Identify the solution set of the following quadratic inequality:
-a^2+4a+7>2
options
(-1,5)
(-∞,-1)∪(5,∞)
(-∞,-1]∪[5,∞)
(-∞,-3]∪[0,∞)

The half of the number is 4.5 .

Given in question as  14 is subtracted from 6 times a number.

Let us suppose a number is x.

First find 6 times of a number = 6*x.

6 times can be defined as x + x + x + x + x + x = 6*x.

We have to subtract from 6 times a number.

14 is subtracted from 6 times a number means 6x - 14.

After subtracting 14 is left.

So 6x - 14 = 40.

Add 14 both side of equal sign.

6x-14+14 = 40+14.

6x = 54.

x = 54/6.

x = 9.

Half of the number x is 9/2 = 4.5.

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Answer:

see explanation

Step-by-step explanation:

(a)

given y is directly proportional to x³ then the equation relating them is

y = kx³ ← k is the constant of proportion

to find k use the condition y = 20h when x = h

20h = kh³ ( divide both sides by h³ )

[tex]\frac{20h}{h^3}[/tex] = k , then

k = [tex]\frac{20}{h^2}[/tex]

y = [tex]\frac{20}{h^2}[/tex] x³ = [tex]\frac{20x^3}{h^2}[/tex]

(b)

when y = 67.5h , then

67.5h = [tex]\frac{20x^3}{h^2}[/tex] ( multiply both sides by h² to clear the fraction )

67.5h³ = 20x³ ( divide both sides by 20 )

3.375h³ = x³ ( take cube root of both sides )

[tex]\sqrt[3]{3.375h^3}[/tex] = x , that is

x = 1.5h

The formula for y in terms of x and h will be y = (20 / h²)x³ and y = 20h. The x in terms of then y = 67.5 h will be x = 1.5h.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

y is directly proportional to the cube of x. Then we have

y ∝ x³

y = kx³

We have y = 20h when x = h, then

20h = k(h)³

k = 20 / h²

The formula for y in terms of x and h is given as,

y = (20 / h²)x³

y = (20 / h²)  (h³)

y = 20h

If y = 67.5 h, then we have

67.5 h = (20 / h²)x³

3.375 h³ = x³

x = 1.5h

The formula for y in terms of x and h will be y = (20 / h²)x³ and y = 20h. The x in terms of then y = 67.5 h will be x = 1.5h.

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The graph y = - 0.5x + 12 has a slope of - 0.5 and decreases in nature.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, harper created a graph of a line by y = - 0.5x + 12.

∴ The graph will have a slope of - 0.5 which is decreasing in nature.

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Answer:

Step-by-step explanation:

A line that is perpendicular to another will have the opposite slope.

y = [tex]-\frac{1}{3}[/tex]a + b

To find b, substitute y and a with the given values

6 =  [tex]-\frac{1}{3}[/tex](-6) + b

6 = 2 + b

-2  -2

4 = b

thus

y = [tex]-\frac{1}{3}[/tex]a + 4

Answer:

r = d(x-e)

or r = dx - de

Step-by-step explanation:

x = e + [tex]\frac{r}{d}[/tex]  subtract e from both sides.

x - e = [tex]\frac{r}{d}[/tex]  Multiply both sides by d

d(x -e) = r

or

dx -de = r

Answer: the space shuttle

Step-by-step explanation:

Answer:

4 x^3 + 24 x^2 = 4 (x^3 + 6 x^2) = 4 x^2 (x + 6)

4 x^2 (x + 6)        seems to be the lowest factor

Answer:(2x+1)(3x-4)

Step-by-step explanation:Factor the expression out first by getting 6x^2+3x-8x-4. From there, factor again to 3x(2x+1)-4(2x+1) to get the answer (2x+1)(3x-4)

Answer:

(3x - 4)(2x - 1)

Step-by-step explanation:

6x^2 - 5x - 4

When factoring, we want to first find the GCF. In this case, the GCF is one so we leave it as that. Next, we want to try and find the sum and the product. Additionally, we have a leading coefficient. We will multiply the leading coefficient by the last term, which is -4. (You will need to remember this to continue on later.)

x^2 - 5x - 24

Now, we can find the sum and the product. To do this, we need to list the factors of 24. (Remember negatives as well!)

