A solid oblique pyramid has an equilateral triangle as a base with an edge length of 4StartRoot 3 EndRoot cm and an area of 12StartRoot 3 EndRoot cm2. What is the volume of the pyramid?

Answer:

Is it B?

Step-by-step explanation:

ab^2 + 2a^2b + 4a + 2b

ab(b+2a) +2(2a+b)

ab(b+2a) +2(b+2a)

(ab+2)(b+2a)

that's why ab+2 is the answer.

Answer:

4 liters.

Step-by-step explanation:

From the question above, we are required to find the amount of water that should be added to a sugar and water solution.

Let x represent the amount of water that would be added by Sharon.

2×36/100= 12/100(2+x)

2×0.36= 0.12(2+x)

Cross multiply both sides

0.72= 0.24+0.12x

Collect the like terms

0.72-0.24= 0.12x

0.48= 0.12x

Divide both sides by the coefficient of x which is 0.12

0.48/0.12= 0.12x/0.12

x= 4

Hence Sharon should add 4 liters of water to 2liters of sugar and water solution that is 36% sugar to form a solution of 12% sugar.

Answer:

4 liters is the correct answer

Step-by-step explanation:

Complete Question

Consider a three-year loan (so we'll assume the numbers 1 through 36) for $5,000 with interest at 10% per year. Using standard amortization, the monthly payment is $161.33. In this example, we will not worry about exact or ordinary interest because the total interest to be paid is $808.13. After the fifth month the borrower decides to prepay the whole loan. Under a standard amortization plan the borrower would have paid $198.28 in cumulative interest. However, using the Rule of 78 a lender would calculate the fraction of the total interest based on two series:

[tex]\dfrac{(n+35)+(n+34)+(n+33)+(n+32)+(n+31)} {(n)+(n+1)+...+(n+35)}[/tex]

Answer:

See below

Step-by-step explanation:

36+35+34+33+32=170

Now, 1,2,3,...36 forms an arithmetic series whose first and last term are 1 and 36 respectively. Its sum is determined using the formula: [tex]S_{n}=\frac{n}{2}(a+l) \\[/tex]

[tex]S_{36}=\frac{36}{2}(1+36) =18*37=666[/tex]

[tex]=\dfrac{170}{666}= 0.255=25.5\% $(to the nearest tenth)[/tex]

The lender will multiply this fraction by the total interest.

The difference between the amount paid under a standard amortization plan and the amount paid under a Rule of 78 plan is:

$206.07-198.28=$7.79

Answer:

If you add 36, 35, 34, 33, and 32, the sum is . If you sum the numbers from 1 to 36, the sum is . The fraction (the first sum / the total sum) to the nearest tenth = %. The lender will multiply this fraction by the total interest. The cumulative interest = (the percentage calculated above) x ($808.13) = $. The difference between the amount paid under a standard amortization plan and the amount paid under a Rule of 78 plan is: $

1

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Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

Two are white.

10 total marbles.

10 - 2

8 are not white.

8/10

Simplify or reduce.

⇒ 4/5

Answer:

46.87

Step-by-step explanation:

V=*(A^3/2

)/36

V=*(46.87^3/2

)/36

Answer:

x >2

Step-by-step explanation:

2x-3> 11 - 5x

Add 5x to each side

2x+5x-3> 11 - 5x+5x

7x -3 > 11

Add 3 to each side

7x-3+3 > 11+3

7x >14

Divide by 7

7x/7 > 14/7

x >2

Answer:

Step-by-step explanation:

hello,

As A and B are two independent events we can say that P(A∩B)=P(A)P(B)

P(A)=P(A∩B)/P(B)=16/13

thanks

Answer: 75

solve:

For gym A

total cost= membership fee+monthly fee

membership fee=25

monthly fee=25

cost of x month=25x

total cost=25+25x

for gym B

membership fee=10

total cost=55+10x

now total cost are same

25+25x=55+10x

15x=30

x=30/15

x=2.

