Solve the inequality:

|x+3|<1

B

note that (f + g)(x) = f(x) + g(x)

f(x) + g(x) = -4x² - 6x - 1 - x² - 5x + 3 ( collect like terms )

               = - 5x² - 11x + 2

Answer:

The correct option is B.

Step-by-step explanation:

The given functions are

[tex]f(x)=-4x^2-6x-1[/tex]

[tex]g(x)=-x^2-5x+3[/tex]

Using the p addition property of functions (f + g)(x) can be written as

[tex](f+g)(x)=f(x)+g(x)[/tex]

Substitute the values of each function in the above equation.

[tex](f+g)(x)=-4x^2-6x-1-x^2-5x+3[/tex]

Combine like terms.

[tex](f+g)(x)=(-4x^2-x^2)+(-6x-5x)+(-1+2)[/tex]

[tex](f+g)(x)=-5x^2-11x+2[/tex]

Therefore the correct option is B.

Answer:

not a rectangle

Step-by-step explanation:

There are several ways to determine whether the quadrilateral is a rectangle. Computing slope is one of the more time-consuming. We can already learn that the figure is not a rectangle by seeing if the midpoint of AC is the same as that of BD. (It is not.) A+C = (-5+4, 5+2) = (-1, 7). B+D = (1-2, 8-2) = (-1, 6). (A+C)/2 ≠ (B+D)/2, so the midpoints of the diagonals are different points.

___

The slope of AB is ∆y/∆x, where the ∆y is the change in y-coordinates, and ∆x is the change in x-coordinates.

... AB slope = (8-5)/(1-(-5)) = 3/6 = 1/2

The slope of AD is computed in similar fashion.

... AD slope = (-2-5)/(-2-(-5)) = -7/3

The product of these slopes is (1/2)(-7/3) = -7/6 ≠ -1. Since the product is not -1, the segments AB and AD are not perpendicular to each other. Adjacent sides of a rectangle are perpendicular, so this figure is not a rectangle.

___

Our preliminary work with the diagonals showed us the figure was not a parallelogram (hence not a rectangle). For our slope calculation, we "magically" chose two sides that were not perpendicular. In fact, this choice was by "trial and error". Side BC is perpendicular to AB, so we needed to choose a different side to find one that wasn't. A graph of the points is informative, but we didn't start with that.

E is located at (-2,-4)

F is located at (2,2)

To find the midpoint, add the 2 X values together and divide by two, then do the same with the y values:

X = -2 + 2 = 0/2 = 0

Y = -4 + 2 = -2/2 = -1

The midpoint is located at (0,-1)

The roots of equation are: x= -3+ √29/2 and x= -3-√29/2.

Quadratic equation's roots The roots of a quadratic equation are the values of the variables that fulfil the equation. In other words, if f(a) = 0, then x = a is a root of the quadratic equation f(x). The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.

given:

x² + 3x - 5 = 0

So, solving for x

x² + 3x - 5 = 0

D= (3)² - 4(1)(-5)= 9 + 20= 29

Now, using the quadratic equation

x= -b ± √ b² -4ac/ 2a

x= -3 ±√(3)² -4(1)(-5) / 2

x= -3±√29/2

x= -3+ √29/2 and x= -3-√29/2

Hence, the roots of equation are: x= -3+ √29/2 and x= -3-√29/2.

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Yes ,

side ×side×side= side^3 =volume of cube  

=>side^3=30

=>side = 30^1/3-answer

The two points on the graph of the function - 7y + 8 = 21x - 6 are;

⇒ (0, 2) and (2, -4)

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

The function is,

⇒ - 7y + 8 = 21x - 6

Now,

We can draw the graph of the function - 7y + 8 = 21x - 6 as shown in figure.

And, The points on the graph are;

⇒ (0, 2) and (2, -4)

Thus, The two points on the graph of the function - 7y + 8 = 21x - 6 are;

⇒ (0, 2) and (2, -4)

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Angles DCE and ACB are vertical angles, hence equal. Both have the value 3x.

Angles ACH and HCB (x) add to give ange ACB, so they sum to 3x. That makes ACH have the value 2x. (2x +x = 3x)

The angles in triangle ACH add to 180°. This sum is ...

... 2x +2x +100° = 180°

... 4x = 80° . . . . . . . . subtract 100°, then divide by 4 to get ...

