 mph

Hope this helps!

Answer:

n will be 6

Step-by-step explanation:

3×n=2×9

substitute n=6 in the above equation

3×6=2×9

18=18

N is 6

Answer:

Therefore the choice is

a) AD/AB=AB/AC

Step-by-step explanation:

In  Δ ADB and Δ ABC  

∠A ≅ ∠A    …………..{Reflexive Property}

∠ ADB ≅ ∠ ABC      ..............{ measure of each angle is 90° given }

Δ ADB ~ Δ ABC ….{Angle-Angle  Similarity test}

If two triangles are similar then their sides are in proportion.

[tex]\frac{AD}{AB} =\frac{AB}{AC}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]  

Therefore the choice is

a) AD/AB=AB/AC

Answer:

Therefore the choice is

a) AD/AB=AB/AC

Step-by-step explanation:

In  Δ ADB and Δ ABC  

∠A ≅ ∠A    …………..{Reflexive Property}

∠ ADB ≅ ∠ ABC      ..............{ measure of each angle is 90° given }

  Δ ADB ~ Δ ABC ….{Angle-Angle  Similarity test}

If two triangles are similar then their sides are in proportion.

Therefore the choice is

a) AD/AB=AB/AC

There are 3 dollars per hour per babysitting job for they will get the same amount.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Jill babysits and makes x dollars per hour plus a $5 transportation charge. Samantha babysits and makes two thousand dollars per hour extra transportation cost of $10

As per the given question, the required system of equations would be as:

Jill: y = 8 - 5

8- 5 = 3

y = 3 dollars per hr per babysitting job

Samantha: 2y = 16 -10

2y = 6

2/2 = 6/2

3 dollars per hr per babysitting job

They will get the same amount regardless of how many hours they babysit

Thus, there are 3 dollars per hour per babysitting job for they will get the same amount.

Learn more about the equation here:

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In this question, we're trying to make an equation for the given scenario and answer a couple of leading questions.

We know that Aiko types at a rate of 70 words per minute

We would represent this as 70x

x = minutes

We are also given more information that he types 210 words in 3 minutes, that still follows our "70x" scenario.

So our equation would be:

y = 70x

The slope of the linear equation would be 70 or 70/1

The slope would be 70 because this is the change that's happening each minute.

A point on a graph would be at (1 , 70)

You would put this equation into a graph, and you would grab a point that's on the linear line. I'll insert a picture of the graph

The linear equation would be written as: y = 70x

The beginning point would be at 0, since Aiko doesn't type anything for 0 minutes.

Answer:

1 The slope of the linear equation is  70

2 One point on the graph of a linear equation will be 3, 210

3,This linear equation can be written as  y-210=70(x-3)

Step-by-step explanation:

The perimeter of rectangle is 16x-2y+4.

Step-by-step explanation:

Given dimensions are;

Length = 5x-y

Width = 3x+2

We know that;

Perimeter of rectangle = 2(Length + Width)

Perimeter of rectangle = [tex]2(5x-y+3x+2)[/tex]

Perimeter of rectangle = [tex]2(8x-y+2)[/tex]

Perimeter of rectangle = [tex]16x-2y+4[/tex]

The perimeter of rectangle is 16x-2y+4.

Keywords: rectangle, perimeter

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Answer:

Step-by-step explanation:

x = small box and y = large box

30x + 40y = 330

y = 2x

30x + 40(2x) = 330

30x + 80x = 330

110x = 330

x = 330/110

x = 3 <===== 3 small boxes

y = 2x

y = 2(3)

y = 6 <=== 6 large boxes

check...

30x + 40y = 330

30(3) + 40(6) = 330

90 + 240 = 330

330 = 330 (correct)

The x-coordinate of the point of intersection for given equations is 2

Step-by-step explanation:

Given equations are:

[tex]2x+y = 7\ \ \ Eqn\ 1\\10x-7y = -1\ \ \ Eqn\ 2[/tex]

The point of intersection is the solution of the system of equations

as we have to find the x-coordinate we will use elimination method to eliminate y

So,

Multiplying equation 1 with 7

[tex]7(2x+y) = 7(7)\\14x+7y = 49\ \ \ \ Eqn\ 3[/tex]

Adding equation 2 and 3

[tex](14x+7y) + (10x-7y) = 49-1\\14x+10x+7y-7y = 48\\24x = 48[/tex]

Dividing both sides by 24

[tex]\frac{24x}{24} = \frac{48}{24}\\x = 2[/tex]

The x-coordinate of the point of intersection for given equations is 2

Keywords: Linear equations, simultaneous equations

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Answer:

The maximum rate of change is between second 15 and second 19.

