Clara solved the equation
7
3
x = −
2
3

Given:

Principal = Rs. 1200

Rate of interest = 25%

To find:

The time in which the interest will became equal to the principal.

Solution:

We have,

[tex]P=1200[/tex]

[tex]r=\dfrac{25}{100}[/tex]

[tex]r=0.25[/tex]

If interest is equal to the principal, then

[tex]Amount=Principal+Interest[/tex]

[tex]Amount=1200+1200[/tex]

[tex]Amount=2400[/tex]

The formula for amount is:

[tex]A=P\left(1+r)^n[/tex]

Substituting [tex]A=2400, P=1200, r=0.25[/tex] in the above formula, we get

[tex]2400=1200(1+0.25)^n[/tex]

[tex]\dfrac{2400}{1200}=(1.25)^n[/tex]

[tex]2=(1.25)^n[/tex]

Taking log on both sides, we get

[tex]\log2=\log(1.25)^n[/tex]

[tex]\log2=n\log(1.25)[/tex]               [tex][\because \log a^b=b\log a][/tex]

[tex]\dfrac{\log2}{\log(1.25)}=n[/tex]

[tex]n\approx 3.11[/tex]

Therefore, the interest will became equal to the principal in about 3.11 years.

Answer:

hello brother or sister can you please send a picture of the graph in provided but if not there are no specific calculations on reflection so you have to be smart on it and try imagining it or have your own scratch

Answer:

x=10.5

Step-by-step explanation:

[tex]\frac{x}{6} =\frac{7}{4} \\x=\frac{7}{4} \times 6\\=\frac{21}{2} \\=10.5[/tex]

Answer:

30.1

Step-by-step explanation:

Have a great summer :)

Answer:

The solution for the system of right triangles are, respectively: [tex]a = 2\sqrt{6}[/tex], [tex]b = 4\sqrt{3}[/tex], [tex]c = 4\sqrt{6}[/tex], [tex]d = 6\sqrt{2}[/tex]

Step-by-step explanation:

By Geometry, we get the following equivalencies:

[tex]a = 2\sqrt{6}[/tex] (45 - 45 - 90 Theorem)

[tex]b = \sqrt{2}\cdot (2\sqrt{6})[/tex] (45 - 45 - 90 Theorem)

[tex]b = 4\sqrt{3}[/tex]

[tex]c = \frac{2\sqrt{6}}{\frac{1}{2} }[/tex] (30 - 60 - 90 Theorem)

[tex]c = 4\sqrt{6}[/tex]

[tex]d = \frac{2\sqrt{6}}{\frac{\sqrt{3}}{3} }[/tex] (30 - 60 - 90 Theorem)

[tex]d = 6\sqrt{2}[/tex]

Answer:

V = 17362.9 ft^3  using 3.14 for the approximation

17371.8 ft^3 using the pi button

Step-by-step explanation:

V = pi r^2 h  where r is the radius and h is the height

V = pi (12)^2 ( 38.4)

V =pi ( 144) 38.4

5529.6pi

Letting  pi be 3.14

V = 5529.6 (3.14)

V =17362.944 ft^3

Rounding to the nearest tenth

V = 17362.9 ft^3

Letting pi = pi button

V =17371.75074 or to the nearest tenth 17371.8 ft^3

Edgar needs 12 cups of masa and 9 cups of water to make 90 tortillas.

A method of dividing something into equal parts is called division.

Given that 2 cups of masa and 1.5 cups of water are needed for 15 tortillas.

Edgar wants to make 90 tortillas.

We can think Edgar wants to make 90/15 = 6 bunches of 15 tortillas.

1 bunch of 15 tortillas needs 2 cups of masa.

So, 6 bunches of 15 tortillas need 6 * 2 = 12 cups of masa.

Again 1 bunch of 15 tortillas needs 1.5 cups of water.

So, 6 bunches of 15 tortillas need 6 * 1.5 = 9 cups of water.

Therefore, Edgar needs 12 cups of masa and 9 cups of water to make 90 tortillas.

Learn more about division here -

https://brainly.com/question/13706292

#SPJ2

Answer:

A

Step-by-step explanation:

2.1 Factoring 4x2+12x+9 The first term is, 4x2 its coefficient is 4 . The middle term is, +12x its coefficient is 12 . The last term, "the constant", is +9 Step-1 : Multiply the coefficient of the first term by the constant 4 • 9 = 36 Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is 12 .

