Solve: Give your answer in set notation.
5-4 |3+6x| > -31

{x|__< x <__}

Answer:

Step-by-step explanation:

Answer:

height of pyramid = 3 cm

height of prism = 9 cm

Step-by-step explanation:

Square Pyramid

surface area of 4 triangular sides of the pyramid = [tex]2a\sqrt{\dfrac{a^2}{4}+h^2}[/tex]

(where [tex]a[/tex] is the base edge and [tex]h[/tex] is the height)

Given [tex]a[/tex] = 8 cm

[tex]\implies \textsf{SA}=2\cdot8\sqrt{\dfrac{8^2}{4}+h^2}[/tex]

            [tex]=16\sqrt{16+h^2}[/tex]

Square Prism

surface area of square prism with one base = [tex]a^2+4ah[/tex]

(where [tex]a[/tex] is the base edge and [tex]h[/tex] is the height)

Given [tex]a[/tex] = 8 cm and [tex]h[/tex] = 3h

[tex]\implies \textsf{SA}=8^2+4\cdot 8\cdot 3h[/tex]

Total surface area

total SA = SA of pyramid + SA of square prism

Given total SA = 432 cm²

[tex]\implies 432=16\sqrt{16+h^2}+64+96h[/tex]

[tex]\implies 368=16\sqrt{16+h^2}+96h[/tex]

[tex]\implies 368=16(\sqrt{16+h^2}+6h)[/tex]

[tex]\implies 23=\sqrt{16+h^2}+6h[/tex]

[tex]\implies 23-6h=\sqrt{16+h^2}[/tex]

[tex]\implies (23-6h)^2=16+h^2[/tex]

[tex]\implies 529-276h+36h^2=16+h^2[/tex]

[tex]\implies 35h^2-276h+513=0[/tex]

[tex]\implies (h-3)(35h-171)=0[/tex]

[tex]\implies h=3, h=\dfrac{171}{35}[/tex]

Inputting both values of [tex]h[/tex] into the equations for SA:

when [tex]h = 3[/tex]:

[tex]\textsf{pyramid}=16\sqrt{16+3^2}=80 \ \sf cm^2[/tex]

[tex]\textsf{square prism}=64+96(3)=352 \ \sf cm^2[/tex]

[tex]\textsf{total SA}=80+352=432 \ \sf cm^2[/tex]

when [tex]h=\dfrac{171}{35}[/tex]:

[tex]\textsf{pyramid}=16\sqrt{16+(\frac{171}{35})^2}=101.0285714... \sf cm^2[/tex]

[tex]\textsf{square prism}=64+96(\frac{171}{35})=533.0285714... \ \sf cm^2[/tex]

[tex]\textsf{total SA}=101.0285714...+533.0285714... =634.0571428... \ \sf cm^2[/tex]

Therefore, h = 3 only (since the total area is 432 cm²)

⇒ height of pyramid = 3 cm

⇒ height of prism = 3h = 3 × 3 = 9 cm

Answer:

2m-8+1=2m-7

Step-by-step explanation:

Answer:

(a) [tex]A=1600(1+\frac{0.0375}{12})^{12t}[/tex]

     (where [tex]A[/tex] is the account balance and [tex]t[/tex] is the time in years)

(b) $1,929.40

Step-by-step explanation:

Compound interest formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where:

Given:

Substituting these values into the formula:

[tex]\implies A=1600(1+\frac{0.0375}{12})^{12t}[/tex]

(where [tex]A[/tex] is the account balance and [tex]t[/tex] is the time in years)

Part (b)

Substitute [tex]t=5[/tex] into the equation created in part (a):

[tex]\implies A=1600(1+\frac{0.0375}{12})^{12\cdot 5}[/tex]

[tex]\implies A=1600(1.003125)^{60}[/tex]

[tex]\implies A=1929.404236...[/tex]

[tex]\implies A=1929.40[/tex]

Therefore, her account balance after 5 years will be $1,929.40

Answer:

can't solve this

Step-by-step explanation:

It's tricky because everybody is used to seeing 50+50=100

50+50=100 Its simple but when u put it like that it makes at trickier and people think its 90 or 103

Answer:

Y=45 X=90

Step-by-step explanation:

B is equal to C so it would be 45. Since the whole triangle must be 180 you subtract 45 and 45 from 180 and you get 90. Another way to tell C and B are the same is the 2 little lines on the sides.

Answer:

y=45°(angles opposite to equal sides are equal)

x+y+45=180(sum of the interior angles of a triangle is 180)

x+45+45=180

y+90=180

y=180-90

y=90

Step-by-step explanation:

Answer:

b) [tex]a_{n}[/tex] = 2 + 2/5n

Step-by-step explanation:

Given :-

a = 12/5

d = 2/5

To Find :-

[tex]a_{n}[/tex]

Solving :-

[tex]a_{n}[/tex] = a + (n - 1)d

= 12/5 + 2/5n - 2/5

= 2 + 2/5n

Solution :-

b) [tex]a_{n}[/tex] = 2 + 2/5n

Answer:

100

Step-by-step explanation:

Lets solve this the easiest way possible :)

120/6 = 20

Now since they sold 5/6 of these copies, lets multiply the 20 by 5 to figure out how much they sold.