24: 1 and 24, 2 and 12, 3 and 8, 4 and 6.

As -24 is also a negative, that means it will have one positive and one negative factor. This must also add up to -5.

One pair that does this is -8 and 3. They multiply together to -24 and add up to -5.

Now, since we multiplied the leading coefficient in the beginning, we must bring it back down into the parenthesis.

(6x - 8)(6x - 3)

We must divide out and try to simplify this as much as we can to match the leading coefficient. The divisors must multiply up to 6.

(6x - 8)/2 and (6x - 3)/3.   3*2 = 6

(3x - 4)(2x - 1)

The test statistic for the given test is t = 2.59.

What is a standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.

Given data:

                    [tex]\bar D[/tex] = 4.1, Sd = 5, n = 10, μd = 0

Now the test statistic can be computed as

                [tex]t=\frac{\bar D-\mu_d}{S_d/\sqrt{n} }[/tex]

                [tex]t=\frac{4.10-0}{5/\sqrt{10}} \\\\t=2.59[/tex]

Hence, the test statistic for the given test would be t = 2.59.

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Answer:

look below

Step-by-step explanation:

Step 1: Determine the amount of pure solvent needed.

100 gallons x 0.5 (50%) = 50 gallons of pure solvent

Step 2: Determine the amount of each solution to use.

30% solution: 50 gallons of pure solvent / 0.3 = 166.67 gallons of 30% solution

80% solution: 50 gallons of pure solvent / 0.8 = 62.5 gallons of 80% solution

Step 3: Total the amount of solution used.

166.67 gallons of 30% solution + 62.5 gallons of 80% solution = 229.17 gallons total

The probability that a point chosen at random lies in the shaded region is 0.28

From the question, we are to find the probability that a point chosen at random lies in the shaded region.

The shaded region is a triangle.

The probability that a point chosen at random lies in the shaded region = Area of the triangle / Area of the circle

First, we will calculate the unknown side of the triangle

Let the unknown side be x.

Then, from the Pythagorean theorem, we can write that

12² = 6² + x²

144 = 36 + x²

x² = 144 - 36

x² = 108

x = √108

x = 6√3

From formula,

Area of a triangle = 1/2 × base × height

Area of the triangle = 1/2 × 6 × 6√3

Area of the triangle = 18√3 square units

Now, we will determine the area of the circle

Area of a circle = πr²

Where r is the radius

From the given information,

Diameter of the circle = 12

But,

Radius = Diameter / 2

Therefore,

r = 12/2

r = 6

Thus,

Area of the circle = 3.14 × 6²

Area of the circle = 113.04 square units

Now,

The probability that a point chosen at random lies in the shaded region = 18√3 / 113.04

The probability that a point chosen at random lies in the shaded region = 0.2758

The probability that a point chosen at random lies in the shaded region ≈ 0.28

Hence, the probability is 0.28

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Answer:

The 8th term of the AP= 113/5 or 22.6

Answer:

22.6

Step-by-step explanation:

Given:

Find the value of a₆:

[tex]\implies a+a_6=20[/tex]

[tex]\implies a_6=20-a[/tex]

[tex]\implies a_6=20-3[/tex]

[tex]\implies a_6=17[/tex]

Therefore:

General form of an arithmetic sequence:

[tex]\boxed{a_n=a+(n-1)d}[/tex]

Where:

Substitute a = 3 and a₆ = 17 into the formula and solve for d:

[tex]\begin{aligned}\implies a_6=3+(6-1)d&=17\\3+5d&=17\\5d&=14\\d&=2.8\end{aligned}[/tex]

Therefore, the equation for the nth term is:

[tex]\implies a_n=3+(n-1)2.8[/tex]

[tex]\implies a_n=3+2.8n-2.8[/tex]

[tex]\implies a_n=2.8n+0.2[/tex]

To find the 8th term, substitute n = 8 into the equation for the nth term:

[tex]\implies a_8=2.8(8)+0.2=22.6[/tex]

Answer:

[tex]\boxed{\tt y=48}[/tex]

Step-by-step explanation:

[tex]\tt \cfrac{3}{16}=\cfrac{9}{y}[/tex]

Cross multiply:-

[tex]\tt 3 \times y=(9)\times (16)[/tex]

[tex]\tt 3y=144[/tex]

Divide both sides by 3:-

[tex]\tt \cfrac{3y}{3}=\cfrac{144}{3}[/tex]

Simplify:-

[tex]\tt y=48[/tex]

_________________

Hope this helps!

Answer:y=48 I hope this is helpful good luck have a good day

Step-by-step explanation:

3/16 = 9/y

Determine the defined range

3/16=9/y y=0 cross out the equal sign y=0

Simplify the equation using cross-multiplication

3y=144

Divide both sides of the equation by 3

y=48

Check if the solution is in the defined range

Answer:3940

Step-by-step explanation:

The value of car after 2 years is $17,008.8, as percent it is 28.2% and depreciation is 27.75%

Value of car after two years will be calculated by calculating the depreciation each year.

Depreciation after first year = 60,320 - 15%×60,320

Depreciation after first year = 60,320 - 9,048

Depreciation after first year = $51,272

Depreciation after second year = 51,272 - 15%×51,272

Depreciation after second year = 51,272 - 7690.8

Depreciation after second year = $43,311.2

Value after depreciation = 60,320 - 43,311.2

Value after depreciation = $17,008.8

Value of car as percentage = 17008.8/60320×100

Value of car as percentage = 28.2%

Depreciation after two years period = 9048 + 7690.8

Depreciation after two years period = 16,738.8

Depreciation as percentage = 16738.8/60320×100

Depreciation as percentage = 27.75%

The correct answers are a) $17008.8, b) 28.2% and c) 27.75%.

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The evaluation of the trendline in line graph of the trendline displaying the value of a 2000 Toyota Camry since the year 2000 are as follows;

a. Independent variable; Time

Dependent variable; Value

b. The equation is; V = 22,500 - 1,166.[tex]\overline 6[/tex]·t

c. The y-intercept is at the point (0, 22,500), which indicates that the value of the 2000 Toyota Camry in the year 2,000 is $22,500

d. The slope of the trendline is -1,166.[tex]\overline {6}[/tex], which indicates that the annual reduction in the price of the 2000 Toyota Camry is $1,166.[tex]\overline 6[/tex]

e. The value of the car in 2017 based on the trendline is $2,666.[tex]\overline{6}[/tex]

A trendline is a line drawn through a scatterplot, minimizing the distances between the points in the chart and the line itself, and shows the trend of the scatterplot.

a. The independent variable is the variable that is the input variable of the function, which the researcher can vary or the value that is controlled.

Therefor;

The dependent variable is the value under study, therefore;

b. The points on the line graph are; (0, 22,500), and (15, 5,000), the slope is therefore;

m = (5,000 - 22,500)/(15 - 0) = -3,500/3

The equation is therefore;

V - 22,500 = -3,500/3·t

V = -3,500/3·t + 22,500

c. The y-intercept of the trend line is (0, 22,500), which indicates that in the year 2,000, the price of the 2,000 Toyota Camry was $22,500

d. The slope of the trend line is -3,500/3 = -1,166.[tex]\overline 6[/tex], which indicates that the value of the Toyota Camry, 2000, reduces at a rate of $1,166.[tex]\overline 6[/tex], each year.

e. In the year 2017, t = 17, therefore;

V = 22,500 - (3,500/3) × 17 = 2,666.[tex]\overline {6}[/tex]

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The inequality given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

Let the number of gigabytes consumed be x,

The total cost per month will be 69.50 + 5x

accoding to the question the bill would not exceed $90.

