Which quadratic expression represents the product of these factors?

(2x + 5)(7 − 4x)

A.
-8x2 + 34x − 35
B.
-8x2 + 6x − 35
C.
-8x2 − 6x + 35
D.
-8x2 − 34x + 35

The ordered pair (z, 11) is not a solution of the inequality.

Explain inequality

An inequality is a statement that compares two values, expressing that one value is greater than or less than the other, or that they are not equal. Inequalities are represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). They are used to describe relationships between numbers, variables, and expressions.

According to the given information

To determine whether the ordered pair (z, 11) is a solution of the inequality 2z < 15, we need to substitute z = 11 into the inequality and see if it is true or false:

2z < 15

2(11) < 15

22 < 15 (this is false)

Since 22 is not less than 15, the ordered pair (z, 11) is not a solution to the inequality.

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Answer:

4.05555555556

Step-by-step explanation:

Answer:

4.05555 (5 repeating)

Step-by-step explanation:

The y-intercept of 80 in the equation (80) represents the estimated number of T-shirts sold when price is set to 0.Implies that if the T-shirts were given away for free, company would sell approximately 80 T-shirts.

The given information provides a scatter plot representing a survey conducted by a T-shirt manufacturing company. Additionally, the equation of the line of best fit is provided as y = -5x + 80, where y represents the number of T-shirts sold and x represents the price of a T-shirt.

To understand and analyze the data further, we can follow these steps:

Interpret the slope: The coefficient of -5 in the equation (-5x) indicates that for every increase of 1 unit in the price of a T-shirt, the number of T-shirts sold decreases by 5 units. This negative slope suggests an inverse relationship between the price and the demand.

Interpret the y-intercept: The y-intercept of 80 in the equation (80) represents the estimated number of T-shirts sold when the price is set to 0. In practical terms, it implies that if the T-shirts were given away for free, the company would sell approximately 80 T-shirts.

By using this line of best fit equation, the company can make predictions about the number of T-shirts they are likely to sell based on different price points, allowing them to make informed decisions about pricing strategies.

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The width of a rectangular frame with a total area of 140 square inches, we set up an equation using the expressions for the length and width, simplify it, solve for x, and substitute the value of x into the expression for the width.

To solve for the width of a rectangular frame with a total area of 140 square inches, we first need to set up an equation using the given expressions for the length and width.
The formula for the area of a rectangle is length x width. Therefore, we can write:
(2x + 10)(2x + 6) = 140
We can then simplify this equation by expanding the expressions in the parentheses:
4x^2 + 32x + 60 = 140
Next, we can move all the terms to one side and simplify further:
4x^2 + 32x - 80 = 0
Now, we can solve for x by factoring or using the quadratic formula. After finding the value of x, we can substitute it into the expression for the width (2x + 6) to get the final answer.

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Answer:

21.9is correct answer

Step-by-step explanation:

please mark as brainlist

Given the next trigonometric identity:

Substituting this identity into the equation:

Subtracting 1 at both sides of the equation:

Replacing with:

we get:

Applying the quadratic formula with a = 1, b = 1 and c = -2:

Recalling that y = sec(x), then we have two options:

By definition:

Therefore, the first option is:

In the interval of x [0,2π), the solution to this equation is 0.

Now, considering the second option:

In the interval of x [0,2π), the solutions to this equation are 2π/3 and 4π/3.

In summary, the solutions to tan^2⁡(x) + sec(x) = 1 are:

=================================================

Explanation:

The number in the upper left corner of the synthetic division table is the test root we're trying out. If it leads to a remainder of 0 (bottom right corner), then we have a winner. In this case, we have a root. Choice A is one of the answers.

Since 4 is a root, this leads to x-4 being a factor. Think of x = 4 becoming x-4 = 0 when we subtract 4 from both sides. Choice C is another answer.

The remaining stuff in the bottom row forms the quotient polynomial. The coefficients 3 and -1 lead to 3x+(-1) which simplifies to 3x-1.