Answer:

(-8 , -2)

Step-by-step explanation:

the coordinates of B’ are (-8 , 2)

then

Since B also is the image of B’ through the reflection across the x-axis

then the coordinates of B are (-8 , -2)

Answer:

(-8, -2)

Step-by-step explanation:

Answer:

I hope the above attachment helps you mate

Have a great day

[tex]#Liliflim[/tex]

Answer:

Solution given;

a⁴-23a²b²+b⁴

making in the form of a²+2ab+b²

a⁴+2a²b²+b⁴-2a²b²-23a²b²

(a²+b²)²-(5ab)²

factoring by using formula

x²-y²=(x+y)(x-y)

(a²+5ab+b²)(a²-5ab+b²)

Answer:

35.75

Step-by-step explanation:

times 65 by 55%

Answer:

5 I think

Step-by-step explanation:

Well, 0.1 and 0.5 goes in anything so I doubt that's it, 2 goes in 10 but not 5, actually. I think if it's division than 2. Not 1,000 percent sure tho

Answer:

0.5

Step-by-step explanation:

So we know the orginal is 10 in size.

The new is 5 in size.

We can think of this as 10 : 5

To find the exact scale, we can divide both by the GCF.

The GCF is the greatest common factor between two numbers.

In this case, the GCF would be 5, now lets divide:

10/5 : 5/5

=

2 : 1

So we can see the ratio is 2 to 1.

Now, the scale is not 2.

The new ratio is 2 : 1, but 2 is the orginal. 1 is the scaled value.

To find the scale, you must divide the new scaled value by the orginal value:

1 / 2

=

1/2

So this is your scale factor.

There is actually another way to do this as well, which is quicker.

Take the new value, 5, and divide it by the orginal value, 10:

5/10

=

1/2

Either way, you get 1/2 as your answer.

Hope this helps!

Answer:

Step-by-step explanation:

The y intercept, also known as 'c' in the formula y = mx + c acts as the coordinate for y when x = 0 [E.g. (0, 24) which c = 24]

Question 1 =  y = -5x + 50

On the graph, c = 50 [ y = mx + 50 ]

30 - 15 = 15

7 - 4 = 3

15/3 = 5 (for the gradient, or 'm', which you may use the formula 'rise/run' on the line shown) [ y = 5x + 50 ]

ALTHOUGH, in question one, the line has a Negative Correlation, it slants downwards on the slope, so the gradient will be negative : y = -5x + 50

If x = 9, y = (9 x -5) + 50, = -5

y = -5

Question 2 =  y = 2.5x + 5

c = 5

m = 5/2 = 2.5

y = 2.5x + 5

when y = 30 > x = 10

30 = 2.5x + 5

30 - 5 = 25

25 = 2.5x

x = 25/2.5

x = 10

Question 3 = y = -10x + 50

c = 50

m = (30 - 20) / 1 = 10

y = -10x + 50

when x = 4 > y = (-10 x 4) + 50

y = -40 + 50

y = 10

Answer:

$31.85

Step-by-step explanation:

total cost of the rafters  = total length of rafters used x cost per foot

total length of rafters used = number of rafters used x length of rafters

7 x [tex]6\frac{1}{2}[/tex]

to solve, convert [tex]6\frac{1}{2}[/tex] to an improper fraction

to convert to improper fraction, take the following steps :  

1. Multiply the whole number  by the denominator

2. Add the numerator to the answer gotten in the previous step

3. divide the number gotten in the previous step by the denominator  

7 x [tex]\frac{13}{2}[/tex] = [tex]\frac{91}{2}[/tex]

cost per foot = 70 cents

100 cents = 1 dollar

70 cents = $0.70

total cost of rafters = $0.70 x [tex]\frac{91}{2}[/tex] = $31.85

Answer:

No solution is possible from the information provided.

