4. June Elloy makes a 22 percent down payment on a home in Rockford,
Illinois. What is the purchase price of the home assuming her down
payment is $35,200?​

[tex]\bf \stackrel{\textit{y-intercept}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-1})}\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-1)}{1-0}\implies \cfrac{1+1}{1}\implies \cfrac{2}{1}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-1)=2(x-0) \\\\\\ y+1=2x\implies \stackrel{\textit{general form}}{-2x+y+1=0}[/tex]

To find the equation of the line with a y-intercept of -1 and passing through the point (1,1), you first determine the slope (which is 2), leading to the slope-intercept form: y = 2x - 1. Then convert this to the general form: -2x + y + 1 = 0.

The general form of the equation of a line is Ax + By + C = 0 where A, B, and C are constants.

To write the equation of a line with a given point (1,1) and a y-intercept of -1, we'll start with the slope-intercept form of the equation, which is y = mx + b. We know that the y-intercept b is -1.

Next, we need to find the slope m, which is the change in y over the change in x. Using the point (1,1), we calculate the slope as (1 - (-1)) / (1 - 0) which equals 2.

Therefore, the slope-intercept form of our line is y = 2x - 1.

To convert this to general form, rearrange the terms and change the equation to have a 0 on one side: -2x + y + 1 = 0.

This is the general form of the equation of the line with the given conditions.

Answer:

(1,12) is correct if you meant [tex]3 \cdot 4^x[/tex].

Please correct if I'm wrong about your expression.  

Step-by-step explanation:

I think you mean [tex]f(x)=3 \cdot 4^x[/tex].

Let's test the point and see.

A. (0,12)?

(0,12)=(x,y)

What happens when x equals 0? Is the result 12?

[tex]3 \cdot 4^0[/tex]

[tex]3 \cdot 1[/tex]

[tex]3(1)[/tex]

[tex]3[/tex]

Yep that isn't 12 so (0,12) is not on the graph of f.

B. (0,0)?

(0,0)=(x,y)

What happens when x equals 0? Is the result 0?

[tex]3 \cdot 4^0[/tex]

We already this and got 3 so (0,0) is not on the graph of f.

C.  (1,12)?

(1,12)=(1,12)

What happens when x equals 1? Is the result 12?

[tex]3 \cdot 4^1[/tex]

[tex]3 \cdot 4[/tex]

[tex]12[/tex]

The result is 12 so (1,12) is on the graph of f.

C.  (12,1)

(12,1)=(x,y)

What happens when x equals 12? Is the result 1?

[tex]3 \cdot 4^{12}[/tex]

This will result in a really big number that isn't 1 so (12,1) is not on the graph of f.

(1,12) is correct if you meant [tex]3 \cdot 4^x[/tex].

Answer:

(1,12)

Step-by-step explanation:

ape x

Answer:

Part 1) [tex]b=8.2\ units[/tex]

Part 2) [tex]a=10.1\ units[/tex]

Part 3) [tex]A=51\°[/tex] and [tex]C=90\°[/tex]

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

Find the side b

we know that

In the right triangle ABC

The function sine of angle B is equal to divide the opposite side angle B (AC) by the hypotenuse (AB)

[tex]sin(B)=AC/AB[/tex]

we have

[tex]AB=c=13\ units[/tex]

[tex]AC=b[/tex]

[tex]B=39\°[/tex]

substitute

[tex]sin(39\°)=b/13[/tex]

solve for b

[tex]b=(13)sin(39\°)[/tex]

[tex]b=8.2\ units[/tex]

step 2

Find the side a

we know that

In the right triangle ABC

The function cosine of angle B is equal to divide the adjacent side angle B (BC) by the hypotenuse (AB)

[tex]cos(B)=BC/AB[/tex]

we have

[tex]AB=c=13\ units[/tex]

[tex]BC=a[/tex]

[tex]B=39\°[/tex]

substitute

[tex]cos(39\°)=a/13[/tex]

solve for a

[tex]a=(13)cos(39\°)[/tex]

[tex]a=10.1\ units[/tex]

step 3

Find the measure of angle A

we know that

In the right triangle ABC

[tex]C=90\°[/tex] ----> is a right angle

[tex]B=39\°[/tex]

∠A+∠B=90° ------> by complementary angles

substitute the given value

[tex]A+39\°=90\°[/tex]

[tex]A=90\°-39\°[/tex]

[tex]A=51\°[/tex]

Answer:

16 un.

