Mathematics High School

Solve the compound inequality 9x ≤ –27 or 4x ≥ 36.

Answers

Answer 1

Answer:

x  ≤ – 3 or x ≥ 9.

Step-by-step explanation:

Given  : 9x ≤ –27 or 4x ≥ 36.

To find : Solve the compound inequality.

Solution : We have given  9x ≤ –27 or 4x ≥ 36.

For 9x ≤ –27 .

On dividing both sides by 9.

x  ≤ – 3.

For ,  4x ≥ 36.

On dividing both sides by 4.

x ≥ 9.

We can write x  ≤ – 3 or x ≥ 9.

Therefore,  x  ≤ – 3 or x ≥ 9.

Answer 2

Answer: x <_ -3 or x >_ 9

Step-by-step explanation:

Related Questions

Jesse ate 100 donughts i 5 days each day she ate 6 more then the day before how many did she eat each day

Answers

506. donuts


hoped it helped! :D



The length of a rectangular plot of land is 10 yards more than its width. If the area of the land 600 square yards , find the dimensions

Answers

Let the width of the rectangular plot of land be 'x' yards. Given that the length of the rectangular plot of land is 10 yards more than its width. So, width of the rectangular plot of land = (x + 10) yards. Also given that the area of the rectangular plot of land is 600 square yards. We know that, area of a rectangle = length * width That is, (x+10) * x = 600 x^2 + 10x = 600 x^2 + 10x - 600 = 0 x^2 + 30x - 20x -600 = 0 x(x + 30) - 20(x + 30) = 0 (x +30)(x -20) =0 Therefore, either (x + 30) = 0 or (x - 20) = 0 If x + 30 = 0, then x = -30 and If x - 20 = 0, then x = 20 Since 'x' represents the width of a rectangular plot of land it cannot be negative. Therefore, width of the rectangular plot of land = 20 yards length of the rectangular plot of land= x + 10 = 30 yards

Final answer:

The dimensions of the rectangular plot of land, where the length is 10 yards more than its width and the area is 600 square yards, are 20 yards by 30 yards. We arrived at this by setting up a quadratic equation and solving for the width.

Explanation:

To find the dimensions of a rectangular plot of land where the length is 10 yards more than its width and the area is 600 square yards, we can set up an equation. Let w be the width of the plot. Then the length is w + 10 yards. The area of a rectangle is given by the formula length × width, which in our case is (w + 10) × w = 600.

Setting up the equation, we get:

w(w + 10) = 600

w^2 + 10w - 600 = 0

To solve the quadratic equation, we can factor it, use the quadratic formula, or complete the square. Factoring the equation, we find that:

(w - 20)(w + 30) = 0

Thus, the width w can be either 20 yards or -30 yards. Since a width cannot be negative, we take w = 20 yards. Then, the length is:

w + 10 = 20 + 10 = 30 yards

The dimensions of the rectangular plot of land are 20 yards by 30 yards.

Which postulate or theorem proves that △JHG and △EFG are congruent?



​ SAS Congruence Postulate ​

​ ASA Congruence Postulate ​

​ HL Congruence Theorem ​

​ AAS Congruence Theorem ​

Answers

the asa congruence postulate

The postulate that proves that △JHG and △EFG are congruent is;

Option B; ​ ASA Congruence Postulate ​

From the given image, we can see two triangles namely;

△JHG and △EFG

Now, we can see that;

FG = GH

That is given because we see that G has divided FH into 2 equal parts.

Also, we see the right angle sign at ∠F and ∠H of both triangles.

Thus, since they are both right angles, then we can say that;

∠EFG = ∠JHG

Also, at point G, we have two vertically opposite angles which are;

∠EGF and ∠JGH

Now, from vertically opposite angle theorem, vertically opposite angles are always equal;

Thus; ∠EGF = ∠JGH

So far, we have;

FG = GH

∠EFG = ∠JHG

∠EGF = ∠JGH

This is 2 corresponding equal angles and 1 corresponding equal side. The side is included between the two angles and as such the proof that  △JHG and △EFG are congruent is the ASA Congruence Postulate.