20 x 5 = 100

They sold 100 copies :)

Hope this helps!!!

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

100

Step-by-step explanation:

5     120

-----   ------

6          1

=

600

-------   =  100

6

Answer:

Dear Friend here is your answer.

Answer:

It is c

Step-by-step explanation:

When you fold it up, it makes a box just like the solid figure.

Have an amazing day!

PLEASE RATE!!

Answer:

0.00000049

I believe this is right if not I apologize

Answer:

All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle

Step-by-step explanation:

Answer:

4. F

5.C

6.G

7.D

8.A

9.E

10.B

Step-by-step explanation:

Step-by-step explanation:

-2 (4a + 4b) + 5a > -35

-8a -8b + 5a > -35

-3a -8b > -35

for a

-3a > -35 + 8b

a < -35 + 8b ÷ -3

a < 35 - 8b ÷ 3

for b

-3a - 8b > -35

-8b > -35 + 3a

b < -35 + 3a ÷ -8

b < 35 - 3a ÷ 8

Answer:

The sum of a number and its additive inverse is equal to 0.

Step-by-step explanation:

Answer:

16 ounces

Step-by-step explanation:

x, quantity of the 5%

24-x, quantity of the 20%

5%x + 20%(24-x) = 10% of 24

.05x + .20(24-x) = .10 * 24

.05x + 4.8 - .20x = .10 * 24

4.8 -.15x = 2.4

2.4 = .15x

.15x = 2.4

x = 2.4/.15

x = 16

Answer: C) Draw segment TU and point R on segment TU.

The construction he set up so far is pretty much almost done. If he draws a ray through points T and U (with T as the endpoint), then ray TU combines with ray TS to get angle STU. This angle is congruent to angle BCD.

The point R is introduced so that we call this angle STR instead of angle STU, but it's the same basic idea. You could also replace "ray" with "line" or "line segment" to get the same basic construction of copying an angle.

Answer:

463.70 or 500.45

Answer:

I don't know which letter answer it is because it is unclear in the question, but the answer is:

28/100 for the fraction

0.28 for the decimal

Step-by-step explanation:

1. ∠EBC = x (Theorem One: The angle at the centre of the circle is twice the angle at the circumference subtended on the same arc. You already have this one labelled)

2. ∠FCD = x (F rule / corresponding angles are equal)

3. ∠CAE = x (Theorem Two: Angles at the circumference subtended by the same arc are congruent)

4. ∠BED = ∠DCF = ∠FCD = x (Theorem Fifteen: The exterior angle of a cyclic quadrilateral is congruent to the interior opposite angle)

5. ∠CDF = ∠BED = x (F rule / corresponding angles are equal)

6. ∠CAE = ∠OAE = ∠OEA = x  (CAE and OAE are the same angles, OF and OA are radii, thus they must both be equivalent in magnitude, therefore making the triangle ΔAOE isosceles. Base angles of an isosceles triangle are always equal, since we knew ∠OAE from '3.' was x, we found that ∠OEA was also x)

Answer:

It would be $45.00.

Step-by-step explanation:

50 divided by 10 would be 5. Subtract that from 50 to get 45.

Answer:

$45.00

Step-by-step explanation:

If an item cost $50 and the discount is 10% then:

Convert 10% to a decimal

10/100 = .1

.1 * $50 = $5

The discount is $5, subtract the discount from the original amount.

$50 - $5 = $45

The item would cost $45.00 after the discount.

Answer:it’s the third answer choice

Step-by-step explanation:

Answer:

Step-by-step explanation:

let us first model the amount that Jaime and Jon will charge

let the total amount be y and let the number of hours be x

Jaime will charge

y=30+4x------1

Jone will charge

y=50x-----2

equating 1 and 2 we can solve for x which is the number of months Jaime and Jon will charge the same price

50x=30+40x

50x-40x=30

10x=30

divide both sides by 10 we have

x=30/10

x=3

Answer:

= 196 cm^2

Step-by-step explanation:

A= bh

= 14X14

= 196 cm^2

Answer:

3. 15 outcomes

5. 72 outcomes

Step-by-step explanation:

5 x 3 = 15

(2 x 3) x 12 = 72

2 x 3 = 6

6 x 12 = 72

Answer:

2.2360679775

Step-by-step explanation:

Answer:

2.2360679775

Step-by-step explanation:

Answer:

0.00000001

Step-by-step explanation:

Answer:

0.000000001

Step-by-step explanation: