Using synthetic division, what is the quotient of this expression?

Answer:

Give the person above me brainliest

Step-by-step explanation:

Step-by-step explanation:

Based on the information given, we have a diagram with two sides labeled as 13.3 mm and 5.5 mm, and another side labeled as X mm.

To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

Perimeter = 13.3 mm + 5.5 mm + X mm

The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.

To find X, we can subtract the sum of the known sides from the perimeter:

X mm = Perimeter - (13.3 mm + 5.5 mm)

Since the value of X is not given, we cannot calculate it without the perimeter value. If you provide the perimeter value, I can help you find the length of X.

Answer: 5(3n+4r)

Step-by-step explanation:You need to find the gcf/factor .So the gcf of 15 and 20 is 5.So know that you know the gcf ,you divide 15n by 5 which gives you 3n and divide 20r by5 which gives you 4r.Now the last thing you do is,take the GCF which is 5 and place a Parentheses and take 3n and 4r and add them together.

So you get 5(3n+4r) as your expression that  is equivalent to  15n + 20r .

Hope it helps . :)

The sketch of the front elevation and the side elevation of the prism are added as an attachment

From the question, we have the following parameters that can be used in our computation:

The prism

Using the figure as a guide, we understand that:

The front elevation is a rectangle of 2m by 0.5m

While the side elevation is a rectangle merged with a trapezoid

Next, we draw the elevations (see attachment)

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The range of the function m is [1, ∞). Thus, B is correct option.

The dοmain οf a functiοn is the cοllectiοn οf values that can be plugged intο it. This set represents the x values in a functiοn like f. (x). A functiοn's range is the set οf values that the functiοn can take οn. This is the set οf values returned by the functiοn when we enter an x value.

Tο determine the range οf functiοn m, we must first determine the set οf all pοssible functiοn οutput values.

Looking at the function graph, we can see that the lowest point is (3, 1) and the highest point is (∞, ∞).

As a result, the function m has a range of [1, ∞).

We can write: in interval notation:

m ∈ [1, ∞) range.

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Answer:

$15353.13

Step-by-step explanation:

The cost of the new car is $25000

It's value decreases by 15% each year

So value of the car after 1 year = (100-15)% of original cost

100 - 15% = 85% which in decimal is 0.85

Cost after 1 year = 25000 (0.85)

Coast after 2 years = 25000(0.85)(0.85) = 25000(0.85)²

After 3 years cost = 25000(0.85)³ = $15353.125 or $15353.13 to the nearest cent

In general, the cost of the car in n years

= 25000(0.85)ⁿ

Answer:

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

Substitute 12 and 24 for n into formula and calculate.

So, the 12th term is 63 and 24th term is 123.

No, his answer is not correct because each of the smaller divisions represents 1/6, not 3.

Mark's answer is not correct.

When dividing a number line into equal sections, the value of each section represents a fraction of the whole.

In this case, Mark divided the number line from 0 to 1 into 3 equal sections and then divided each of those sections into 2 equal parts.

Initially, the whole number line from 0 to 1 represents the number 1. When Mark divided it into 3 equal sections, each section represents 1/3 (one-third) of the whole.

So far, this is correct.

However, when Mark further divided each of the 1/3 sections into 2 equal parts, each part represents 1/2 (one-half) of the 1/3 section.

So, each of these smaller divisions represents 1/2 \(\times\) 1/3 = 1/6 (one-sixth) of the whole.

Therefore, the correct representation of each of the smaller divisions is 1/6, not 3.

Mark made an error by mistakenly assuming that each smaller division represents the number 3.

In summary, Mark's answer of 3 is incorrect because each of the smaller divisions represents 1/6, not 3.

The correct representation for dividing the number line as described is 1/6.

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The outcomes that are contained in the events are

1 - P(X) = 4/5 and 1 - P(X) is the same as P(Not X)

From the question, we have the following parameters that can be used in our computation:

X = gray colours

Given that

gray colours = 3 and 10

We have

X = 3 and 10

Not X =1, 2, 4, 5, 6, 7, 8

The probability is then calculated as

P(X) = 2/10 = 1/5

For P(Not X), we have

P(Not X) = 1 - 1/5 = 4/5

In (a), we have

P(Not X) = 1 - 1/5 = 4/5

This means that

P(Not X) = 1 - P(X)

So, the solution is

1 - P(X) = 4/5

Using the above (a) and (b) as a guide, we have the following:

1 - P(X) is the same as P(Not X)

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Answer:

find the given numbers on the number line

x⁴ - 8x² + 17 is the function that represents the fog(x).

To find fog(x), we first need to find g(f(x)), which means we need to substitute the expression for f(x) into the expression for g(x):

g(f(x)) = g(x² - 4)

Now, we can substitute the expression for g(x) into the above expression:

g(f(x)) = (x² - 4)² + 1

Expanding the squared term, we get:

g(f(x)) = x⁴ - 8x² + 17

Therefore, fog(x) = g(f(x)) = x⁴ - 8x² + 17.

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Complete question:

f(x) = x² - 4 and g(x)= x^2 + 1  find fog(x).

In this exercise we have to use the knowledge of function to write the minimum production cost, so we have to:

\(K=13.975\)

Thus writing the function that corresponds to this will be:

\(MPK = Q'(K) = 50L^{0.5}/K^{0.5} = 25\\MPL = Q'(L) = 50K^{0.5}/L^{0.5} = 100\)

Now calculating the minimum production cost we have:

\(MPK/r = MPL/w\\MPK/40 = 100/50\\MPK =80\\MPK = 50L^{0.5}/K^{0.5} = 80\\K=(1.118/80)= 13.975\)

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Answer:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

-3*x+y-(10)=0

Pull out like factors :

-3x + y - 10 = -1 • (3x - y + 10)

The top angle is right (90 degrees, kinda looks like a bent elbow).

The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).

The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).

4th is acute.

5th is straight because it's a straight line.

6th is also obtuse.

Have a good day :)

Answer:

  9

Step-by-step explanation:

After 81 passengers get off, only 9 passengers remain on the train of the original 90.

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Answer:

C)  I, III, IV, II

Step-by-step explanation:

Convert each number into a decimal:

\(\textsf{I.} \quad \dfrac{58}{67}=0.86567...\)

\(\textsf{II.} \quad 0.58\%=\dfrac{0.58}{100}=0.0058\)

\(\textsf{III.} \quad 58\%=\dfrac{58}{100}=0.58\)

\(\textsf{IV.} \quad 5.8\%=\dfrac{5.8}{100}=0.058\)

Comparing the tenths of all the numbers, 8 is the biggest tenth, so 58/67 is the largest number.

The next biggest tenth is 5, so 58% is the next largest number.

The two remaining numbers have zero tenths, so compare their hundredths. 5 is the largest hundredth, so 5.8% is the next largest number.  Therefore, 0.58% is the smallest number.

Therefore, the given set of numbers in order from greatest to least is:

Answer:

c) I, III, IV, II

Step-by-step explanation:

Values of l, ll, lll & lV respectively,

→ 58/67, 0.58%, 58%, 5.8%

→ 0.87, 0.0058, 0.58, 0.058

Arranging them in descending order,

→ 0.87 > 0.58 > 0.058 > 0.0058

→ 0.87, 0.58, 0.058, 0.0058

→ l, lll, lV, ll

Hence, the option (c) is correct.

The determinant of the given matrix is bc²-cb²+ac²-ab²+a²c-a²b.

The given matrix is \(\left[\begin{array}{ccc}1&a&a^2\\1&b&b^2\\1&c&c^2\end{array}\right]\).

Determinants are considered as a scaling factor of matrices. They can be considered as functions of stretching out and the shrinking in of the matrices. Determinants take a square matrix as the input and return a single number as its output.

Here, 1(bc²-cb²)+a(c²-b²)+a²(c-b)

= bc²-cb²+ac²-ab²+a²c-a²b

Therefore, the determinant of the given matrix is bc²-cb²+ac²-ab²+a²c-a²b.

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Answer:

3)  A = 35.2°, B = 38.6°, C = 106.2°

4)  B = 70.4°, C = 31.6°, a = 18.7

Step-by-step explanation:

To solve for the remaining angles of the triangle ABC given its side lengths, use the Law of Cosines for finding angles.

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}\)

Given sides of triangle ABC:

Substitute the values of a, b and c into the Law of Cosines formula and solve for angle C:

\(\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}\)

\(\implies \cos(C)=\dfrac{12^2+13^2-20^2}{2(12)(13)}\)

\(\implies \cos(C)=\dfrac{-87}{312}\)

\(\implies \cos(C)=-\dfrac{29}{104}\)

\(\implies C=\cos^{-1}\left(-\dfrac{29}{104}\right)\)

\(\implies C=106.191351...^{\circ}\)

To find the measure of angle B, swap b and c in the formula, and change C for B:

\(\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}\)

\(\implies \cos(B)=\dfrac{12^2+20^2-13^2}{2(12)(20)}\)

\(\implies \cos(B)=\dfrac{375}{480}\)

\(\implies B=\cos^{-1}\left(\dfrac{375}{480}\right)\)

\(\implies B=38.6248438...^{\circ}\)

To find the measure of angle A, swap a and c in the formula, and change C for A:

\(\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}\)

\(\implies \cos(A)=\dfrac{20^2+13^2-12^2}{2(20)(13)}\)

\(\implies \cos(A)=\dfrac{425}{520}\)

\(\implies A=\cos^{-1}\left(\dfrac{425}{520}\right)\)

\(\implies A=35.1838154...^{\circ}\)

Therefore, the measures of the angles of triangle ABC with sides a = 12, b = 13 and c = 20 are:

\(\hrulefill\)

Given values of triangle ABC:

First, find the measure of side a using the Law of Cosines for finding sides.

\(\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}\)

As the given angle is A, change C for A in the formula and swap a and c:

\(\implies a^2=c^2+b^2-2cb \cos (A)\)

Substitute the given values and solve for a:

\(\implies a^2=10^2+18^2-2(10)(18) \cos (78^{\circ})\)

\(\implies a^2=424-360\cos (78^{\circ})\)

\(\implies a=\sqrt{424-360\cos (78^{\circ})}\)

\(\implies a=18.6856038...\)

Now we have the measures of all three sides of the triangle, we can use the Law of Cosines for finding angles to find the measures of angles B and C.

To find the measure of angle C, substitute the values of a, b and c into the formula:

\(\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}\)

\(\implies \cos(C)=\dfrac{(18.6856038...)^2+18^2-10^2}{2(18.6856038...)(18)}\)

\(\implies \cos(C)=0.852040063...\)

\(\implies C=31.565743...^{\circ}\)

To find the measure of angle B, swap b and c in the formula, and change C for B:

\(\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}\)

\(\implies \cos(B)=\dfrac{(18.6856038...)^2+10^2-18^2}{2(18.6856038...)(10)}\)

\(\implies \cos{B}=0.334888270...\)

\(\implies B=\cos^{-1}(0.334888270...)\)

\(\implies B=70.434256...^{\circ}\)

Therefore, the remaining side and angles for triangle ABC are:

Answer:

I think the answer is A as well

Step-by-step explanation:

Answer:

a a a a a a a a  a a a a  a

Step-by-step explanation:

Answer:

=10t-6-7.5t = 6-0.5t

= 2.5t- 6 = 6-0.5t

= 2.5t+0.5t = 6+6

= 3t = 12

= t = 12/3

t = 4

Therefore the answer is 4

This equation has the next form:

To find if the equation has two complex solutions we have to check if the discriminant is negative, as follows:

Then, the first case has two complex solutions.

In the second case,

The discriminant in this case is:

Then, the second case has two complex solutions.

In the third case,

The discriminant in this case is:

Then, the third case has two real solutions.

In the fourth case,

The discriminant in this case is:

Then, the fourth case has two complex solutions.

Answer: Scalene

Step-by-step explanation:

The triangle doesn't have any equal side

Answer:

This is a scalene triangle. Hope this helps.

For the given similar triangles the value of x is 16/7.

What is similar triangles?

If the respective sides of two triangles are proportional and the corresponding angles are congruent, then the triangles are said to be comparable. To put it another way, similar triangles have the same shape but may differ in size. In addition, if the corresponding sides of the triangles are identical in length, the triangles are congruent.

Let the triangles ΔABD and ΔADE are similar.

Since ratios of sides of similar triangles are in proportion.

⇒

\(\frac{AB}{AD} = \frac{BC}{DE}\\ \frac{4}{7} =\frac{x}{4} \\16 = 7x\\x = \frac{16}{7}\)

Hence, the value of x is 16/7.

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Answer:

\( y = 2x + 5 \)

Step-by-step explanation:

Using the slope-intercept form equation, \( y = mx + b \), where,

y = total cost

x = hour

m = slope, which is the hourly charge = $2

b = y-intercept, which is the flat fee, or starting fee paid for bring your car into the garage = $5

Substitute m = 2 and b = 5 into \( y = mx + b \).

✅Thus, the equation that represents the problem situation would be:

\( y = 2x + 5 \)

From the given number line, the variable "m" could take the values of -2, -3.5, 0, and -5

To determine which values the variable "m" could take from the given number line, we need to identify the points or intervals on the number line that correspond to the possible values of "m".

Looking at the number line, we can see the following values:

-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

From this list, the values that "m" could take are:

-2, -3.5, 0, -5

These values are present on the number line, indicating that they are possible values for "m".

Therefore, the variable "m" could take the values -2, -3.5, 0, and -5 from the given number line.

It's important to note that the values -7 and 4 are not present on the number line, so they are not possible values for "m" based on the information provided.

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