Which of the following vectors are orthogonal to (2,1)? Check all that apply.
A. (1,-2)
B. (-3,6)
C. (1,2)
D. (-2,-3)

Answer:

[tex]y=x^{2} -\frac{48}{7}x+\frac{64}{7}[/tex]

Step-by-step explanation:

step 1

Find the roots of the quadratic equation

we know that

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]x^{2} -6x+7=0[/tex]  

so

[tex]a=1\\b=-6\\c=7[/tex]

substitute in the formula

[tex]x=\frac{6(+/-)\sqrt{-6^{2}-4(1)(7)}} {2(1)}[/tex]

[tex]x=\frac{6(+/-)2\sqrt{2}} {2}[/tex]

[tex]x=3(+/-)\sqrt{2}[/tex]

[tex]x1=3(+)\sqrt{2}[/tex]

[tex]x2=3(-)\sqrt{2}[/tex]

The roots of the equation are a and b

so

[tex]a=3(+)\sqrt{2}[/tex]

[tex]b=3(-)\sqrt{2}[/tex]

step 2

Find a quadratic equation with roots a+1/b and b + 1/a

so

[tex]a+\frac{1}{b} =(3+\sqrt{2})+\frac{1}{3-\sqrt{2}} =\frac{9-2+1}{3-\sqrt{2}} =\frac{8}{3-\sqrt{2}}=\frac{8}{3-\sqrt{2}}*(\frac{3+\sqrt{2}}{3+\sqrt{2}})=\frac{8}{7}(3+\sqrt{2})[/tex]

[tex]b+\frac{1}{a} =(3-\sqrt{2})+\frac{1}{3+\sqrt{2}} =\frac{9-2+1}{3+\sqrt{2}} =\frac{8}{3+\sqrt{2}}=\frac{8}{3+\sqrt{2}}*(\frac{3-\sqrt{2}}{3-\sqrt{2}})=\frac{8}{7}(3-\sqrt{2})[/tex]

The quadratic equation is equal to

[tex]y=(x-\frac{8}{7}(3+\sqrt{2}))(x-\frac{8}{7}(3-\sqrt{2}))[/tex]

[tex]y=x^{2} -\frac{8}{7}(3-\sqrt{2})x-\frac{8}{7}(3+\sqrt{2})x+\frac{64}{49}(7)[/tex]

[tex]y=x^{2} -\frac{48}{7}x+\frac{64}{7}[/tex]

Answer:

Step-by-step explanation:

The length is described as 4(-9 +w/2), which simplifies to 2w-36. The area is the product of length and width, so is ...

  Area = width×length

  126 = w(2w -36) = 2w² -36w

__

This equation can be divided by 2, then the square completed to give ...

  w² -18w = 63

  w² -18w +81 = 144 . . . . add 81 to complete the square

  (w -9)² = 12² . . . . . . . . . show as squares

  w -9 = 12 . . . . . . . . . . . . take the positive square root

  w = 12 +9 = 21

The width of the placemat is 21 inches.

Answer:

[tex]126in^2=2w^2-36w[/tex] and w= 21 inches.

Step-by-step explanation:

The placemat has an area of [tex]126in^2[/tex]. Now, let's call w to the width, the exercise says that the length of the placemat is four times the quantity of nine less than half its width, that is

length = 4(w/2-9).

Now, the area is length*width, so

[tex]A=w*4(\frac{w}{2}-9)= \frac{4w^2}{2}-36w = 2w^2-36w.[/tex]

and we know that [tex]A=126in^2[/tex], so

[tex]126in^2=2w^2-36w.[/tex]

Now, let's find the solution.

[tex]2w^2-36w-126=0[/tex] is a quadratic formula of the form [tex]ax^2+bx+c[/tex] with a=2, b= -36 and c = -126. The solutions will be

[tex]w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]w=\frac{-(-36)\pm\sqrt{36^2-4(2)(-126)}}{2a}[/tex]

[tex]w=\frac{36\pm\sqrt{1296+1008}}{2*2}[/tex]

[tex]w=\frac{36\pm\sqrt{2304}}{4}[/tex]

[tex]w=\frac{36\pm48}{4}[/tex]

[tex]w=\frac{36+48}{4}[/tex] or [tex]w=\frac{36-48}{4}[/tex]

[tex]w=\frac{84}{4}[/tex] or [tex]w=\frac{-12}{4}[/tex]

as we are searching a distnace, we are going to use the positive solution, that is

[tex]w=\frac{84}{4}= 21.[/tex]

Then, the width is 21 inches.

Answer:

That's [tex] y = \ln x[/tex]

Step-by-step explanation:

[tex]f(1) = \ln 1 = 0[/tex]

[tex]f(e) = \ln e = 1[/tex]

[tex]f(1/e) = \ln (1/e) = -1[/tex]

Seems right.