2 months

and amount =25+25*2=75

Answer:

2 months, they will have paid 75 dollars

Step-by-step explanation:

Gym A

25+ 25m  where m is the number of months

Gym B

55 + 10m

Set them equal

25+25m = 55+10m

Subtract 10m from each side

25+25m-10m = 55+10m-10m

25+15m = 55

Subtract 25 from each side

25+15m-25 = 55-25

15m = 30

Divide by 15

15m/15 = 30/15

m=2

After 2 months

25+25(2) = 25+50 = 75

The cost is 75 dollars

Answer:

Answer:

option 4

Step-by-step explanation:

Simplify the equation,

9x² + 6x = 3x ( 3x + 2)

9x² + 3x = 3x*(3x + 1)

9x² + 9x + 2 =9x² + 3x + 6x + 2*1

                    = 3x(3x + 1) + 2(3x + 1)

                  = (3x+ 1)(3x +2 )

[tex]\frac{10}{9x^{2}+6x}-\frac{1}{9x\frac{}{}+3x}=\frac{10}{3x(3x+2)}-\frac{1}{3x(3x+1)}\\\\=\frac{10(3x+1)}{3x(3x+1)(3x+2)}-\frac{1(3x+2)}{3x(3x+1)(3x+2))}\\\\=\frac{10(3x+1)-(3x+2)}{3x(3x+1)(3x+2)}\\\\\\\frac{5}{9x^{2}+9x+2}= \frac{10(3x+1)-(3x+2)}{3x(3x+1)(3x+2)}\\\\\frac{5}{(3x+1)(3x+2)}=\frac{10(3x+1)-(3x+2)}{3x(3x+1)(3x+2)}\\[/tex]

Both sides (3x+1)(3x+2) will get cancelled

[tex]5=\frac{10(3x+1)-(3x+2)}{3x}\\[/tex]

Cross multiply,

5(3x) =10(3x+1)-(3x+2)

When x = -2/3, LHS = 5(3x) = [tex]5*3*\frac{-2}{3}[/tex]

                                 = -10

When x= -2/3, RHS = 10(3x+1)-(3x+2)

                                = [tex]10(3*\frac{-2}{3}+1)-(3*\frac{-2}{3}+2)\\[/tex]

                                = 10(-2+1) - (-2+2)

                                = 10 * (-1) -0

                               = -10

LHS = RHS

So, -2/3 is a solution

Answer:b the probabilty that it contains nuts and is white

Step-by-step explanation:im sorry if this is wrong but its the only one that makes sense to me

Conditional probability is represented by probability that the candy is blue

The concept of the conditional probability formula is one of the quintessential concepts in probability theory. The conditional probability formula gives the measure of the probability of an event, say B given that another event, say A has occurred.  

The Bayes' theorem is used to determine the conditional probability of event A, given that event B has occurred, by knowing the conditional probability of event B, given that event A has occurred, also the individual probabilities of events A and B.

: In case P(B)=0, the conditional probability of P(A | B) is undefined.  (the event B did not occur)

Given:

Some red, white, and blue candies were placed in a bowl.

Some contain nuts, and some do not

Here we are only focusing on the red candy which shows we have reduce the sample space.

Learn more about conditional probability here:

https://brainly.com/question/13044823

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Answer:

y = 4

Step-by-step explanation:

We simply have to find the y-value when x = -3. When x = -3 on the graph, our y value would be 4.

Answer:

4

Step-by-step explanation:

Answer:

Hello!

____________________

Your answer would be (C).

Hope this helped you!

Answer:

y = [tex]\frac{2}{3}[/tex] x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, 4)

m = [tex]\frac{4-2}{3-0}[/tex] = [tex]\frac{2}{3}[/tex]

The line crosses the y- axis at (0, 2) ⇒ c = 2

y = [tex]\frac{2}{3}[/tex] x + 2 ← equation of line

Answer:

Question 1:

The letter x or any letter used when writing an expression is representative of  unit of an idea, quantity or measure, such that it can be translated in the expression to provide information about a related idea

Question 2:

The expression can be translated as two times the expression three (variable) x minus two (variable) y plus the constant 7

Question 3:

In the first expression, the like terms are;

10y and (-2y),

3x and x

In the second expression, the like terms are;

-y and -2y

3x and 4x

The first expression simplifies to 8y + 4x + 10

The second expression simplifies to  7x - 3y + 6

Question 4:

The expression is evaluated as 122

Question 5:

The equivalent expression of the expression 3(4x + 2y) + 5x, is 17x + 6y

To prove when x = 1 and y = 2 we have;

3(4×1 + 2×2) + 5×1 is 29

17×1 + 6×2 is 29 which are equivalent in value

Step-by-step explanation:

Question 1:

The letter x or any letter used when writing an expression is representative of  unit of an idea, quantity or measure, such that it can be translated in the expression to provide information about a related idea

Example;

If x is the symbol representing the average number of oranges sold in 1 hour, then the expression for the number of oranges sold per day of 24 hours  = 24·x

