Alice took out a $15,000 loan for college. She is borrowing money from two banks. Bank A charges an interest rate of 6%, and Bank B charges an interest rate of 7%. After one year, Alice owes $960 in interest. How much money did she borrow from Bank A?

It’s (x-6)(x+4) so the first one and last one

For this case we must factor the following expression:

[tex]x ^ 2-2x-24[/tex]

We must find two numbers that when added together give "-2" and when multiplied by "-24"

These numbers are:

[tex]-6\ and\ +4\\-6 + 4 = -2\\-6 * + 4 = -24[/tex]

So:

[tex]x ^ 2-2x-24 = (x-6) (x + 4)[/tex]

Answer:

[tex](x-6) (x + 4)[/tex]

Option A and D

Set it up.

Make the equations equal to 180° because they are on a straight line. And a straight line adds up to 180°

Answer:

y = 54.1

Step-by-step explanation:

The big triangle is divided in two: one on  the left and one on the right. Lets start working with the right one.

We know the right triangle is a right triangle with legs 24 and 36, so we can use Pitagoras to find the hypotenuse (h), in a way that:

24^2 + 36^2 = h^2

1872 = h^2

Applying sqr root in both sides:

h = 43.27

So, the hypotenuse measures 43.27 or 43.3.

Now lets do the same with the triangle of the right which legs are 36 and y, lets find it hypotenuse (g):

36^2 + y^2 = g^2

1296 + y^2 = g^2

Now we will pass to the large triangle, which is composed by the left and the right triangles and has legs of 43.3 and g, and the hypotenuse is 24+y. Lets apply Pitagoras:

43.3^2 + g^2 = (24+y)^2

1875 + 1296 + y^2 = 24^2 + 48y + y^2

3171 + y^2 = 576 + 48y + y^2

As we have y^2 in both sides we can eliminate them

3171 + = 576 + 48y

Now subtract 576 in both sides:

3171 -576 = 576 + 48y - 576

2595 = 48y

Divide both sides by 48:

2595/48 = 48y/48

54.1 = y

So, the large hypotenuse measures 54.1+24 = 78.1. Lets verify:

43.3 ^2 + 1296 + 54.2^2 = 6,108.53

And the sqrd root of 6,108.53 is approximately 78.1. Verified!!!!

So, we can confirm: y = 54.1

The area is 168 yd²

The area of Trapezoid is given by

A= (a+b)/2 * h

Putting the values

A = (5+23)/2 * 12

A = 168 yd²

Answer:

A = 168 Square Yards

Answer:

11

Step-by-step explanation:

8 plus 3 i dunno know if it is forsure but yeah.

Answer:

[tex]\large\boxed{15x+42-8y+20-4x=11x-8y+62}[/tex]

Step-by-step explanation:

[tex]15x+42-8y+20-4x\\\\\text{combine like terms}\\\\=(15x-4x)-8y+(42+20)\\\\=11x-8y+62[/tex]

You add like terms together.

Ex. You would add 15x and(-4x) together, giving you 11x

So to simplify it, you need to do 15x-4x, 42+20, and 8y would be left by itself since there are no like terms for 8y.

So the simplified version would be: 11x+62+8y

Habeas corpus is the right to have one’s detention reviewed by a judge

Answer:

a prisoner’s right to inquire why he or she is being detained

Step-by-step explanation:

Answer: option D.

Step-by-step explanation:

To solve this exercise you must apply the proccedure shown below:

- Apply the Distributive property (Remember that when you multiply two powers with the same base, you must add the exponents).

[tex]b^m*b^n=b^{(m+n)}[/tex]

- Add the like terms.

Therefore, you obtain that the product is:

[tex](2x^2+5x-3)(3x+7)=6x^3+14x^2+15x^2+35x-9x-21\\=6x^3+29x^2+26x-21[/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. The product of (2x²+5x-3) and (3x+7) is 6x³ + 29x² + 26x - 21.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The product of (2x²+5x-3) and (3x+7) can be done as,

(2x²+5x-3) × (3x+7)

= 3x(2x²+5x-3) + 7(2x²+5x-3)

= 6x³ + 15x² - 9x + 14x² + 35x - 21

= 6x³ + 29x² + 26x - 21

Hence, the product of (2x²+5x-3) and (3x+7) is 6x³ + 29x² + 26x - 21.

Learn more about Expression:

https://brainly.com/question/13947055

#SPJ2

Answer:

"The values for y are square roots of negative numbers"

Step-by-step explanation:

The steps shown are correct. But at the end we can see that we have to "take the negative square roots".

