Six less than five times a number is at least thirty- four

a) solve the inequality

b) graph the solution on a number line

c) write the solution in interval notation

Answer:

14

Step-by-step explanation:

8 + 3e

Let e =2

8 + 3(2)

8 + 6

14

Answer:

-3c

Step-by-step explanation:

The given expression is:

[tex]\frac{\frac{6c^{2}+3c}{-4c+2}}{\frac{2c+1}{4c-2}}[/tex]

We need to simplify this expression. The rational expression in the denominator can be multiplied to numerator by taking its reciprocal as shown below:

[tex]\frac{\frac{6c^{2}+3c}{-4c+2}}{\frac{2c+1}{4c-2}} \\\\ =\frac{6c^{2}+3c}{-4c+2} \times \frac{4c-2}{2c+1}\\\\=\frac{3c(2c+1)}{-(4c-2)} \times \frac{4c-2}{2c+1}\\\\ =-3c[/tex]

Thus, the given expression in simplified form is equal to -3c

Answer:

-3c

Step-by-step explanation:

We are given that an expression

[tex]\frac{\frac{6c^2+3c}{-4c+2}}{\frac{2c+1}{4c-2}}[/tex]

We have to find an expression which is equal to given  expression

Taking common 3c from nominator and -2 from denominator in dividened  and 2 common in divisor then we get

[tex]\frac{\frac{3c(2c+1)}{-2(c-2)}}{\frac{2c+1}{2(2c-1)}}[/tex]

[tex]\frac{3c(2c+1)}{-2(2c-1)}\times \frac{2(2c-1)}{(2c+1)}[/tex]

By reciprocal divisor

By canceling same factor

Then ,we get

[tex]\frac{\frac{6c^2+3c}{-4c+2}}{\frac{2c+1}{4c-2}}[/tex]

=-3c

Answer:

The mass of 150 books = 41.7kg

The number of books that have mass 20kg = 72 books

Step-by-step explanation:

(I) Number of identical books = 108

Mass of  books = 30 kg

Mass of 150 books = ?

Let the mass of 150 books = x kg

To find the mass of 150 books we will use ratio and proportion:

108 books: 30kg = 150 books: x kg

You can also write it like this because ratio can be written in division:

108/30 = 150/x

By cross multiplication:

108x = 150*30

108 x= 4500

Divide both sides by 108

108 x/108 = 4500/108

x= 41.7

Thus the mass of 150 books = 41.7kg

( ii ) The number of books that have a mass of 20 kg = ?

Let assume that the number of books of mass 20 kg = y books

We will again use ratio and proportion method.

108 books: 30kg = y: 20kg

We can write it as:

108/30 = y/20

By cross multiplication:

108 *20 = 30y

2160= 30y

Divide both the terms by 30

2160/30 = 30y/30

72 = y

Therefore the number of books that have mass 20kg = 72 books ....

Answer:

(-12, 0) and (5, 0)

Step-by-step explanation:

f(x) = x² + 7x − 60

Here, a = 1, b = 7, c = -60.  Using the AC method, we need to find factors of a×c that add up to b.

12 × -5 = -60

12 + -5 = 7

The factors are 12 and -5.

f(x) = (x + 12) (x − 5)

The zeros are:

x + 12 = 0, x − 5 = 0

x = -12, x = 5

The zeros are (-12, 0) and (5, 0).

[tex]x^2+7x-60 =0\\x^2-5x+12x-60=0\\x(x-5)+12(x-5)=0\\(x+12)(x-5)=0\\x=-12 \vee x=5[/tex]

The probability of an event and its complement add up to 1. If the probability of an event is 0.3, the probability of its complement is 0.7.

The probability of an event and its complement always add up to 1. So, if the probability of an event is 0.3, the probability of its complement can be calculated by subtracting the probability of the event from 1. In this case, the probability of the complement would be 1 - 0.3 = 0.7. Therefore, the probability of the complement is 0.7.

