The sum of two numbers is 27. One of the numbers is three more than the other. Find the numbers. A) 20 and 7 B) 12 and 15 C) 13 and 14 D) -12 and -15

multiply through the equation by 7

x - 14 = x

collect like term

x - x = 14

But 0 is not equal to 14

so, this implies that there is no solution

The correct option is c.

Answer:

B, (6,0)

Take the average of the x values and the average of the y values:

(3+9)/2 = 6

(-2+2)/2 = 0

This means the answer (the average (midpoint) of the two points) is (6,0)

Answer:

(x + 2)² + (y - 2)² = 3²

Step-by-step explanation:

Equation of a circle is (x - a)² + (y - b)² = r²,

where a is the x-coordinate of the centre of the circle, b is the y-coordinate of the centre of the circle, r is the circle's radius.

So, we have (x - -2)² + (y - 2)² = 3²

subtract a minus means we add.

(x + 2)² + (y - 2)² = 3²

Answer: 162°

Step-by-step explanation:

To find the answer to this question, we need to find what 45% of 360 degrees (a circle) is.

First, a percent divided by 100 becomes a decimal.

       45% / 100 = 0.45

Next, "of" means multiplication in mathematics.

       0.45 * 360 = 162

The central angle will be 162°.

An ISOSCELES triangle has two sides equal, and two base angles are also equal.

The two sides on the left and the right are equal. The right side measures 11 inches, therefore the left side also measures 11 inches.

The correct answer option is 11 inches

Answer: 4/5 * 7^1/2 ==> 1st option

Step-by-step explanation:

3(7/25)^1/2-(28/25)^1/2+(63/25)^1/2=

3(7)^1/2 / 5 -(4*7)^1/2 / 5 +(9*7)^1/2 / 5=

3(7)^1/2 / 5 -2(7)^1/2 / 5 +3(7)^1/2 / 5=

(3-2+3)(7^1/2 / 5)=

4(7^1/2 / 5)=4/5 * 7^1/2 ==> 1st option

The Integral \(\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt = i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)\)

Given integral;

\(\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt\)

By solving the above integral, we have;

⇒ \(\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt\)

By applying the sum rule,

⇒ \(\int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\)

\(=\int \sec ^2\left(t\right)idt+\int \:t\left(t^2+1\right)^4jdt+\int \:t^6\ln \left(t\right)kdt\)

\(\int \sec ^2\left(t\right)idt=i\tan \left(t\right)\)

\(\int \:t\left(t^2+1\right)^4jdt = \frac{j\left(t^2+1\right)^5}{10}\)

\(\int \:t^6\ln \left(t\right)kdt = k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)\)

⇒ \(i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)\)

Therefore, the integral \(\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt = i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)\)

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Answer:

54

Step-by-step explanation:

13.5/0.25=54

Hey there! I'm happy to help!

We'll call our weeks w and call our total savings s.

We have an initial $85 and then we add 7 every week. This means that we will be adding 7 for every week, so we will put this in our equation as 7w.

Therefore, our equation would be s=7w+85

Now, we plug in 8 for our w value to see how much money she will have after 8 weeks.

s=7(8)+85

s=56+85

s=141

Therefore, Aubrey will have saved $141 after 8 weeks.

I hope that this helps! Have a wonderful day! :D

Answer:

$ 71.83  

Step-by-step explanation:

This year's earnings=last year's earnings*(1+growth rate)=$2*(1+20%)=$2.4

This year's dividend=2.4 *payout ratio=2.4 *20%=$0.48

Next year's earnings=$2.4*1.2=$2.88

Next year's dividend=2.88 *0.2=$ 0.58  

Year 3 earnings=$2.88*1.2=$ 3.46  

Year three dividend= 3.46*0.2=$0.69  

year 4 earnings =$3.46*1.08=$ 3.74  

Dividend from year 4 onward= 3.74  *0.5=1.87

From year 4 terminal value=1.87 /(cost of equity-growth rate)=1.87/(10%-8%)=$93.5

Share price is present value of the above dividends amnd terminal value=0.48/(1+0.1)^0+0.58/(1+0.1)^1+0.69/(1+0.1)^2+93.5/(1+0.1)^3=$ 71.83  

Answer:

the answer is 21

Step-by-step explanation:

first you need to find which function that -5 belongs in.

you will see that you need to plug -5 into the first equation -4x+1

-4(-5)+1=21

Check the picture below.

Answer:

Step-by-step explanation:

An easy way is to substitute values into both equations and compare:

A. x = 0.8

B. x = 0.9

C. x = 1.9

D. x = 1.1

As we see the most accurate one is A

Let's graph both function(Attached)

Let's round 0.775

\(\\ \sf\longmapsto 0.775\)

\(\\ \sf\longmapsto 0.77\)

\(\\ \sf\longmapsto 0.8\)

Option A is correct

ANSWER and EXPLANATION

We are given a function and its inverse function:

To solve the problems, we have to substitute the values of x in the brackets into the appropriate function (or inverse function).

Therefore, we have that the value of the function for x = 2:

For x = 1, we have that the value of the inverse function is:

For x = -2, we have that the value of the inverse function is:

For x = -4, we have that the value of the function is:

For the fifth option, substitute the value of the function at x = 2 into the inverse function.

