Mathematics High School

How many integers satisfy the inequality (x 2 – 4)(x 2 – 10) < 0?

none
two
four
an infinite number

Answers

Answer 1

Answer:

4

Step-by-step explanation:

solution: −√10<x<−2 or 2<x<√10

√10=3.16

-3,-2,2,3

Answer 2

The 2 and -2 are the integers satisfy the inequality.

It is required to find the number of integers .

What is inequality?

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

For (x²– 4)< 0;

x²<4

By taking the square root of both sides we have,

√x²<√4

x < ±2

x<2 and x<-2

Also,

x²<10

By taking  the square root of both sides we get,

√x²<±√10

x < ±√10

x<√10 and x<-√10

The √10 is not an integer but an irrational number. An integer  is a whole number (not a fractional number) that can be positive, negative, or zero.

So we can't take the integer of ±√10.

Therefore, the 2 and -2 are the integers satisfy the inequality.

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Related Questions

What is
2
- ---- x times 15
3

Answers

If you are asking what 2/3 times 15 is its 10

for line segment ac, point b is between points a and c. points abc are collinear. if ab=x-7, bc=2x-2, and ac=x+13. solve for bc

Answers

Answer:

           BC = 20

Step-by-step explanation:

Point B is between points A and C and points A, B, C are collinear so

AB + BC = AC

x-7 + 2x-2 = x + 13

  3x - 9  =  x + 13

      +9           +9

   3x  =  x + 22

   - x       - x

   2x  =  22

BC = 2x - 2 = 22 - 2 = 20

If a gold bar has a length of 17.78 cm, a width of 9.208 cm, a height of 4.445 cm, and the density of gold is 19.3 g/cm^3, what is the
mass of the gold bar. Answer with the correct number of significant figures. Use the rounding rules.

A. 1.40x10^4 grams
B. 14 040 grams
C. 14 045.142 grams
D. 14 045 grams

Answers

Answer:

17.78×9.208×4.445=727.7275768

D=mass÷volume

mass=density×volume

mass=19.3g/cm3×727,7275768=14045,14223224=14045grams

You are shopping for T-Shirts on your favorite site. You choose 3 shirts, and the site
tells you they will cost $15.50 each, and shipping will cost $12.60
The website then suggests you can save some money by buying a 4th shirt, because
the cost per shirt will reduce to $14.00 each, AND shipping will be free.
How much money will you save by buying 4 T-Shirts?
Your answer will be a positive decimal value. You do NOT NEED the $ sign.

Answers

Answer:You will be saving $3.10

Answer:

Step-by-step explanation:

3 T-Shirts price= 15.50

mean 1 T-Shirt price=5.16

3 T-Shirts shipping=12.60

mean 1 T-Shirt Shipping=4.2

If I get 4 then

4 T-Shirts price will be 5.16 x 4 = 20.65

4 T-Shirts shipping will be 4.2 x 4 = 16.8

Total cost will be = 37.45

So Company offers

4 T-Shirts in 14$ with free shiping

you will save 23.45

Julio is payed 1.2 times his normal hourly rate for each hour he works over 30 hours in a week. Last week he worked 40 hours and earned $495.60 enter and solve an equation to find julios hourly rate, r. Complete the explanation how you know that your answer is reasonable

Answers

Answer: $10.33

Step-by-step explanation:

Given: Julio is payed 1.2 times his normal hourly rate for each hour he works over 30 hours in a week.

Last week he worked 40 hours ( > 30 hours by 10 ) and earned $495.60.

Let r = Julio's hourly rate

if he worked over 30 hours in a week, then hourly rate = 1.2r

According to the question

[tex](1.2r)\times 40=495.60\\\\\Rightarrow\ r=\dfrac{495.60}{1.2\times 40}\\\\\Rightarrow\ r=10.325\approx10.33[/tex]

Hence, his hourly rate = $10.33

Here is a system of linear equations:
6x+21y=103
-6x+23y=51

Would you rather use subtraction or addition to solve the system? Explain your reasoning.