The angle measure of GIH is 35 degrees. The corresponding angles theorem guarantees that when two angles are formed by intersecting lines and share the same endpoints at an arc, they will have equal measures.

Since angles HJG and GIH contain the same endpoints at arc GH, they are corresponding angles formed by intersecting lines with a transversal. According to the corresponding angles theorem, when two lines are intersected by a transversal, the corresponding angles are congruent.

Given that angle HJG measures 35 degrees, we can conclude that angle GIH also measures 35 degrees. This is because they are corresponding angles and share the same endpoints at arc GH.

Therefore, the angle measure of GIH is 35 degrees. The corresponding angles theorem guarantees that when two angles are formed by intersecting lines and share the same endpoints at an arc, they will have equal measures. In this case, both angles HJG and GIH have an angle measure of 35 degrees.

To know more about angle measure:

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Answer: i believe y = f because you are doing f x 1 and y = f x 1

Step-by-step explanation:

1 to the power of 1 is 1

Answer:

1

Step-by-step explanation:

You have the function f(x) [pronounced "f of x"]

"f(x) is equal to" is the same as saying "y is equal to"

The problem wants you to find f(x) when x = 1.

So, substitute 1 in for x.

This is your equation:

f(x) = 1^x

Now substitute 1 in for x:

f(1) = 1^1

1 to the power of 1 is equal to 1.

So, when f(x) = 1 when x = 1.

I hope this helps! :)

Answer:

so you can simplify the ratio

Step-by-step explanation:

Answer:

The height of the building is [tex]100\ ft[/tex]

Step-by-step explanation:

Let

h ----> the height of the building in feet

we know that

Using proportion

[tex]\frac{6}{4.5}=\frac{h}{75}\\ \\h=6*78/4.5\\ \\h=100\ ft[/tex]

I took the test and got 100 ft correct

Answer:

(x + 10)(x - 7)

Step-by-step explanation:

It is 3 and 10 in some order. The difference is 7 and it is plus, so the larger number is +10 and the smaller one - 3

(x + 10)(x - 3) should be the answer

10x - 3x = 7x

The trinomial [tex]x^2+7x-30[/tex] can be factored into (x+10)(x-3) by finding two numbers that multiply to -30 and add to 7.

To factor the trinomial [tex]x^2+7x-30[/tex] we are looking for two numbers that multiply to -30 (the constant term) and add up to +7 (the coefficient of the linear term).

These two numbers are +10 and -3, as -

10 * -3 = -30 and

10 + (-3) = 7.

So, we can rewrite the trinomial as (x+10)(x-3), which are the factors of the lowest possible order.

Answer:

f maths lah chibai i hate maths sorry cannot answer your question

Answer:

- 77

Step-by-step explanation:

Given

- (a - b)(a - bc) ← substitute given values for a, b and c

= - (3 - (- 4))(3 - (- 4 × 2))

= - (3 + 4)(3 - (- 8))

= - (7)(3 + 8)

= - 7 × 11

= - 77

A. It is a many-to-one function.

Hello! It will be a pleasure to help to figure out what's the correct answer to this problem. First of all, we have the following function:

[tex]f(x) = 2x^3 + 2x^2-x[/tex]

When plotting this function, we get the red graph of the function shown below. So let's solve this as follows:

True

A function is said to be many-to-one there are values of the dependent variable (y-values) that corresponds to more than one value of the independent variable (x-values). To test this, we need to use the Horizontal Line Test. So let's take the horizontal line [tex]y=0.5[/tex], and you can see from the first figure below that [tex]y=0.5[/tex] is mapped onto [tex]x=-1.241 \ x=-0.344 \ and \ x=0.585[/tex]. so this is a many-to-one function.

Since this is a many-to-one function, it can't be a one-to-one function.

False

Indeed, this is a function

False

It passes the vertical line test because any vertical line can intersect the graph of the function at most once. An example of this is shown in the second figure below.

Answer:

AB = CD = 3√5

Step-by-step explanation:

We use Pythagoras' Theorem.

AB² = CD² = 3²+6² = 9+36 = 9·(1+4) = 9·5

=> AB = CD = √(9·5) => AB = CD = 3√5

Answer:

18x²y²√6xy²

Step-by-step explanation:

3x∛648x⁴y⁸  = 3x ∛ 2 * 2 * 2 * 3 * 3 * 3 * 3 * x⁴ * y⁸

                      = 3x * 2 * 3 * x * y * y √2 * 3 * x * y * y

                      = 18x²y²√6xy²

Answer:

5, -1/4, -3, and 5/2

Step-by-step explanation:

All you need to do is look at leading term and constant term.  The possible rational zeros are the factors of 15 over (fraction bar) factors of 8.

