Leila is considering buying her first home. The house she is interested in buying is priced at $125,000. Leila can put down a $20,000 payment, and she qualifies for a 30-year mortgage at 6%. What will her monthly mortgage payment be?

Answer:

  98 ft²

Step-by-step explanation:

There are a couple of ways you can think about this one. Perhaps easiest is to treat it as a square with a triangle cut out of it. The cutout triangle has a base (across the top) of 14 ft and a height of 14 ft, so its area is ...

  A = (1/2)(14 ft)(14 ft) = 98 ft²

Of course the area of the square from which it is cut is ...

  A = (14 ft)² = 196 ft²

So, the net area of the two triangles shown is ...

  A = (196 ft²) - (98 ft²) = 98 ft²

_____

Another way to work this problem is to attack it directly. Let the base of the left triangle be x. Then the base of the right triangle is 14-x, and their total area is ...

  A = A1 + A2 = (1/2)(x ft)(14 ft) + (1/2)((14-x) ft)(14 ft)

We can factor out 7 ft to get ...

  A = (7 ft)(x ft + (14 -x) ft)

  A = (7 ft)(14 ft) = 98 ft²

Answer:

4

Step-by-step explanation:

Count

Answer:

domain; x<0 or x>0

Step-by-step explanation:

We have been given the following function;

f(x) = 2x + 6/x^2 + 5x + 6

We need to evaluate the values of f(x) for the following domain values;

{-3, -2, 0, 2, 3}

f(-3) = 2(-3) + 6/(-3)^2 + 5(-3) + 6

      = -43/3

f(-2) = 2(-2) + 6/(-2)^2 + 5(-2) + 6

      = -6.5

f(0) = 2(0) + 6/(0)^2 + 5(0) + 6

     = undefined

f(2) = 2(2) + 6/(2)^2 + 5(2) + 6

     = 21.5

f(3) = 2(3) + 6/(3)^2 + 5(3) + 6

     = 83/3

The function is real and defined for every value of x in its domain except where x = 0 . This is a point of discontinuity.

Find the attachment below;

Answer:

0

Step-by-step explanation:

From the graph of the function f(x) we have:

        When f(x)=0  ,   x= -1.8

By looking at the graph we observe that the graph first increases in the interval (-∞,-1.2) and then it decreases in the interval (-1.2,0.6) and then again it increases in the interval (0.6,∞).

Hence, the graph of the function is neither strictly increasing nor strictly decreasing in the whole of the real line.

Also, when x=0 the value of the function is: f(x)=5

( Since, the graph passes through the point (0,5) )

Also, when f(x)=0

then x= -1.8

( Since, the graph of the function passes through the point (-1.8,0) )

Answer:

answer is 25t I DID THE TEST!!

Answer: 25F i did the test

Step-by-step explanation:

Hey there! :)

(0, 2) & (-1, -2)

Slope-intercept form is : y=mx+b , where m=slope, b=y-intercept

First, we must find the slope using the slope formula, which is :

m = y2-y1/x2-x1

Where y2 = -2 ; y1 = 2 ; x2 = -1 ; x1 = 0

Now, let's plug and chug! :)

m = (-2 - 2) / (-1 - 0)

Simplify.

m = -4/-1 --> Therefore, our slope is : m = 4

Now that we have the slope, we can plug this (and our original coordinates) into point-slope form, which is : y - y1 = m(x - x1) -> use the coordinates (0, 2)

y - 2 = 4(x - 0)

Simplify.

y - 2 = 4x

Add 2 to both sides.

y = 4x + 2

Hope this helped! :)

Answer:

The quotient is (10x - 5) and the reminder is -50 ⇒ 1st answer

Step-by-step explanation:

* Lets solve the long division by easiest way

∵ (10x² - 85x - 10)/(x - 8)

∵ (10x² - 85x - 10) is the dividend

∵ (x - 8) is the divisor

- Divide the first term of the dividend by the first term of the divisor

∴ 10x² ÷ x = 10x ⇒ first term of the quotient

- Multiply 10x by the the divisor

∴ 10x(x - 8) = 10x² - 80x

- Subtract the answer from the dividend

∴ (10x² - 85x - 10) - (10x² - 80x) =

# 10x² - 10x² = 0

# -85x - -80x = -85x + 80x = -5x

# -10

∴ (10x² - 85x - 10)/(x - 8) = 10x + (-5x - 10)/(x - 8)

