Given f(x) = 5x – 3, find f(2).

y = 5x

and x = y/5

you can then put any value for x and y and it will make sense

Congruent triangles have congruent corresponding sides and angles

The true statement is (c) yes, because of ASA or AAS

Start by adding the angles of the triangles

[tex]\mathbf{\theta = 98 + 35 + 47}[/tex]

[tex]\mathbf{\theta = 180}[/tex]

The angles add up to 180 degrees,

This means that, the triangles have congruent corresponding angles and a congruent corresponding side

Hence, the triangles are congruent by AAS or ASA.

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Answer:

Yes, because of ASA or ASA

Step-by-step explanation:

Tooken note so their right trust me

We have been given that a cylinder was enlarged by a scale factor of 4. The new volume is 2,240 cubic units. We are asked to find the volume of original cylinder.

We know that a cylinder is a three dimensional object. Since scale factor is 4, so each side of new cylinder will be 4 times the side of original side of cylinder.

Due to 3 dimensions, the volume of new cylinder is [tex]4^3[/tex] times the volume of original cylinder.

[tex]\text{Volume of original cylinder}\times 4^3=\text{Volume of new cylinder}[/tex]

[tex]\text{Volume of original cylinder}\times 64=2240[/tex]

[tex]\frac{\text{Volume of original cylinder}\times 64}{64}=\frac{2240}{64}[/tex]

[tex]\text{Volume of original cylinder}=35[/tex]

Therefore, the volume of the original cylinder is 35 cubic units.

Answer:

40 cm

Step-by-step explanation:

a square has 4 equal length sides, to get area you multiply two of those sides, 10 x 10 = 100, so each side is 10cm long, adding all of the sides together gets you 40cm.

Answer:

40cm

Step-by-step explanation:

We know that the formula for area of a square is side length squared or [tex]s^2[/tex]

In this case, [tex]s^2=100[/tex]. So we can go through the following steps in order to solve for s

[tex]s^2=100\\\sqrt{s^2} =\sqrt{100} \\\\s=10[/tex]

If one side equals 10, and we know all squares have 4 equal sides, then we can multiple 10 * 4 or add 10+ 10 + 10 + 10.

Our outcome is 40!

Answer:

Option A. 2

Step-by-step explanation:

From the question given, we were told that the total outcome in event A is 5.

Now if region 2 is 6, 7 or 8, as given in the other options, it therefore means that the total out in event A will be more than 5. So region 2 must be 2 in order to satisfy the event A.

Further more, considering the diagram, event B is bigger than event A. With this idea we can give the summary in diagram as follow:

Region 1 => 3 outcomes

Region 2 => 2 outcomes

Region 3 => 4 outcomes

Region 4 => 6 outcomes

Total => 15 outcomes

Now we can see that the total outcome correspond to the total outcome of 15 given in the question.

Therefore, region 2 has 2 outcome

Given the information, we can determine that B has 4 outcomes, but the number of outcomes specifically in region 2 cannot be found without additional information.

Let's break down the given information one piece at a time. The sample space (S) consists of 15 equally likely outcomes. Out of these, we know that 5 outcomes are in region A, and 6 outcomes neither belong to event A nor to event B.

Since events A and B are independent, they do not share outcomes. Now, we can calculate the number of outcomes in event B by subtracting the outcomes not belonging in A or B and belonging in A from the total outcomes. Hence, there are 15 - 5 - 6 = 4 outcomes in event B.

However, the question requires us to find outcomes in the second region (2). Since the regions were not specified concerning events A and B, we cannot identify the precise number of outcomes in region 2. Therefore, we cannot accurately answer the question with the given information.

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Answer:

he theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse.

The missing length is 35 feet.

Step-by-step explanation:

i just did it

Answer: 1:sum 2:equal to 3:35

Step-by-step explanation:

I did the assignment on edge and got it right.

Answer:

The volume of the prism is 476 cm^3

Step-by-step explanation:

Mathematically, the volume of a right prism can be calculated using the formula area of the base * height of the prism

Here, the base is a parallelogram and thus, the area of the base can be calculated using the formula A = bh where b is the parallelogram base and h is the height

in the question the parallelogram has a base of 8.5cm with the height at that point as 4cm

The area of that parallelogram is thus 4 * 8.5 = 34 cm^2

the volume of the right pyramid is thus 34 * 14 = 476 cm^3

By using the combination formula to calculate the number of unique ways a group can be formed, we find that a coach can divide her 9-player squad into three equal groups in 5600 ways.