So the factors of 15:

-1,1,-3,3,-5,5,-15,15

The factors of 8:

-1,1,-2,2,-4,4,-8,8

So the possible rational zeros.... I'm just going to put the factors of 15 over the factors of 8 like so:

-1/-1=1

-1/1=-1

-1/-2=1/2

-1/2=-1/2

-1/-4=1/4

-1/4=-1/4

-1/-8=1/8

-1/8=-1/8

Now I'm going to go to 1 and put it all over the factors of 8.

Anyways I can see some of your choices there 5/1=5 , I already listed the -1/4 above, -3/1=-3, and 5/2.

If you are still confused what I did all I'm doing is putting the first list of factors I made over (fraction bar) the second list of numbers I made.

Answer: 5, -1/4, 5/2, -3

Step-by-step explanation:

Answer:

h = 55

Step-by-step explanation:

Each of the angles adjacent to 2h° on the straight line = (180° - 2h°)

We also know that all internal angles of a triangle add up to 180

Hence,

40 + (180-2h) + (180-2h) = 180

40 + 180 -2h + 180 - 2h = 180

220 -4h = 0

4h = 220

h = 55

Answer:

H=55

Step-by-step explanation:

Answer:

U = -1/6

How to solve:

Multiply both sides by 2U to get rid of the denominator and you should end up with

[tex] - 5 = 15(2u)[/tex]

then multiply and devide to get your U by itself.

you should then get

[tex]u = - \frac{1}{6} [/tex]

after symplifying.

Answer:

Answer:

u=−10

Step-by-step explanation:

Let's solve your equation step-by-step.

u− 5 /2 u=15

Step 1: Simplify both sides of the equation.

u− 5/ 2 u=15

u+ −5 /2 u=15 (u+ −5 2 u)=15

(u+ −5 2 u)=15(Combine Like Terms)

−3 /2 u=15

−3 /2 u=15

Step 2: Multiply both sides by 2/(-3).

( 2 −3 )*( −3 2 u)=( −3 )*(15)

u=−10

Hey there! :)

If the temperature was at -41 F then warmed by 52 F, then what is our current temperature?

Simply do -41+52. Another way that your mind can do this is by rearranging this to look like this : 52 - 41

Because we are already very accustomed to doing this, we know that 52-41 is equal to 11. Therefore, -41+52 is very simply 11.

This means that our current temperature is 11 degrees Fahrenheit.

Hope this helped! :)

The solution set for the quadratic expression given is : (-8, 5)

Using the expression given :

divide through by 2

y = x² + 3x - 40

As a quadratic expression ;

x² + 3x - 40 = 0

factors whose product gives -40 and addition gives 3

x² + 8x - 5x - 40

factorize

x(x + 8) -5(x + 8)

(x + 8) = 0 or (x - 5) = 0

x = -8 or x = 5

Hence, the solution set is (-8 or 5)

The fraction 12/16 simplifies to 3/4 after dividing both the numerator and the denominator by 4. This concept is related to finding equivalent measurements through simplification and the use of proportions.

The student's question is about identifying a measurement that is equal to 12/16. To solve this, we need to simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which in this case is 4. So, the simplified form of 12/16 when reduced gives us 3/4.

To provide an example, if the scale factor is 1:4, and the scale measurement is given as 4, the actual measurement can be found with this proportion: 1:2 = 4:x. By cross-multiplying, we get x = 8, showing the application of scale factors and proportions in finding equivalent measurements.

if the answer for b is 4 square meters of fabric then both a and b will be the right answer. If you look at the graph, it starts at the points (0,0) which proves that it costs $0 for 0 square foot of fabric. Sames goes for choice b.

Answer:

a and b

Step-by-step explanation:

khan

Step-by-step explanation:

T = time in seconds

H = distance

Tground = time to return to ground

Tmax = time at maximum height

H = -16T^2 + 672T...eqn 1

projectile returns to ground at H =0,

subs for H in eqn 1...

0 = -16T^2 + 672T

solving for T we get...

16T^2 = 672T

=> Tground = 42secs

Tmax = 0.5 Tground = 21secs

Step-by-step explanation:

all work is shown and pictured

The GCF of 12x^2y and 27xy^3z is 3xy.

The full sort of GCF is greatest divisor. it's also referred to as highest  common factor.

we have to seek out GCF of

We can write them as:

1)2*2*3*x*x*y

2)3*3*3*x*y*y*y*z

GCF=3*x*y

=3xy

Hence the best common measure of 12x^2y and 27xy^3z is 3xy.

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First, distribute the negative to the second set of parentheses:

(9x2+10x+4)+(-9x2-5x+1)

Now, add like term:

9x2-9x2=0

10x-5x=5x

4+1=5

Recombine each sum for the final answer:

5x+5

Hope this helps!!