So this means dividing 3x^2-13x+4 over x-4 yields the quotient 3x-1 with a remainder of 0. Therefore, choice E is the correct equation compared to choice D which is close but not quite there.

The equation combines these two joint probabilities to express the probability of event E given event F hence the proof.

To understand the proof, let's consider events E, F, and G. The left side of the equation, \(\(P(E \mid F)\)\), represents the probability of event E occurring given that event F has occurred.

The right side of the equation involves conditional probabilities. The term\(\(P(E \mid F G) P(G \mid F)\)\) represents the joint probability of events E and G occurring given that event F has occurred. It takes into account the probability of both E and G occurring together given F.

The term\(\(P(E \mid F G^{c}) P(G^{c} \mid F)\)\) represents the joint probability of events E and G complement (not G) occurring given that event F has occurred. It considers the probability of both E and G complement occurring together given F.

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The solution of the circle is 3.204

We are given that;

\(mTN = (62-47), \\m/TKN = 33 \\mYM = (32-6),\\ mMX = (4x+10)\)

Now,

The theorem states that if two chords intersect inside a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. Using this theorem, we get:

\(TK \times KN = MY \times MX (62 - 47) \times (47 + 33) = (32 - 6) \times (4x + 10) 15 \times 80 = 26 \times (4x + 10) \\1200 = 104x + 260 \\104x = 940 \\x = 9.038\)

Since RY is a tangent to the circle H at Y, and YM is a secant to the circle H, we can use the tangent-secant theorem to find a relationship between their lengths and the length of the intercepted arc MX.

\(RY^2 = MY * MW (9r - 75)^2 = (32 - 6) * (32 - 6 + 4x + 10) \\(9r - 75)^2 = 26 * (46 + 4x) (9r - 75)^2 = 1196 + 104x\\ 81r^2 - 1350r + 5625 = 1196 + 104x \\81r^2 - 1350r + 4429 = 104 * 9.038 \\81r^2 - 1350r + 4429 = 940.952 \\8r^2 - 1350r + 3488.048 = 0\)

To solve this quadratic equation for r, we can use the quadratic formula. We get:

r = (-b ± √(b² - 4ac)) / (2a)

r = (-(-1350) ± √((-1350)² - 4 * 81 * 3488.048)) / (2 * 81)

r = (1350 ± √(1822500 - 1131918.752)) / 162

r = (1350 ± √(690581.248)) / 162

r ≈ (1350 + 831.032) / 162 or

r ≈ (1350 - 831.032) /162

r ≈ 13.407 or r ≈ 3.204

Therefore, by the given circle the answer will be 3.204

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Answer:

4(5x-2)= 6(x+8)

20x-8=6x+48

20x-6x=48+8

14x=56

\(x = \frac{56}{14} \)

x=4

Step-by-step explanation:

hope this helps you!!

XXITSCHOCOLOVERXX

Answer:

x = 4

Step-by-step explanation:

\(\frac{5x-2}{6}=\frac{x+8}{4} < == cross\ multiply\\\\4(5x-2)=6(x+8) < ==distribute\\\\4(5x)+4(-2)=6(x)+6(8)\\\\20x-8=6x+48 < ==subtract\ 6x\ from\ both\ sides\\-6x\ \ \ \ -6x\\\\14x-8=48 < == add\ 8\ to\both\ sides\\\ \ \ +8 \ \ \ \ \ \ \ +8\\\\14x=56 < ==divide\ both\ sides\ by\ 14\\/14 \ \ \ /14\\\\x=4 < ==final\ answer\)

Check your answer:

\(\frac{5x-2}{6}=\frac{x+8}{4}\\\\\frac{5(4)-2}{6}=\frac{4+8}{4}\\\\\frac{20-2}{6}=\frac{12}{4}\\\\\frac{18}{6}=\frac{12}{4}\\\\3=3\)

This statement is correct

Hope this helps!