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PLEASE HELP!!!! WILL MARK THE BRAINLIST!!!! PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE


a) The shoe store manager borrowed $17,000.00 from the bank to purchase 1000 pairs of shoes. The bank charges a simple interest rate of 5% per year on a loan to a business. If it takes 3 years to pay back the loan and interest, what is the total amount of interest that the shoe store will pay? (2 points)


b) What is the total amount, including interest, that the shoe store must pay on the loan? (2 points)


c) How could you use estimation to determine if your answer is reasonable? Explain. (2 points)

Answers

A) 17000*(1+(0.05*3) = 19550

19550-1700 = $2,550 total interest


B)  $19,550 total amount


C) multiply 5 by 3  = 15 than multiply by 17 = 17 * 15 = 255 , then make it a thousands amount by adding a zero at the end


Answer:

A)

p = 17000

r = 5% or 0.05

t = 3

Simple interest formula = p x r x t

Interest paid in 3 years = [tex]17000\times0.05\times3=2550[/tex] dollars

B)

Total amount to be paid = [tex]17000+2550=19550[/tex] dollars

C)

You can first multiply the years and rate that is 5 and 3 to make 15. Then you can multiply by 17. Then put proper decimals as per the values.

PLZ HELP ILL GIVE A BRAINLIEST SHOW ALL WORK!!!!

Answers

Step 1. Collect like terms
(√3 + 2√3) + √7
Step 2. Simplify 
3√3 + √7
That's all.

MATH PLEASE HELP 50 POINTS 1 QUESTION
Complete the reasons in the proof below.

Given: ∠1 and ∠5 are supplementary.
Prove: a ∥ b


Statements
1. ∠1 and ∠5 are supplementary
2. ∠1 ≅ ∠2
3. ∠2 and ∠5 are supplementary
4. a ∥ b

Answers

For 1, ∠1 and ∠5 are supplementary is a given, so you can just write 'Given'
For 2, due to that 1 and 2 are vertical angles (angles that are opposite to each other when two lines cross according to Math is Fun)
For 3, since ∠1=∠2, ∠1 can be substituted by ∠2 in ∠1+∠5=180 to get ∠2+∠5=180. Therefore, they are supplementary.

For 4, due to that we have Consecutive Interior Angles (they are angles that are on one side of a transversal, which is the line that cuts through a and b,but inside the two lines according to Math is Fun) adding up to 180 degrees, a  || b

Feel free to ask if you have any questions!

Each of ten tickets is marked with a different number from 1 to 10 and put in a box. if you draw a ticket from the box, what is the probability that you will draw 2, 8, or 4?

Answers

10% would be you chance of get one of those numbers but together its 30%

Answer: [tex]\dfrac{3}{10}[/tex]

Step-by-step explanation:

Given : Each of ten tickets is marked with a different number from 1 to 10 and put in a box.

i.e. The total number of outcomes : 10

Favorable outcomes : 2, 8, or 4

i.e. Number of favorable outcomes = 3

Now, the probability that you will draw 2, 8, or 4 is given by :-

[tex]=\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}\dfrac{3}{10}[/tex]

An automobile manufacturing organization noted a drop in sales after an incident occurred due to the lack of a safety feature in their cars. Many customers began considering other brands of cars after this incident. How can the organization avoid losing customers

Answers

By paying the person who was involved in the incident

Recalling the effected car and fixing the issue

Answer:

introducing customer retention strategies

Step-by-step explanation:

Which postulate or theorem proves that these two triangles are congruent?

Answers

the answer would be AAS (angle angle side) theorem

Answer:

option B  

Step-by-step explanation:

Given in the question are ∠x ≅ ∠y and ∠zwx ≅ ∠ ywz and wz is common in both.

These angles are adjacent angles of triangles.

We know theorem for congruence is Angle - Angle - Side

Therefore, for the congruence of these two triangles option B, AAS congruence theorem is the answer.

i need someones help please?

Answers

y = mx + b

m = slope

plug in 1 and -7 to it's respective places

y (-7) = -2/3(x + 1)

D is your answer

hope this helps


Hey there!