That is:

For the sixth option, substitute the value of the inverse function at x = -2 into the function.

That is:

To find the general form of the function:

either substitute the function for x in the inverse function or substitute the inverse function for x in the function.

Therefore:

That is the answer.

The inverse function of f(x) = 3x + 5 is given as follows:

C. p(x) = 1/3x - 5/3.

The function in the context of this problem is defined as follows:

f(x) = 3x + 5.

To obtain the inverse function, first we must exchange the variables x and y, hence:

y = 3x + 5

x = 3y + 5.

Now we must isolate the variable y, hence:

3y = x - 5

y = (x - 5)/3.

p(x) = 1/3x - 5/3.

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Hello !

   D

   I\
   I  \  
   I    \
   I      \    7cm
   I        \
   I          \
   I            \

 E    4cm     F  

The ratio = hypotenuse ; opposite

⇒ calculate sin(D)

sin(D) = opposite/hypotenuse = 4/7

arcsin(4/7) ≈ 34,84.. ≈ 35°

The angle D measures 35°.

Answer:

$675.00

Step-by-step explanation:

4500 x 0.05 x 3 = 675

Answer:

x = 5 - 2a

Step by step explanation:

2x + 4a = 10

So, 2x = 10 - 4a

=> x = (10 - 4a)/2

=> x = 5 - 2a

Hope this answer helps, if it does help, please mark me as brainliest,

Thank you.

Aquí, queremos escribir ecuaciones donde el resultado de la variable es el número 41;

El valor de x en la ecuación anterior es 41

Escribamos una segunda ecuación;

El valor de 'y' aquí también es 41

Answer: 283.3333333% (283.3%)

Step-by-step explanation:

First, lets turn 2 5/6 into and improper fraction. It becomes 17/6.

Now, we divide 17/6

17/6 = 2.833333333

Now, to turn it into a percent, we multiply it by 100, or move the decimal point 2 places to the right. That gives us 283.3333333% (283.3%)

Hope this helps!

Answer:

Step-by-step explanation:Angles 1 and 2 form a linear pair and are supplementary. So to find m∠2, subtract m∠1 from 180o. m∠2 = 180o - 135o = 45o.

...

Solution

m∠1 + 32 = 90 Substitute 32 for m∠2.

m∠1 = 58 Subtract 32 from each side.

m∠1 + m∠ 2 = 90 Definition of complementary angles.

Answer:

Step-by-step explanation:

What is 20 as a decimal? To write 20 as a decimal you have to divide numerator by the denominator of the fraction. 20 is not a fraction so it is a decimal already. And finally we have: 20 as a decimal equals 20

The value of 'n' is 18 in the given equation 8n - 5 = 139.

We have to find the value of 'n'.

To do so, we need to solve the given equation.

Let us see how we can solve the given equation.8n - 5 = 139

We need to find the value of 'n'.

Let us bring the constant term to the right side by adding 5 to both the sides of the equation.8n - 5 + 5 = 139 + 5On simplifying, we get8n = 144Now, we need to isolate 'n' to find its value.

To do so, we divide both the sides by 8.8n/8 = 144/8On simplifying, we get n = 18

Therefore, the value of 'n' is 18.

Hence, the value of 'n' is 18 in the given equation 8n - 5 = 139.

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You can either transform this quadratic equation into a vertex form which would rather painful or use derivatives.

I'll use dervatives. We know that vertex of a quadratic function is either its maxima or its minima, since the leading coefficient \(-x^2\) has a negative prefix that means we get a downward turned parabola with minima being the vertex.

First we take the derivative with respect to x,

\(\dfrac{d}{dx}-x^2-2x+3=-2x-2\)

The derivative is esentially information what is the slope of a function at a particular x. When the slope is 0 we reached some sort of turning point, such as minima.

We therefore do,

\(-2x-2=0\implies x=-1\)

So at \(x=-1\) there appears to be a minima or x-coordinate of the vertex of the function.

Plug the coordinate into the function to get y,

\(y=f(-1)=-1+2+3=4\)

So the vertex of the function is at \(\boxed{(-1,4)}\).

Assuming you don't know derivatives, there is another way.

First compute the roots of the function,

\(-x^2-2x+3=0\)

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

\(x_1=1,x_2=-3\)

In the middle between \(x_1,x_2\) is an x coordinate of a vertex,

\(x=\dfrac{x_1+x_2}{2}=\dfrac{1-3}{2}=-1\)

Just like we had before, we compute for y, \(h(-1)=4\) and again the result is \(\boxed{(-1,4)}\).

Hope this helps :)

Answer:

  z = √35

Step-by-step explanation:

In this geometry, all of the right triangles are similar, so corresponding sides are proportional.

  long side / hypotenuse = 5/z = z/(2+5)

  z² = 5(7) = 35

  z = √35

Step-by-step explanation:

\( \frac{a}{b} c = \frac{a}{ \frac{b}{c} } \)

\( \frac{a}{b} c = a \times \frac{c}{b} \)

Answer:

Step-by-step explanation: change A/B/C to A÷B/C then change the division sign into a multiplicmultiplication sign so that you will have A×C/Bwhich will make your left equation = to your right equation