So the inequality,

69.50 + 5x ≤ 90

Simplification for the maximum gigabyte he can buy,

5x ≤ 90 - 59.90

5x ≤ 20.5

x ≤ 4.1

Hence, the required inequality is given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.

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      idddddddddddddddkkkkkkkkkkkkkkkkkkkkkkkk annnnthinggggggg            

The value   of   x≥2  are: 2,4,5,6

Inequality—the state of not being equal, particularly in status, rights, and opportunities1—is central to social justice theories. However, it is prone to misunderstanding in public debate because it means different things to different people. Some distinctions, however, are universal.

An inequality compares two values to determine whether one is less than, greater than, or simply not equal to the other. a b indicates that a is not equal to b.

Given ,

2x - 4≥1

State the values of x within 1 and 6

2x - 4≥1

2x ≥ 1 +4

2x ≥ 5

Divide both sides by 2

2x/2 ≥  5/2

x = 2

(1,6) is an open interval which means that 1 and 6are not inclusive of the values of x.

So:

therefore the values of   x≥2  are: 2,4,5,6

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Answer: Side of an empty cubicle carton = 9 cm.

Now as we know that volume of the cube is the cube of its side.

So the volume of an empty cubicle carton having side 9 cm, V = (9)3=729 cm3.

Now we have to find out can 1000 cubes of side 1cm fit in it.

So the volume of the cube of side 1 cm is, V’ = (1)3=1 cm3

So the volume of the 1000 such cubes = 1000 (1) = 1000 cubic centimeters.

Now if the ratio of the volume of the empty cubicle carton to the volume of 1000 cubes of 1 cm is greater than 1 then we can will 1000 cubes of side 1 cm into an empty cubicle carton otherwise not.

So the ratio of the volume of the empty cubicle carton to the volume of the 1000 cubes is,

⇒VV′=7291000=0.729 < 1

So as we see that the ratio is less than one so we cannot fit 1000 cubes of side 1 cm into an empty cubicle carton of side 9 cm.

Step-by-step explanation:

I really hope this works!

                                      Hope you Have a Great Day!! :)

If the three sides of the triangle is (x + 5), (2x - 3), (21 - x), then the perimeter of the triangle is 23 + 2x

The perimeter of the triangle is the summation of all three sides of the triangle

Perimeter = a + b + c

= (x + 5) + (2x - 3) + (21 - x)

= 2x + 23

= 23 + 2x

Therefore, if the three sides of the triangle is (x + 5), (2x - 3), (21 - x) then the perimeter of the triangle  23 + 2x.

Any two-dimensional figure's perimeter is determined by the space surrounding it. By adding the lengths of the sides, we can determine the perimeter of any closed shape.

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The image with line segment AB is dilated from (6, 3) and (3, 3) with scale factor of 1.8

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape. Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor.

In this case, the image with endpoints of line segments AB which are (9, 4) and (5, -4) and dilated to become (6, 3) and (3, 3) would have a scale factor of;

scale factor = 9 * x = 5

x = 9 / 5 = 1.8

The scale factor is 1.8

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The current age of Angela and Khali by the formation of the equation will be 2 and 7 years old.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Suppose the current age of Angela is A while Khali is K.

In 5 years,

A + 5 = K

In 3 years,

K + 3 = 2(A + 3)

K + 3 = 2A + 6

K + 3 = 2(K - 5) + 6

K + 3 = 2K - 10 + 6

2K - K = 3 + 4

K = 7 years old,

A = 7 - 5 = 2 years old.