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Answer:

The correct answer is first option

x = 12, y = 10

Step-by-step explanation:

From the figure we can see that a triangle ADC, and EB is parallel to side DC.

To find the value pf x

From the given figure we get,

<ABC = <BCD  [ corresponding angles are equal]

3x + 9 = 4x - 3

4x - 3x = 9 + 3

x = 12

To find the value of y

<ABE and <EBC are linear pairs.

Therefore, <ABE + <EBC = 180

(3x + 9)  + (14y - 5) = 180

(3 * 12 + 9) + 14y - 5 = 180

45 + 14y - 5 = 180

14y = 180 -40

14y = 140

y = 140/14 = 10

y = 10

Therefore x = 12 and y = 10

The correct answer is first option

Answer:

don´t exist

Step-by-step explanation:

The slant asymptote only exist under two condition:

1) Don't exist horizontal asymptote  

2) If the degree of the denominator is n, the degree of the numerator should be n+1

In this case, the degree of the numerator is n+2, for that the slant asymptote don´t exist

Answer:

See below.

Step-by-step explanation:

You take the absolute value of the negative number  and add.

For example the difference between - 2 and + 3 is |-2|

= 3 + 2 = 5.

+4 and - 6: we have   4 + |-6| = 10.

Answer:

[tex]log_{7} \frac{7}{x^{2} }[/tex]

Step-by-step explanation:

We need to write [tex]1 - 2log_{7}x[/tex] as a single logarithm.

We know that

[tex]log_{7}7 = 1[/tex]

Therefore we have:

[tex]log_{7}7 - 2log_{7}x[/tex]

→ [tex]log_{7}7 - log_{7}x^{2}[/tex]

→ [tex]log_{7} \frac{7}{x^{2} }[/tex]

The solution is: [tex]log_{7} \frac{7}{x^{2} }[/tex]

Answer:

14

Step-by-step explanation:

Plug the 5 into the equation

2(5) + 4 = 14

Answer:

f(5)= 2(5) + 4 = 10 + 4 = 14

Answer:

The radius is [tex]\frac{\sqrt{74}}{2}[/tex].

The center is (5/2 , 9/2).

Step-by-step explanation:

The radius is half the diameter.  We aren't given the length of the diameter but we are given endpoints to one of them.

So let's find the length of that diameter using the distance formula.

The distance formula is

[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex].

I just do big x minus small x or big y minus small y.

Anyways the points are (-1,7) and (6,2).

The x distance is 6-(-1)=7.

The y distance is 7-2=5.

So we have this using the distance formula so far:

[tex]d=\sqrt{(6-(-1))^2{(7-2)^2}[/tex]

[tex]d=\sqrt{7^2+5^2}[/tex]

[tex]d=\sqrt{49+25}[/tex]

[tex]d=\sqrt{74}[/tex]

So the radius is half that much because that was the distance between the endpoints of a diameter.

So the radius is [tex]\frac{\sqrt{74}}{2}[/tex].

Now the center of a circle will lie on the midpoint of a diameter, any given diameter.

We have the endpoints of one, so we just need to use midpoint formula.

Midpoint formula says the midpoint is (average of x, average y).

Midpoint formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex].

So average of x's is (-1+6)/2=5/2.

The average of y's is (7+2)/2=9/2.

So the midpoint of the diameter or the center of the circle is at (5/2 , 9/2).

Answer:

135°

Step-by-step explanation:

To convert from radian measure to degree measure

degree measure = radian measure × [tex]\frac{180}{\pi }[/tex], so

degree = [tex]\frac{3\pi }{4}[/tex] × [tex]\frac{180}{\pi }[/tex]

Cancel π on numerator/denominator and 4, 180 by 4, leaving

degree = 3 × 45 = 135°

Answer:

1 radian = 180 / PI degrees

3 PI / 4 radians * 180 / PI the "PI's" cancel and we get

3 / 4 * 180 = 135 degrees

Step-by-step explanation:

Answer:

14 ft/sec

so 14 feet in one second.