* Repeat the same steps again with the new dividend -5x - 10

- Divide the first term of the dividend by the first term of the divisor

∴ -5x ÷ x = -5 ⇒ second term of the quotient

- Multiply -5 by the divisor

∴ -5(x - 8) = -5x + 40

- Subtract the answer from the dividend

∴ (-5x - 10) - (-5x + 40) =

# -5x - -5x = -5x + 5x = 0

# -10 - 40 = -50

∴ (-5x - 10)/(x - 8) = -5 + -50/(x - 8)

∴ (10x² - 85x - 10)/(x - 8) = 10x - 5 + -50/(x - 8)

- The quotient is the answer of the division

∴ The quotient is (10x - 5) and the reminder is -50

Answer:

The quotient is 10x - 5 and the reminder is -50

Step-by-step explanation:

Answer:

[tex]\large\boxed{x^3-5x^2+8x-6}[/tex]

Step-by-step explanation:

[tex]f(x)=x^2-2x+2\\\\g(x)=x-3\\\\f(x)\cdot g(x)=(x^2-2x+2)(x-3)\qquad\text{use}\ \bold{FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\f(x)\cdot g(x)=(x^2)(x)+(x^2)(-3)+(-2x)(x)+(-2x)(-3)+(2)(x)+(2)(-3)\\\\f(x)\cdot g(x)=x^3-3x^2-2x^2+6x+2x-6\qquad\text{combine like terms}\\\\f(x)\cdot g(x)=x^3+(-3x^2-2x^2)+(6x+2x)-6\\\\f(x)\cdot g(x)=x^3-5x^2+8x-6[/tex]

Answer:

B

Step-by-step explanation:

V=4/3 x 3.14 x 3^3

V= 113.04

SA= 4 x 3.14 x 3^2

SA= 113.04

Answer:

The answer is V=SA

Step-by-step explanation:

V=4/3 x 3.14 x 3^3

V= 113.04

SA= 4 x 3.14 x 3^2

SA= 113.04

So the relationship should be V=SA, because the equaled amount on both ends was the same.

Answer:

1.what number should be added to both sides of the equation? 1

2. how many of the solutions to the equation are positive? one, x=3.031

3.what is the approximate value of the greatest solution to the equation rounded to the nearest hundredth? 3.03

Step-by-step explanation:

The question is on solving for quadratic equations using the completing square method

The equation given is ;

4x²+8x+27=88...........rewrite the equation

4x²+8x+27-88=0

4x²+8x+-61=0...................divide every term of the equation by 4

4x/4²+8x/4+-61/4=0/4

x²+2x-15.25=0..................rewrite the equation as;

x²+2x=15.25.......................complete square on both sides

x²+2x+ (2/2)²= 15.25 +(2/2)²

x²+2x+1 = 15.25+1

x²+2x+1=16.25................factorize the left hand side

(x+1)²=16.25.....................eliminate the root on the left hand side

x+1=±√16.25

x+1= ± 4.031

solutions

x+1= +4.031

x= +4.031-1 =3.031

or

x+1= -4.031

x= -4.031-1 = - 5.031

Answer:

The first box is 1, the second box is 1, and the third box is 3.03

Step-by-step explanation:

Answer: $360

Step-by-step explanation:

Let Mp the manufacturing price.

First step:

Manufacturer sells at a profit of 25% = Mp + Mp·0.25 = Mp·1.25

Second step:

Agency sells at a profit of 10% = 1.25Mp + 1.25Mp·0.10 = Mp·1.375

Third step:

Shopkeeper sells at a profit of 20% = 1.375Mp + 1.375Mp·0.20 = Mp·1.65

Then the final price = 1.65·Mp

1.65Mp = $594

Mp = $594/1.65 = $360 ►Manufacturer price

Answer: $360

Verification

Manufacturer sells at a profit of 25% = 25/100 = 0.25:

$360 + $360·0.25 = $360(1 + 0.25) = $360 + $90 = $450

Agency sells at a profit of 10% = 10/100 = 0.10:

$450 + $450·0.10 = $450(1 + 0.10) = $450 + $45 = $495

Shopkeeper sells at a profit of 20% = 20/100 = 0.20

$495 + $495·0.20 = $495(1 + 0.20) = $495 + $99 = $594 Checked!