Answer:

ANSWER: 59/ 60

Step-by-step explanation:

What should be subtracted to get 1 / 2 ?( 3 / 4 + 1 / 3 + 2 / 5 )

to get 1 / 2A.3 / 4 = 3.00 ÷ 4 = .75 *.1 / 3 = 1.000 ÷ 3 = .333 * .2 / 5 = 2.0 ÷ 5 = .4 * ..75 + .33 + .4 = 1.48…75+.33.40 == 1.48 *OR3 / 4 = 45 / 60+1 /3 = 20 / 602 / 5 = 24 / 60 ======== 89 / 60 = 1 29/601 29 /60 = 1 29/60 === 0 89/60—0 1/2 ==== 0 30/ 60=—0 30/60 =====================0 59/ 60

Answer:

1. Pour the mixture through a filter to separate the sand; 2. Evaporate the liquid to separate the salt.

Step-by-step explanation:

Answer(s):

\(\displaystyle y = 4cos\:(2x - \frac{\pi}{2}) - 1 \\ y = 4sin\:2x - 1\)

Explanation:

\(\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{4}} \hookrightarrow \frac{\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4\)

OR

\(\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4\)

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = 4cos\:2x - 1,\) in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted \(\displaystyle \frac{\pi}{4}\:unit\) to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD \(\displaystyle \frac{\pi}{4}\:unit,\) which means the C-term will be positive, and perfourming your calculations, you will arrive at \(\displaystyle \boxed{\frac{\pi}{4}} = \frac{\frac{\pi}{2}}{2}.\) So, the cosine graph of the sine graph, accourding to the horisontal shift, is \(\displaystyle y = 2cos\:(2x - \frac{\pi}{2}) - 1.\) Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits \(\displaystyle [-\frac{\pi}{4}, -5],\) from there to \(\displaystyle [\frac{3}{4}\pi, -5],\) they are obviously \(\displaystyle \pi\:units\) apart, telling you that the period of the graph is \(\displaystyle \pi.\) Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = -1,\) in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

3x^2 + 3  -->  6, 15, 30, 51

2x^2 - 1    -->  1, 7, 17, 31

x^2 + 2     -->  3, 6, 11, 18

Step-by-step explanation:

Let's start with the first equation; 3x^2 + 3

Substitute 1 (the first digit in a sequence) for x.

3(1^2) + 3

3(1) + 3

3 + 3 = 6

3(2^2) + 3 Then the second digit.

3(4) + 3

12 + 3 = 15

Since the two numbers we have so far are 6 and 15, there is only one sequence this could match. 6, 15, 30, 51.

2(1^2) - 1

2(1) - 1

2 - 1 = 1

This equation represents 1, 7, 17, 31.

These same steps apply to the other equation as well.

1^2 + 2, then 2^2 + 2, then 2^2 + 2, and so on. (But we don't need to do extra work to figure that out.)

Yes, there is evidence to suggest that the average diameter is greater than 2.30 cm.

To perform a hypothesis test for the population mean at alpha, use a two-tailed t-test. Assume the null hypothesis is that the average is equal to 2.30 cm and the alternative hypothesis is that the average is greater than 2.30 cm. Calculate the test statistic and then compare it to the critical value.

If the test statistic is greater than the critical value, then you can reject the null hypothesis and conclude that the average is greater than 2.30 cm.

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Answer:

3c+8

Step-by-step explanation:

Add the numbers of seeds together

c + 2c+8

Combine like terms

3c+8

The simplest form of 3x + 14 – x + \(1\frac{1}{2}\) is  2x + \(15\frac{1}{2}\). Both given expressions are not equivalent.

What is an expression?