An expression is a written mathematical symbolic statement that shows the the finite merging together of representative symbols by the mathematical operations that govern the present constraints

An equation is a statement that two expressions are equal

Question 2:

The given expression is 2(3x - 2y) + 7

The parts are;

The coefficient of (3x - 2y) = 2

The constant term = 7

The variables are x and y

Which gives

The coefficient of the variable x = 6

The coefficient of the variable y = -4

The expression can be translated as two times the expression three (variable) x minus two (variable) y plus the constant 7

or

The expression can be translated as two times the bracket open three times (variable) x minus two times (variable) y bracket close plus the constant 7

or

The expression can be expanded as 2(3x - 2y) + 7 → 6·x - 4·y + 7 which is expressed verbally as follows;

Six times (variable) x minus four times (variable) y plus the constant 7

Question 3:

The expressions are;

10y + 3x + 10 + x  - 2y..........................(1)

3x - y + 4x + 6 - 2y,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(2)

In the first expression, the like terms are;

10y and (-2y),

3x and x

In the second expression, the like terms are;

-y and -2y

3x and 4x

They are like terms because they can be simply added together to simplify the expressions as follows

10y + 3x + 10 + x  - 2y gives 10y - 2y + 3x + x  10  to give 8y + 4x + 10

Also

3x - y + 4x + 6 - 2y  gives  3x+ 4x - y  - 2y + 6 to give 7x - 3y + 6

Question 4:

The expression 8x² + 25·y when x = 3 and y = 2 is evaluated by replacing (putting) the value x and y (into the expression)

The expression is then evaluated as 8×3² + 25×2 which is the same as 72 + 50 or 122

Question 5:

To write the equivalent expression of the expression 3(4x + 2y) + 5x, we expand the expression as follows;

3×4x + 3×2y + 4x which is 12x + 6y + 4x

We combine like terms;

12x + 5x + 6y which is 17x + 6y

To prove we can check by substituting a value for each of the variables x and y such as x = 1 and y = 2

3(4×1 + 2×2) + 5×1 is 29

17×1 + 6×2 is 29

Answer:

Step-by-step explanation:

numbers to find perimeter = perimeter

Side + Side + 2 unknown sides = perimeter

12 + 7.8 + 2t = 50.2

19.8 + 2t = 50.2

19.8 + 2t = 50.2

-19.8        - 19.8

2t = 30.4

12 + 7.8 + t + t = 50.2

12 + 7.8 + (15.2) + (15.2) = 50.2

Hope this helped,

Kavitha

Answer:

t = 15.2 miles

Step-by-step explanation:

First, let's add the top and bottom numbers together.

7.8 + 12 = 19.8 mi

Next, we subtract that from 50.2 to get the combined value of both t's.

50.2 - 19.8 = 30.4 mi

Finally, we can divide 30.4 by 2 to get the value of t.

30.4 ÷ 2 = 15.2 mi

To check our answer, we can add all the sides up to see if they equal to 50.2. 15.2 + 15.2 = 30.4

30.4 + 12 + 7.8 = 50.2

Answer:

Kindly check attached picture for number line.

Step-by-step explanation:

Total time Allen would love to complete race is less than 5.5 hours

Time elapsed = 3 hours

Inequality representing the problem above :

3 + t < 5.5

Where t will mean the time left.

Solving for t

t < 5.5 - 3

t < 2.5

Time left is < 2.5 hours.

Answer:

Open Circle to the left from 2.5

Step-by-step explanation:

Answer:

2:30

Step-by-step explanation:

58+32=90

90-60=30

2:30 is the answer

Answer: she will get home at 2:30

Step-by-step explanation:

If you start at 1:32 then take 28 min from 58 then you get 2:00

Finally add 30 yo that and get 2:30.

Answer:

A

Step-by-step explanation:

If you put your function in a graphing calculator you will get (6,0)

Answer:

75%

Step-by-step explanation:

Percentage of planets having moons = 6 /8 *100 = 75%

Answer:

52

Step-by-step explanation:

Since the sum of interior angles in a quadrilateral is 360°, you have to subrtact all those numbers from 360° in order to get angle D. What I mean is:

360 - (128+126+54)

360 - 308

52

Answer:

52°

Step-by-step explanation:

The trapezoid is a closed figure, meaning all the angles must equal 360°.