Step-by-step explanation:

In right triangle ABC:

m∠C = 90°;

m∠BAC = 2m∠ABC;

BC = 24;

AL is a bisector of angle A.

The sum of the measures of all interior angles in triangle  is always 180°, then

In right triangle the leg that is opposite to tha angle 30° is half of the hypotenuse. This means that

By the Pythagorean theorem,

Let AL be the angle A bisector. By bisector property,

Use the Pythagorean theorem for the right triangle ACL:

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Answer:

AL=24 cm

Step-by-step explanation:

We are given that a triangle ABC,

[tex]m\angle C=90^{circ}[/tex]

[tex]m\angle BAC=2m\angle ABC[/tex]

BC=24 cm

AL is angle bisector

We have to find the value of AL

Let [tex]m\angle ABC=x[/tex]

In triangle ABC

[tex]m\angle BAC+m\angle ABC+m\angle ACB=180^{\circ}[/tex]

[tex]2x+90+x=180[/tex]

[tex]3x=180-90[/tex]

[tex]3x=90[/tex]

[tex]x=\frac{90}{3}=30[/tex]

[tex]m\angle ABC=30^{\circ}[/tex]

[tex]m\angle BAC=2\times 30=60^{\circ}[/tex]

AL is a bisector of angle A

Then [tex]m\angle CAL=30^{\circ}[/tex]

BL=LC=12 cm

In triangle ACL

[tex]sin\theta =\frac{perpendicular side }{hypotenuse}[/tex]

[tex]sin30^{\circ}=\frac{12}{AL}[/tex]

[tex]\frac{12}{AL}=\frac{1}{2}[/tex]

[tex]AL=12\times 2=24 cm[/tex]

Hence, AL=24 cm

Answer:

1. D y = 8

2. C y = −8

Step-by-step explanation:

1.

Both points have y-coordinate 8, so the line is horizontal.

A horizontal line has equation

y = k

where k is the y-coordinate of all of its points.

The y-coordinate of all points on this line is 8.

Answer: y = 8

2.

A line with 0 slope is a horizontal line. All points on a horizontal line have the same y-coordinate.

A horizontal line has equation

y = k

where k is the y-coordinate of all of its points.

The y-coordinate of the given point is -8, so all points must have -8 as the y-coordinate.

Answer: y = -8

The equation of a line through two given points can be found using the point-slope form. A slope of 0 indicates a horizontal line.

To find the equation of a line that contains the points (0, 8) and (8, 8), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). Here, (x1, y1) represents one of the points and m represents the slope. Since the y-coordinates of both points are 8, we can see that the line is horizontal. Therefore, the equation of the line is y = 8.

For the second question, a slope of 0 indicates a horizontal line. The equation of a horizontal line is y = b, where b is the y-coordinate of any point on the line. Since our point is (0, -8), the equation of the line is y = -8.

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Answer:

1. 3x + 6

2. [tex]\frac{99}{14}[/tex] or 7.071

3. [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

1. 3 consecutive even integers

If the first is x, the 2nd is x+2, and the 3rd is x+4

x + (x+2) + (x+4)

= 3x + 6

2. The equation for circumference is

[tex]C=2\pi r[/tex]

If the diameter is [tex]1\frac{4}{5} = \frac{9}{5}[/tex]

The the radius is half of that.