[tex]\textit{\textbf{Spymore}}[/tex]

In a standard shuffled deck of 52 cards, half of the cards are black and half of the cards are red: (26 black cards, 26 red cards).

Since we are interested in pulling a black card first, the probability is 26/52.

Without replacing the card we have chosen, we are left with 51 total cards in the entire deck (25 black cards, 26 red cards).

Now that we want to pull a red card, we know that the probability will be 26/51.

Since we are interested in both events occurring simultaneously, we must multiply the probability of the first by the probability of the second, aka: (26/52) * (26/51)

The answer we are given is 0.2549

The probability of picking a black card and then a red card from a standard deck without replacement is 13/51.

To calculate the probability of selecting a black card and then a red card from a standard deck without replacement, we need to consider the sequence of the two events. Initially, the deck contains 26 black cards (spades and clubs) and 26 red cards (diamonds and hearts). The probability P(A) of picking a black card first is 26/52 or 1/2.

After one black card has been removed, there are now 51 cards left in the deck with 26 red cards remaining. The probability P(B) of then picking a red card is 26/51. To find the overall probability of both events happening in sequence, we multiply the probabilities:

[tex]P(A and B) = P(A) \times P(B) = (\frac{1}{2}) \times (\frac{26}{51})[/tex]

This simplifies to P(A and B) = [tex](\frac{26}{102})[/tex] which can be further simplified to [tex](\frac{13}{51}).[/tex]

5x=45

divide by 5 for 5x and 45 to get the answer

5x/5= 45/5

x=9 ( Answer)

The solution to the equation 5x = 45 is x = 9.

To solve the equation 5x = 45, you want to find the value of x that satisfies the equation.

Here's how you can solve it step by step:

Step 1: Start with the equation 5x = 45.

Step 2: To isolate x, divide both sides of the equation by 5. This step cancels out the multiplication by 5 on the left side of the equation.

(5x) / 5 = 45 / 5

Simplifying further:

x = 9

Explanation: In Step 2, when you divide both sides of the equation by 5, you are essentially undoing the multiplication operation on the left side.

By dividing both sides by the same number, you maintain the equality of the equation.

On the left side, the 5s cancel out, leaving you with just x. On the right side, 45 divided by 5 equals 9.

Thus, x = 9 is the value that satisfies the equation.

Therefore, the solution to the equation 5x = 45 is x = 9.

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Answer:

x=9 and x=-2

Step-by-step explanation:

GFC = 9 => 9(x²-6x-16) =0

9(x-8)(x+2) = 0

x-b=0    x+2= 0

x=8 and x = -2

Solving the quadratic equation, it is found that the company needs to sell 8 products for the net income to be equal $0.

It is given by:

f(x) = 9x² - 54x - 144.

It can be simplified as follows:

f(x) = 9(x² - 6x - 16)

Then:

f(x) = 9[(x + 2)(x - 8)]

It has a net income equals to 0 when:

f(x) = 0, hence:

The amount of products sold is positive, hence, the company needs to sell 8 products for the net income to be equal $0.

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Final answer:

To calculate the temperature of the liquid after 7 hours, you can use Newton's cooling model. By plugging in the initial temperature, the surrounding temperature, and the cooling constant into the equation T = T0 + (T1 - T0) * e(-kt), you can calculate the temperature after 7 hours. In this case, the temperature after 7 hours is approximately 152.85°F.

Explanation:

In this problem, we can use Newton's cooling model to determine the temperature of the liquid after 7 hours. Newton's cooling model states that the rate of heat loss or gain is directly proportional to the temperature difference between the object and its surroundings. Using the equation T = T0 + (T1 - T0) * e(-kt), where T is the temperature at time t, T0 is the initial temperature, T1 is the surrounding temperature, k is the cooling constant, and e is the base of the natural logarithm, we can calculate the temperature after 7 hours.

Convert the initial temperature, the surrounding temperature, and the time to Kelvin.

Plug the values into the equation and calculate the temperature after 7 hours.

Using the given values of T0 = 170°F, T1 = 76°F, and k = 0.34, we can calculate the temperature after 7 hours.

T0 = 170°F + 459.67 = 629.67 K

T1 = 76°F + 459.67 = 535.67 K

T = 629.67 + (535.67 - 629.67) * e⁻°³⁴*⁷

T ≈ 152.85°F

Answer:first one is dependent

second one is independent

Step-by-step explanation:

I do exercises on it

solve it with a system

x=screwdriver

y=cutter

x+y=29

2x+15.2y=150.40

ANSWER

(-5,1) is the correct answer

EXPLANATION

The given inequality is:

[tex]y \: > \: |x|- 6[/tex]

If any point satisfies this inequality, then it is a solution.

We need to substitute each point into the given inequality.

We substitute (-5,1) to get:

[tex]1\: > \: | - 5|- 6 \implies1\: > \: - 1[/tex]

This statement is true. Hence (-5,1) is a solution.

For (-1,-5), we have

[tex] - 5\: > \: | - 1|- 6 \implies - 5\: > \: - 5[/tex]

This is false.

For (5,-1), we have

[tex] - 1\: > \: | 5|- 6 \implies - 1\: > \: - 1[/tex]

This is also false.

Answer:

(-5,1) is the correct answer

Answer:

a)  4x +7y =100             b)  4x = 100-7y

Step-by-step explanation:

students = 4x

teachers  = 7y

4x +7y = 100

4x =100 -7y

Final answer:

The equation is solved to determine the number of students Mr. Bean gave money to as 2.

Explanation:

a) Equation:

Let x be the number of students and y be the number of teachers Mr. Bean gave money to.

Equation: 4x + 7y = 100

b) Solving the equation:

Given that Mr. Bean only gave out $100, we substitute this into the equation:

4x + 7y = 100

4x + 7(14-x) = 100

4x + 98 - 7x = 100

98 - 3x = 100

-3x = 2

x = -2/-3 = 2/3

Therefore, Mr. Bean gave money to 2 students.

Learn more about Equation solving here:

Answer:

an increase then a pause then anotha increase

Step-by-step explanation:

Answer:

{x while x ≠2, -2}

Step-by-step explanation:

First let's define domain,

Domain is the set of all values on which the function is defined i.e. the function doesn't approach to infinity.

Given function is:

[tex]y = \frac{2x-4}{x^{2} -4}[/tex]

We will look for all the values of x on which the function will become undefined:

We can see that x= 2 and x=-2 will make the denominator zero as there is x^2 involved. The denominator zero will make the function undefined.

So, the domain of the function is set of all real numbers except 2 nd -2 {x while x ≠2, -2} ..

Answer:

[tex](-\infty,-2)\cup (-2,2)\cup (2,+\infty)[/tex]

Step-by-step explanation:

The given rational expression is:

[tex]y=\frac{2x-4}{x^2-4}[/tex]

We factor this expression to obtain:

[tex]y=\frac{2(x-2)}{(x-2)(x+2)}[/tex]

We can see that, this rational function has a hole at x=2 and a vertical asymptote at x=-2

Therefore the domain is

[tex]x\ne 2\: and\:x\ne -2[/tex]

Or

[tex](-\infty,-2)\cup (-2,2)\cup (2,+\infty)[/tex]

Answer:

+ 6

Step-by-step explanation:

The constant term in the function is the term which is only numeric and has no variable attached to it.

f(y) = 8y² - 7y + 6 → has constant term + 6

Answer:

b) There is translation 3 units to the right and 1 unit up

c) The domain is {x I x > 3}

   The equation of the asymptote is x = 3

Step-by-step explanation:

* Lets revise the rule of the translation

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Now lets solve the problem

b) ∵ f(x) = [tex]log_{2} (x-3)+1[/tex]