1. Set up the equation

128° + 126° + 54° + ∠D = 360°

2. Solve for ∠D

360 - 128- 126- 54 = 52

∠D = 52°

You can also solve this by knowing that in a trapezoid:

∠A + ∠D = 180° and ∠B + ∠C = 180°

1. Set up the equation

128 + ∠D = 180°

2. Solve

180 - 128 = 52

∠D = 52°

Answer:

Area of ABCD = 959.93 units²

Step-by-step explanation:

a). By applying Sine rule in the ΔABD,

  [tex]\frac{\text{SinA}}{46}=\frac{\text{Sin}\angle{DBA}}{35}[/tex]

  [tex]\frac{\text{Sin110}}{46}=\frac{\text{Sin}\angle{DBA}}{35}[/tex]

 Sin∠DBA = [tex]\frac{35\times \text{Sin}(110)}{46}[/tex]

 m∠DBA = [tex]\text{Sin}^{-1}(0.714983)[/tex]

 m∠DBA = 45.64°

 Therefore, m∠ADB = 180° - (110° + 45.64°) = 24.36°

                  m∠ADB = 24.36°

c). Area of ABCD = Area of ΔABD + Area of ΔBCD

  Area of ΔABD = AD×BD×Sin([tex]\frac{24.36}{2}[/tex])

                           = 35×46Sin(12.18)

                           = 339.68 units²

   Area of ΔBCD = BD×BC×Sin([tex]\frac{59.92}{2}[/tex])°

                            = 46×27×(0.4994)

                            = 620.25 units²

   Area of ABCD = 339.68 + 620.25

                            = 959.93 units²

Answer:

The postulates are as follows:

Answer:4x2−6x−4

Step-by-step explanation:

(4x+2)(x−2)

=(4x+2)(x+−2)

=(4x)(x)+(4x)(−2)+(2)(x)+(2)(−2)

=4x2−8x+2x−4

=4x2−6x−4

Answer:

(4x+2)(x-2)

= 4x(x-2) +2(x-2)

=4x^2-8x + 2x-4

=4x^2 - 6x -4

Hey there! I'm happy to help!

There is a rule in trigonometry that says that the sine of one angle is equal to the cosine of that angle's complement.

Complementary angles are ones that equal 90 degrees when added.

We see that L and M are complementary angles, so we can apply this rule.

The sine of L is 19/20. We know that the sine of angle L is equal to the cosine of L's complement from our rule, which is M. This means that the cosine of M is equal to 19/20.

Have a wonderful day!

Answer:

45 degrees

Step-by-step explanation:

central angle = the arc

inscribed angle = 1/2 the arc

Answer:

x=26 degrees (D)

Step-by-step explanation:

Let's say x is the angle.

90-x would be the complement of the angle

180-x is the supplement

We can make the equation

supplement-26=2complement as the question states that twice the complement is 26 less than the supplement.

We can now substitute the 90-x and 180-x in their respective positions to get (180-x)-26=2(90-x) if we simplify this we get 180-x-26=180-2x which if we take away 180-x from both sides we get that -26=-x or 26=x

Answer:

x          |          y

− 2                − 6

− 1                − 3

0                    0

1                     3

2                    6

hope this helps!

The table of values for the equation y = 3x - 1, is attached.

x y

-2 -7

-1 -4

0 -1

1 2

2 5

3 8

Equations are relations between two or more variables, used to find the value of an unknown variable from the known value of other variables.

We are given the equation y = 3x - 1. We are asked to complete the table, for the given values of x: -2, -1, 0, 1, 2, 3.

To find the y variable, for the given x's, we substitute each value of x, one at a time in the equation.

We put all these values of y, for the corresponding value of x in the table. The completed table is attached.

Learn more about equations at

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Answer:

27.44 square cm

Step-by-step explanation:

If the length of parallelogram is a and b and angle between side a and b is [tex]\alpha[/tex].

Then area of parallelogram = [tex]a*b*sin(\alpha ) = ab sin(\alpha )[/tex]

Given side length 4 cm and 7 cm

angle between them = 100°

value of sin(100°) = 0.98

Thus, area of given parallelogram = 4*7*sin(100°) = 28*0.98 = 27.44

Thus, area of given parallelogram is 27.44 square cm.

Answer:

D

Step-by-step explanation:

The number of months in two years is 24 months.

Now, with a repayment plan of $400 per month, the total amount returned will be 400 * 24 = $9,600

Now, $8,000 was borrowed but $9,600 was returned

The amount of interest is 9600-8000 = 1600

So what percentage of 8,000 is 1600?

1600/8000 * 100 = 16/80 * 100 = 1/5 * 100 = 20%