... x = 20°

Divide 100 from 2000

2000/100 = 20

20 counted to get to 2000 by skip counting by 100

hope this helps

Answer:

x can take any value less than 3.

Step-by-step explanation:

This is an inequality.

[tex]2x < 6[/tex]

Lets solve the inequality for x

[tex]x < 3[/tex]

This means x can take any value less than 3.

We can show this by using a number line.

Notice how number 3 is not fully shaded, this means x cannot be 3. And all the numbers less than 3 to infinity is shaded, meaning x can take any value in that range.

We won't have a function if for same value of x in (x,y) we get different values y.

So first step: figure out k so that the first coordinate (x) is the same:

3k-4=4k    | solve for k

k = -4

no check the values y for the elements of the relation

x = 3k-4 = -12-4=-16

so at -16 we get (-16,16) and (-16, 32), which mean for k=-4 the relation is not a function.

Let me know if you have any questions.

Answer:

K= -4

Step-by-step explanation:

Since it isn't possible that (3k-4, 16) is going to be equal to (4k, 32) in terms of positive numbers, you will have to go to the negative side of the number line.

K has to equal 4 because 3 · -4 = -12, and -12 minus 4 is equal to -16.

And since 4 · -4 = -16, K has to equal - 4.

25x²-16 is the difference of two squares, so can be written as the product ...

... (5x -4)(5x +4)

or

... (5x +4)(5x -4)

Answer:

[tex](5x+4)(5x-4)[/tex]

Step-by-step explanation:

25x^2- 16

To find out the product that is equivalent to the given expression we need to factor the given expression

we write the numbers in square form

25 = 5*5 = 5^2

16 = 4*4 = 4^2

5^2x^2 - 4^2

[tex](5x)^2- 4^2[/tex]

we apply difference in square formula

a^2 - b^2 = (a+b)(a-b)

[tex](5x)^2- 4^2=(5x+4)(5x-4)[/tex]

The angle of elevation of the ladder is approximately 70.35°

How do we find the angle of elevation?

To find the angle of elevation of the ladder, we can use trigonometric functions.

The angle of elevation can be found using the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle.

opposite side is the height from the ground to the window = 14 feet,

adjacent side is the distance from the house to the base of the ladder= 5 feet.

tan(θ) = opposite/adjacent

tan(θ) = 14/5

θ = arctan(14/5)

θ =  70.35 degrees

​

Full question
Jack is using a ladder to hang lights up on his house. He places the ladder 5 feet from the base of his house and leans It so it reaches a window 14 feet above the ground. Find the angle of elevation of the ladder.
A) 65.5

B) 68.4

C) 70.3

D) 71.5

E) 72.9

depth = 3.3 cm

the volume (V ) of a cuboid is

V = Ah ( A is the area and h the depth )

A = 20 × 28 = 560 cm², thus

h = [tex]\frac{V}{A}[/tex] = [tex]\frac{1843}{560}[/tex] ≈ 3.3 cm

It can't be proven because it isn't so.

You can show that A'B' = C'D' because each is half of AC (from the midsegment theorem).

The set of seashell weights that Mirna collected (12, 13, 16, 17, 18, 20) does not have a mode because all values appear only once.

The mode of a set of data refers to the number that appears most frequently. In the case of the weights of the seashells Mirna collected in Florida, the data set is: 12, 13, 16, 17, 18, 20. To find the mode, we look for the value that occurs the most:

Since all numbers occur only once, there is no number that appears more frequently than the others. Therefore, this set of data does not have a mode.

Hello...

Z = total area (1)

___-z___0.9544___z

z = 0.0288

Normal,

z = 2

The value of z is 2.  the probability that is closest to 0.0228, where the outliner is a -2 and z equals 2.

The decimal numeral system is widely used to express both integer and non-integer numbers. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A number that has been divided into a whole and a fraction is called a decimal. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

The word decimus, which means tenth in Latin, is derived from the base word decem, or 10. As a result, the decimal system, often known as a base-10 system, has 10 as its fundamental unit. A number expressed using the decimal method is also referred to as being "decimal."

Given ,

0.9544/2= 0.4772

.5- 0 .4772=0.0228

the probability that is closest to 0.0228, where the outliner is a -2 and z equals 2.

Therefore value of z is 2.

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Answer:

Points (0,-3) and (-3,-1) work, I got a 100% on the test.

If s = 1/4 unit and A = 80s^2

A = 80 (1/4)^2

A = 80 (1/16)

A = 5

Answer

5 square units

5 square units

substitute s = [tex]\frac{1}{4}[/tex] into the equation

A= 80 × ([tex]\frac{1}{4}[/tex])² = 80 × [tex]\frac{1}{16}[/tex] = [tex]\frac{80}{16}[/tex]= 5 square units

slope = [tex]\frac{1}{12}[/tex]

the slope is the value of f' (36)

f(x) = √x = [tex]x^{\frac{1}{2} }[/tex]

f'(x) = [tex]\frac{1}{2}[/tex] [tex]x^{-\frac{1}{2} }[/tex] = [tex]\frac{1}{2\sqrt{x} }[/tex]

f'(36) = [tex]\frac{1}{2(6)}[/tex] = [tex]\frac{1}{12}[/tex]

Answer:

[tex]slope = \frac{1}{12}[/tex]

Step-by-step explanation:

Here is another method to solve your problem. I am showing this method because this is the first method normally taught and a student might not of had the chance yet to learn the other methods

We can solve this problem by using limits and the following function

[tex]\lim_{h\to 0} \frac{f(x+h) - x}{h}[/tex]

[tex]\lim_{h\to 0} \frac{\sqrt{x+h} - \sqrt{x}}{h}[/tex]

Next multiply by the conjugate of the numerator.

[tex]\lim_{h\to 0} \frac{\sqrt{x+h} - \sqrt{x}}{h} * \frac{\sqrt{x+h} + \sqrt{x}}{\sqrt{x+h} + \sqrt{x}}[/tex]

[tex]\lim_{h\to 0} \frac{x + h - x}{h(\sqrt{x+h} + \sqrt{x})}[/tex]

Cancel the x - x

[tex]\lim_{h\to 0} \frac{h}{h(\sqrt{x+h} + \sqrt{x})}[/tex]

Divide out the h

[tex]\lim_{h\to 0} \frac{h}{h(\sqrt{x+h} + \sqrt{x})}[/tex]

[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x+h} + \sqrt{x})}[/tex]

Plugin 0 where h is located

[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x+h} + \sqrt{x})}[/tex]

[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x+0} + \sqrt{x})}[/tex]

[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x} + \sqrt{x})}[/tex]

Combine Like terms in denominator

[tex]\lim_{h\to 0} \frac{1}{(\sqrt{x} + \sqrt{x})}[/tex]

[tex]\lim_{h\to 0} \frac{1}{2\sqrt{x}}[/tex]

Now lets use our derivative and plugin 36 where x is located and solve

[tex]\frac{1}{2\sqrt{x}}[/tex]

[tex]\frac{1}{2\sqrt{36}}[/tex]

[tex]\frac{1}{2(6)}[/tex]

[tex]\frac{1}{12}[/tex]

Note, this is a harder method but it is normally the first method taught in Calculus 1.

We can treat inequalities like standard algebraic equations.

7x - 9 > 2x + 6

Add 9 to both sides.

7x > 2x + 15

Subtract 2x from both sides.

5x > 15

Divide both sides by 5.

x > 3

Answer:

x>3 is the answer

Step-by-step explanation:

We are given one inequality

7x-9>2x+6

To solve this we can do additions and subtraction as we do for equations.

Only for multiplication if negative number is used inequality changes

So let us add 9 to both the sides

7x>2x+6+9

Now subtract 2x from both the sides

7x-2x >15

5x>15

We divide by a positive number 5 without disturbing inequality sign.

X>3 is the answer

In interval notation we can write this as open interval

(3,∞)

In number line this is the region to the right of 3, not includig 3

Step-by-step explanation:

6/8 / 3/4 = 1

Hi!

[tex]3x=18[/tex]

[tex]\frac{3x}{3}=\frac{18}{3}[/tex]

[tex]x=6[/tex]

Explanation: This question is super easy on this question. First you had to divide by 3 from both sides. And simplify, it gave us the answer is x=6 is the right answer. Hope this helps! And thank you for posting your question at here on Brainly. And have a great day. -Charlie

You need to pick from each column depending on what makes sense - they are mixed (some numbers are roots, some cubes, in the same column).

On the order:

3 - 27

4 - 64

5 - 125

512 - 8

8 - 2

729 - 9

216 - 6

1 - 1

Answer:

as>JDKFas;lkdjfsa;lkdfjas;kldfjlakdjfalsdkfjakdkdkdlddd

Step-by-step explanation:

Amount of down payment = $650.