The answer would be y+7= -2/3(x-1)

Hope this helps!

Find three consecutive odd integers whose sum is negative 465

Answers

465 / 3 = 155

so -153 + -155 + -157 = -465

Find the 31st term of the following sequence.

9, 15, 21, ...

Answers

Notice that the above sequence is arithmetic because the common difference: d is constant.

d = second term - first term.

= 15 - 9

= 6

The general term of an arithmetic sequence is,

a_{n} =a_{1} +(n-1)d

Where , nth term = [tex] a_{n} [/tex]

[tex] a_{1} [/tex] = First term

and d = common difference.

The given sequence is: 9, 15, 21, ...

Here a_{1} = 9,

d = 6

We need to find the 31st term. So, n = 31.

Next step is to plug in these values in the above formula. Therefore,

[tex] a_{31} =9 +(31-1)*6 [/tex]

= 9 + 30* 6

= 9 + 180

= 189

So, 31st term of this sequence is 189.

Hope this helps you.

Answer:

189

Step-by-step explanation:

If f(x)=5x^0+4x^-3 then f(a)=?

Answers

x=a
f(a)=5(a^0)+4a^-3          a^0=1
=5(1)+4/a^3
=5+4/(a^3)
Final answer:

To find f(a) for the given function, substitute a for x in the function and simplify the expression.

Explanation:

Given the function f(x) = 5x0 + 4x-3, we need to find f(a). To find f(a), we substitute a for x in the function. Plugging in a, we get f(a) = 5a0 + 4a-3. Since any number raised to the power of 0 is equal to 1, we have f(a) = 5(1) + 4a-3. Simplifying further, we get f(a) = 5 + 4/a3.

Learn more about Functions here:

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does anyone know how to do this?

Answers

You're looking for values to factor this equation into (x+p)(x+q)
such that pq=12 and p+q=b

Assuming we're looking for simple values, you can start by factorizing 12:

12 = 3*4 = 2*6 = 12*1 = -3*-4 = -2*-6 = -12*-1

For 3 and 4, b would be 7
2 and 6 => b=8
12 and 1 => b=13

and for the negatives

b can be -7, -8 or -13

So the total set is -13, -8, -7, 7, 8, 13
It is factorable if you can solve it when it equals 0. 
There are many ways to do this. 

X^2+bx+12=0 

[tex](-b +- \sqrt{ b^{2} -4*12 } )/2 [/tex]

This equation gives a good answer if 
[tex]b ^{2} \geq 48[/tex]

Given:
AC = BC
∠3 = ∠4

Based on the given information and the algebraic and geometric properties presented or proven thus far, choose the congruence theorem that could be used to prove that triangle ACM is congruent to triangle BCM. If it is not possible to prove the triangles are congruent, choose "not possible".

Choices:
SSS
SAS
ASA
not possible

Answers

SAS You've been given that AC = BC. So that's the first side or S of the proof. Then you've been given â 3 = â 4, which is the angle. And finally, CM = CM, which is the second S. So you have AC=BC, and â 3 = â 4, and finally CM = CM. So SAS can be used to prove that triangle ACM is congruent to triangle BCM.

Answer:

SAS Postulate

Step-by-step explanation:

You were assigned to read 5⁄8 of your book. how many sixteenths is that? fraction

Answers

5/8 = 10/16

You just multiply the numerator and the denominator by 2

Hope I helped :)

Find the 20th term in arithmetic sequence -4, 1, 6, 11, 16,

Answers

91, I just kept adding 5 until I got to the 20th term

Emily has 32 grams of a 25% sugar syrup, but this is just too sweet for her! How much pure water should she add to have a 10% syrup?

Answers

32 grams = water mass + sugar mass . 100% syrup=75% water+ 25%sugar 
original water content= 32*75/100=24 grams
original sugar content= 32*25/100= 8grams 

total mass at 10% syrup:
8grams/total mass=10%=0.1
total mass=8/0.1=80grams
total mass of water=80grams- 8grams of sugar content= 72 grams
total mass of water added=72grams- 24grams original water content= 48grams.

answer: 48grams

By this information, we know: (just so you know, when I will write the equation, the multiplication sign will be ^)

25%+0%=10%
32g    xg   (32+x)g
Now, we create an equation:

(0.25^32)+(0^x)=0.1^(32+x)
8+0=3.2+0.1x
8=3.2+0.1x
4.8=0.1x
48=x
Answer: 48 gram.