Answers

Step-by-step explanation:

6x + 21y = 103

-6x + 23y = 51

The signs of the x coefficients are opposite.  So adding the equations will eliminate the x terms.

44y = 154

y = 3.5

Combining the equations will remove the x terms because the x coefficients have inverse signs. The solution to the given system of linear equations is x = 4.92 and y = 3.5.

What is the equation?

The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.

Here is a system of linear equations:

⇒ 6x + 21y = 103

⇒ -6x + 23y = 51

Inverse signs can be seen in the x coefficients. The x terms will therefore be removed after adding the equations.

⇒ 44y = 154

⇒ y = 3.5

Substitute the value of y = 3.5 in the equation 6x + 21y = 103

⇒ 6x + 21(3.5) = 103

⇒ 6x + 73.50 = 103

⇒ 6x = 103 - 73.50

⇒ 6x = 29.50

⇒ x = 4.92

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Bryan has a prepaid cell phone with a balance of $75. He is charged the same rate per minute. Which function represents the balance on the phone after (n) minutes?

Answers

Answer:

36 minutes

Step-by-step explanation:

i have a different saying this so dont get mad

An ice cream truck drive truck driver made $23 in one hour. She the spent $35 for gas. What is the difference?

Answers

Answer:

$12

Step-by-step explanation:

Step 1:

$35 - $23

Answer:

$12

Hope This Helps :)

-2x+5=24 I need help!!!

Answers

Answer:

[tex]x=-\frac{19}{2}[/tex]

Step-by-step explanation:

hope that was the answer you were looking for :/

Answer:

x = -19/2

Step-by-step explanation:

[tex]-2x+5=24[/tex]

Then subtract 5 from 24

[tex]-2x=19[/tex]

Then divide -2 by 19 to get:

[tex]x = -\frac{19}{2}[/tex]

Hope this helps!

Describe the steps of constructing a segment that is TWICE as long as the given segment BD.

Answers

Answer:

See below

Step-by-step explanation:

From the segment BD, I will consider the point B as the begin and D as the end of the vector, therefore [tex]\overrightarrow{BD} = \vec{v}[/tex]

Once you want a segment that is twice as long as the given segment, we may say that the magnitude of the vector is

[tex]||2\vec{v} || = \sqrt{(2x)^2 + (2y)^2} = \boxed{ \sqrt{4x^2 + 4y^2} }[/tex]

Note: I'm assuming [tex]\vec{v} \in E^2[/tex], which means the segment is in the plain.

Determine which of the following statements about rigid transformations is false.

Question 5 options:

In a translation, the segments joining points of the pre-image and their images are perpendicular.


In a reflection, the segments joining points of the pre-image and their images are perpendicular to the line of reflection.


In a rotation, the points of the pre-image are always the same distance away from the center of rotation as the corresponding points of the image.


In a reflection, the points of the pre-image are always the same distance away from the line of reflection as the corresponding points of the image.

Answers

Answer:

The false statement about rigid transformation is;

In a translation, the segments joining points of the pre-image and their images are perpendicular

Step-by-step explanation:

The direction of a rigid transformation involving a translation can vary from changes in the values of one of the two coordinates of the vertex points in the figure with the same change value for all the vertices or

The translation can also be made by changing the values of both coordinates of the vertex each coordinate having equal value of change which may be different from the value of change of the other coordinate, maintaining the size of the figure.

In the second case, the translation can be in other directions other than vertical or horizontal, such that, the segments joining the points of the pre-image with the corresponding point on the image are parallel.

The false statement about rigid transformation is;

In a translation, the segments joining points of the pre-image and their images are perpendicular

The direction of rigid transformation:

It includes a translation that could be varied from changes in the values of one of the two coordinates of the vertex points having the same change value for all the vertices. The translation could also be made via changing the values of both coordinates of the vertex every coordinate that contains the equal value of change.

