Find the slope of a line perpendicular to a line through the given points. E(5, 7), F(3, 1)

Answer:

Step-by-step explanation:

Givens

x intercept =

The vertex is at 3, 4

The vertex is upside down.

Solution

(x - 1) and (x - 5) produce the two roots.

There must be 1 minus somewhere so that the quadratic goes upside down.

Answer

y = - (x -1)(x - 5)

Answer:

The range of the function f(x) :  is y > 0.

The correct option is (A)

Step-by-step explanation:

The definition of range is the set of all possible values that the function will give when we give in the domain as input.

Given function is :

If we draw the graph for this, then we can see that the horizontal asymptote is 0.

So,  the range is real numbers higher than 0.

Hence, the range should be y > 0.

Answer: 3/4

Step-by-step explanation:

The monthly payment for purchasing the home will be $457.85.

The term loan refers to a sort of credit vehicle in which a sum of money is lent to another party in exchange for the value or principal amount being repaid in the future.

Then the formula of monthly payment (MP) will be

[tex]\rm MP = P \times \dfrac{r(1+r)^n}{(1+r)^n - 1}\\[/tex]

In order to purchase a home, a family borrows $110,000 at 2.9% for 30 years.

We have

P = $110,000

r = 0.029 / 12 = 0.0024

n = 30 × 12 = 360

Then the monthly payment will be

[tex]\rm MP = 110,000\times \dfrac{0.0024(1+0.0024)^{360}}{(1+0.0024)^{360} - 1}\\\\[/tex]

On further solving, we have

MP = 110000 × 0.0024 × 1.723

MP = $ 457.85

More about the monthly payment link is given below.

https://brainly.com/question/14064255

#SPJ1

I consider the original fraction: x/y.

If the numerator "x" increases by 20%, it can be interpreted in this way:

"x" represents 100% (the unit) and when increasing by 20% we have that the value of "x" becomes 120%

120% of "x" is [tex]\bf{\frac{120*x}{100}=1,2x }[/tex]

This is what we have left in the numerator.

By the same reasoning, in the denominator "y" remains:

100% - 40% = 60% of "and"

60% of "y" is...[tex]\bf{\frac{60*y}{100}=0.6 y }[/tex]

The new fraction is: 1,2x / 1,6y.

...simplifying by dividing top and bottom by 0.6,... 2x / y

To find out the percentage by which the original fraction has changed, we first find the relationship or ratio between the original fraction and the new fraction with the fraction quotient:

[tex]\bf{\dfrac{\frac{2x}{y} }{\frac{x}{y} }=\frac{2xy}{xy}=2 }[/tex]

... that is to say that the new fraction has doubled in relation to the original.

Therefore, the percentage of variation per increase is 100%.

Answer:

0.9668 USD

Step-by-step explanation:

1 USD=1.0343 AUD 1AUD=0.9668 USD.

Answer:

29a² - 3a - 12

Step-by-step explanation:

Given expression:

(6a+2)(6a-5)-(7a-1)(a-2)

Solution:

Apply distributive property.

[tex] \rm=(6a)(6a)+(6a)(-5)+(2)(6a)+(2)(-5)-7a^2+15a-2[/tex]

[tex] \rm= 36a {}^{2} - 30a + 12a - 10 - 7a {}^{2} + 15a - 2[/tex]

Combine like terms:

[tex] \rm=(36a {}^{2} - 7a {}^{2} )+( - 30a+12a+15a)+( - 10 - 2)[/tex]

[tex] = \boxed{ \rm \: 29a {}^{2} - 3a - 12}[/tex]

Done!

The value of [tex]38 \frac{22}{75} + 3\frac{11}{15}[/tex] is [tex]42\frac{2}{75}[/tex]

The summation expression is given as:

[tex]38 \frac{22}{75} + 3\frac{11}{15}[/tex]

Rewrite as:

[tex]38 + 3 + \frac{22}{75} + \frac{11}{15}[/tex]

Evaluate the sum and take LCM

[tex]41 + \frac{22 + 5 * 11}{75}[/tex]

Evaluate the sum

[tex]41 + \frac{77}{75}[/tex]

Express as mixed number

[tex]41 + 1\frac{2}{75}[/tex]

Add

[tex]42\frac{2}{75}[/tex]

Hence, the value of [tex]38 \frac{22}{75} + 3\frac{11}{15}[/tex] is [tex]42\frac{2}{75}[/tex]

Read more about fractions at:

https://brainly.com/question/11562149

#SPJ1

Answer:

48π

Step-by-step explanation:

→ State the formula for the surface area of a a cylinder

2π × r × h + 2π × r²

→ Substitute in the numbers

2π × 3 × 5 + 2π × 3²

→ Simplify

48π

The correct answer is A.

