The volume of the rectangular pyramid below is 56 units³. Find the value of x.
Height=7
Width=6
Length=x

7 raised to the power of 4 equals 2,401, and the exponent we were looking for is 4.

What is meant by power?

Power is a function that represents the number of times a base number is multiplied by itself. It is the rate at which work is done or energy is transferred, measured in watts.

What is meant by exponent?

An exponent is a mathematical notation used to indicate the number of times a quantity is multiplied by itself. It is written as a superscript and represents the power to which a number or expression is raised.

According to the given information

To find the value of the exponent that satisfies the equation 7ˣ = 2,401, we can take the logarithm of both sides of the equation with respect to base 7. This gives us:

log7(7ˣ) = log7(2,401)

x = log7(2,401)

Using a calculator, we can find that log7(2,401) is approximately 3. Therefore, the value of x that satisfies the equation 7ˣ = 2,401 is 3.

Alternatively, we could also use the fact that 2,401 is equal to 7⁴ - 2, which can be written as:

7⁴ - 2 = (7²)² - 2

= 49² - 2

= 2,401

To know more about exponent visit

brainly.com/question/15993626

#SPJ1

Answer:10907

Step-by-step explanation 10907

Answer:

The answer is 28

Step-by-step explanation:

Hope this helps,

have a great day

To show that the angle bisector of an equilateral triangle is perpendicular to the base​, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.  

After getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.

We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.

Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.

Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.

Learn more about the angle bisector of an equilateral triangle here:

https://brainly.com/question/30341397

#SPJ1

Answer:Yes

Step-by-step explanation:His complaint is valid.

Answer:

Jay

Step-by-step explanation:

by the graph, after 10 hours, Jay melts 95 ft³

by the equation y = 17/3x, after 10 hours, Michelle melts 0.57 ft³

The coordinate of point R after the rotation is determined as = ( - 4, 7).

option A.

A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.

You can turn a figure 90°, a quarter turn, either clockwise or counterclockwise. When you spin the figure exactly halfway, you have rotated it 180°. Turning it all the way around rotates the figure 360°.

When a figure is rotated 180 degrees, each point of the figure is moved to a new position that is exactly opposite its original position with respect to a fixed center of rotation.

The initial coordinate of point R = ( 4, 7),

The new coordinate of point R after the rotation = ( - 4, 7)

Learn more about rotation of figures here: https://brainly.com/question/13286537

#SPJ1

(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

for more questions on down payment

https://brainly.com/question/1698287

#SPJ8

To divide 30 into five parts such that the first and last parts are in the ratio of 2:3, we can follow these steps:

1. Determine the ratio between the first and last parts. In this case, it is 2:3.

2. Add the ratio values together to find the total number of parts: 2 + 3 = 5.

3. Divide the total value (30) by the total number of parts (5) to find the value of each part: 30 / 5 = 6.

4. Multiply the value of each part by the respective ratio values to obtain the individual parts:

- First part: 2 * 6 = 12

- Second part: 6

- Third part: 6

- Fourth part: 6

- Last part: 3 * 6 = 18

Therefore, the five parts of 30, with the first and last parts in the ratio of 2:3, are 12, 6, 6, 6, and 18.

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

Option D is the correct answer.

We have,

We need to isolate the absolute value |x + 2| on one side of the inequality.

We subtract 7 from both sides.

|x + 2| > 3

Next, we can split this inequality into two separate inequalities, one for when the expression inside the absolute value is positive, and one for when it is negative:

x + 2 > 3

or

- (x + 2) > 3

Solving for x in the first inequality.

x > 1

Solving for x in the second inequality.

-x - 2 > 3

Adding 2 to both sides and multiplying by -1.

x < -5

So the solution set for the inequality |x + 2| + 7 > 10 is the set of all x-values that satisfy either x > 1 or x < -5.

Using interval notation.

(-∞, -5) U (1, ∞)

Thus,

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ1

Answer:

Option C

Step-by-step explanation:

have a great Day

Answer:

2.98

Step-by-step explanation:

First find 3% of 16.05 which is 0.48.

Then add 0.48 to 16.05 which is 16.53.

Then multiply .18 by 16.53 which gets you 2.98

Hope it helps

Answer:

To find the amount of the sales tax, we need to multiply the bill amount by the tax rate of 3% or 0.03:

Sales tax = 0.03 x $16.05 = $0.48

To find the total amount of the bill after the sales tax was added, we need to add the bill amount to the sales tax:

Total bill = $16.05 + $0.48 = $16.53

To find the amount of the tip, we need to calculate 18% of the total bill after the sales tax was added:

Tip = 0.18 x $16.53 = $2.98

Rounding to the nearest cent, Penelope left a tip of $2.98.