The difference is 5x + 5

First, remove the parentheses by distributing the negative sign:

9x² + 10x + 4 - 9x² - 5x + 1

Combine like terms:

10x + 4 - 5x + 1 = 10x - 5x + 4 + 1 = 5x + 5

Therefore, the difference is 5x + 5

First divide 5 to both sides to isolate p. Since 5 is being multiplied by p, division (the opposite of multiplication) will cancel 5 out (in this case it will make 5 one) from the right side and bring it over to the left side.

20 ≥  5p

20 ÷ 5 ≥ 5p ÷ 5

4 ≥  1p

4 ≥  p

For the graph will you have a empty or colored in circle?

If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.

If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.

Which direction will the ray go?

If the variable is LESS then the number then the arrow will go to the left of the circle.

If the variable is MORE then the number then the arrow will go to the right of the circle.

In this case your inequality is:

4 ≥ p OR p ≤ 4

aka 4 is greater then p OR p is less then 4

This means that the graph will have an colored circle and the arrow will go to the left of 4. Look at image below.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

B. Select a random sample of students who go to the work laboratory

Step-by-step explanation:

The best way to get acurate results is by selecting a random sample of students. If the students administers a survey to the students that are seated at the front of the laboratory he could get biased results.

The students that are seated in fron of the laboratory could obey to a certain characteristic (ie. They could be very applied students), which could definitely provide us with a different result.

The survey is just fine. We don't need any instrument to test statistical analysis understanding. Also, using a larger sample size of students seated in front of the laboratory won't make much difference. Finally, Administering instruments to a group who does not go to the work  laboratory makes no sense. You can not measure effectiveness on people that don't assist to class.

Answer:

Select a random sample of students who go to the work laboratory

verified on a p e x

The probability that two 1-6 number cubes both land on an even number is calculated by multiplying the individual probabilities for each cube (1/2 x 1/2), resulting in a final probability of 0.25, or answer 'C. 0.25.'

To determine the probability that two 1-6 number cubes land on an even number, we first recognize that there are three even numbers on each cube (2, 4, and 6), and thus three favorable outcomes out of six possible outcomes for each individual number cube roll. To calculate the probability of two independent events both occurring (in this case, both number cubes landing on an even number), we multiply the probabilities of each event.

The probability for one cube is 3/6, or 1/2. Therefore, for two cubes, the probability is (1/2) x (1/2) = 1/4. Expressed as a decimal, 1/4 is equivalent to 0.25.

The correct answer to the question is 'C. 0.25.'

Answer:

C. [tex]y=\sqrt[3]{-x} -1[/tex]

Step-by-step explanation:

Consider the eparent function [tex]y=\sqrt[3]{x}[/tex] The graph of this function is shown in the attached diagram - red curve.

Reflect this graph across the y-axis, you'll get the blue line which equation is

[tex]y=\sqrt[3]{-x}[/tex]

Translate this graph 1 unit down, then you'll get green line (that is exactly the graph from your image) and the function for this line is

[tex]y=\sqrt[3]{-x} -1[/tex]

Answer:

  it depends: $197,591.00 if you count 52 weeks per year; $198,851.28 if you count 365.25 days per year and 7 days per week.

Step-by-step explanation:

If we consider a year to be 52 weeks, then the total number of payments is ...

  25×52 = 1300

The total amount paid is then ...

  1300×$315.07 = $409,591.00

The difference between this and the loan amount is the interest paid:

  $409,591 - 212000 = $197,591

__

If you take into account the extra days in each year and the leap years, very likely there would be 4 more payments in 25 years. Then the total interest is ...

  1304×$315.07 -212,000.00 = $198,851.28

Follow below steps;

To convert temperature from Celsius to Rankine, the formula is:

R = (C + 273.15) x 9/5

So, to find the temperature in Celsius corresponding to R degrees Rankine, the correct formula is option B. 9/5(C + 273).

4) Answer: 512cm^3

6) Answer: 13,642.5in^3

7) What bathtub?

8) Answer: Height = 3 feet

9) Answer: Volume = 64/729 ft^3

10) Answer: Volume = 7/20 m^3

Answer:

[tex]\large\boxed{-5\dfrac{2}{5}=-\dfrac{27}{5}}[/tex]

Step-by-step explanation:

[tex]\bold{Method\ 1}:\\\\5=\dfrac{5\cdot5}{5}=\dfrac{25}{5}\\\\-5\dfrac{2}{5}=-\left(5+\dfrac{2}{5}\right)=-\left(\dfrac{25}{5}+\dfrac{2}{5}\right)=-\dfrac{25+2}{5}=-\dfrac{27}{5}\\\\\bold{Method\ 2:}\\\\\text{Multiply the integer by the denominator and add it to the numerator.}\\\\-5\dfrac{2}{5}=-\dfrac{(5)(5)+2}{5}=-\dfrac{25+2}{5}=-\dfrac{27}{5}[/tex]

Answer:

5 x 5 + 2

= -27/5 (5 is denominator)