 

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How do you do #14abc?

Answers

Answer:

220 10 4

Step-by-step explanation:

3x + 2y + -2x + 8y pls help

Answers

Answer:

x+10y

Step-by-step explanation:

3x+2y+(-2x)+8y

First of all you cannot substitute x with y, so what u do u make the numbers with the same letters they have,and I put -2x because + &amp; - equals to -(minus) :-

3x-2x+2y+8y= x+10y

I don't add 1 to x coze when x alone stands for 1, I added +10y because both the y equations had + they were positive so I add a +.

Hope it helps

In February, Paul's electric bill was three dollars more then one-half his gas bill. If the electric bill was ninety-two dollars, what was the gas bill?

Answers

Answer:

49$

Step-by-step explanation:

Shambrekia put down $800 on a used car. She took out a loan to pay off the balance of the cost of the car. Each month she will pay $175. After 9 months how much will she have paid for the car?

Answers

Answer:

$1,575

Step-by-step explanation:

Find the distance between the points (6, 9) and (0, 1).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
units

Answers

Answer:

D= 10

Step-by-step explanation:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d=\sqrt{(0-6)^2+(1-9)^2}\\d=\sqrt{(-6)^2+(-8)^2}\\d=\sqrt{(36)+(64)}\\d=\sqrt{100}\\d=10[/tex]

EASY BUNCH OF POINTS & WILL GIVE BRAINLIEST:) Find the distance FG between the points F(2,7) and G(4, -1). Round your answer to the nearest tenth, if necessary. FG=

Answers

Answer:

2 between 2 and 4 and 8 between 7 and -1

Mr. Alfred’s car gets 12 miles per gallon. He drives to West Harlem for a weekend to visit his grandmother. He uses 6 gallons of gas. How many miles did he drive?

Answers

Answer:

72 miles.

Step-by-step explanation:

If he uses 6 gallons of gas, you would do 6 (gallons he used) x 12 (miles per gallon) equaling 72.

How many cm in 92.4 inches?

Thank you!

Answers

Answer:

234.696 cm

Step-by-step explanation:

Answer: 234.696

Step-by-step explanation:

1 inch = 2.54 centimeters so

92.4 times 2.54 is 234.696

What is the volume of a rectangular prism with l = 412 cm, w = 312 cm, and h = 6 cm?

Answers

Answer:

Step-by-step explanation:

V = l · w · h

V = (412)(312)(6)

V = (1872)(412)= 771,264 cm^3

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{771264 \: \: {cm}^{3} }}}}}[/tex]

Step-by-step explanation:

[tex] \star{ \sf{ \: length \: of \: a \: rectangular \: prism(l) = 412 \: cm}}[/tex]

[tex] \star{ \sf{ \: width \: of \: a \: rectangular \: prism \: ( \: w \: ) = 312 \: cm}}[/tex]

[tex] \star{ \sf{ \: height \: of \: a \: rectangular \: prism \: ( \: h \: ) = 6 \: cm}}[/tex]

Finding the volume of a rectangular prism having length ( l ) of 412 cm , width ( w ) of 312 cm and height ( h ) of 6 cm :

[tex] \bold{\boxed{ \sf{volume \: of \: a \: rectangular \: prism = lwh}}}[/tex]

[tex] \hookrightarrow{ \sf{volume \: of \: a \: rectangular \: prism \: = 412 \times 312 \times 6}}[/tex]

[tex] \hookrightarrow{\boxed{ \sf { volume \: of \: a \: rectangular \: prism = 771264 \: {cm}^{3} }}}[/tex]

Volume of a rectangular prism = 771264 cm³

Hope I helped!

Best regards! :D

~TheAnimeGirl

THIS IS HARD HELP....