So the circumference is

[tex]\pi * \frac{9}{4} *\frac{1}{2} * 2\\= \pi * \frac{9}{4}\\=\frac{22}{7} * \frac{9}{4}\\= \frac{198}{28}\\ =\frac{99}{14} \\=7.071[/tex]

3. To divide we multiply by the reciprocal.  So flip the fraction that we are dividing by.

[tex]\frac{1}{7} / -\frac{2}{7}\\ = \frac{1}{7} * -\frac{7}{2} \\= -\frac{1}{2}[/tex]

Answer:

$7,434.57

knewton alta 2023

Step-by-step explanation:

Edgar will owe approximately $6,360.92 on his credit card debt in 2 years with continuous compounding.

To calculate the amount Edgar will owe on his credit card debt in 2 years with continuous compounding, we can use the formula for compound interest:

A = P*e^(rt)

Where:

Plugging in the values, we have:

A = $5,000 * e^(0.20*2)

Calculating this expression gives the approximate value of $6,360.92. Therefore, Edgar will owe approximately $6,360.92 on his credit card debt in 2 years with continuous compounding.

Answer: B. It would be shifted up.

Step-by-step explanation: We are changing the last number only. This number determines where the y-intercept is, which is on the vertical axis. Since the number increases by 4, the y-intercept would be shifted up by 4, without changing the slope. Therefore, the answer would be B. It would be shifted up.

Answer:

60,000/ -30,000 (read explanation)

Step-by-step explanation:

8% of 10,000 is 800, 800 x 50(years) = 40,000, 100,000 -40,000 = 60,000, I believe you meant 100,000, cause if not, the answer is -30,000

Hope this helped

Answer:

[tex]\large\boxed{-1\dfrac{1}{2}}[/tex]

Step-by-step explanation:

The points on the graph are collinear (they lie on one straight line).

Therefore, average of change is the same as a slope.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We choose two points and put the coordinates to the formula

[tex](1, 4), (3, 1)\\\\\dfrac{1-4}{3-1}=\dfrac{-3}{2}=-1\dfrac{1}{2}[/tex]

The average rate of change for the sequence given is [tex]-1\frac{1}{2}[/tex].

The average rate of change formula is used to find the slope of a graphed function. To find the average rate of change, divide the change in y-values by the change in x-values.

The points on the graph are collinear (they lie on one straight line).

Therefore, average of change is the same as a slope.

The formula of a slope:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

We choose two points and put the coordinates to the formula

(1, 4), (3, 1)

[tex]\frac{1-4}{3-1} =\frac{-3}{2} =-1\frac{1}{2}[/tex]

The average rate of change for the sequence given is [tex]-1\frac{1}{2}[/tex].

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Answer:

$2322.59

Step-by-step explanation:

Given

mortgage amount=$470,000

Interest rate annually=4.6%

Time=30 years

Monthly payments=?

Formula to apply

[tex]M=\frac{P(1+r)^n*r}{(1+r)^n-1}[/tex]

where

M=monthly payment for the mortgage

P=Principal amount =$470,000

i=rate per month=4.6÷12=0.3833%

n=30×12=360

Applying the formula

[tex]M=\frac{P(1+r)^n*r}{(1+r)^n-1} \\\\\\M=\frac{470000(1+0.004)^{360}*0.004 }{(1+0.004)^{360} -1} \\\\\\M=\frac{7452.235}{3.209} =2322.59[/tex]

Answer:

Third choice.

Step-by-step explanation:

Trinomial means you have 3 terms.

You don't have 3 terms in first two choices so let's not look at them.

Anything of the form [tex]a^2x^2+2abxy+ b^2y^2[/tex] is a perfect square trinomial because it can be written as [tex](ax+by)^2[/tex].

Let's this this:

[tex](ax+by)^2[/tex]

[tex](ax+by)(ax+by)[/tex]

Now foil!