Hope this helps you :)

Good Luck :)))

Answer:

14 feet per second

Step-by-step explanation:

If a ball travels on a straight surface at 20 ft/sec and begins to decrease at 6 ft/sec, it will travel 14 feet per second.

Answer:

I got you.Use pemdas to solve this expression. First, evaluate the exponets, then multiply them together. Finally, divide that by 100.

Answer:

256

Step-by-step explanation:

First evaluate the exponents

100 ÷ 25 × 64

Division and multiplication are of equal precedence

When they appear together in a mixed calculation then evaluate from left to right, that is

100 ÷ 25 × 64

= 4 × 64

= 256

Answer:

4pi or 12.57 cm

Step-by-step explanation:

Step 1 : Write the formula of arc length

Arc length = x°/360° x Circumference

Circumference = 2pir

Arc length = x°/360° x 2pir

Step 2 : Substitute the given values in the formula

x = 48°

r = 15 cm

Arc length = 48°/360° x 2pi(15)

Arc length = 4pi or 12.57 cm

!!

Answer:212.5

Step-by-step explanation:85/100×250

=212.5

85 percent of 250 results in 212.5.

To find 85 percent of 250, follow these steps:

Change the percentage to a decimal by dividing by 100: 85% = 85 / 100 = 0.85

Multiply the decimal by the number: 0.85 x 250

Calculate the product: 0.85 x 250 = 212.5

Therefore, 85 percent of 250 is 212.5.

For example, if 250 students are surveyed, then 212.5 students would represent 85 percent of the surveyed group.

Answer:

Up down and side to side on the graph

Step-by-step explanation:

If a is 1, since it is positive the parabola moves up. If a is -1, since it is negative the parabola moves down. (not sure about side to side because I can't back that one up but I'm 100% sure about up and down)

When a is between 0 and 1, the parabola gets wider.

A parabola is a mathematical curve that is defined by a point and a line. The point is known as the focus, and the line is called the directrix. The parabola has the property that all points on it are equidistant from the focus and the directrix.

Here,

When a is negative, the parabola flips 180°.

When |a| is less than 1, the parabola opens wider.

When |a| is greater than 1, the parabola opens more narrow.

When a is between 0 and 1, the parabola gets wider, when it is greater than 1, it gets narrower, and when it is less than 0 it is reflected across the x-axis.

Therefore, when a is between 0 and 1, the parabola gets wider.

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Answer:

I believe it would be C I don't have much experience with these problems but I'm good at them for what I did

Answer:

ASA Postulate.

Step-by-step explanation:

Two angles and  a corresponding side make the triangles congruent.

The answer is A.75°

The sum of all the angles of a triangle is 180°

75+35+x = 180.

x = 180-75-35

x = 75

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle.

The sum of all three angles of the triangle is equal to 180 degrees.

The angles of a triangle always add up to 1800 degrees because one exterior angle of the triangle is equal to the sum of the other two angles in the triangle. When all the angles are added up, the sum obtained should be 180 degrees.

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[tex]\huge{\boxed{25}}[/tex]

The radius is the distance from the center of the circle to its edge.

The diameter is the distance from one point on the edge to the opposite point on the edge, so it is twice as much as the radius.

This means we just need to multiply the radius by two to get the diameter. [tex]2r=d[/tex]

[tex]2(12.5)=d[/tex]

[tex]\boxed{25}=d[/tex]

Answer:

Range is y > 0

Step-by-step explanation:

We need to find the range of y = e^4x

The range is defined as a set of values of dependent variable for which the function is defined.

The exponential function of form c. n^x + k has range f(x) > k

in the given function y = e^4x ,k =0

so Range is y > 0

Answer:

6x + 8 = 32

Step-by-step explanation:

Let the number be= x

So 6 times a certain number is added to 8 which gives the answer 32.

6( x ) + 8 = 32

6x + 8 = 32

Hence this is the equational form.

On further solving we get,

6x = 32 - 8

6x = 24

x = 24 / 6

x = 4....