Hence "The current age of Angela and Khali by the formation of the equation will be 2 and 7 years old".

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Tamar raise $15

What is division ?

One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.

A group is divided into equal portions when it is divided. For a game or activity, division can be used to divide a class into equal groups. It can also be used to divide a pizza among friends in equal pieces. Divided into partitive and quotative, there are two forms of division.

There are 2 ways one by writing equation and the other by using logic

1. by using equation

3*x=45

x=45/3

 = 15

2. Logically

If Jack has $45 which is 3 times Tamara's we can reverse the statement:

45/3

=15

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The area under the curve r²=50sin2Θ is (15.71)unit square

A parabola is defined as a plane curve that is mirror-symmetrical and approximately U-shaped.

The given parabola is r²=50sin2∅,

where r=5

Where r=radius of the circle of the parabola

Substitute r=5 in the parabola

5²=50sin2∅

Simplifying the equation to find the value of ∅25=50sin2∅[tex]\frac{25}{50}[/tex]=sin2∅

Finding the sine inverse, we havesin[tex]^{-1} 0.5=2[/tex]∅30⁰=2∅∅=15⁰

The angle made by the parabola is 15⁰

note r=5

Area = 22/7 × 5

Area = 15.71 unit²

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Answer:

y = - [tex]\frac{3}{2}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

6x + 4y = 16 ( subtract 6x from both sides )

4y = - 6x + 16 ( divide through by 4 )

y = [tex]\frac{-6}{4}[/tex] x + [tex]\frac{16}{4}[/tex] , that is

y = - [tex]\frac{3}{2}[/tex] x + 4 ← in slope- intercept form

The most petunias Ying Ying will ever purchase is 28.

Given data;

Using x as the total amount of money in her wallet and m as the price per petunia

The money remaining in the wallet after buying 2 petunias equals $6.50 according to the provided table.

Now,

6.50 = x - 2m ⇒ (I)

In addition, $5 was left in the wallet after the purchase of 8 petunias,

5 = x - 8m ⇒ (II)

Here, (I) - (II);

6.50 - 5 = x - 2m - x + 8m

1.50 = 6m

m = 0.25

One petunia costs $0.25.

Therefore, the total number of petunias Ying Ying buys at most is,

When 14 petunias brought money left in the wallet is $3.50.

Now,

→ 3.50/0.25 = 14

The total number of petunias Ying Ying buys at most is 14 + 14 = 28

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Answer:

1/2 x 1/10^-9

Step-by-step explanation:

(1.5x10^-5)/(3.0x10^4)

=> 1.5/3 x 10^-5/10^4

=> 1/2 x 10^-9

Answer:

= 5

Step-by-step explanation:

(1.5*10⁵) / (3.0*10⁴)

1.5*10⁵ = 15*10⁴

Then:

(1.5*10⁵) / (3.0*10⁴) = (15*10⁴) / (3*10⁴) = 15/3

= 5

The given expressions are equivalent.

What is equivalent expression?

Expressions that function identically despite having different appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).

Consider the given expressions,

-(-3m + 6 - 12 + 15m) and 2(1 - 2m)

First simplify the expression -(-3m + 6 - 12 + 15m)

= 3m - 6 + 12 - 15m

= -12m + 6

Divide the expression by 3,

= -4m + 2

= 2 + 4m            ..(1)

Now, consider the expression,  2(1 - 2m)

Simplifying this,

2(1 - 2m) = 2 - 4m         ..(2)

From (1) and (2) we can see that the expressions are equivalent.

Hence, the given expressions are equivalent.

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Answer:

[tex]7\sqrt{5}[/tex]

Step-by-step explanation:

Using the geometric mean theorem, [tex]n=\sqrt{28 \cdot 7}=14[/tex].

Using the Pythagorean theorem, [tex]m=\sqrt{7^2+14^2}=7\sqrt{5}[/tex]