Step-by-step explanation:

A. 0

Answer:

Solution given

(x1,y1)=G(3, -2),

(x2,y2)=H(7, -2)

now

slope=(y2-y1)/(x2-x1)=(-2+2)/(7-3)=0/4=0

Answer:

0

Step-by-step explanation:

To find the slope

m= ( y2-y1)/(x2-x1)

 = ( -2 - -2)/ ( 7-3)

   = (-2+2)/(7-3)

   = 0/4

Answer:

jk

Step-by-step explanation:

Answer:

nxgxhdhdjdkdkdjdjjddbdvd f fvfbfbfnfjjfcjjfjfjfjfjdjdjdjdjdjdjdjdjdjjjdjdjfjfjfjfjffjfjfjfjfjf

Answer:

8%/100×500=$40

Kathleen pays $40 sales tax

Answer:

[tex]\frac{\sqrt{47}}{10}[/tex]

Step-by-step explanation:

First you find the missing side using the Pythagorean theorem of [tex]a^{2} +b^{2} =c^{2}[/tex].

Which is [tex](\sqrt{53})^{2} + b^{2} = 10^{2}[/tex].

do the squares to make it 53 + [tex]b^{2}[/tex] = 100 and solve for b.

[tex]b^{2} = 100-53\\b^{2} = 47\\b= \sqrt{47}[/tex]

Sine of an angle is Opposite over Hypotenuse to get

[tex]\frac{\sqrt{47} }{10}[/tex]

Answer:

Step-by-step explanation:

1) Step 4: Marc has converted radical form to exponent form

Step 5: He has evaluated the value of the radical

3)

[tex]x = \sqrt[3]{8}[/tex]

Here, 3 is index and 8 is radicand.

Prime factorize 8 and for every 3 numbers we can take one number outside the radical

Solution:

[tex]x = \sqrt[3]{2*2*2}\\\\x = 2[/tex]

4) No,my equation does not have an extraneous solution.

My solution, satisfies the equation

Answer:

The workout ratio of the online sales to shop sales is 1:3

Step-by-step explanation:

Given:

A jewelry shop sells 240 necklaces in a month. 180 of the necklaces were sold via the shops website. The rest were sold in a High Street shop.

To find:

Work out the ratio of online sales to shop sales.

Solution:

Total no necklaces = 240

Necklace sold on website = 180

Remaining necklace sold via street = 240 - 180 = 60

Ratio = 60 : 180 = 1 : 3

Answer:

12

Step-by-step explanation:

The equation

2x(50) = 24

x(50) = 12

Answer:

y = 12

Step-by-step explanation:

36 - 24 = 12.

24 calories were burned in 100 minutes. 36 calories were burned in 150 minutes. That means that in 50 minutes (150 - 100) 12 calories were burned.

Answer:

going clockwise from upper left the correct graph is the 2nd one

Step-by-step explanation:

asymptote at -2

[tex]{ \bf{ \underbrace{Given :}}}[/tex]

Area of the circle = 2464 cm².

[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]

The radius of the circle.

[tex]{ \bf{ \underbrace{Solution :}}}[/tex]

[tex]\sf\orange{The\:radius \:of\:the\:circle\:is\:28\:cm.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

Let "[tex]r[/tex]" be the radius of the circle.

We know that,

[tex]\sf\purple{Area\:of\:a\:circle \:=\:πr²}[/tex]

[tex]⇢ 2464 \: {cm}^{2} = \frac{22}{7} \times {r}^{2} \\\\ ⇢  {r}^{2} = 2464 \: {cm}^{2} \times \frac{7}{22} \\ \\⇢  {r}^{2} = \frac{17248}{22} \: {cm}^{2}\\ \\⇢  {r}^{2} = 784 \: {cm}^{2} \\ \\⇢ r = \sqrt{784 \: {cm}^{2} } \\ \\⇢ r = \sqrt{28 \times 28 \: {cm}^{2} } \\ \\⇢ r = 28 \: cm[/tex]

[tex]\boxed{Therefore,\:the\:radius \:"r"\:of\:the\:circle\:is\:28\:cm.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\blue{Happy\:learning }}{\blue{!}}}}}[/tex]

Answer:

3, -1

Step-by-step explanation:

just set f(x) = g(x)

x^2 + 3x + 4 = 5x + 7

combine like terms

x^2 - 2x - 3 = 0

factor

(x-3)(x+1)=0

x = 3, x = -1

so, f(x) = g(x) when x = 3 or -1