Please help with these questions thank you.

Answers

1.D
2. B
3.A
these should be correct

Solve x ym = y x3 for m.

Answers

xym-yx3m = 0
xym (1-1x2) = 0
xym (1 (un cuadrado)-1x2)=0
xym(1+x)(1-x)=0
1+x=0
1-x=0
m= 0
x=-1
x=1
Is true 
m=0;x= -1;1

given a line whose slope is, m, is -6/5, and passes through point (-5,3), the graph will?

Answers

Using the point-gradient form y - y₁ = m ( x - x₁ )
y₁ = 3;  x₁ = -5;  m =  [tex]- \frac{6}{5} [/tex]

 ⇒  y - 3 =  [tex]- \frac{6}{5} [/tex] ( x - (-5))
 ⇒  y - 3 =  [tex]- \frac{6}{5} [/tex] (x + 5)

Now, you can approach here in two ways: put it in the y-intercept form or the general form.

In the y-intercept form;
      y - 3 = [tex]- \frac{6}{5} [/tex]x + ([tex]- \frac{6}{5} [/tex] (5))
      y - 3 =  [tex]- \frac{6}{5} [/tex]x - 6
           y =  [tex]- \frac{6}{5} [/tex]x - 3

In the general form;
    y - 3 =  [tex]- \frac{6}{5} [/tex] (x + 5)
       by multiplying through by 5
⇒    5 ( y - 3 ) = -6 ( x + 5)
⇒       5y - 15 = -6x - 30
⇒      5y + 6x = -15

∴ the line that passes through (-5, 3), with gradient [tex]- \frac{6}{5} [/tex] is 
 y =  [tex]- \frac{6}{5} [/tex]x - 3 (y-intercept form)  OR  5y + 6x = -15 (general form).

Which expression is a perfect cube?

A. -8x21y8

B. -64x64y64

C. -125x9y20

D. -216x9y18

Answers

Finding the cube root of each expression

Expression A:

[tex] \sqrt[3]{-8x^{21}y^{8}} [/tex]
[tex] \sqrt[3]{-8} [/tex] [tex] \sqrt[3]{x^{21}[tex] \sqrt[3]{y^8} [/tex]} [/tex] 
[tex]-2x^ \frac{21}{3} y^ \frac{8}{3} [/tex]
[tex]-2 x^7 y^ \frac{8}{3} [/tex]

the term [tex]y^ \frac{8}{3} [/tex] is not a perfect cube, therefore expression A is not a perfect cube.

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

Expression B
[tex] \sqrt[3]{-64x^{64}y^{64}} [/tex]
[tex] \sqrt[3]{-64} \sqrt[3]{x^{64}} \sqrt[3]{y^{64}} [/tex]
[tex]-4 x^ \frac{64}{3} y^ \frac{64}{3} [/tex]

The term [tex]x^ \frac{64}{3} [/tex] and [tex]y^ \frac{64}{3} [/tex] are not perfect cube because 64/3 doesn't give whole number
----------------------------------------------------------------------------------------------------------------

Expression C

[tex] \sqrt[3] {-125x^9y^{20}} [/tex]
[tex] \sqrt[3]{-125} \sqrt[3]{x^9} \sqrt[3] {y^{20}} [/tex]
[tex]-5 (x^ \frac{9}{3}) (y^ \frac{20}{3})[/tex]
[tex]-5 (x^3) (y^ \frac{20} {3}) [/tex]

The term [tex]y^ \frac{20}{3} [/tex] are not perfect cube because 20/3 doesn't give whole number
---------------------------------------------------------------------------------------------------------------

Expression D

[tex] \sqrt[3]{ -216 x^{9} y^{18} } [/tex]
[tex] \sqrt[3]{-216} \sqrt[3]{x^9} \sqrt[3]{y^{18}} [/tex]
[tex]-6 ( x^ \frac{9} {3} ) ( y^ \frac{18} {3} ) [/tex]
[tex]-6 (x^3) (y^6)[/tex]

All terms are perfect cubes

ANSWER: OPTION D

Merry and pippin were working on a project in carpentry class. they needed to cut 4 lengths of 1 5/8 feet from a board. how long must the board be to allow this?