Step-by-step explanation:

Answer:

$61.92

Step-by-step explanation:

Given data

Charge for food= $48

Tax= 9%

Tip=20%

Let us find the amount of the tax and the tip

Tax

=9/100*48

=0.09*48

=$4.32

Tip

=20/100*48

=0.2*48

=$9.6

Hence the total amount paid is

=48+4.32+9.6

=$61.92

Step-by-step explanation:

Sam's cookies = $16 for 12

Charlie's cookies = $21 for 12

$5 more when buying Charlies other than Sam's

Answer:

1. 7.3

2. 33.3

3. 21.3

4. 31.9

5. 25.6

6. 11.0

7. 42°

8. 64°

9. 13°

10. 51°

Step-by-step explanation:

make sure if you're using a math calculator that it is in degree mode.

SIN, COS, OR TAN. SOH CAH TOA. Sin is Opposite/hypotenus.

Cos is Adjacent(next to it)/hypotenus.

Tan is Opposite/Adjacent.

~~

PROBLEM 1:

So we have 63°, 16 as hypotenus, and x as one of the legs.

1. Figure out whether it is Sin, Cos, or Tan. (It's adj and hyp. of the angle degree (63° listed so it's cos.)

2. Once you set it up, it is Cos 63°= x/16 then flip it around. which makes it 16 COS 63= X.

3. Input it into your calculator as 16cos(63, then it will give you.. 7.263847996

4. Don't forget to round to the nearest tenth, which gives you

x = 7.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 2:

Given: 39°, 27 is opposite of the °, and adj is x. So this is Tan.

1. Set it up, Tan 39° = 27/x can't solve this way so fix it.

2. rewritten as X = 27/tan39

3. round ur answer.

x = 33.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 3:

Given: 49°, adj is 14, hyp is x. So this is Cos.

1. Set up according to CAH, Cos 49=(14/x).

We can't solve it this way since the X is on the bottom. So we have to fix it!

2. Turns into X Cos 49 = 14, which then turns into X= 14/cos49.

3. Put it in your calculator as 14 DIVIDED BY cos 49. ( Put image example)

4. Round.

x= 21.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 4:

Given: 15°, 33 hyp, adj x. Which is Cos.

1. Cos 15= x/33 and rewrite.

2. Input as 33 cos(15 into calculator = 31.875...

3. Round to tenth.

x = 31.9

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 5:

Given: 52°, 20 adj of °, and x opp of °. Will use TAN.

1. Tan 52° = x/20

2. 20 Tan(52 into calculator

3. Round

x = 25.6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 6:

Given: 27°, opp of ° is 5, hyp is x. Will use Sin.

1. Write out as I have the last few times, Sin 27 = 5/x rewrite cause x can't be at the bottom.

2. Input into calculator as: 5/sin 27 which equals 11.01...

3. Round.

x = 11.0

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 7:

Given: x°, 6 as hyp, 4 opp. now we have to solve this different since we don't know the degree. Now when we input into the calculator you will press 2nd, then sin/cos/tan so it will be negative this is depending on which one ur solving for.

We will be using SIN, x is still a °.

1. Sin X = 4/6 Rewrite.

2. X= Sin^-1 (4/6)

Make sure ur sin is negative in calculator when doing this.

3. It SHOULD give you 41.81, round.

x = 42°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 8:

Given: x°, 29 opp, 14 adj. TAN.

1. Tan x°= 29/14 or..

2. X = Tan^-1(29/14) solve..

3. gives u 64.23.... round.

x = 64°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 9:

Given: x°, hyp 54, opp 12. SIN

1. Sin x°=(12/54)

2. X= Sin^-1(12/54) solve. (dont put x= into calculator.)

3. Don't Forget to round, answer unrounded: 12.839..

x = 13°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 10:

Given: x°, adj 25, hyp 40. COS

1. Cos x°=25/40 rewrite.

2. X= Cos^-1(25/40) Solve.

3. Round.

X= 51°

The length of the arc defined by the central angle of 312 degrees is 26π cm.

The formula for the arc length of a circle is given by:

L = (θ/360) × 2πr

where L is the length of the arc, θ is the central angle in degrees, and r is the radius of the circle.

Substituting the given values, we get:

L = (312/360) × 2π(30)

L = (26/30) × π × 30

L = 26π cm

Therefore, the length of the arc defined by the central angle of 312 degrees is 26π cm.

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ1

Answer:

$270 will be you compound interest after 3 years

Answer: I have two days to finish this class I need points I’m sorry

Step-by-step explanation:

Answer:

(10, 27)

Step-by-step explanation:

We have to solve the given set of equations :

As both equations are equal to y, equate the RHS of both of the equations.

Writing an ordered pair

Answer:

\(\displaystyle [10, 27]\)

Step-by-step explanation:

Set each equation equivalent to each other:

\(\displaystyle 3x - 3 = 2x + 7 \\ \\ \frac{-10}{-1} = \frac{-x}{-1} \\ \\ \boxed{10 = x, 27 = y}\)

I am joyous to assist you at any time.

Answer:

c the answer is c

Step-by-step explanation:

Answer:

C

I hope this helps

Answer:

B. 5 + 2(3 + 2x) = x + 3(x + 1)

Step-by-step explanation:

5 + 6 + 4x = x + 3x + 3

11 + 4x = 4x + 3

4x - 4x = 3 - 11

0 = - 8

There are no solutions.