Step - by - step answer:

Mario will travel a distance equal to 1 circumference of the wheel for each complete revolution of the wheel.

Circumference of Mario's wheel, C = πD, where D is the diameter of the circle.

Hence, C = 26π inches

Speed = Distance / Time

Distance for 200 revolutions in ft = 26π x 200 x 1/12

Time in sec = 60

So, speed =  (26π x 200)/(12 x 60)

= 65π/9

=22.69 is the average speed.

P.s: Answer is copied from https://www.myactguide.com/math/mario-was-riding-a-bicycle-with-wheels-26-inches-in-diameter

Answer:

Option C.  [tex]g(x)=(\frac{1}{3}x)^2[/tex]

Step-by-step explanation:

Given a function to start with, extra operations that are done outside of the given function, cause vertical transformations, whereas operations that are done inside of the function cause horizontal transformations.

Transformations on the outside

Ex. [tex]g(x)=(x^2)-3[/tex]  is subtracting 3 outside, so its transformation is vertical.

Transformations on the inside

Ex. [tex]g(x)=(x-7)^2[/tex] is subtracting 7 inside, so its transformation is horizontal.

For any function, stretches or compressions occur by multiplying by positive numbers larger or smaller than 1.

Multiplying by numbers larger than one, quantities get larger, and multiplying by a positive number less than one, quantities get smaller.

For example, [tex]\$10*2 = \$20[/tex], but [tex]\$10*\frac{1}{2} = \$5[/tex]

For transformations, this intuition needs a small modification:

Multiplying on the outside

When multiplying outside of the function, things outside happen normally, and since it is happening outside, it is in a vertical direction.

Ex. Multiplying outside by 3, things get larger (stretch) vertically to 3 times as much as (300% of) normal (away from a height of zero).

Multiplying outside by [tex]\frac{1}{2}[/tex] , things get smaller (compress) vertically down to [tex]\frac{1}{2}[/tex] as much as (50% of) normal (toward a height of zero).

"g" is lower than "f", so it may have been compressed vertically (see alternative solution at end).

Looking at the only options with multiplication outside (A & B), option B multiplies by 3 (greater than 1), so it would stretch "f" even taller.

Option A, does compress "f" vertically (by 1/3), but doesn't compress it enough to arrive at the point (3,1) defined on function "g". Note ordered pair (3,1) on "g", meaning when you input "3", you get out "1".  

Putting 3 into the "f" function, f(3)=9.  Since one-third (the transformation in Option A) of 9 is 3, not 1, Option A doesn't compress "f" enough.

Multiplying on the inside

When multiplying inside, transformations happen horizontally, and inside things happen "backwards".

So, if multiplying inside by 4, (...normally things get bigger...) things actually get smaller (compressed) horizontally, reduced to 1/4 (the reciprocal of 4) the size (toward a horizontal distance of zero).

If multiplying by a number less than one (but positive), like [tex]\frac{1}{3}[/tex] , (...things normally get smaller...) things will actually get larger (stretch) in the horizontal direction out to triple (the reciprocal of [tex]\frac{1}{3}[/tex]) as much as normal.

Looking options C & D (where multiplication happens inside), both have multiplication by a positive number less than one (... normally would make things smaller...), which will stretch "f" out horizontally.

Looking at the red point (3,1), the blue function does have a height-matched point at (1,1).

Measuring horizontal distances, (3,1) is 3-units from the y-axis, whereas (1,1) is only 1-unit away.  Thus, the "g" is 3 times as far as "f", meaning a horizontal stretch outward by 3.

Answer C multiplies inside by [tex]\frac{1}{3}[/tex], so it actually makes things 3 times bigger horizontally.

The correct answer is option C.

To verify, from (3,1), put 3 into the option C g(x) --  it gives "1" as an output.

[tex]g(x)=(\frac{1}{3}x)^2\\g(3)=(\frac{1}{3}(3))^2\\g(3)=(1)^2\\g(3)=1\\[/tex]

This function could have been compressed vertically to obtain the red graph.

