Given: ⅓ (18x + 27) = 81 Prove: x = 12

Answer:

x = 1 or x = −6

Step-by-step explanation:

Step 1: Subtract 18 from both sides.

3x2+15x−18=18−18

3x2+15x−18=0

Step 2: Factor left side of equation.

3(x−1)(x+6)=0

Step 3: Set factors equal to 0.

x−1=0 or x+6=0

x=1 or x=−6

Answer:

A. 7/14, 2/5, 32%, and .25

Answer:

the cost is $26

i think ths answer would be help full

Answer:

69.39  kilometers

Step-by-step explanation:

total kilometres driven on each trip = total kilometres driven on all trips / total number of visits

6,870.1 / 99 = 69.394949

To the nearest hundredth means we are rounding off the third number after the decimal point. The second number after the decimal is the hundredth. The third number is less than 4, so zero would be added to the preceding number

69.39 kilometers

Answer:

[tex] \boxed{ \tt{the \: adult \: giraffe \: is \to \: 14 \: ft}}[/tex]

The height of the giraffe standing near it which casts a shadow of 7 feet is 14 feet.

Scale factor is the ratio of the dimension of the given original object and the dimension of the new object from the original.

Given that,

Actual height of the tree = 18 feet

Height of the shadow = 9 feet

Actual height = 2 × Shadow height

So, here the scale factor is 2.

Given Shadow height of the giraffe = 7 feet

Actual height of the giraffe = 2 ×  height of shadow of the giraffe

                                             = 2 × 7 feet

                                             = 14 feet

Hence the height of the giraffe is 14 feet.

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Answer:

15 different sums.

Step-by-step explanation:

1+2

1+3

1+4

1+5

1+6

2+3

2+4

2+5

2+6

3+4

3+5

3+6

4+5

4+6

5+6

There is 15 different sums.

Answer:

B; 2.5x + 45 = 62.5

Step-by-step explanation:

Since the current height is 62.5, and the starting height is 45, then all you have to do is subtract 45 from 62.5, then divide that by 2.5 to get your answer, which should be 7 years.

Hopefully this helps- let me know if you have any questions!

Answer:

0.7

Step-by-step explanation:

The total probability is equal to 1

To find the probability of player b we take the probability of player a and subtract it from the total probability of 1

Hence 1-0.3=0.7

Answer:

0.7

Step-by-step explanation:

→ Minus 1 from the probabilities as all probabilities add up to 1

1 - 0.3 = 0.7

Answer:

.

Step-by-step explanation:

Answer:

50p

Step-by-step explanation:

you can add them all up together. 27+3+6+14=50!

Answer:

50kg

Step-by-step explanation:

25 kg of a 15% salt solution

25kg * 15%

25kg * 15/100 = 3.75 kg

3.75kg * 100/5

3.75 * 20 = 75

Mass of water in kg increased from 25kg to 75kg

75kg - 25kg = 50kg of water must be added.

Answer:

the question is blurry and it has a glare

The three main trig functions are sine (written as sin), cosine (written as cos), and tangent (written as tan).

Sine of an angle = the length of the side opposite (aka across) the angle / the length of the hypotenuse

Cosine of an angle = the length of the side adjacent (aka the side next to which isn't the hypotenuse) to the angle / the length of the hypotenuse

Tangent of an angle = the length of the side opposite of the angle / the length of the side adjacent to the angle.

The acronym to remember this is SOHCAHTOA

SOH | CAH | TOA

SOH means sin(x) = opposite/hypotenuse

CAH means cos(x) = adjacent/hypotenuse

TOA means tan(x)= opposite/adjacent

cosB = length of adjacent side/length of hypotenuse = 7/25

tanB = length of opposite/length of adjacent = 24/7

sinB = length of opposite/length of hypotenuse = 24/25

Answer:

1.6; 2.4

Step-by-step explanation:

five or more round up

4 or less leave as is

Answer:

we know all angles are 90° in the rectangle

therefore, angle d = bdc+bda = 90

=> 31+bda = 90

=>angle bda= 59

The measurement of the angle ADB should be considered as the 59 degrees.

Since we know that all angles in the rectangle should be of 90 degrees

So,

Here angle d = bdc + bda

= 90

Now

31 + bda = 90

So, bda = 90 - 31

= 59

hence, The measurement of the angle ADB should be considered as the 59 degrees.

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Answer:

Remember that for a triangle rectangle we have the Pythagorean's theorem, it says that the square of the hypotenuse is equal to the sum of the squares of the catheti.

Then if the catheti of a triangle rectangle are A and B, and the hypotenuse is H, we have:

H^2 = A^2 + B^2

In the smaller triangle we can see that:

H = 10

A = 6

Then:

10^2 = 6^2 + B^2

100 = 36 + B^2

100 - 36 = B^2

64 = B^2

√64 = B = 8

And we know that the perimeter of a triangle is equal to the sum of the lengths of it's sides, then the perimeter of the smaller triangle is:

P = 10 + 6 + 8  = 24

Now we know that the triangles are similar and related by a factor of 4/3, then each measurement of the larger triangle will be equivalent to 4/3 times the corresponding measurement of the smaller triangle, then if the measures of the larger triangle are A', B', and H', we can write these as:

A' = (4/3)*A = (4/3)*6 = 8

B' = (4/3)*B = (4/3)*8 = 10.67

H' = (4/3)*H = (4/3)*10 = 13.33

Then the perimeter of the larger triangle is:

P' = 8 + 10.67 + 13.33 = 32

Answer:

hypotenuse is about 33 ft long

Step-by-step explanation:

a^2+b^2=c^2

a= 30

b=14

30^2+14^2= 1096 =c^2

[tex]\sqrt{1096}[/tex]=c

33.1=c

hypotenuse is about 33 ft long

Answer:

No, the Hypotenuse is 33.11

Step-by-step explanation:

The formula for finding a hypotenuse is:

[tex]\sqrt{x^2+y^2}[/tex]

x=30 and y=14 here

[tex]x^2=900[/tex]

[tex]y^2=196[/tex]

[tex]x^2+y^2= 1,096[/tex]

[tex]\sqrt{1,096} = 33.11[/tex]

So it would be about 33, not 39

Answer:

0 = -16t² + 3200 → 16t²= 3200 → t² = 200 → t = 10√2 s ≈ 14 s

The time taken by the skydiver to reach the ground is 14.1 second.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

Given that, the height of a skydiver jumping out of an airplane is given by n = -16t² + 3200.

Here, n=0

-16t² + 3200=0

-16t²=-3200

t²=200

t=√200

t=14.14

t=14.1 second

Therefore, the time taken by the skydiver to reach the ground is 14.1 second.

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Answer:

Hi friend I am new can you show me how post question pls

Step-by-step explanation:

Answer:

x=11

Step-by-step explanation:

step 1- add 6 to both sides

2x-6+6=16+6

step 2- divide both side by 2

2x/2 22/2

x=11

I suggest using a calculator called Math Papa that's what I use for equations

9514 1404 393

9514 1404 393

Answer:

  1) (1 1/2)(7/5) = g

  2) (1 1/2)/(5/7) = g

Step-by-step explanation:

1) Tyler has painted 5/7 of the 7/7 of the fence. So the total amount of the fence is (7/7)/(5/7) = 7/5 as much as what was already painted.

The total amount of paint needed is then 7/5 the amount already used:

  g = (7/5)(1 1/2) . . . . . gallons of paint needed for the whole fence

__

2) If g gallons are required for the whole fence, the amount used so far for 5/7 of the fence is 5/7 of the quantity required:

  (5/7)g = 1 1/2

  g = (1 1/2)/(5/7) . . . . division expression for the paint needed

Answer:

55m

Step-by-step explanation:

A scale model is a reduced sized of the actual model

If 2m represents 110m, then 1m = 110/2 = 55m

Answer:

y = 2x + 8

Step-by-step explanation:

Recall that two parallel lines have the same slope.

Thus, if we begin with y = 2x - 4, we know that this new line through (-1, 6) will also have slope 2.

Starting from the slope-intercept form y = mx + b, we substitute 2 for m, -1 for x and 6 for y:

6 = 2(-1) + b

and solve for the new y-intercept, b:

6 = -2 + b, or

b = 8

Then the new line has the equation y = 2x + 8

Answer:

You need to rent

14

videos, and you'll pay the same amount for both. Renting

15

will make the membership a better method of payment.

Explanation:

We can create an equation. Say the number of videos you rent is given by

n

. We can write that, if we rent

n

videos without membership, we'll have to pay

4

n

. If we rent the same amount of videos with membership, we'll have to pay

21

+

2.5

n

.

To find the value of

n

such that the amount you pay without membership is equal to the amount you pay with, we write:

4

n

=

21

+

2.5

n

1.5

n

=

21

n

=

21

1.5

n

=

14

You need to rent

14

videos, and you'll pay the same amount for both. Renting

15

will make the membership a better method of payment.

Answer:

21x +11 is the answer hope this helps

Answer:

the probability of getting exactly 2 fours is 0.16

Step-by-step explanation:

The probability of obtaining a number that is four = ¹/₆

The probability of obtaining a non 4 number = 1 - ¹/₆ = ⁵/₆

The number of ways 2 fours can be arrange in five numbers = ⁵C₂ = 10 ways

If the die is tossed five times, the probability of the events is calculated as;

P = 10 x (¹/₆)² x (⁵/₆)³

P = 10 x (¹/₃₆) x  (¹²⁵/₂₁₆)

P = 10 x 0.02778 x 0.5787

P = 0.16

Therefore, the probability of getting exactly 2 fours is 0.16

The probability of exactly [tex]2[/tex] four's in [tex]5[/tex] tosses is [tex]0.1608[/tex].

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are to happen, using it.

Let [tex]X[/tex] be the number of fours in [tex]5[/tex] coin tosses.

We have no. of tosses [tex]n=5[/tex].

Probability of a success i.e., getting four [tex](p)=\frac{1}{6}[/tex] and probability of not getting a four [tex](q)=\frac{5}{6}[/tex].

[tex]X[/tex] follows a binomial distribution. So,

[tex]P(X=x)=\binom{n}{x}p^{x}q^{n-x}[/tex]

[tex]\therefore[/tex] the probability of exactly [tex]2[/tex] four's in [tex]5[/tex] tosses is given by,

[tex]P(X=2)=\binom{5}{2}\left ( \frac{1}{6}^{2} \right )\left ( \frac{5}{6} \right )^{3}[/tex]

               [tex]=0.1608[/tex]

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Answer:

please send an image so I can further assist