Solve for x: −2x + 5 < 7
A:) x > −1
B:) x < −1
C:) x > −6
D:) x < −6

Please answer ASAP :]​

The coordinates of D are: B. (2.5, 0.5).

The product of the slopes of CD and AB is: C. -1.

This shows that AB is perpendicular to CD. Therefore, C lies on the perpendicular bisector of AB.

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Substituting the given parameters into the midpoint of a line segment formula, the midpoint of line AB is given by;

Midpoint AB = [(4 + 1)/2, (-2 + 3)/2]

Midpoint AB = [5/2, 1/2]

Midpoint AB = (2.5, 0.5).

5, 2

Next, we would determine the slopes of line segment CD and AB:

Slope (m) of CD = (0.5 - 2)/(2.5 - 5)

Slope (m) of CD = -1.5/-2.5 = 3/5

Slope (m) of AB = (-2 - 3)/(4 - 1)

Slope (m) of AB = -5/3 = 0.6

Product of the slopes = 3/5 × -5/3 = -3/3 = -1.

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Answer:

Step-by-step explanation:

Answer: 36

Step-by-step explanation: Gail needs 9 yards of fabric for a quilt. How many different patterns of fabric does she need if she buys

1

4

of a yard of each pat

patterns

Since ∠BDA is an inscribed angle measuring 25°, the arc it intercepts, AB, must measure 50°. For the same reason, the arc intercepted by ∠BDA must measure 64°. That's a total of 114° out of the semicircle ABCD, which leaves 66° out of the 180° half-circle. That's the measure of arc BC.

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Since ∠BDA is an inscribed angle measuring 25°, the arc it intercepts, AB, must measure 50°. For the same reason, the arc intercepted by ∠BDA must measure 64°. That's a total of 114° out of the semicircle ABCD, which leaves 66° out of the 180° half-circle. That's the measure of arc BC.

Define measurement?

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The discriminant and the point of tangency are used to find the values of the variables as follows;

7. The line y = m·x is tangent to the curve x² + 2·x·y + 2·x = 1 when m = 1

8. The line y = 2·x - k is tangent to the curve x² + y² = 5, when k = ±5

Exercise 11.

1. The discriminant of the equation x² - 6·x + y² - 2·y + 2 = 0 is zero when y = x - 6, therefore the line x - y = 6 is tangent to the curve x² - 6·x + y² - 2·y + 2

2. The exact values of k for which the line 2·x + 3·y = k is tangent to the curve C = 4·x² + 9·y² = 36 is k = ±6·√2

The discriminant is the values which are within the radical sign of the quadratic formula.

7. At the point of tangency, the discriminant is 0

The equation is; x² + 2·x·y + 2·x = 1

The equation of the line is; y = m·x

Rewriting the equation of the curve, we get;

x² + 2·x·y + 2·x = 1

2·x·y = 1 - x² - 2·x

\(y = \dfrac{1 - x^2 - 2 \cdot x}{2\cdot x}\)

At the point of tangency, we have;

\(y = \dfrac{1 - x^2 - 2 \cdot x}{2\cdot x} = m\cdot x\)

1 - x² - 2·x - 2·m·x² = 0

1 - x² - 2·m·x² - 2·x  = 0

1 - x²·(1 - 2·m) - 2·x  = 0

The discriminant is zero at the point of tangency, which gives;

((-2²) - 4× (-(1 - 2·m)) × 1) = 0

8 - 8·m = 0

8 = 8·m

m = 8 ÷ 8 = 1

8. The line y = 2·x - k is tangent to the curve, x² + y² = 5 where we have;

y² = 5 - x²

y² = (2·x - k)²

5 - x² = (2·x - k)²

Which gives;

k² - 4·k·x + 5·x² - 5

5·x² - 4·k·x + k² - 5

At a tangent point the discriminant is therefore;

(-4·k)² - 4 × 5 × (k² - 5) = 100 - 4·k² = 0

100 - 4·k² = 0

4·k² = 100

k² = 100 ÷ 4 = 25

k = √(25) = ±5

Exercise 11

1. The equation of the line is; x - y = 6

The equation of the curve is; x² - 6·x + y² - 2·y + 2 = 0

From the equation, x - y = 6, we get; y = x - 6

Which gives; x² - 6·x + (x - 6)² - 2·(x - 6) + 2 = 0

x² - 6·x + (x - 6)² - 2·(x - 6) + 2 = 2·x² - 20·x + 50 = 0

2·x² - 20·x + 50 = 0

x² - 10·x + 25 = 0

The discriminant is; (-10)² - 4 × 1 × 25 = 0

Therefore;