Note that f(3)=9.

The point (3,1), on the red function, is only at a height of 1 ... 1/9th the height of the blue function.  We could compress the "f" vertically by 1/9th to transform the blue function into the red function.

Vertical transformations come from operations outside, and outside things behave "normally", so to vertically compress by 1/9th, just multiply on the outside by 1/9th.

Thus, an alternative answer to transform f(x) to g(x) is [tex]g(x)=\frac{1}{9}(x^2)[/tex]

Two last things:

Simplifying this function we just obtained we get [tex]g(x)=\frac{1}{9}x^2[/tex]

Returning to the function that we chose for our answer in option C, [tex]g(x)=(\frac{1}{3}x)^2[/tex]

[tex]g(x)=(\frac{1}{3}x)(\frac{1}{3}x)[/tex]

[tex]g(x)=\frac{1}{9}x^2[/tex]

Note that the transformation answer for this problem (Option C) and our alternative solution both simplify and match perfectly, so they both represent the same end result.

Step-by-step explanation:

2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)

2x+4+5x+25=4x-32+2x-4

7x+29=6x-36

7x-6X=-36-29

X=-65

Answer:

x = -65

Step-by-step explanation:

2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2) ​

Distribute:

2(x + 2): 2x + 4

5(x + 5): 5x + 25

=

4(x - 8): 4x - 32

2(x - 2): 2x - 4

Combine like terms:

(2x + 4) + (5x + 25) = (4x - 32) + (2x - 4)

5x + 2x: 7x              =  4x + 2x: 6x

4 + 25 = 29             =  -32 - 4: -36

7x + 29 = 6x - 36

Now we want to separate like terms,

subtract 29 from both sides

subtract 6x from both sides

7x + 29 - 29 - 6x = 6x - 29 - 6x- 36

7x - 6x = - 29 - 36

x = -65

Answer:

1277

Step-by-step explanation:

350 * (1.04)^33 =

1276.93338385

algebracom

theo(12211)

Answer:

[tex]20a^3b^3[/tex]

Step-by-step explanation:

Binomial Series

[tex](a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n[/tex]

Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Example:  4! = 4 × 3 × 2 × 1

Therefore, the fourth term in the binomial expansion (a + b)⁶ is:

[tex]\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3[/tex]

[tex]\implies \dfrac{6!}{3!(6-3)!}a^{6-3}b^3[/tex]

[tex]\implies \dfrac{6!}{3!3!}a^{3}b^3[/tex]

[tex]\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3[/tex]

[tex]\implies \left(\dfrac{120}{6}\right)a^{3}b^3[/tex]

[tex]\implies 20a^3b^3[/tex]

Answer:

All the possible zeroes of the polynomial: f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex] are  ±1 , ±2 ,  ±4 ,  ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex]  , ±[tex]\frac{4}{3}[/tex] by using rational zeroes theorem.

Step-by-step explanation:

Rational zeroes theorem gives the possible roots of polynomial f(x) by taking ratio of p and q where p is a factor of constant term and q is a factor of the leading coefficient.

The polynomial f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex]

Find all factors (p) of the constant term.

Here we are looking for the factors of 4, which are:

±1 , ±2 and ±4

Now find all factors (q) of the coefficient of the leading term

we are looking for the factors of 3, which are:

±1 and ±3

List all possible combinations of ± [tex]\frac{p}{q}[/tex]  as the possible zeros of the polynomial.

Thus, we have ±1 , ±2 ,  ±4 ,  ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex]  , ±[tex]\frac{4}{3}[/tex] as the possible zeros of the polynomial

Simplify the list to remove and repeated elements.

All the possible zeroes of the polynomial: f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex] are  ±1 , ±2 ,  ±4 ,  ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex]  , ±[tex]\frac{4}{3}[/tex]

Learn more about Rational zeroes theorem here -https://brainly.ph/question/24649641

#SPJ10

Answer:

0.5

Step-by-step explanation:

well you can just take one of the sides and in this case I'll use AC which originally is 8 and then in AC prime it's 4. You can simply divide the new length by the original length which is 4/8 or 0.5. So if you multiply any of the original side lengths by 0.5 you'll get the new side length.

Answer:

1/2

Step-by-step explanation:

edge 23

0.21094 is the probability that the surgery is successful on exactly 3 patients.