Answers

Answer: you can google the Four 4’s assignment and there will be several sites and documents giving you all the answers

Step-by-step explanation:

4-3= 1
4x4= 16
4x5= 20

here’s a start

What is the absolute value of –7.5?

Answers

Answer: 7.5

Step-by-step explanation:

Absolute value is the distance from 0.

-7.5 is is 7.5 units away from 0.

W/-4 + 17=9. Solve for w what is w

Answers

Answer:

w=-32

Step-by-step explanation:

Answer: w=32

Step-by-step explanation:

Given

w/-4 + 17=9

Subtract 17 on both sides

w/-4 + 17 - 17=9-17

w/-4=-8

Multiply -4 on both sides

w/-4 × -4=-8×-4

w=32

What is the sum of 2/3 + (-1/3) in fraction form?

Answers

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \frac{1}{3}}}}}} [/tex]

Step-by-step explanation:

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

We know that [tex] \sf{( + ) \times ( - ) = ( - )}[/tex]

[tex] \dashrightarrow{ \sf{ \frac{2}{3} - \frac{1}{3}} }[/tex]

While performing the addition or subtraction of like fractions , you just have to add or subtract the numerator respectively in which the denominator is retained same.

[tex] \dashrightarrow{ \sf{ \frac{2 - 1}{3}}} [/tex]

[tex] \dashrightarrow{ \boxed{ \sf{ \frac{1}{3}}}} [/tex]

Hope I helped!

Best regards! :D

The sum of 2/3 + (-1/3) in fraction form is 1/3 after applying the arithmetic operation, the answer would be 1/3.

What is a fraction?

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The number expression is:

= 2/3 + (-1/3)

= 2/3 - 1/3

Taking 3 as LCM

After simplification:

= (2 - 1)/3

= 1/3

Thus, the sum of 2/3 + (-1/3) in fraction form is 1/3 after applying the arithmetic operation, the answer would be 1/3.

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Compare the quantity in Column A with the quantity in Column B. Choose the best
answer.
Column A
The distance from
(-11, 2) to (5, 10)
Column B
The distance from
(0, -8) to (16,0)
O A. The quantity in Column A is greater.
O B. The quantity in Column B is greater.
O C. The two quantities are equal.
O D. The relationship cannot be determined from the information given.

Answers

Answer:

option :c is correct..ok

Answer:

c

Step-by-step explanation: got it right prommispromise

Keith had two hundred sixteen dollars to spend on six books. After
buying them he had eighteen dollars. How much did each book cost ? _____________

Answers

Answer:

$34.66

Step-by-step explanation:

216-8= 208 divided by 6 = 34.666666

Answer: 33$ each

Step-by-step explanation:

you start by subtracting 18 from 216 to get rid of the leftover money.

you'll have ended up with the number 198

divide 198 by 6 and that will be your answer.

11 times 11 in exponential expression

Answers

Answer:

11^2

Step-by-step explanation:

bc there is two eleven it's 11 to the power of two

the diving distance between manchester and london is 195 miles faris inteneds to travels from manchester to london by coach the coach will leave manchester at 3.30 pm faris assumes that the coach will travel at an average speed of 50 mph work out farris arrival time in london

Answers

Answer:

Faris' arrival time = 3:30 pm + 3 h 54 mnt = 7:24 pm

Answer:

19.24

Step-by-step explanation:

Solve for the equation for x 3x+y/=2

Answers

Answer: x= 2/3 - 1/3y


Explanation step by step:

Step 1: Move variable to the right hand side and change its sign.

3x = 2-y

Step 2: divide both sides of the equation by 3.

x= 2/3 - 1/3y

rote x+18=x-2 what is the answer

Answers

Answer:

no solution

Step-by-step explanation:

Given

x + 18 = x - 2 ( subtract 18 from both sides )

x = x - 20 ( subtract x from both sides )

0 = - 20 ← not possible

This indicates the equation has no solution

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