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the expression 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given expression is 3x + 14 – x + \(1\frac{1}{2}\)

Now combine like terms:

= (3x - x) + (14 + \(1\frac{1}{2}\))

= 2x +  (14 + \(1\frac{1}{2}\))

Convert mixed fraction to improper fraction:

= 2x +  (14 + 3/2)

= 2x + 31/2

= 2x + \(15\frac{1}{2}\)

The equivalent expression of 3x + 14 – x + \(1\frac{1}{2}\) is  2x + \(15\frac{1}{2}\). Therefore, 3x + 14 – x + \(1\frac{1}{2}\) is not equivalent to 4x + \(1\frac{3}{4}\).

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Answer:

Step-by-step explanation:

This is the sum of perfect cubes. There is a pattern that can be followed in order to get it factored properly. First let's figure out why this is in fact a sum of perfect cubes and how we can recognize it as such.

343 is a perfect cube. I can figure that out by going to my calculator and starting to raise each number, in order, to the third power. 1-cubed is 1, 2-cubed is 8, 3-cubed is 27, 4-cubed is 64, 5-cubed is 125, 6-cubed is 216, 7-cubed is 343. In doing that, not only did I determine that 343 is a perfect cube, but I also found that 216 is a perfect cube as well. Obviously, x-cubed and y-cubed are also both perfect cubes. The pattern is

(ax + by)(a^2x^2 - abxy + b^2y^2) where a is the cubed root of 343 and b is the cubed root of 216. a = 7, b = 6. Now we fill in the formula:

(7x + 6y)(7^2x^2 - (7)(6)xy +6^2y^2) which simplifies to

(7x + 6y)(49x^2 - 42xy + 36y^2)

Answer: wheres the table

Step-by-step explanation:

Alleen's mom is not correct because if her friend reads 20 pages, she can read 30 pages in the same time period.

To answer this question, we need to use the terms "ratio" and "proportion". The given ratio of Alleen's reading speed to her friend's speed is 1.5:1. If Alleen's friend reads 20 pages, we can use proportion to find how many pages Alleen can read:

1.5 / 1 = x / 20

To solve for x (the number of pages Alleen reads), we can cross-multiply:

1.5 * 20 = 1 * x
30 = x

So, if Alleen's friend reads 20 pages, Alleen can read 30 pages in the same time period.

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Answer:

m∠U = 36°

m∠V = 75°

m∠T = 69°

Step-by-step explanation:

(2x+14)+(6x+9)+(6x+3)=180

Combine like terms: 14x+26=180

Solve this equation: x=11

Use x=11 to find angles

∠U = 36°

∠V = 75°

∠T = 69°

You can add up all of these measurements to check. =180°

Answer:

Step-by-step explanation:

The Triangle Sum Theorem states that the 3 angles of a triangle must add up to 180°.

We don't know the angles of the triangle, but we do know that the sum of all three unknown angles is 180°.

We set the three expressions together as equal to 180°.

6x + 3 + 6x + 9 + 2x + 14 = 180

Simplify

14x + 26 = 180

Subtract 26

14x = 154

x = 11

Now, we check our answer for x.

6(11) + 3 + 6(11) + 9 + 2(11) + 14 = 180

69 (measure of angle T) + 75 (measure of angle V) + 36 (measure of angle U) = 180

180 = 180 ✅

Note that once we found x, would substitute it in and get the needed measures. Since the needed measures add up to 180°, we know that our answer is correct.

Answer:

depends on the rate you work and how much you make during that time

Step-by-step explanation:

Answer:

just depends on how long and or how slow u go

Step-by-step explanation:

Answer:

If the x-coordinate is (0,0) and the y-coordinate is positive, it is not technically in any quadrant because it is located on the line and not in any quadrant.

Step-by-step explanation:

The graph is a vertical line

The equation of the vertical line is x = a, where a is the x-coordinate of all points lie on the line

In our graph the x-coordinate of any point on the lie is 6, so

Answer: 11

Step-by-step explanation:

5 + 7(6-4) - 2(5 - 1)

P E M/D A/S

5 + 7(2) - 2(4)

P E M/D A/S

5 + 14 - 8

P E M/D A/S

11

Given

Procedure

Now for y

The answer would be x = 2.75 and y = 1.25