This means we have to take the square root of -1. In the real number system, we CANNOT take the square root of any negative number. Hence, there is NO SOLUTION to the system.

2nd answer choice, "The values for y are square roots of negative numbers", is right.

Answer:

(6y+17)

Step-by-step explanation:

1. Subtract 4y from 10y to get 6y

2. 9 is positive and 8 is negative but to subtract a negative is basically adding so you would add 9 to 8

3. You final equation would be (6y+17)

4. (10y+9)-(4y-8)= (6y+17)

Answer:

Step-by-step explanation:

[tex](10y+9)-(4y-8)\\\\=10y+9-4y-(-8)\\\\=10y+9-4y+8\qquad\text{combine like terms}\\\\=(10y-4y)+(9+8)\\\\=6y+17[/tex]

Answer:

The correct answer option is x = -16 and x = 16.

Step-by-step explanation:

We are given the following equation and we are to find the solution for this equation:

[tex] | \frac { x } { 2 } | = 8 [/tex]

For the given equation, involving the modulus, we will have a positive as well as a negative value for it in order to find its solution set.

[tex] \frac { x } { 2 } = - 8 [/tex] and [tex] \frac { x } { 2 } = 8 [/tex]

[tex] x = 8 \times 2 [/tex] and [tex] x = - 8 \times 2 [/tex]

x = -16 and x = 16

Answer:

The correct answer is last option

x = -16 or x = 16

Step-by-step explanation:

it is given that,

|x/2| = 8

To find the solution set

From this we can understand that , the value of x/2 = - 8 or x/2 = 8

If x/2 = -8 then  x = -8 * 2 = = -16

If x/2 = 8 then x = 8 * 2 = 16

Therefore the solutions are

x = -16 or x = 16

Answer:

342

Step-by-step explanation:

Let's see the difference is each successive values:

232 - 217 = 15

252 - 232 = 20

277 - 252 = 25

307 - 277 = 30

As we can see, each month the increase is 5 more than previous months' increase. Clearly from the pattern we can surmise that the next month (August), it will increase by 35 from the value of July.

Number of visitors in August = Number of Visitors in  July + 35 = 307 + 35 = 342

Answer:

342

Step-by-step explanation:

Answer:

D. $240,000

Step-by-step explanation:

find $40,000 on the chart - then find 45 years old / 60% - go down the chart and over to the right and you'll find 6.0

multiply 40,000 * 6.0 = 240,000

hope this helps!!

The answer is D. 240,000

Hope this helps : )

The slope is

[tex] - \frac{1}{3} [/tex]

Answer:

81 is the answer

Step-by-step explanation:

Answer:

Hold up im solving it

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

We will solve the equation by using quadratic formula.

x=  (-b ± √(b^2-4ac))/2a

The standard form of quadratic equation is:

ax^2+bx+c=0

So by comparing with the standard form, we get:

a=1

b= -4

c=18

Putting the values in the formula

x=  (-(-4)± √((-4)^2-4(1)(18)))/2(1)  

x =  (4± √(16-72))/2

x =  (4± √(-56))/2

The minus sign in square root will introduce the imaginary symbol.  

x =  (4± √(14*4*(-1)))/2

The minus 1 can be replace by the imaginary i => i^2 = -1

x =  (4± √(14*2^2*i^2 ))/2

The terms with squares can be brought out of the square root

So,

x =  (4± 2i√14)/2

Taking 2 as common

x =  (2(2± i√(14)))/2

x = 2± i√14

Answer:

B. .12 is the decimal

Step-by-step explanation:

What you do is you divide 25 by 3. That will already give you a decimal and when you divide it out your answer is .12.

3/25=.12.

Answer:

The correct answer is 0.12

Step-by-step explanation:

3 = numerator

25 = denominator

Divide the numerator by the denominator to convert a fraction to a decimal.

3 ÷ 25 = 0.12  

as a decimal is  

0.12

.

Answer: The answer is B. 0.12

Step-by-step explanation:

answer :

y=-1/4x+5

my work:

y=mx+b

2=-1/4(12)+b

2=-3+b

+3 +3

5=b

y=-1/4x+5

Answer:

y = - [tex]\frac{1}{4}[/tex] x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{1}{4}[/tex], hence

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

To find c substitute (12, 2) into the partial equation

2 = - 3 + c ⇒ c = 2 + 3 = 5

y = - [tex]\frac{1}{4}[/tex] x + 5 ← equation of line

(6, -5)

(5, -6) --> (-5, 6)

Hope this helps!!

I'd right the key concepts for future reference!

