Directions: Solve the following inequalities. Be sure to follow the rules for operations with signed numbers.

1. -4x + 2 > 0

2. +5x > x + 4

3. 3x + 4 < 10

4. -10x + 5 -4 > 4x + 3

5. 6x + 3 < 7x - 10

6. 2x - 4 < 8x + 2

7. -3s + 3 > 3

8. 4s + 2s > 6

9. 6t < 12

10. 11x < 121

11. 3x > 36

12. 25x < 500

13. 16r < 8 (10)

14. 6s > 216

15. 8x < 64

Answer:

a) 100

b) Mango

c) Shop A = 90 and Shop B= 80

d) Shop B

e) chocolate

f) 330 ice-creams

g) 30

h) Mango

Your welcome~

The Volume of crystals is 160 mm³ while the area of the base is 20 mm².

Volume is the amount of space occupied by a three dimensional shape or object.

Area of triangle = (1/2) * DF * height

Height = 10 - 6 = 4 mm, DF = AC = AB + BC = 2 + 3 = 5 mm

Area of triangle = (1/2) * 5 * 4 = 10 mm²

Volume of triangle prism = Area of triangle * AG = 10 * 4 = 40 mm³

Volume of rectangular prism = A to F * AC * AG = 6 * 5 * 4 = 120 mm³

Volume of crystals = 120 + 40 = 160 mm³

Area of base = AC * AG = 5 * 4 = 20 mm²

The Volume of crystals is 160 mm³ while the area of the base is 20 mm².

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[tex]AB=BC=>\angle A=\angle C=49а\\\angle CBA=180а-\angle A-\angle C=180а-49а-49а=82а[/tex]

Answer:

C is the formula you should use and the rest of the answers are below

Step-by-step explanation:

Hence, the formulae to calculate the variance are -

[tex]\sigma^2 = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n}[/tex]     for a complete population and [tex]s^{2} = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n-1}[/tex]  for a sample population.

We have Variance.

We have to specify the formula of variance.

Variance is a measure of dispersion that takes into account the spread of all data points in a data set.

According to the question, the following formulae for variance are used according to the need.

For a Complete Population divide by the size n -

[tex]\sigma^2 = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n}[/tex]

For a Sample Population divide by the sample size minus 1

[tex]s^{2} = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n-1}[/tex]

Hence, the the formulae to calculate the variance are -

[tex]\sigma^2 = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n}[/tex]     for a complete population and [tex]s^{2} = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n-1}[/tex]  for a sample population.

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Answer:

95 degrees!!!

Step-by-step explanation:

add 5 to 90. or if you look at the protractor, after the 90, its on the 5 marker, which is why you add 5.

Answer:

81(x + 2y)(x - 2y)

Step-by-step explanation:

[tex]81 {x}^{2} - 324 {y}^{2} \\ \\ = {(9x)}^{2} - {(18y)}^{2} \\ \\ = (9x + 18y)(9x - 18y) \\ \\ = 9(x + 2y) \times 9(x - 2y) \\ \\ = 81(x + 2y)(x - 2y)[/tex]

Answer:

I don't have a clue and :3 is your 1st-period teacher named Mrs. SIKE I AINT GONNA EXPOSE MY DEAR TEACHA NAME!!

Step-by-step explanation:

Answer:

6

i started with 9 and counted up untell i got to 15

Answer:

A, B, and C

Step-by-step explanation:

The solution is, The true statements are F and E.

i.e.  F. The x-intercept is (1,0).

E. It is increasing.

The logarithm can be stated as the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

here, we have,

We need to graph the log function. F(x) = log6x

Domain: x>0 All real number greater than 0.

Range: All real number.

y-intercept: Put x=0 and solve for y. (Does not exist)

y-intercept: Put y=0 and solve for x. (1,0)

Log function is increasing function.

F is true. (It is increasing)

D is False. (Because Range is all real number)

E is true. (x-intercept (1,0))

A is false. (It is decreasing.)

B is false. (The y-intercept is (0, 6))

C is false. (Domain is x>0)

Hence, F and E are true.

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The false statement:

a° + d° = 180°

The correct option is B.

Corresponding angles are those formed at matching or corresponding corners with the transversal when two parallel lines are crossed by another line (i.e. the transversal).

Given:

Two pairs of parallel lines j and k, and r and s traverse each other.

d° = f° {opposite angles}

a° + d° = 180°

This is an incorrect statement.

a° = c° {Corresponding angles}

b° + e° = 180° (Sum of linear pair)

Therefore, a° + d° = 180°.

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Step-by-step explanation:

I assume we are simplifying

1) -6k+7k = k

2) 12r-8-12 = 12r-20

3) n-10+9n-3 = 10n-13

4) -4x-10x = -14x

Answer:

x=37

Step-by-step explanation:

Area of triangle = x+x+x=180
= 78+65+x=180
=143+x=180
=x=180-143 (bring 143 to the otherside)
x=37

In the given figure, We are to find the respective value of x .