First=ax(ax)=a^2x^2

Outer=ax*by=abxy

Inner=by*ax=abxy

Last=by*by=b^2y^2

Add together and this gives you a^2x^2+2abxy+b^2y^2.

So looking at third choice you can write it as 4^2x^2+24xy+3^2y^2.

Is 2*4*3 equal to 24?  If it is then you have your answer. It is.

We have our answer.

Answer: y=-16

Step-by-step explanation:

Y/-2+5=13

Y/-2=8

Y=-16

Answer:

[tex]\large\boxed{(n^3)^2\times(n^5)^4=n^{26}}[/tex]

Step-by-step explanation:

[tex](n^3)^2\times(n^5)^4\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=(n^{3\cdot2})\times(n^{5\cdot4})=n^{6}\times n^{20}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\=n^{6+20}=n^{26}[/tex]

Answer:

360

Step-by-step explanation:

Answer:

39 tables

Step-by-step explanation:

Given:

third grade= 134

fourth grade=167

total=134+167=301

Now no. of students is 7 times no. of adults,

no. of adults= 301/7

                    =43

Total no. of people =301+43

                                 =344

Each picnic table can seat 9 people, so

No. of tables for 344 people= 344/9

                                              =38.222

39 tables picnic tables will need to be set up for the picnic!

Answer:

[tex]x_{1=} \frac{-1+i\sqrt{35} }{6} \\\\x_{2=} \frac{-1-i\sqrt{35} }{6}[/tex]

Step-by-step explanation:

Using the quadratic formula:

[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]

We will have two solutions:

[tex]x_{1}\\ x_{2}[/tex]

-3x^2-x-3=0     a=-3    b=-1   c=-3

We have:

[tex]x_{1}=\frac{1+\sqrt{-35} }{-6}\\\\x_{2}=\frac{1-\sqrt{-35} }{-6}\\[/tex]

we can write:

[tex]x_{1}=\frac{-1+\sqrt{-35} }{6}\\\\x_{2}=\frac{-1-\sqrt{-35} }{6}\\[/tex]

The solutions are not real numbers.

So, we know: [tex]i=\sqrt{-1}[/tex]

Finally we have:

[tex]x_{1}=\frac{-1+i\sqrt{35} }{6}\\\\x_{2}=\frac{-1-i\sqrt{35} }{6}\\[/tex]

Answer:

[tex]y=\frac{1}{30}(x-7)+1.5[/tex]

2.8 million is what we get in 2047

Step-by-step explanation:

Ok I see the following given in 2007, the medium salary is 1.5 million and in 2013 the medium salary is 1.7 million.

It says let x=7 represent 2007 so that means x=13 would represent 2013.

It also says y is in millions so y=1.5 means 1.5 million and y=1.7 means 1.7 million.

So we have these points that we need to find a line for:  (7,1.5) and (13,1.7).

The slope can be found by using the slope formula given two points.  This looks like this (y2-y1)/(x2-x1).

I like to line the points up and subtract then put 2nd difference over 1st difference.

Let's do that.

(13, 1.7)

-(7, 1.5)

-----------

6       .2

The slope is .2/6 or 2/60 (after multiplying top and bottom by 10) or 1/30 (after dividing top and bottom by 2)

So point slope form for this line is [tex]y-1.5=\frac{1}{30}(x-7)[/tex].

To get the point slope form for this line I just entered my m (the slope) and point (x1,y1) I knew on the line (like (7,1.5) ). Point slope form is [tex]y-y_1=m(x-x_1)[/tex].

So adding 1.5 on both sides of  [tex]y-1.5=\frac{1}{30}(x-7)[/tex] gives me  [tex]y=\frac{1}{30}(x-7)+1.5[/tex]

So now it says what is the medium salary in 2047 I believe. So we are going to plug in 47.

This gives us

[tex]y=\frac{1}{30}(47-7)+1.5[/tex]

[tex]y=\frac{1}{30}(40)+1.5[/tex]

[tex]y=\frac{4}{3}+1.5[/tex]

[tex]y=2.833333333333333333333333[/tex]

So 2.8 million

Set up an equation:

Numerator is the top number and denominator is the bottom number in a fraction.

(6x)^5 / d = 36

(6x)^5 can be rewritten as 6^5x^5

6^5x^5 / d = 36

Raise 6 tot he power of 5:

7776x^5 /d = 36

Multiply both sides by d:

7776x^5 = 36d

Divide both sides by 36:

d = 7776x^5 / 36

d = 216x^5

Check the picture below.

Answer:

6^(32)

Also I don't see your choices.

Step-by-step explanation:

I'm going to apply this law of exponents: (x^a)^b=x^(a*b).

It justs says to multiply the exponents in this case so we have 6^(-8*-4)=6^(32).

Answer:

It would be 1/6^32

Step-by-step explanation:

Answer:

Step-by-step explanation:

x^2 - 36 is the difference of two squares and factors as follows:

        (x - 6)(x + 6)

x^2 - 16 is the difference of two squares and factors as follows:

        (x - 4)(x + 4)

x^2 - 7x + 12 is an easily factored quadratic; the factors are

         (x - 3)(x - 4)

x^2 - x - 20 is an easily factored quadratic; the factors are

         (x - 5)(x + 4)

I conclude that none of the four expressions is prime.

Answer:

B. [tex]x^2+16[/tex]

Step-by-step explanation:

We are asked to find the prime polynomial from our given choices.

We know that a polynomial is prime, when it has only two factors that are 1 and polynomial itself.

Upon looking at our given choices, we can see that each polynomial can be factored except [tex]x^2+16[/tex].

We can see that [tex]x^2+16[/tex] is sum of squares and sum of squares cannot be factored, therefore, polynomial [tex]x^2+16[/tex] is a prime polynomial.

Answer:

93

Step-by-step explanation:

A quadrilateral's 4 angles add to 360 degrees

70 + 92+<1 + 105 = 360

Combine like terms

267 + <1 = 360

Subtract 267 from each side

267-267 + <1 = 360-267

<1 = 93

Answer:

93

Step-by-step explanation:

OK it's simple...

The interior angles of ANY quadrilateral (a shape with 4 sides) add up to 360.

So all you have to do is add up the angles you already know (70+92+105=267) and subtract that from 360. (360-267).

Answer:

R(- 12, 22 )

Step-by-step explanation:

Using the midpoint formula

[tex]\frac{1}{2}[/tex](8 + [tex]x_{R}[/tex] ) = [tex]x_{M}[/tex] = - 2

Multiply both sides by 2

8 + [tex]x_{R}[/tex] = - 4 ( subtract 8 from both sides )

[tex]x_{R}[/tex] = - 12

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

[tex]\frac{1}{2}[/tex](- 10 + [tex]y_{R}[/tex] ) = [tex]y_{M}[/tex] = 6

Multiply both sides by 2

- 10 + [tex]y_{R}[/tex] = 12 ( add 10 to both sides )

[tex]y_{R}[/tex] = 22

The coordinates of R = (- 12, 22 )

Answer:

Terry has 20 quarters and 18 dimes

Step-by-step explanation:

Let

x -----> the number of quarters

y ----> the number of dimes

Remember that

1 quarter=$0.25

1 dime=$0.10

we know that

x=y+2 ----> equation A

0.25x+0.10y=6.80 -----> equation B

Substitute equation A in equation B and solve for y

0.25(y+2)+0.10y=6.80

0.25y+0.50+0.10y=6.80

0.25y+0.10y=6.80-0.50

0.35y=6.30

y=18 dimes

Find the value of x

x=y+2 -----> x=18+2=20 quarters

therefore

Terry has 20 quarters and 18 dimes

To determine the number of quarters and dimes Terry has, set up two equations based on the information provided, solve one of the equations for one variable, and substitute this into the second equation. Solve the equation to get the number of dimes and substitute it into the first equation to get the number of quarters.