∵ The parent function is [tex]log_{2} x[/tex]

∴ x is changed to (x - 3), that means there is a translation 3 units

  to the right

∵ We add the parent function by 1, that means there is a translation

  1 unit up

* There is translation 3 units to the right and 1 unit up

c) To find the domain of the function, find the values of x which

    make the function undefined

∵ [tex]log_{2}(0)[/tex] is undefined

∴ x - 3 can not be 0

∵ x - 3 = 0 ⇒ add 3 to both sides

∴ x = 3

∴ The domain of the function is all real number greater than 3

* The domain is {x I x > 3}

∵ x can not be 3

∴ There is a vertical asymptote, its equation is x = 3

* The equation of the asymptote is x = 3

# Look to the attached graph for more understand for the domain

  and the equation of the asymptote

The circumference of the circle with a diameter of 16 units is approximately 50.26544 units.

To find the circumference of a circle, you can use the formula C = πd, where C represents the circumference and d is the diameter of the circle. In this case, the diameter of the circle is given as 16 units.

Substituting the value into the formula, we have C = π(16). Using the value of π (pi) as approximately 3.14159, we can calculate the circumference.

C = 3.14159 x 16 = 50.26544 units.

Therefore, the circumference of the circle with a diameter of 16 units is approximately 50.26544 units.

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Answer: distance = rate x time

Step-by-step explanation: divided by distance then multiply by rate

Answer:

True, ∠1 and ∠2 are adjacent angles. True

Explanation:

Definition of adjacent angles: Two angles are called adjacent angles if

1. They have a common side

2. Common vertex (corner point)

3. They don't overlap.  

Further Explanation:

In the given figure two lines are intersecting each other and form 4 angles, ∠1, ∠2, ∠3  and ∠4.

From the given figure it is clear that, the common vertex of all angles is the point of intersection of both lines. The pairs of adjacent angles are

(i) ∠1 and ∠2

(ii) ∠2  and ∠3

(iii) ∠3  and ∠4

(iv) ∠1  and ∠4

Therefore, ∠1 and ∠2 are adjacent angles and the given statement is true.

Learn More:

Adjacent angles :  https://brainly.com/question/11933939  (Answered by MollieToliver)

Adjacent angles :  https://brainly.com/question/12256805  (Answered by ApusApus)

Keywords:

Adjacent angles, Intersection of two lines.

When we have an intersection of two lines, four angles are created in that intersection.

With this, we define two adjacent angles as a pair of angles that is separated by one of the lines.

In the image, we can see that:

∠1 and ∠2 are adjacent

∠2 and ∠3 are adjacent

∠3 and ∠4 are adjacent

∠4 and ∠1 are adjacent.

Then the statement:

"∠1 and ∠2 are adjacent"

Is true, by definition of adjacent angles.

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Answer:

2 time 5 squared is simplified form of 60 they both get the end result of 7.4

Step-by-step explanation:

Answer:

The correct answer is second option

2√15

Step-by-step explanation:

From the attached question we can see that,

√60

To find the value of √60

We know that, 60 = 4 * 15

and √4 = 2

Therefore √60 can be written as,

√60 = √(4 * 15)

 = 2√15

The correct answer is 2√15

Therefore the correct option is second option.

√60 = 2√15

Second from top down

Answer:

9x^2-4

Step-by-step explanation:

use FOIL

9x²-4 is represented by the factorization.

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

Given

(3x+2)(3x - 2)

= 9x² + 6x - 6x -4

= 9x² -4

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Final answer:

The binomial equivalent to (xy + z)(xy - z) is found by applying the difference of squares formula, resulting in x²y² - z².

Explanation:

The question asks which binomial is equivalent to the expression (xy + z)(xy - z). This can be simplified using the difference of squares formula, which is a² - b² = (a + b)(a - b). In this case, a is xy and b is z.

Applying the formula, we have:

First, square a: (xy)² = x²y²

Then, square b: z²

Subtract the square of b from the square of a to get the answer: x²y² - z²

Therefore, the binomial equivalent to (xy + z)(xy - z) is x²y² - z².