:D

Answer:

(6,-5)

Step-by-step explanation:

Yea it’s the second one

Answer:

Answer is yes

Step-by-step explanation:

Given in the picture are two circles which are congruent.

This suggests that the radii of the two circles are equal.

Also the central angle of the two circles are congruent (given)

Consider triangles ABC and XYZ,

AC =XY:  AB = YZ:

Angle A = Angle X

By SAS theorem, the two triangles are congruent.

Hence BC = YZ

So yes is answer.

Answer:

Step-by-step explanation:

Unfortunately not...

The shape is a triangle, and the area formula is A=[tex]\frac{1}{2}[/tex]bh.

b = 5 ft.

h = 4 ft.

Therefore:

A = [tex]\frac{1}{2}[/tex](5)(4)=10ft

Answer:

[tex]y^{5}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

Hence

[tex]y^{2}[/tex] × [tex]y^{3}[/tex] = [tex]y^{(2+3)}[/tex] = [tex]y^{5}[/tex]

Find two "dots" where the line crosses the X and Y axis at real numbers.

(0,3) and (6,-1)

Now find the slope which is the difference in Y over the difference in x.

Slope = (-1 - 3) / (6-0) = -4 / 6 = -2/3

The answer is D.

Answer:

[tex]\large\boxed{h=10\dfrac{2}{7}}[/tex]

Step-by-step explanation:

The formula of an area of a triangle:

[tex]A=\dfrac{bh}{2}[/tex]

We ahve b = 14 and A = 72. Substitute:

[tex]72=\dfrac{14h}{2}[/tex]             multiply both sides by 2

[tex]144=14h[/tex]          divide both sides by 14

[tex]h=\dfrac{144}{14}\\\\h=\dfrac{144:2}{14:2}\\\\h=\dfrac{72}{7}\\\\h=10\dfrac{2}{7}[/tex]

Answer:

200ml

Step-by-step explanation:

5+2+3=10

400/10=40

Since lemon's ratio is 5, you multiply 40 by 5 to get 200.

Answer:

(x+1)(x2+1)

Step-by-step explanation:

Factor x3+x2+x+1

x3+x2+x+1

=(x+1)(x2+1)

also a great website for your problems is called mathpapa-algebra calculator

Answer:

The solution is [tex]x=6\ cm[/tex]

Step-by-step explanation:

we know that

The area of rectangle is equal to

[tex]A=LW[/tex]

we have

[tex]A=56\ cm^{2}[/tex]

so

[tex]56=LW[/tex] ------> equation A

[tex]L=x+2[/tex] -----> equation B

[tex]W=2x-5[/tex] -----> equation C

Substitute equation B and equation C in equation A

[tex]56=(x+2)(2x-5)[/tex]

solve for x

[tex]56=(x+2)(2x-5)\\56=2x^{2}-5x+4x-10\\2x^{2}-x-66=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]  

in this problem we have

[tex]2x^{2}-x-66=0[/tex]  

so

[tex]a=2\\b=-1\\c=-66[/tex]

substitute in the formula

[tex]x=\frac{1(+/-)\sqrt{-1^{2}-4(2)(-66)}} {2(2)}[/tex]

[tex]x=\frac{1(+/-)\sqrt{529}} {4}[/tex]

[tex]x1=\frac{1(+)23} {4}=6[/tex]

[tex]x2=\frac{1(-)23} {4}=-5.5[/tex]  

The solution is [tex]x=6\ cm[/tex]

[tex]L=6+2=8\ cm[/tex]

[tex]W=2(6)-5=7\ cm[/tex]

answer = 42

if you look at the triangle you see a small square in the corner indicating that the triangle is a 90 degree angle, therefore all the sides add up to 90. With this knowledge just add the values of the two known sides, 18 and 30, which is 48 and then subtract 48 from 90 which gives you the value of x, 42

➷ Find the total number of pens:

5 + 3 + 2 = 10

The probability of taking a red the first time is 5/10

The probability of taking a blue the first time is 3/10

The probability of taking a green the first time is 2/10

If you want to take the same colored pen again, there would be 1 less of the total pen (as it hasn't been replaced) and there would be one less of that color (as one has already been taken)

Therefore:

The probability of taking a red again is 4/9

The probability of taking a blue again is 2/9

The probability of taking a green again is 1/9

Multiply the values for the same color together:

5/10 x 4/9 = 20/90

3/10 x 2/9 = 6/90

2/10 x 1/9 = 2/90

Add these values together:

20/90 + 6/90 + 2/90 = 28/90

Your answer is 28/90

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

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