It is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

According to the given question,

Let Y = The number of patients who respond yes: [tex]Y - Bin (n,p)[/tex]

Given , [tex]n = 4 , p = 0.75 , q = 1 - p = 0.25[/tex]

[tex]P (Y = 3) = \left(\begin{array}{ccc}4\\3\\\end{array}\right) (0.75)^{2}(0.25)^{4-3} \\ = 0.21094\\\\[/tex]

The probability that the surgery is successful on exactly 3 patients is 0.21094

Learn more about Probability here:

https://brainly.com/question/23345093

#SPJ1

Answer:

width is 30, and the length 69.

Step-by-step explanation:

In order to do this, we need to do ALGOOBRAA

lets say x is equal to the width of the room

then, that means the length is (9+2x) Sooooo,

198=2x+2(9+2x)

Using the distributive property, we know that

2(9+2x)=18+4x

If you dont know what that is, then go search it up :/

so,

198=2x+18+4x

198=6x+18

180=6x

30=x

BAM

Now, we know that the width is 30, bro.

That means the length is 60+9, Which is 69.

Therefore, the width is 30, and the length 69.

Sry if im wrong btw.

The width of rectangle is 30, and the length is 69.

A rectangle is a quadrilateral. The opposite sides of a rectangle are equal and parallel to each other. The interior angle of a rectangle at each vertex is 90°. The sum of all interior angles is 360°. The diagonals bisect each other.

Here, lets say x is equal to the width of the room

then, that means the length is (9+2x) So,

              198 = 2x+2(9+2x)

Using the distributive property, we know that

                 2(9+2x)=18+4x

If you don't know what that is, then go search it up :/

so,

               198 = 2x+18+4x

                198=6x+18

                 180=6x

                  30=x

Now, we know that the width is 30,

That means the length is 60+9, Which is 69.

Thus, the width of rectangle is 30, and the length is 69.

Learn more about Rectangle from:

https://brainly.com/question/15019502

#SPJ1

Answer:

70%

$571.41

Step-by-step explanation:

100% means 1, or a whole thing.

Since the discount is 30% of the original price, and the original price is 100% of the original price, then

100% - 30% = 70%

With a 30% discount, you actually pay 70% of the original price.

$399.99 is 70% of the original price.

399.99 / 70% = x / 100%

70x = 100 × 399.99

x = 571.41

The original price was $571.41.

Answer:

franchise fast-food restaurant located in the Northeast specializing in halfpound hamburgers, fish sandwiches, and chicken sandwiches. Soft drinks and French fries are

also available. The planning department of Bun-and-Run Inc. reports that the distribution of

daily sales for restaurants follows the normal distribution and that the population standard

deviation is $3,000. A sample of 40 showed the mean daily sales to be $20,000. Find the 95%

confidence interval for the population mean.

Answer:

Approximately $594.38

Step-by-step explanation:

Use the formula: y = a(1 + r)^t
a is the initial amount
r is the percent of interest in decimal form
t is the time in years
y is the money after t years

Substitute the values given in the problem into the equation:
400(1+0.02)^20
Use a calculator or solve manually
Around 594.38

Answer:

Polynomial, 6. Constant. The highest value of the exponent in the expression is known as the Degree of Polynomial. The degree of a polynomial is the largest exponent. It is also known as an order of the polynomial. While finding the degree of the polynomial, the polynomial powers of the variables should be either in ascending or descending order.

Step-by-step explanation:

A term is defined as a part of an equation separated by a +/- operation. Because there is a + operation separating two terms (-x^6 and 7x^5), the expression is a binomial, meaning the expression has two terms.

The highest exponent or degree, present in the expression is to the power of 6. Therefore, the expression is in the sixth degree.

Taken together, the expression is a sixth-degree binomial.

The options are not mentioned , but the correct graph is plotted and attached with the answer.

A function is a mathematical statement that relates a dependent variable with an independent variable .

It is given to find among the options which is the correct graph for

y = log₃ (x-1)

The options are not mentioned , but the correct graph is plotted and attached with the answer.

To know more about Function

https://brainly.com/question/12431044

#SPJ1

Therefore, the equation of the hyperbola with a given origin has vertices at (0, ±9) and foci at  (0, ±10) is [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].

Given, that a hyperbola centred at the origin has vertices at (0, ±9)  and foci at  (0, ±10).