To solve this, we can use algebra, setting up equations to represent the problem and then solve it.

Let F represent the number of dimes (since a dime is worth $0.10) and let Q represent the number of quarters (since a quarter is worth $0.25). We have two key pieces of information:

From the first equation, we can substitute F + 2 for Q in the second equation: 0.10F + 0.25(F + 2) = 6.80.

Solve this equation to find the value of F, representing the number of dimes, Terry has. Then, substitute the value of F into the first equation to determine the number of quarters Terry has.

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Answer:

Given a function f(x), the function f(x) + k will be translated k units down if k<0. In this case, if we want to produce a vertical translation by 4 units down of the function f(x) = 2x, therefore the new function is:

f(x) = 2x - 4.

Now, we can graph the function like we normally do. Attached you will find the graph made with the help of a graphing calculator.

Answer:

0.5

Step-by-step explanation:

there are 26 black cards

26/52=

0.5

Answer:

0.5

Step-by-step explanation:

A deck of cards has 52 cards. Out of which 26 are red and 26 are black. The black cards are further divided into two suits.

So,

total sample space = n(S) = 52

Let A be the event that the drawn card is a black card

Then,

n(A) = 26

So, the probability of A will be:

[tex]P(A) = \frac{n(A)}{n(S)}\\ = \frac{26}{52}\\ =\frac{1}{2}\\ =0.5[/tex]

Hence the theoretical property of drawing a black card is 0.5 ..

[tex]\huge{\boxed{y=-3x+4}}[/tex]

Slope-intercept form is [tex]y=mx+b[/tex], where [tex]m[/tex] represents the slope and [tex]b[/tex] represents the y-intercept.

Substitute in the values. [tex]\boxed{y=-3x+4}[/tex]

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

In this case the slope (m) is -3 and the y-intercept (b) is 4

Your equation is:

y = -3x + 4

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

(a + b)(a + b - 2c)

Step-by-step explanation:

Note that

(a + b)² = a² + b² + 2ab

Given

a² + b² + 2(ab - ac - bc) ← distribute parenthesis

= a² + b² + 2ab - 2ac - 2bc

= (a + b)² - 2ac - 2bc ← factor out - 2c from each term

= (a + b)² - 2c (a + b) ← factor out (a + b) from each term

= (a + b) [ a + b - 2c ]

= (a + b)(a + b - 2c) ← in factored form

The expression a² + b² + 2(ab - ac - bc) cannot be factorized using standard factorization techniques over real numbers, as a² + b² is not factorizable over the reals and there's no common factor for all terms.

To factorize the expression a² + b²+ 2(ab - ac - bc). To factorize this, we will look for a common factor and regroup the terms. Let's see if there's a way to rearrange the terms to resemble a known pattern or factor by grouping.

First, let's rewrite the expression by grouping terms with a common factor:

a² + 2ab - 2ac

b² - 2bc

However, we notice that the expression does not fit into a perfect square or any other easily factorizable form like (a + b)² or (a - b)² due to the nature of the terms a², b², and 2(ab - ac - bc). The expression is already in its simplest factored form as it stands because a²+ b² is not factorizable over the real numbers, and there's no common factor for all terms.

Therefore, the expression a² + b² + 2(ab - ac - bc) does not factorize further using real numbers and the usual factorization techniques.

Answer:

Yes.

Step-by-step explanation:

If we add a fixed number to each term of an arithmetic sequence, we are still going to be having an arithmetic sequence.

For example, given the following sequence:

1, 3, 5, 7, 9, 11...

The difference between consecutive terms  is 2, therefore the pattern is adding two to the previous term.

If we add a fix number, let's say '3':

1+3, 3+3, 5+3, 7+3, 9+3, 11+3...

4, 6, 8, 10, 12, 14...

We notice that the pattern is the same, and it's still an arithmetic sequence.