3. The curve 4·x² + 9·y² = 36 has the tangent line 2·x + 3·y = k, when we have;

4·x² + 9·y² = 36

9·y² = 36 - 4·x²

y² = (36 - 4·x²)/9 = 4 - (4/9)·x²

y² = 4 - (4/9)·x²

2·x + 3·y = k

3·y = k - 2·x

y = (k - 2·x)/3

y² = ((k - 2·x)/3)²

4 - (4/9)·x² = ((k - 2·x)/3)²

4 - (4/9)·x² - ((k - 2·x)/3)² = 0

8·x² - 4·k·x + k² - 36 = 0

(-4·k)² - 4 × 8 × (k² - 36) = 0

1152 - 16·k² = 0

16·k² = 1152

k² = 1152 ÷ 16 = 72

k = √(72) = ±6·√2

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Answer:

Y is 90 and x is 90

Step-by-step explanation:

Answer:

  x = 25

Step-by-step explanation:

The given angles, x° and (6x+5)° form a linear pair. You want the value of x.

Two angles that together form a straight line are called a linear pair. A linear pair of angles has a total measure of 180°.

  x° +(6x +5)° = 180°

  7x +5 = 180 . . . . . . . . . divide by °, collect terms

  7x = 175 . . . . . . . . . . subtract 5

  x = 25 . . . . . . . . . . divide by 7

The value of x is 25.

\({ \boxed{ \red{ \bold{3072}}}}\)

Step-by-step explanation:

Given,

\({ \green{ \sf{ {ar}^{2} = 24}}} \: { \to} \: { \tt{ {eq}^{n} (1)}}\)

\({ \green{ \sf{ {ar}^{5} = 192}}} \: { \to} \: { \tt{ {eq}^{n} (2)}}\)

From Eqⁿ (2),

\({ \green{ \sf{ {ar}^{2}. {r}^{3} = 192}}}\)

\({ \green{ \sf{24. {r}^{3} = 192}}}\)

\({ \green{ \sf{ {r}^{3} = \frac{192}{24}}}} \)

\({ \green{ \sf{ {r}^{3} = 8}}}\)

\({ \green{ \sf{ {r}^{3} = {2}^{3}}}} \)

\({ \boxed{ \purple{ \sf{r = 2}}}}\)

From Eqⁿ (1)

\({ \blue{ \sf{ {ar}^{2} = 24}}}\)

\({ \blue{ \sf{a {(2)}^{2} = 24}}}\)

\({ \blue{ \sf{4a = 24}}}\)

\({ \blue{ \sf{a = \frac{24}{4}}}} \)

\({ \boxed{ \purple{ \sf{a = 6}}}}\)

10th term is,

\({ \orange{ \sf{ {ar}^{9} }}}\)

\({ \orange{ \sf{6 {(2)}^{9}}}} \)

\({ \orange{ \sf{6(512)}}}\)

\({ \bold{ = }}{ \boxed{ \red{ \bold{3072}}}}\)

Answer:

20

Step-by-step explanation:

(25-5)/(1-0)

20/1

20

Answer:

20

Step-by-step explanation:

use y2-y1/x2-x1 by finding 2 points on the graph

(0,5) and (2,45)

45-5/2-0

40/2

20

Hopes this helps please mark brainliest

The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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Hello !

Answer:

\(\Large \boxed{\sf length=13cm}\)

Step-by-step explanation:

The volume of a pyramid is given by \(\sf V_{pyramid}=\frac{1}{3} \times B\times h\) where B is the area of the base and h is the height.

This is a rectangular pyramid. We have where \(\sf B=l\times w\) l is the length and w is the width (breadth).

So \(\sf V_{pyramid}=\frac{1}{3} \times l\times w\times h\)

Given :

Let's replace h, w, l, \(\sf V_{pyramid}\) with their values in the previous formula :

\(\sf 728=\frac{1}{3} \times x\times 8 \times 21\\728=56x\)

Let's solve for x !

Divide both sides by 56 :

\(\sf \frac{56x}{56} =\frac{728}{56}\\ \boxed{\sf x=13cm}\)

Have a nice day ;)

Answer:

b. -3

Step-by-step explanation:

30 - 3 = 27

27 - 3 = 24

24 - 3 = 21....

Answer:

answer big no l

x=-6

y=10

Step-by-step explanation:

answer of 4

x 30

Answer:

Step-by-step explanation:

1) 5x + 4 + 3x - 8 = 180 ( co - interior angles )

8x - 4 = 180

8x = 184

x = 184 / 8

x = 23°

y = 3x - 8 ( vertically opposite angles )

y = 3 × 23 - 8

= 69 - 8

= 61°

4) 5 x + 7 = 2x + 97 ( vertically opposite angles )

5x - 2x = 97 - 7

3x = 90

x = 90 / 3

x = 30°

Hope this helps

plz mark as brainliest!!!!!