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

The formula for a hyperbola centred at the origin is [tex]\frac{(x-h)^{2} }{a^{2} } -\frac{(y-k)^{2} }{b^{2} } =1[/tex]

Where (h, k) is the center = (0, 0)

Distance from centre to vertices a = 9 ⇒ a² = 81

Distance from centre to vertices which is given from the foci c = 10

⇒ c² = 100

Using the Pythagorean formula, c²= a²+ b²

Substituting the values 100 = 81 + b²

So we get, b²= 100 - 81 = 19

Substituting the values in the standard form [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].

Therefore, the equation of the hyperbola with a given origin has vertices at (0, ±9) and foci at  (0, ±10) is [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].

To learn more about hyperbola visit:

brainly.com/question/27799190.

#SPJ1

Answer:

see the attachment photo!

The interest rate will be equal to 24% in 2 years.

Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-

Given that:-

The interest rate will be calculated by using the following formula:-

[tex]A = P[1+\dfrac{r}{n}]^{nt}[/tex]

[tex]50=32[1+\dfrac{r}{1}]^{2}[/tex]

[tex]\dfrac{50}{32}=(1+r)^2[/tex]

1.56 = ( 1 + r )²

√1.56 = ( 1 + r )

r = 1.24 - 1

r = 0.24

r = 24%

Therefore  interest rate will be equal to 24% in 2 years.

To know more about Compound interest follow

https://brainly.com/question/24924853

#SPJ1

Answer:

Step-by-step explanation:

current total of hours work earnings (7hrs): $140

total earnings: $980 per week

49 hours work per week (no overtime)

immagine you're working another 4 hours for overtime payment everyday:
current total of hours work earnings (11hrs): $280 including 4 hours overtime ($120)

total working hours: 77 hours per week

total earnings: $1,960 per week

The value of x, y and z will be 1, 5 and 2 respectively

An augmented matrix in linear algebra is a matrix created by joining the columns of two supplied matrices, often so that the same basic row operations may be applied to each of the given matrices individually.

Lets write the augmented matrix by writing the coefficients of all the variables:

3      -4    -5      -27              Row 1

5        2     -2      11               Row 2

5       -4      4      -7               Row 3

We need to get

1   0   0

0   1    0

0   0   1

then the values of x, y, and z will be in the last column.

The row operation (R1=R1/3) is used to get the identity matrix.

1      -4/3    -5/3      -9              Row 1

5        2        -2      11               Row 2

5       -4        4      -7               Row 3

Add row 2 to row 1 and multiply by 5 (R2=R2(5)R1).

1      -4/3      -5/3      -9              Row 1

0     26/3      19/3     56              Row 2

5       -4             4      -7               Row 3

Add row 3 to row 1 and multiply by 5 (R3=R3(5)R1).

1      -4/3      -5/3      -9              Row 1

0     26/3      19/3     56              Row 2

0      8/3       37/3    38               Row 3

Multiply row 2 by 326 (R2=(3/26)R2)

1      -4/3      -5/3        -9              Row 1

0     1       19/26    84/13              Row 2

0      8/3       37/3    38               Row 3

Add row 2 multiplied by 4/3 to row 1 (R1=R1+(4/3)R2)

1      0        -9/13     -5/13              Row 1

0     1       19/26    84/13              Row 2

0      8/3       37/3    38               Row 3

Add row 3 to row 2 and multiply the result by 8/3 (R3=R3(8/3)R2).

1      0        -9/13     -5/13              Row 1

0     1       19/26    84/13              Row 2

0    0       135/13    270/13           Row 3

Multiply row 3 by 13/135 (R3=(13/135)R3)

1      0        -9/13     -5/13              Row 1

0     1       19/26    84/13              Row 2

0    0          1         2                    Row 3

Add row 3 multiplied by 9/13 to row 1 (R1=R1+(9/13)R3)

1      0       0            1                  Row 1

0     1       19/26    84/13              Row 2

0    0          1         2                    Row 3

Row 2 is reduced by row 3 multiplied by 19/26 (R2=R2(19/26)R3).

1      0       0            1                  Row 1

0     1          0          5                 Row 2

0    0          1         2                    Row 3

Hence the value of x, y and z will be 1, 5 and 2 respectively

Learn more about augmented matrix here:

https://brainly.com/question/12994814

#SPJ10