Answer:

A

4(x+3)+2x=6(x+2)

4x+12+2x=6x+12

6x+12=6x+12

6x-6x=12-12

0=0

As per the given percentage of 20, the total number of bees is 200 and on the second day, he caught 40 unique bees so the total unique bees are 140

Percentage:

Percentage refers the amount of something is expressed as if it is a part of the total which is a hundred. and the ratio can be expressed as a fraction of 100.

Given,

Sara wants to estimate the number of bees in a beehive. She catches 100 bees from the hive and marks each one with a dye. She then lets the bees go. The next day, Sara catches 50 bees from the hive. 10 of these bees have been marked with dye.

Here we need to determine the number of bees in the beehive.

Let us consider she catches 100 bees from the hive and marks each one with a dye. And then lets the bees go.

Then the next day, she catches 50 bees from the hive. 10 of these bees have been marked with dye.

So, the percentage of the dye bees in the hive will be

P = 10/50 x 100

P = 20%

Now, let the total number of the bees be x, then the total number of the bees will be

=> 100 x 2 = 200

Therefore, the total number of bees is 200.

Now, the number of unique bees will be

Unique bees = 100 + (50 - 10)

Then, the number of unique bees = 100 + 40

Therefore, the number of unique bees is 140.

To know more about Percentage here.

https://brainly.com/question/28269290

#SPJ1

answer

-z•1=-3-1

z=-3•-1

z=3

The amount that was invested in each account is:

Maricopa Success invested $47,858 in stocks.

Maricopa Success invested $63,571 in bonds.

Maricopa Success invested $47,571 in CDs.

Let c represent Cds

Let b represent bonds

Let s represent stocks

Equations:

b = c + 15000

s = 160000 - b - c = 160000 - c - 15000 - c = -2c + 145,000

0.08(-2c + 145000) + 0.036(c + 15000) + 0.04c = 7520

-0.16c + 11600 + 0.036c + 540 + 0.04c = 7520

-0.084c = -4,080

Divide both side by -0.084

c = -4,080 / 0.084

c= $48,571 (CDs)

b = 48,571+ 15000

b=$63,571 (bonds)

s = 160,000 - $63,571- 48,571

s= $47,858 (stock)

Therefore Maricopa Success invested $47,858  in stocks,Maricopa Success invested $63,571 in bonds and Maricopa Success invested $47,571 in CDs.

Learn more about amount invested here:https://brainly.com/question/25300925

#SPJ1

The coordinates of the triangle after transformation are:

L′(1, −5), M′(1, 0), N′(2, −5)

There are different methods of transformation such as:

Translation

Rotation

Reflection

Dilation

Now, a rotation of 180 degrees counterclockwise about the origin is equivalent to the coordinate transformation given as (x, y) → ( −x, −y) . Meanwhile, a rotation of 270 degrees counterclockwise about the origin is equivalent to the coordinate transformation (x, y) → ( y, -x) .

Applying the rule for rotation of 180 degrees counterclockwise to the coordinates L(−1, 5), M(−1, 0), N(−2, 5) gives us:

L'(1, -5), M'(1, 0), N'(2, -5)

Read more about transformed coordinates at: https://brainly.com/question/27224272

#SPJ1

Answer:

I think you're missing some basic operations... but i'd love to help you so if you could let me know what the operations are I'd love to help :)

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

508/72=49

127/18=49

127=884

Answer:

5x7 = 35 + 3 = 38 :)

Step-by-step explanation:

If you were asking how much he would have each week its 35$ but dont foget to add 3

Applying the central angle theorem, we have:

a. angle BAC.

b. arc BEC

c. arc BC

d. Measure of arc BEC = 260°

e. Measure of arc BC = 100°

According to the central angle theorem, the central angle that is suspended at the center of a circle by two line segments (usually radii) have a measure that is equal to the measure of the intercepted arc. That is:

Measure of central angle = measure of intercepted arc.

A major arc have a measure that is greater than 180 degrees or half a circle, while minor arcs have a measure that is less than 180 degrees or half a circle.

a. A central angle in the image given is: angle BAC.

b. One major arc in the given circle is arc BEC (greater than half a half a circle/180 degrees).

c. One minor arc in the given circle is arc BC (less than half a half a circle/180 degrees).

d. m∠BEC = 360 - 100

m∠BEC = 260°

m∠BEC = measure of arc BEC [central angle theorem].

Measure of arc BEC = 260°

e. Measure of arc BC = m∠BAC [central angle theorem].

Measure of arc BC = 100°

Learn more about the central angle theorem on:

https://brainly.com/question/5436956

#SPJ1

Answer:

The answer would be B

Step-by-step explanation:

Answer:

55860

Step-by-step explanation:

This way super dupper easy

Answer:

V is approximately 11.81

Step-by-step explanation:

We use the sine rule

V/sin 98 = 10/sin 57

Cross multiply

V * sin 57 = 9.90268068

V = 9.90268068/sin 57

V= 11.80759295

V ~ 11.81