Answer:

The required equation is 6x+8=32

Step-by-step explanation:

Consider the provided information.

6 times a certain number is added to 8, the result is 32

Let the number is represents by x.

6 times of a number can be written as: 6x

Add 8 to the above expression.

6x+8

The expression is equal to 32.

Thus, the required equation is 6x+8=32

The correct option is b). The statement is False, it incorrectly describes the method for converting minutes to seconds.

To convert minutes to seconds, you multiply by 60 because there are 60 seconds in one minute.

So, to convert 5.25 minutes to seconds:

[tex]\[ 5.25 \text{ minutes} \times 60 \text{ seconds/minute} = 315 \text{ seconds} \][/tex]

Therefore, 5.25 minutes is equal to 315 seconds.

Regarding your original question about the statement:

To convert 5.25 minutes to seconds, you would use the ratio  [tex]\( \frac{1 \text{ second}}{60 \text{ minutes}} \).[/tex]

This statement suggests using a ratio, which is not correct for converting minutes to seconds. Instead, you should use multiplication by 60 seconds per minute.

Answer:

The binomial 2d + 3 represents the length of the swimming pool

Step-by-step explanation:

Let

l ----> the length of the swimming pool

w ---> the with of the swimming pool

d ---> the depth of the swimming pool

we know that

[tex]w=2d[/tex] -----> equation A

[tex]l=w+3[/tex] ----> equation B

substitute equation A in equation B

[tex]l=2d+3[/tex] -----> equation C

The volume of the swimming pool is equal to

[tex]V=lwd[/tex]

Substitute equation A and equation C in the formula of Volume

[tex]V=(2d+3)(2d)d\\ \\ V=4d^{3}+6d^{2}[/tex]

therefore

The binomial 2d + 3 represents the length of the swimming pool (equation C)

Answer:

C; The left end goes up; the right end goes down

Step-by-step explanation:

If you expand the function, you end up with a polynomial with a negative coefficient and it has an odd power. According to polynomial behaviors of a function that is odd negative, the graph will rise to the left (y → ∞ and x → -∞) and falls to the right (y → -∞ and x → ∞).

ANSWER

C. The left end goes up; the right end goes down.

EXPLANATION

The given function is

[tex]f(x) = - 2( {x - 2)}^{5} [/tex]

We analyze the end behavior of this function using the leading term.

The leading term of this function is:

[tex] - 2 {x}^{5} [/tex]

Since the degree(5) is odd and the leading coefficient (-2) is negative, the graph rises on the left and falls on the right.

In other words, the left end of the graph goes up and the right end goes down.

The correct option is C.

Answer:

9

Step-by-step explanation:

8.5*9(h)=76.5

76.5+15=91.5

Answer:

10 cm

Step-by-step explanation:

If the length of a rectangle is equal to triple the width, the width of the rectangle is 10 cm if the perimeter is 80 centimeters.​

L = 3w

P = 80

Formula: a = l × w

8W = 80 cm

W = 80 / 8 = 10 cm

Therefore, the width of the rectangle is 10 centimeters.

The width of the rectangle is found to be 10 centimeters, obtained by solving the equation created based on the fact that the perimeter of a rectangle is 2(length + width) and the given data that length is thrice the width and perimeter is 80 cm.

To figure out the width of the rectangle, we first need to understand the relationship between the length and width, and how they relate to the perimeter. The length of the rectangle is triple the width. Let's define the width as 'w'. Therefore, the length would be '3w'.

The formula for the perimeter of a rectangle is 2(length + width).

Given that the perimeter is 80 centimeters, we can set up the equation 2(3w + w) = 80. Simplifying this gives 8w = 80. To find the width 'w', we divide both sides of the equation by 8, giving us w = 10 centimeters.

Therefore, the width of the rectangle is 10 centimeters.

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Write it out as an equation:

3 < 1/3P

Rewrite so P is on the left side:

1/3P >3

Multiply each side by 3:

1/3P x 3 > 3 x 3

Simplify:

P > 9