Step-by-step explanation:

See the attached table.

The table shows the total distance a spider traveled after a light was turned on.

Now, the average rate of change between two consecutive times in the table is given by  

= [tex]\frac{\textrm {Total change in Distance in feet}}{\textrm {Total change in Time in seconds }}[/tex]

Therefore, between second 5 and second 11, the average rate of change = [tex]\frac{7 - 4}{11 - 5} = 0.5[/tex]

Between second 11 and second 15, the average rate of change = [tex]\frac{13 - 7}{15 - 11} = 1.5[/tex]

Between second 15 and second 19, the average rate of change = [tex]\frac{20 - 13}{19 - 15} = 1.75[/tex]

Between second 19 and second 28, the average rate of change = [tex]\frac{24 - 20}{28 - 19} = 0.44[/tex]

Therefore, the maximum rate of change is between second 15 and second 19. (Answer)

Answer:

1 : 4 and 6 : 24

Step-by-step explanation:

We can generate equivalent ratios by dividing or multiplying each part of the ratio by the same value

Divide both parts by 3 , then

3 : 12 = 1 : 4 ← in simplest form

Multiply both parts by 2

3 : 12 = 6 : 24

Step-by-step explanation:

Solve the system via elimination (add the equations):

-10y + 9x = -9

+ (10y + 5x = -5)

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

14x = -14

x = -1

Plug in the value for 'x' into the second equation:

-10y + 5(-1) = -5

Solve for y:

-10y - 5 = -5

--> -10y = 0

--> y = 0

x = -1

y = 0

WAR is given as 57 degrees.

If you draw a line from W to R, the angle WRA would also be 57 degrees.

57 + 57 = 114

The measure of AR = 180 -114 = 66 degrees.

Answer:

66.

Step-by-step explanation:

If You See W.And R., They Are The Same Angle's, So If They Are Little And Big At The Same Time, You Can Notice It Will Be 66* :)

Tell Me If You Have Any Problomes With These!!!!

Hope This Information Helps!!!

Answer:

8x+24

Step-by-step explanation:

8(x+3)=8x+24

16π

Step-by-step explanation:

The area within a circle is given by the formulae;

πr²

Since this circle is part of a full circle will multiply the area by teh appropriate fraction;

90/360 = ¼

¼ πr²

r = 8 according to the illustration

¼ π*8²

1/4 * π * 64

= 16π

Area = 16π

Learn More:

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Answer:

length is 28 meters

width is 15 meters

Step-by-step explanation:

Write out formulas and assign variables:

Width: w

Length: l = 2w - 2

Here is a diagram:

            2w - 2              

|                                     |  w

|_________________|

The perimeter formula for rectangle is P = 2(l +w). Substitute the perimeter and the formula for length into the formula.

P = 2(l +w)

86 = 2(2w - 2 + w)       Simplify inside the brackets

86 = 2(3w - 2)            Divide both sides by 2

43 = 3w - 2              Add 2 to both sides

45 = 3w                  Divide both sides by 3

w = 45/3               Variable on left side is standard formatting

w = 15                 Width of basketball court

Substitute width into the length formula to fin length.

l = 2w - 2

l = 2(15) - 2

l = 30 - 2

l = 28           Length of basketball court

Therefore the length is 28 meters and the width is 15 meters.

The dimensions of the basketball court are 28 meters in length and 15 meters in width.

We need to find the dimensions of the rectangular court where the length (L) is 2 meters less than twice the width (W), given that the perimeter is 86 meters. We can set up the equations as follows:

First, substitute the value of L from the first equation into the second equation:

Simplify and solve for W:

Now, find the length (L):

Thus, the dimensions of the court are 28 meters in length and 15 meters in width.