Answers

Attached the solution and work.

Answer:

Hence, the length of board is:

6.5 feet

Step-by-step explanation:

Merry and pippin were working on a project in carpentry class.

They needed to cut 4 lengths of 1 5/8 feet from a board.

That means each of the  piece  is of length 1 5/8 feet which could be written in fraction as:

[tex]1\frac{5}{8}=\dfrac{13}{8} feet[/tex]

Hence, the otal length of the board is addition of length of each board.

i.e.

[tex]\dfrac{13}{8}+\dfrac{13}{8}+\dfrac{13}{8}+\dfrac{13}{8}=4\times \dfrac{13}{8}=\dfrac{13}{2}feet=6.5feet[/tex]

Hence, the length of board is:

6.5 feet

Two integers with the sum of -17 and the product of 52?

Answers

let the integers be x and y
you have x+y=-17 ---------(1)
xy=52 ---------(2)
from eqn (1) x=-17-y --------(3)
, so subsitute eqn (3) in to eqn(2)
(-17-y)y=52
-17y-y²=52
:
-y²-17y-52=0 same as y²+17y+52=0
y²+13y+4y+52=0
y(y+13)+4(y+13)=0
(y+4)(y+13)=0
therefore y=-4 or -13
now substitute y=-4 or -13 in eqn (3)
x=-17-(-4) or -17-(-13)
x= -13 or -4
so when x=-13 ,y=-4 and when x=-4 ,y=-13

so the integers are -13 and -4

What is the value of N?

-10= N over -0.2

Answers

The answer would be N= -10.2

Which ordered pair comes from the table ? HELPPP!

Answers

It's (4,2). Can you comment why you're having a struggle with this? I might be able to help you.
The answer is B.(4,2). Hope this helps.

The point MegaMarket sold 450 organic pears last season. this season they only sold 360 What was the percent decrease in sales

Answers

First, you would need to determine the difference between last season's pear sales and this season's pear sales.  
450 - 360 = 90

Next, you would need to create an equation to determine what percentage 90 is of 450. Let x represent the unknown sales decrease percentage. 
[tex] \frac{90}{450} [/tex] = [tex] \frac{x}{100} [/tex]

Cross multiply. 
450x = 9,000

Now, all you would need to do is isolate the x. To do this, you would divide both sides of the equal sign by 450. 
x = 20
x = 20%

The percent decrease was 20%.

I hope this helps!


Which of the sets of ordered pairs represents a function? (4 points)

A = {(−4, 5), (1, −1), (2, −2), (2, 3)}
B = {(2, 2), (3, −2), (9, 3), (9, −3)}

you can do both or neither as well THX

Answers

neither set of ordered pairs here is a function

Find the value of x so that the line passing through (10, 5) and (x, 9) has a slope of -2.

Answers

Ok, so here, we need to use the slope formula which is:

(y2 - y1)/(x2-x1)

y2 = 9
y1 = 5

x2 = x
x1 = 10

So:

(9-5)/(x-10) = -2

Now, we just solve for x,

9-5  =  -2(x-10)

4  =  -2x+20

2x  =  16

x  =  8

Given that a line has a slope of -3 and a point on the line is (2,-4),
1.what is the equation of the line in point-slope form?
2.how do we create slope-intercept form?
*please show all work, step by step.

Answers

The equation in Point Slope Form is

y + 4 = -3(x - 2)

We can convert this to Slope-Intercept Form by isolating y.

y + 4 = -3(x - 2)
y + 4 = -3x + 6
Subbtract 4 from both sides.
y = -3x + 2

The equation in Slope-Intercept Form is y = -3x + 2.
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