Answer:

-7x + 5

General Formulas and Concepts:

Distributive Property

Combining Like Terms

Step-by-step explanation:

Step 1: Write expression

-5(2x - 1) + 3x

Step 2: Simplify

Using multiplication, the total length of all the sunflowers in the garden is 1,260 inches.

Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.

Multiplication operation involves the multiplicand, the multiplier, and the product.

The total number of sunflowers in the garden = 210

The length of each sunflower = 6 inches

The total length of all the sunflowers = 1,260 inches (210 x 6)

Thus, based on multiplication operation, the total length of the sunflowers in the garden can be stated to be 1,260 inches.

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Assume that each sunflower measures 6 inches in length and there are 210 sunflowers in the garden.

Answer:

23. Similar as well as congruent triangle

25. Conguent triangle

Step-by-step explanation:

Answers:

23. Not enough information

25. Congruent (by the HL theorem)

HL = hypotenuse leg

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

Explanation for problem 23.

Check out figure 1 shown below.

I have marked the given diagram with light blue and light pink to show which angles are congruent.

Because lines UN and TC are parallel, we know the following alternate interior pairs are congruent.

Therefore, we can establish one link of paired congruent angles of the triangles LNU and TCH. However, we cannot determine any other angle pairings. Why not? Because we don't know if segment UL is parallel to segment TH. If they were parallel, then we could establish something like angle LUN = angle CHT as one alternate interior pairing.

But again, we don't know if UL is parallel to TH. The arrow markers aren't shown for these segments.

Therefore, we simply don't have enough information to determine if the triangles are similar or congruent.

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

Explanation for problem 25.

Luckily this problem will provide sufficient info to prove the triangles KSR and ISR are congruent.

We start with the given info that KR = SI due to the identical tickmarks. This represents one node in the flowchart (see figure 2).

Another node is angle RKS = angle RIS because both are right angles, aka 90 degree angles.

A third node is SR = SR because of the reflexive property.

Those three nodes then feed into the final conclusion node that triangle KSR = triangle ISR. The reasoning is "HL theorem" where HL = hypotenuse leg. This theorem works for right triangles only.

Take note how I structured the proof so that it flows from top to bottom. The three nodes side by side are related so they share the same row.

There are many other ways to make the flowchart, so don't feel obligated to use this format. Use whatever works best for you.

The simplified expression when a polynomial is divided by a monomial is \(y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).\)

A polynomial expression can be represented as a product of other, smaller polynomial expressions through the algebraic process of factoring. The process of factoring can be used to simplify expressions and solve problems. A polynomial equation's roots can be found by factoring, as can the common factors in an expression that can be eliminated. Factoring occasionally enables us to spot trends and connections between several expressions.

Depending on the kind of polynomial and the degree of the terms involved, there are several ways to factor. S

For the given expression \((12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)\) factor the common term.

\((12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)\\-4y^5u^2(3y^2 - 8u^4 - 3y^2u^4) / (-4y^2u^5)\)

Cancelling the -4:

\(= y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2)\)

Hence, the simplified expression is \(y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).\)

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Answer:

The bottom choice.

Step-by-step explanation:

Evaluate the behavior relating to when x goes into the negatives (-∞), f(x) goes towards the positives or negatives.

Do the same for when x goes into the positives (∞).

So, as x approaches -∞, f(x) approaches -∞ because f(x) goes deeper into the negatives.

And, as x approaches ∞, f(x) approaches -∞ as well, meaning that your answer is the bottom choice.

Answer:

The return on stockholders' equity is 11.3% and the return on common stockholders' equity is 20.1%.

Step-by-step explanation:

To calculate the return on stockholders' equity and the return on common stockholders' equity, we can use the following formulas:

Return on Stockholders' Equity = Net Income / Average Stockholders' Equity

Return on Common Stockholders' Equity = Net Income - Preferred Dividends / Average Common Stockholders' Equity

Using the given values, we can calculate:

a. Return on Stockholders' Equity:

Return on Stockholders' Equity = $135,000 / $1,194,690

Return on Stockholders' Equity = 0.113 or 11.3%

b. Return on Common Stockholders' Equity:

Return on Common Stockholders' Equity = ($135,000 - $5,400) / $644,776

Return on Common Stockholders' Equity = $129,600 / $644,776

Return on Common Stockholders' Equity = 0.201 or 20.1%

Therefore, the return on stockholders' equity is 11.3% and the return on common stockholders' equity is 20.1%.

SOLUTION:

Step 1:

In this question, we are given the following:

Which equation represents the line passing through the point (-5, 12) and perpendicular to the line y=2/3x +14 ?

Step 2:

The details of the solution are as follows:

Step 3:

CONCLUSION:

The final answer is:

Problem 1

The variable "favorite style of sweatshirt" is a qualitative variable instead of a quantitative one. This is because the categories "hoodie", "pullover" and "zip-up" are not quantitative in nature. They are simply labels or names. Yes we can assign a frequency tally for each one, which is likely what she's doing, but that's a slightly different story from what your teacher is asking.

An example of a quantitative variable is "height". This variable can take on any positive numeric value, within realistic reason of course. Theoretically there are infinitely many possible height values if we allow as much precision as we want. Even in a more finitely restricted space, we still have a lot of values to work with. We don't consider each number a different label or category or class. It's just a number. So that's what makes "height" a quantitative variable.

Keep in mind that just because you have a number, doesn't mean it's automatically quantitative. A phone number or a basketball player jersey number are two examples of numbers that are labels. We cannot add up a bunch of phone numbers to get something meaningful. Ask yourself "can I do math operations on these numbers?". If the answer is "yes", then you have quantitative data. Be careful to ask this question for any kind of data you have. Going back to Dyani's data, the category names cannot have math operations applied to them, so that's more evidence we're not dealing with quantitative data.

In short, Dyani has qualitative data instead of quantitative data. Specifically, she has nominal data because each label can be thought of as a name. There is no order to each choice, which means the data is not ordinal.

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

Problem 2

The answer to this question is found at the top, in the very first sentence. She wants to know what the most common car is. The population is the set of all student drivers at that school. Let's say there are 400 students who drive to school. That would mean the population would be those 400 people.

Because it's likely too time consuming to survey every member of the population, a sample is used instead to make the best estimate of what the population is. So this is what she's doing when she asks every 10th student to take part of the survey. This is known as systematic sampling because there's a pattern or rule to her choices. This form of sampling can be fairly unbiased assuming that she does this on various different days to get a good snapshot. If she only did it on one day, then it could be likely that some students skipped school or some were out sick. The more she samples, the better look she'll have at the population.

Answer:

x = 116

x° = 116°

(x - 52)° = 64°

Step-by-step explanation:

this shape is a right angle trapezoid and there are two 90° angles

the sum of all interior angles is 360°

90 + 90 + x + x - 52 = 360

2x - 52 = 180

2x = 232

x = 116

Answer:

0.31

Step-by-step explanation:

the area of shaded region =

(2×½×8×10) = 80

the total area of fig. =

½×(34+18)×10 = 260

the probability = 80/260 = 0.31

Step 1: Isolate the Sin Operator

\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)

Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable

Note that since trig functions have 2 general solutions, this will give us one of our general solutions.

\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)

x₁= 0.48

Solving for x₂

Use the period identity for Sin Functions

\(sin(x)=sin(\pi -x)\)

X in this case is arcsin(0.25)

\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)

So our two general solutions are 0.48 and 5.52

Step 3: Period

Trig Functions have periodic behavior and this function period is

\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)

So our general solutions are

0.48±12k, where k is an integer

5.52±12k, where k is an integer

Let k=1, and we get our next set of solutions:

12.48 and 17.52

So our answer is 0.48,5.52,12.48,17.52

Answer:

you have nice handwriting

Step-by-step explanation:

no answer

Answer:

$4.25

Step-by-step explanation:

We can create a proportion to find how much 25 oz will cost:

\(\frac{2.79}{16.4}\) = \(\frac{x}{25}\)

We can cross multiply to find x.

16.4x = 69.75

x = 4.25

So, this means 25 ounces of cereal will be $4.25

Answer:

37 feet

Step-by-step explanation:

9 1/2 × 4 = 37

...........

Answer:

The value of the test statistic is \(t = -1.61\)

Step-by-step explanation:

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Our test statistic is:

\(t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the expected mean, \(\sigma\) is the standard deviation and n is the size of the sample.

A publisher reports that 52% of their readers own a laptop.

This means that \(\mu = 0.52\)

Sample of 180:

Means that \(n = 180\)

By the Central Limit Theorem:

\(\frac{\sigma}{\sqrt{n}} = s = \sqrt{\frac{0.52*0.48}{180}} = 0.0372\)

A random sample of 180 found that 46% of the readers owned a laptop.

This means that \(X = 0.46\)

Find the value of the test statistic.

\(t = \frac{X - \mu}{s}\)

\(t = \frac{0.46 - 0.52}{0.0372}\)

\(t = -1.61\)

The value of the test statistic is \(t = -1.61\)