Jordan gets money by mowing lawns = $25 per lawn.

Sharla gets money by selling handmade necklaces for = $15 each necklace.

The number of lawns Jordan mows = x.

The number of necklaces Sharla sells = y.

A) Total money raised by Jordan to move x lawns at the rate $25 per lawn = 25x.

Total money raised by Sharla by selling y handmade necklaces for $15 per necklace = 15y.

Total money Sharla can raise by selling 40 necklaces at the rate $15 each = 40 × 15 = $600.

Answer:

See the attached.

Step-by-step explanation:

A graph of f' is a graph of the slope of the function. Your function f(x) is piecewise linear, so different sections of its graph have different constant values of slope.

In the intervals (-5, -2) and (0, 2), the slope is -1. (The graph has a "rise" of -1 for each "run" of 1.) So, in those intervals, the graph of f' looks like a graph of y=-1.

In the interval (-2, 0), the rise is 2 for a run of 2, so the slope is 2/2 = 1. The graph of f' in that interval will look like a graph of y=1.

In the interval (2, 5), the rise of f(x) is 1 for a run of 3, so the slope in that interval is 1/3. There, the graph of f' will look like a graph of y=1/3.

If you want to get technical about it, the slope is undefined at x=-2, x=0, and x=2. Therefore, the line segments that make up the graph of f' ought to have open circles at those points, indicating that f' is not defined.

When you replace the comparison symbol (<) with an equal sign (=), you get the equation of a line in slope-intercept form:

... y = mx + b

where m is the slope, and b is the y-intercept.

Your equation has m = -1/4 and b = -1. To graph this line, find the point (0, -1) on the y-axis. To find another point on the line, you can use the slope value (rise/run = -1/4), which tells you the line "rises" -1 for each "run" of +4. That is, another point on the line will be 4 units to the right and 1 unit down, at (4, -2). Working in the other direction (to the left, instead of to the right), the -1/4 slope tells you the point 4 units left and 1 unit up (-4, 0) will also be on the line. Draw a dashed line through these points,

The dashed line you just drew is the boundary of the solution region. It is dashed because the line itself is not part of the solution. (Those points do not meet the requirement for "less than.")

Appropriate values of y are ones that are less than those on the line, so the solution region is indicated as being the half-plane below the line. You indicate this by shading the solution region. (See the attachment for an example of the way this can be graphed.)

_____

If the comparison is ≤ instead of <, then the line is solid (not dashed), indicating it is part of the solution region. If the comparison is > or ≥, then the shaded region is above the line, where y-values are greater than those on the line.

All the numbers shown are real.

The answers to problems 4, 7, 11 are irrational, because they are square roots of numbers that are not perfect squares.

The remaining numbers are rational because they are terminating decimals or the square root of a square number.

(1)

C

d + q = 250 ( total number of coins ) and

d + 0.25q = 137.50 ( total value of coins )

(2)

G

consecutive integers have a difference of 1 between them

let the integers be n and n + 1 then

2n + 3(n + 1) = 153 (distribute and simplify )

2n + 3n + 3 = 153

5n + 3 = 153 ( subtract 3 from both sides )

5n = 150 ( divide both sides by 5 )

n = 30 and n + 1 = 31

the 2 consecutive integers are 30 and 31

(3)

E

let x be the shortest side then longest side = 2x and middle side = x + 4

2x + x + 4 + x = 52

4x + 4 = 52 ( subtract 4 from both sides )

4x = 48 ( divide both sides by 4 )

x = 12

the longest side = 2x = 2 × 12 = 24

The system of equations for a parking meter are -

d + q = 250

100d + 25q = 137.50

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a a parking meter in downtown Seattle takes dollar coins and quarters only.

Assume that there are [d] dollar coins and [q] quarter coins. Then, we can write the system of equations as -

d + q = 250

100d + 25q = 137.50

Therefore, the system of equations for a parking meter are -

d + q = 250

100d + 25q = 137.50

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Answer:

  y -8 = -5(x -6)

Step-by-step explanation:

The point-slope form of the equation for a line is generally written ...

  y -k = m(x -h)

for slope m and point (h, k).

The slope of your parallel line is the same as the slope of the reference line, -5. So your equation is ...

  y -8 = -5(x -6)