Solution :

We know that,

Sum of all the angles of the triangle = 180°

So,

[tex] \qquad \sf \dashrightarrow{ x {}^{ \circ} + 65 ^{ \circ} +78 ^{ \circ} = 180}[/tex]

[tex] \qquad \sf \dashrightarrow{ x ^{ \circ} + 143^{ \circ} = 180^{ \circ}}[/tex]

[tex] \qquad \sf \dashrightarrow{ x ^{ \circ} = 180^{ \circ}} - 143^{ \circ}[/tex]

[tex] \qquad \bf \dashrightarrow{ x ^{ \circ} = 37^{ \circ}}[/tex]

Therefore, The value of x is 37°

Answer:

$1540

Step-by-step explanation:

base cost = $60
1 mile = $40
$40 x 37m = $1480
$1480 + $60
= $1540

Answer:

  x = 117

Step-by-step explanation:

The sum of the interior angles of a pentagon is 180°(5 -2) = 540°. This means ...

  x +59 +138 +140 +86 = 540

  x +423 = 540 . . . simplify

  x = 117 . . . . . . . . subtract 117

4 units

Step-by-step explanation:

I did the quiz, hope it helped! <3

Answer:

the kilograms of apples sold is 33/5 and in decimal is 6.6

Answer:

Yes because everytime y increases by 150 x increases by 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The second equation tells you ...

  ♧ = 21/3 = 7

The third equation tells you ...

  ♢ = 20 -2(7) = 6

Then the first equation tells you ...

  ♤ = 15 -7 -6 = 2

Finally, the last equation tells you ...

  ♡ = 13 -6 -2 = 5

Answer

Club = 7

Diamond = 6

Spade = 2

Heart = 5

Step-by-step explanation

Here it shows that 1 club + 1 diamond + 1 spade is equal to 15. Ok, let's get back to that one later.

In the next hint it shows that 3 clubs equals 21. So, in order to get the value of the club, divide 21 by 3, and you'll get 7. This means that 7 is the value of the club.

Now on to the third hint. Here it shows that 1 diamond plus 2 clubs are equal to 20. We already got the value of the club, which is 7, so add 7+7 and you'll get 14. Then, subtract 14 from 20 and you'll get the value of the diamond, which is 6.

Finally, the fourth hint. Here it shows that 1 diamond + 1 heart + 1 spade = 13. So, inorder to get the value of the heart, add the value of the diamond and the spade, which sums up to 8. Then subtract 8 from 13 and you'll get the value of the heart, which is 5.

Answer:

50% decease

Step-by-step explanation:

A change from 8 to 4 represents a negative change (decrease) of -50%

Use the formula found below on this webpage to find the percent change by replacing the given values:

Percent = New - Old/Old x 100

Percent = 4-8/8 x 100

Where: 8 is the old value and 4 is the new value. In this case we have a negative change (decrease) of -50 percent because the new value is smaller than the old value.

Hence, 50% decrease

Check Answer:

8 x 50% = 4

8 - 4 = 4

Hence, 50% decrease is the correct answer.

[RevyBreeze]

Answer:

please attach a photo to your question

Answer:

2.22

Step-by-step explanation:

2 + 0.22

2.22

None of them are equivalent to 2 + 0.22.

[tex]\\ \tt\hookrightarrow 2+0.22[/tex]

[tex]\\ \tt\hookrightarrow 2+22/100[/tex]

[tex]\\ \tt\hookrightarrow 200+22/100[/tex]

[tex]\\ \tt\hookrightarrow 222/100[/tex]

[tex]\\ \tt\hookrightarrow 2.22[/tex]

Answer:

p(3,3)

Q(6,3)

s(-2,-2)

R(-8,-2)

Answer:

He will get there in time

Step-by-step explanation:

Superman speed = 20miles per second and there are 60 seconds per minute, so Superman's speed is 1,200 miles per minute

1,200miles/minute * 5 minutes = 6,000 miles

6,000 miles > 5,000 miles so our boi will make it within 5 minutes

Answer:

8 m²

Step-by-step explanation:

1/2 × d1 × d2

= 1/2 × 4m × 4m

= 8 m²

Answer:

0.5, 7

Step-by-step explanation:

y=mx+b

-2y=0.5x+7

slope is m

yintercept is b

slope= 0.5

yintercept= 7

Answer:

£59.25

Step-by-step explanation:

It appears you can measure the height of the trapezoid [trapezium  :-)  ??].  If you can't, you can use the Pythagorean Theorem (image attached).  Draw a line from the upper right-hand corner down to the baseline--the 20m side.  You'll form a right triangle with one leg  h , hypotenuse 17m and the other leg  8m  (the difference between 20m and 12m).

(leg)^2 + (leg)^2 = (hypotenuse)^2

h^2 + 8^2 = 17^2

h^2 + 64 = 289

h^2 = 225

h = 15m

The area of the trapezium is [tex]A=\frac{1}{2}h\left(b_1+b_2\right)[/tex]  where the b's are the lengths of the two bases (upper and lower sides).

[tex]A=\frac{1}{2}(15)(12+20)=\frac{1}{2}(480) = 240[/tex] m^2

One can of weedkiller covers 100 m^2 of area.  You'll need 3 cans (2 cans isn't enough, and you can't buy a fraction of a can).  Tricky question!

Three cans will cost  3 x 19.75 pounds = £59.25

Answer:

24 square feet

Step-by-step explanation:

There are four "triangles" of the rhombus. If you find the area of each triangle by multiplying the height by the width and dividing by two, you get 6. You then multiply that by 4 to get 24.

Answer:

for 7 its A, B, E. For 8 its D

Answer:

Step-by-step explanation:

One vertex is given (5, 4).

The side of the square is 3. So other vertices may have ± 3 difference on either one coordinate.

Possible options are:

Point M is 6 units away from the origin.

Possible (x, y) coordinates have the sum of squares equal to 6².

The only correct option is D. (0, 6)