The two triangles are similar. What is the value of x?

Answer with Step-by-step explanation:

We are given that u and v are a basis for the two dimensional vector space.

To prove that w=u+v and x=u-v is also a basis .

By using matrix we prove w and x are basis of vector space.

We make a matrix from w and x

[tex]\left[\begin{array}{cc}1&1\\1&-1\end{array}\right][/tex]

Apply operation

[tex] R_1\rightarrow R_1-R_2[/tex]

[tex]\left[\begin{array}{cc}0&2\\1&-1\end{array}\right][/tex]

Apply [tex] R_2\rightarrow R_2-+R_1[/tex]

[tex]\left[\begin{array}{cc}0&2\\1&1\end{array}\right][/tex]

Apply [tex]R_1\rightarrow \frac{1}{2}R_1[/tex]

[tex]\left[\begin{array}{cc}0&1\\1&1\end{array}\right][/tex]

Apply [tex]R_2\rightarrow R_2-R_1[/tex]

[tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex]

Rank is 2 .Therefore, row one and second row are linearly independent.

Hence, first and second row are linearly independent because, any row is not a linear combination of other row.

Therefore, w and x are formed basis of given vector space.

Answer:

  exponential: y = 2^(-x)

Step-by-step explanation:

The y-differences are not constant, and the x-y products are not constant. For each increase in x, y is divided by 2, so this is a geometric sequence that can be described by an exponential model. The common factor is 1/2.

A simple way to write the model for this is ...

  y = 2^(-x)

Answer:

D. 0.7611

Step-by-step explanation:

The area is:

P(z<1.60) − P(z<-0.90)

Looking up the values in a z-score table:

0.9452 − 0.1841

0.7611

Answer:

D. 0.7611

Step-by-step explanation:

We have been given a graph of a normal standard distribution curve. We are asked to find the area of the shaded region under the given standard distribution curve.

The area of the shaded region under the standard distribution curve would be area of a z-score of 1.60 minus area of a z-score of [tex]-0.90[/tex] that is [tex]P(-0.90<z<1.60)=P(z<1.60)-P(z<-0.90)[/tex]

Using normal distribution table, we will get:

[tex]P(-0.90<z<1.60)=0.94520-0.18406[/tex]

[tex]P(-0.90<z<1.60)=0.76114[/tex]

Therefore, the shaded area under the curve is 0.7611 and option D is the correct choice.

Answer:

The most common source of income is business ownership. A. True.

Step-by-step explanation:

The most common source of income is employment. Other sources of income may include investments, business profits, or government assistance.

The statement "The most common source of income is employment" is true.

Employment is the main source of income for the majority of people worldwide. It refers to a person's work for which they receive financial compensation in the form of wages or salary. Other sources of income may include investments, business profits, or government assistance, but employment is the most common and reliable.

Examples of employment include working in various sectors such as healthcare, technology, education, manufacturing, and services.

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Answer:

g = 28,000 - 700t

Step-by-step explanation:

This solution reads, in words,

"the amount of water remaining in the pool is equal to 28,000 gallons minus 700 gallons per hour", which is what your situation is asking you.  You start with 28,000 gallons and are pumping out (subtracting) 700 gallons per hour.

g is what remains

Answer: [tex]g=28000-700t[/tex]

Step-by-step explanation:

Given : A 28,000-gallon swimming pool is being drained using a pump that empties 700 gallons per hour.

i.e, Remaining gallons = 28,000- 700 × Number of hours.

Let g be the number of gallons remaining in the pool and t is the amount of time in hours the pool has been draining.

Then, the equation models this situation  will be :-

[tex]g=28000-700t[/tex]

Answer:

Step-by-step explanation:

This is a combination problem from stats.  We have a total of 12 English books from which you have to 3.  The order in which you pick them doesn't matter, you only need to determine how many different combinations are available to you.  This is the combination formula, then:

₁₂C₃ = [tex]\frac{12!}{3!(12-3)!}[/tex]

I'm just going to simplify the right side and leave off the left side til the end of the algebra because it's easier.  The right side simplifies to

[tex]\frac{12*11*10*9!}{3*2*1*9!}[/tex]

The 9!'s cancel each other out, leaving you with

[tex]\frac{12*11*10}{3*2*1}=\frac{1320}{6}[/tex]

Therefore,

₁₂C₃ = 220 possible different combinations of English books from which to pick.

We'll do the same for History, which has a combination formula that looks like this:

₈C₂= [tex]\frac{8!}{2!(8-2)!}[/tex]

That right side expands to

[tex]\frac{8*7*6!}{2*1*6!}[/tex]

The 6!'s cancel each other out, leaving you with:

[tex]\frac{8*7}{2*1}=\frac{56}{2}[/tex]

Therefore,

₈C₂ = 28 possible different combinations of History books from which to pick.

You may or may not need to add those together to get the answer your teacher is looking for.

The value of a salary of $12,000 in 1964 would be approximately $84,000 in 2016 dollars when adjusted for inflation as measured by the Consumer Price Index.

To calculate the value of your grandfather's salary in 2016 dollars, the relative rates of Consumer Price Index (CPI) for both years need to be compared. The salary of $12,000 in 1964, adjusted for inflation through 2016, would be:

$12,000 * (219 / 31)

This formula indicates the change in CPI from 1964 to 2016 and multiplies it by the salary in 1964 dollars. Therefore, your grandfather's salary in 2016 is approximately $84,000 when accounting for inflation.

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Final answer:

The value of your grandfather's salary in 2016 dollars is approximately $84,687.10

Explanation:

The value of your grandfather's salary in 2016 dollars is approximately $84,687.10

. To calculate this, you need to adjust the 1964 salary for inflation using the Consumer Price Index (CPI) for 1964 and 2016. First, find the inflation factor by dividing the CPI of 2016 by the CPI of 1964. Then, multiply the 1964 salary by this factor to get the equivalent value in 2016 dollars.

Answer:

102 an hour

Step-by-step explanation:

all you do is add all of them together

Answer:

3,604 books

Step-by-step explanation:

We have 2 situations:  situation A and situation B.  What we are looking for is the number of books that has situation A equal to situation B.  So the game plan is to write the equations for A and B, set them equal to each other, and then solve for the unknown number of books, x.

Situation A:  If each book costs 19.25 to produce and the number of books is x, we express that as 19.25x.  The fixed cost to use that company, regardless of the number of books it produces for you, is 22,427.  Which means it is going to charge you 22,427 whether you produce 1000000 books or no books at all.  The equation for A is:

C(A) = 19.25x + 22,427

Situation B uses the exact same reasoning, with the cost of each book being 10.50x and the flat rate cost of 53,962.  Therefore, the equation for B:

C(B) = 10.50x + 53,962

We need the number of books where A = B, so we set the equations equal to each other and solve for x:

19.25x + 22,427 = 10.50x + 53,962 so

8.75x = 31,535 and

x = 3604

Answer: (1, -7) (11, -7)

Step-by-step explanation:

The foci of the hyperbola whose equation is (1,−7) and (11,−7).

The hyperbola is horizontal, we will count 5 spaces left and right and plot the foci there.

We need to use the formula [tex]\rm c^ 2 =a^ 2 +b^ 2[/tex] to find c.

The given equation of the hyperbola is;

[tex]\rm \dfrac{(x-6)^2}{16}-\dfrac{(y+7)^2}{9}=1[/tex]

Here a^2 is 16 and b^2 =9.

Substitute all the values in the formula

[tex]\rm c^ 2 =a^ 2 +b^ 2\\\\\rm c^ 2 16+9\\\\\rm c^2=25\\\\c^2=5^2\\\\c=5[/tex]

The center of the hyperbola is (6, -7).

The foci of the hyperbola whose equation is;

( 6 +5 , -7), (6-5, -7)

(11, -7), (1, -7)

Hence, the foci of the hyperbola whose equation is (1,−7) and (11,−7).

Learn more about hyperbola here;

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Answer:

shortest length of fence is 8485.2 ft

Step-by-step explanation:

Given data

area =  3,000,000 square feet

to find out

shortest length of fence

let length L and width is W

so area is L × W

W = 3 × [tex]10^{6}[/tex] /L    ............1

2W = 6 × [tex]10^{6}[/tex] /L

rectangular field and then divide it in half

so fencing will be 3 × L + 2 × W

i.e.  3 L + 2W

fencing =  3 L  + 6 × [tex]10^{6}[/tex] /L

fencing minimum = 3 L  -  6 × [tex]10^{6}[/tex] /L²

fencing minimum length will be zero

3 L  -  6 × [tex]10^{6}[/tex] /L² = 0

3 L² = 6 × [tex]10^{6}[/tex]

L² =  2 × [tex]10^{6}[/tex]

L  =  1414.2

so from equation 1

W = 3 × [tex]10^{6}[/tex] /L

W = 3 × [tex]10^{6}[/tex] /1414.2

W = 2121.3

so fencing will be  3 L +2 W

so fencing =   3 × 1414.2  +2 × 2121.3

fencing =  4242.6 +4242.6

fencing =  8485.2

shortest length of fence is 8485.2 ft

The shortest length of fence the rancher can use is approximately 6104 feet. This is derived by setting up the area and perimeter equations, differentiating to find the minimum perimeter, and substituting the values back into the equation.

This problem is a basic optimization problem in mathematics. Given that the area of the field to be fenced is 3,000,000 square feet, we can use the formula for the area of a rectangle, which is length multiplied by width. Since the rancher wants to divide the field in two with a fence running parallel to one side, the total amount of fencing will be two lengths and three widths.

Let's denote the length of the rectangle as 'l' and the width as 'w'. The area is thus l*w = 3,000,000. The perimeter is defined as 2*l + 3*w. Given that the area is fixed, w can be expressed in terms of l as 3,000,000/l.

Therefore, the perimeter becomes 2*l + 3*(3,000,000/l). The minimum fence length or perimeter occurs when the derivative of this equation is zero. By differentiating and setting the equation to zero, we get l=sqrt(1,500,000), approximately 1224.74 feet. Substituting this value into the equation for w gives us w also as 1224.74 feet.

The shortest length of fence that the rancher can use is thus 2*l + 3*w = 2*1224.74 + 3*1224.74 = 6103.7 feet.

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Answer:

The third side can be any length as long as it is greater than 4 in and less than 26 in

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that The sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

x ----> the length of the third side

Applying the triangle inequality theorem

1) 11+15 > x

26 > x

rewrite

x < 26 in

2) 11+x > 15

x> 15-11

x > 4 in

therefore

Aziza's claim is incomplete

The third side can be any length as long as it is greater than 4 in and less than 26 in

Answer:

Aziza’s claim is not correct. The third side must be between 4 in. and 26 in.

Step-by-step explanation:

Answer:

  y = (-4/3)(x +4) +4

Step-by-step explanation:

Between the given points, the "rise" is -8 and the "run" is 6. The rise/run ratio is then -8/6 = -4/3. So, a version of the point-slope equation can be written:

  y = m(x -h) +k . . . . . . . line with slope m through point (h, k)

  y = (-4/3)(x +4) +4

_____

Comment on the answer

The image asks for "an equation", which seems to allow for any equation format. The equation shown above can be put into other forms.

  y -4 = -4/3(x +4) . . . . different point-slope form

  y = -4/3x -4/3 . . . . . . slope-intercept form

  4x +3y = -4 . . . . . . . . standard form

  4x +3y +4 = 0 . . . . . . general form

  x/(-1) +y/(-4/3) = 1 . . . . intercept form

Answer:

  A, D, E (probably preferred)

  B, C, F (also true)

Step-by-step explanation:

"This situation" problems are almost always ambiguous. The first problem is to figure out what it is about "this situation" that you want to model.

__

If we want to model concession stand revenue in a general way, then statements B, C, and F could represent "this situation." No specific values can be determined from this model.

__

More likely, we want to model the details of sales and revenue, so we want to know the exact numbers of water bottles and hamburgers that were sold. For "this situation," we can assign variables to the numbers of items of each type, and write equations for the total number of items and for the revenue their sales generates. Appropriate statements about this interpretation of the problem are those of A, D, and E:

  A: x could represent bottles sold

  D: y could represent hamburgers sold

  E: The system of equations could be 2.50x +5.50y = 1325; x +y = 350.

_____

The solution to the last model is 200 bottles were sold for revenue of $500, and 150 hamburgers were sold for revenue of $825.

Answer:

A-The variable x could represent the number of bottles of water sold.

D-The variable y could represent the number of hamburgers sold.

E-The system of equations that could represent the concession sales is

2.50x + 5.50y = 1,325

x+y=350

Step-by-step explanation:

When doing a system of equations you need variables and constants, in this case it´s easy to know what are the constants, since they are given directly to you by the problem, the constan 1 is the cost of the bottled water, the cost of each hamburger, the number of items sold and the total sum of the sells.

The only variables that we have are the number of items sold, we are going to express them with X and Y, the cost of the number of bottles of water sold will be expressed with the letter X and the number of hamburgers sold will be expressed by the letter Y.

Assuming pure chance, on a 12 question multiple choice test with 3 options per question, it would be unusual to get 5 or more questions correct by guessing alone.

The question pertains to the probability of guessing correctly on a multiple-choice test with 3 options per question, assuming pure chance. On a 12-question test, the probability of guessing correctly on a single question is 1/3. Hence, for 12 questions, the expected number of correct guesses would be the total number of questions times the probability of getting each question right, which is 12 * 1/3 = 4. Therefore, it would be unusual to get 5 or more questions correct by guessing alone.

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In a 12-question multiple choice test with 3 possible answers for each, a student randomly guessing is expected to get roughly 4 correct answers. Getting 6 or more questions correct by random guessing would be considered unusual.

When taking a 12-question multiple choice test where each question has 3 possible answers, the probability of getting a question correct by simply guessing is 1/3. Here, we want to calculate the unusual scenario of how many or more questions correct by simply guessing.

If we apply the principle of probability, under normal circumstances where guessing is purely random, the expected number of correct answers would be the total number of questions times the probability of getting a question correct. This equates to 12 × (1/3) which is 4 correct answers. This means on average, if the student were to guess all their answers, they are likely to get around 4 correct answers.

However, getting 6 or more questions right by guessing alone would be considered unusual due to the low probability of guessing correct answers repeatedly. Keep in mind, that these calculations hold if all the guesses are random and there is no elimination of wrong answers based on known information.

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For this case we have the following equation:

[tex]\sqrt [4] {2x-8} + \sqrt [4] {2x + 8} = 0[/tex]

If we subtract both sides of the equation [tex]\sqrt [4] {2x + 8}[/tex] we have:

[tex]\sqrt [4] {2x-8} = - \sqrt [4] {2x + 8}[/tex]

To eliminate the radical we raise both sides of the equation to the fourth power:

[tex](\sqrt [4] {2x-8}) ^ 4 = (- \sqrt [4] {2x + 8}) ^ 4[/tex]

Answer:

Option D

Answer:

diagonal is 20.68 ft; shorter base is 17.21 ft

Step-by-step explanation:

If base angles add up to 140, then each is 70 since this is an isosceles trapezoid.  We can use the Law of Cosines now to find the length of the diagonal which I will call d:

[tex]d^2=7^2+22^2-2(7)(22)cos(70)[/tex] and

[tex]d^2=533-308cos(70)[/tex] and

[tex]d^2=533-105.3422041[/tex],

[tex]d^2=427.6577959[/tex]

so the length of the diagonal is

d = 20.68 ft

The length of the shorter base is a little more tedious.  First drop an altitude from each of the upper vertices to the base measuring 22 ft.  We have 2 smaller right triangles now, each with unknown height (we need to find this), each with unknown base measures (we need to find this, too!), each with a base angle of 70 degrees, and each with a hypotenuse of 7.  We need only work with one of these since they are both the same.  

We will first find h, the height of each of these right triangles.  Using the sin ratio:

[tex]sin(70)=\frac{h}{7}[/tex] and

[tex]7 sin(70)=h[/tex] so

h = 6.577848

Now we can use that along with the hypotenuse measure to find the base measure, b:

[tex]7^2-6.577848^2=b^2[/tex],

[tex]b^2=5.731911137[/tex] so

b = 2.394141002

Because we have 2 identical small right triangles with base measures of 2.394141002 each, we can subtract 2(2.394141002) from 22 to get the measure of the shorter base, which I will call x:

22 - 2(2.394141002) = x so

x = 17.21 ft

Answer:

not really sure maybe 12

Answer:

8 / 12 = x / 18

8 * 18 / 12 = x

x = 12

Step-by-step explanation:

Answer:

North pacific and south pacific.

Step-by-step explanation:

D.

The Pacific Ocean's two major gyre systems are found in the North Pacific and South Pacific.

The Pacific Ocean is divided into two sets of gyres, notably in the North Pacific and South Pacific. Gyres are large systems of circulating ocean currents; the gyres in the Pacific Ocean play significant roles in influencing climate and marine life. The North Pacific Gyre, encircling the area between Asia and North America, and the South Pacific Gyre, contained mostly between Australia, South America and Antarctica, are the two main gyre systems in the Pacific Ocean.

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Answer:

79 ft

Step-by-step explanation:

The formula for the circumference of a circle is

C = 2πr.  If it's the diameter that is known, then C = πd.  We will use the latter formula to find the circumference of this pool:

C = π(25 ft) = 78.54 ft, approx., which, to the nearest foot, is 79 ft

Answer:

8.3

Step-by-step explanation:

Let Ao be the original amount and A the amount after t days.

Then we have the exponential function

     A = Ao(1 - x)^t or

A/Ao = (1 - x)^t

When t = 8, A/Ao = 0.5

         0.5 = (1 - x)^8

(0.5)^(1/8) = 1 - x

     0.917 = 1 - x

            x = 1 - 0.917 = 0.083 = 8.3 %

The substance decays by 8.3 % each day.

Answer:

(B)  this is not binomial function

Step-by-step explanation:

Given data

sample card n = 4 cards

total card number N =  52 cards

red card = 26

black card = 26

to find out

X be the number of cards that are red. (A) Binomial(B) Not binomial

solution

we know that 4 is selected with out replacement from 52 cards

we can say that R item is as success , here R is Red card

so that  52 - R items will be as failures

and we know

failure = 52 - 26 = 26 that is equal to 26 black card

we know this is Hyper geometric function

so this is not binomial function

Answer:

  a. 3093

Step-by-step explanation:

The missing two terms in the 5-term sequence are ... 300 + 750.

You can add up these 5 terms directly, or you can recognize that the sum will be more than the last term (not C), but cannot be more than double the last term (not B or D). The sum must be 3093, choice A.

_____

If you use the formula for the general term of the series, you can find the number of terms.

The common ratio is 120/48 = 2.5

The general term is ...

  an = a1·r^(n -1)

Solving for n, we get ...

  n = log(an/a1)/log(r) +1 = log(1875/48)/log(2.5) +1 = 5 . . . . the number of terms

Then the sum is given by ...

  Sn = a1(r^n -1)/(r -1) . . . . . using a1=48, r=2.5, n=5

  S5 = 48(2.5^5 -1)/(2.5 -1) = 48(96.65625/1.5)

  S5 = 3093

_____

The sum of a geometric sequence with a common ratio of 2 is double the last term, less the first term. When the common ratio gets larger, the sum gets smaller than double the last term.

  Sn = a1(r^n -1)/(r -1) = (a1·r^n -a1)/(r -1) = (r·an -a1)/(r -1)

  Sn = (r/(r -1))an -a1/(r -1) . . . . . . verifies the above comment

In our case, this evaluates to ...

  S5 = (2.5/1.5)(1875) -48/1.5 = (5/3)(1875) -(2/3)(48)

  = 3125 -32 = 3093

Using the first and last terms this way, we only need the common ratio and don't need to know the number of terms.

Answer:

1_ scalene

2_isoscelous

Answer:

13a. scalene

13b. isosceles

13c. right

Step-by-step explanation:

i took geometry hope this helps

Answer:

1.6 hours or 1 hour 36 minutes.

Step-by-step explanation:

The rate at which the trains are moving apart is 55 + 75 = 130 mph.

Speed = distance / time so:

130 = 208 / t

130t = 208

t = 1.6 hours.

Answer:

  A = 15t +15

Step-by-step explanation:

The amounts have a common difference of $15, so that is apparently the amount Jasmine is saving each week. Week 1, however, is $15 more than $15×1. The function ...

  A = 15t +15 . . . . dollars

seems to fit the data.

Answer:

65

Step-by-step explanation:

The outlier made the mean bigger/greater. Rounded to the nearest tenth it would be 40.8.

Answer:

Step-by-step explanation:

According to the problem

[tex]\angle N + \angle O =180\°[/tex]

[tex]\angle O + \angle P = 180\°[/tex]

[tex]\angle M + \angle P = 180\°[/tex]

Which means,

[tex]\angle N + \angle O = \angle O + \angle P\\\angle N = \angle P[/tex]

And,

[tex]\angle O + \angle P = \angle M + \angle P\\\angle O = \angle M[/tex]

Therefore, the right answer is the last choice.

Answer:

The sum of the vectors is <8 , 6>

The magnitude of the resultant vector is 10

The direction of the resultant vector is 37°

The answer is the 1st answer: <8 , 6> ; 10 ; 37°

Step-by-step explanation:

* Lets explain how to solve the problem

∵ The first vector is <7 , -2>

∵ The second vector is <1 , 8>

∴ The sum of the 2 vectors = <7 , -2> + <1 , 8>

∴ Their sum = <7 + 1 , -2 + 8> = <8 , 6>

* The sum of the vectors is <8 , 6>

- The magnitude of the resultant vector = √(x² + y²)

∵ x = 8 and y = 6

∴ The magnitude of the resultant vector = √(8² + ²)

∴ The magnitude of the resultant vector = √(36 + 64) = √100 = 10

* The magnitude of the resultant vector is 10

- The direction of the vector = tan^-1 (y/x)

∵ x = 8 and y = 6

∴ The direction of the vector = tan^-1 (6/8) = 36.869 ≅ 37°

* The direction of the resultant vector is 37°

Answer:

The answer is A. ⟨8,  6⟩;  10;  37°

Answer:

ABC ~ FED

Step-by-step explanation:

A ~ F

B~E

C~D

If you're still confused, look at the angles. No lines match to A and F, 1 line matches to B and E, and 2 lines match to C and D.

The correct answer is ΔABC ~ ΔDEF, where the corresponding congruent angles are matched to affirm triangle similarity, making option A correct.

To determine which triangles are similar, we need to match the angles from ΔCBA to ΔFDE. Since angle D is congruent to angle B and angle E is congruent to angle A, we need to ensure that the order of the vertices corresponds to the congruent angles in the similar triangles. Therefore, the correct order that names the similar triangles is ΔABC ~ ΔDEF, which makes option A correct. In ΔABC, angle A corresponds to angle E in ΔDEF, and angle B corresponds to angle D. This order maintains the sequence of corresponding congruent angles in both triangles.

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