Answer:

The value of log  43is 1.633

Step-by-step explanation:

Explanation:

Suppose you know that:

[tex]\begin{array}{l}{\log 2 \approx 0.30103} \\{\log 3 \approx 0.47712}\end{array}[/tex]

Then note that:

[tex]43=\frac{129}{3} \approx \frac{128}{3}=\frac{2^{7}}{3}[/tex]

So

[tex]\log 43 \approx \log \left(\frac{2^{7}}{3}\right)=7 \log 2-\log 3 \approx 7 \cdot 0.30103-0.47712=1.63009[/tex]

We know that the error is approximately:

[tex]\log \left(\frac{129}{128}\right)=\log 1.0078125=\frac{\ln 1.0078125}{\ln 10} \approx 0.00782 .3=0.0034[/tex]

So we can confidently give the approximation:

[tex]\log 43 \approx 1.633[/tex]

Answer:

1.6

Step-by-step explanation:

It's 1.633, when you round to the nearest tenth, it's B) 1.6

Answer:22

Step-by-step explanation:

Answer:maximize p = profit = 2 L + 1 C >/= 25

L >/= 5

C>/=5

start with L = 5

10+C >/= 25

C >/= 15

if L = 6

12 + C >/= 25

C >/= 13

so

L 7, C 11

L 8 ,C 9

L 9 , C 7

L 10, C 5

are your MINIMUM combinations. Of course you can always sell more

Step-by-step explanation:

Answer:

$1862 ÷9=$207(each lot)

$207 ×4=$828

Answer:

increase is 37.5%

Step-by-step explanation:

3000/8000 *100= 37.5%

Answer:

0.

Step-by-step explanation:

We can do this by substitution of -2  The numerator will tend to 0.

The denominator  will always be positive so the limit is 0.

Answer:

x - 0.8y

Step-by-step explanation:

5.20/6.5 = $0.80 per pound

x = total cost of potatoes

y = number of potatoes

x = 0.8y

Answer: x = 6

Step-by-step explanation: To solve for x, we must first isolate the term containing x which in this problem is -3x.

Since 28 is being added to -3x, we subtract 28 from both sides of the equation to isolate the -3x. On the left, the +28 and -28 cancel out and on the right 10 - 28 is -18 so we have -3x = -18.

Now we can finish things off by just dividing both sides of the equation by -3. On the left the -3's cancel and we have x. On the right, -18 divided by -3 is 6 so we have x = 6 which is the solution to our equation.

Answer:

g(x) = - (x² + 3x + 2) = - x² - 3x - 2

Step-by-step explanation:

The graph represents the function f(x) = x² + 3x + 2.

Now, g(x) is the function which is obtained by reflecting f(x) across the x-axis.

While a graph of a function reflects across x-axis then its y-values will change sign for a fixed value of x.  

Therefore, the function g(x) will be given by  

g(x) = - (x² + 3x + 2) = - x² - 3x - 2 (Answer)

Answer:

[tex]\frac{1}{4} lbs/person[/tex]

Step-by-step explanation:

Here is the complete question: Find the rate of change for the situation:

A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.

Given: 1st situation, A chef cook 9 lbs chicken for 36 people.

           2nd situation, chef cook 17 lbs chicken for 68 people.

∴ 1st situation, weight of chicken per person= [tex]\frac{9\ lbs}{36\ person} = \frac{9}{36}[/tex]

  Weight of chicken per person= [tex]\frac{1}{4} lbs/ person[/tex]

2nd situation, weight of chicken per person= [tex]\frac{17\ lbs}{68\ person} = \frac{17}{68}[/tex]

Weight of chicken per person= [tex]\frac{1}{4} lbs/ person[/tex]

In both the situation chef cook same amount of chicken per person, which is [tex]\frac{1}{4} lbs/ person[/tex]

∴ Rate of change is [tex]\frac{1}{4} lbs/ person[/tex]

Answer:

i guess 1/4

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

The last two parts of the function help see where the curve is and where the vertical asymptote would be. The (x-3) says that it was moved 3 units to the right, and the -5 says that it was moved 5 units down:

                                                 /\        *  ]

                                                  |         *  [

                                                  |         *  ]

                                                  |         *  [

             <--|--|--|--|--|--|--|--|-- |--|--|--|--|--3*-]-|--|--|--|--|--|--|--|--|-->

                                                  |        *   [

                                                  |       *    ]

                                                  |*5         [

                                                  \/           ]        

So the vertical asymptote would be where it crosses the x-axis and then goes straight up: 3    

[

]   = vertical asymptote

[

__________________________________

*

*   = function graphed

*

__________________________________

(By the way, I got this correct on my quiz!)

Hope this helps!

The vertical asymptote of the given function h(x)=6log4(x−3)−5 is x=3.

The vertical asymptote of a function is the value of x at which the function approaches infinity or negative infinity. For a logarithmic function h(x)=a*logb(x−c)−d, the vertical asymptote is x=c. Consequently, in the given function h(x)=6log4(x−3)−5, the vertical asymptote is x=3.

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