The student's question is about a concept in mathematics called combinations. A combination is a selection of items without regard to the order in which they are selected. In this particular problem, the tennis coach is dividing her 9-player squad into three equal groups. The number of ways this can be done uses the formula for combinations (nCr) where n equals the total number of items (in this case, players) and r equals the number of items being chosen at a time (in this case, the number of players in each group).

First, the coach can choose the first trio from the nine players using the combination formula 9C3. The second trio is chosen from the remaining 6 players, so this uses the formula 6C3, and for the third trio, which is chosen from the remaining 3 players, the formula is 3C3. Multiplied out, 9C3 x 6C3 x 3C3 equals 280 x 20 x 1 which is 5600. Therefore, there are 5600 unique ways the coach can divide her 9-player squad into three 3-player groups with each player in only one group.

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Answer:

D 64

Step-by-step explanation:

f(x) = 4^x

Let x = 3.

f(3) = 4^3

    = 4*4*4

   = 64

Answer:

Greg pays more interest than Linda

He pays $17.45 more

Step-by-step explanation:

Greg

P=$1975

R=5%=0.05

T=3 years

Simple interest=P×R×T

=$1975×0.05×3

=$296.25

Linda

P=$1975

r=4.5%=0.045

n=1

t=3

Linda's Interest is compounded once per period, so we this formula

Compound Interest =P(1+r)^t

=$1975(1+0.045)^3

=$1975(1.045)^3

=$1975(1.141166125)

=$2,253.80

Interest paid=$2,253.80-$1975

=$278.8

Answer:

$659.25

Step-by-step explanation:

Since its 25 percent off we need to see what it would look as a decimal

1-.25=.75

879times.75= 659.25

Answer:

224.25

Step-by-step explanation:

think of quarters, one is 25 cents, and it takes four to make a dollar. Then if you have a dollar and you want a quarter of it, you divide the dollar by 4, divide $879.00 by four to get 224.25!

Answer:

3 < x

Step-by-step explanation:

3(8 - 4x) < 6(x - 5)?

Distribute

24 -12x< 6x -30

Add 12x to each side

24-12x+12x < 6x+12x-30

24 < 18x-30

Add 30 to each side

24+30 < 18x-30+30

54 < 18x

Divide each side by 18

54/18 < 18x/18

3 < x

Answer:

Length of area is 857.14 ft

Width of area is 857.14 ft

Length of dividing fence is 857.14 ft

Step-by-step explanation:

Here we have

Area of rectangle = Length × Width

The dimension, of the rectangle with the largest area is the dimension of a square, hence we have;

Length of rectangle = Width of rectangle = x

Hence,  the perimeter of the area = 4·x, while the width of the dividing fence = x

Therefore, since the we have;

Cost of the perimeter fence = $15/foot

Cost of the dividing fence = $10/foot

Then;

4·x × 15 + x × 10 = 60000

60·x + 10·x = 60000

x = 60000/70 = 857.14 ft

Which gives the following dimensions;

Length of area = 857.14 ft

Width of area = 857.14 ft

Length of dividing fence = 857.14 ft.

Answer:

C

Step-by-step explanation:

16 times 2 equals 32, 52 minus 32 equals 20.

Answer:

ok i agree

Step-by-step explanation:

Answer:

-6 and -10.

Step-by-step explanation:

Added together you get -16, multiplied together results in 60.

The value of two numbers gives multiplied by 60, but added to -16 are - 10 and - 6.

Given that,

The multiplication of two numbers is 60

And, the addition of two numbers is - 16.

Let us assume that the two numbers are x and y.

Hence we get;

[tex]x y = 60[/tex]  ... (i)

And, [tex]x + y = - 16[/tex]  .. (ii)

From equation (ii);

[tex]y = - 16 - x[/tex]

Substitute the above values in (i);

[tex]x (- 16 - x) = 60[/tex]

[tex]- 16x - x^2 = 60[/tex]

[tex]x^2 + 16x + 60 = 0[/tex]

[tex]x^2 + (10 + 6)x + 60 = 0[/tex]

[tex]x^2 + 10x + 6x + 60 = 0[/tex]

[tex]x(x + 10) + 6 (x + 10) = 0[/tex]

[tex](x + 10) (x + 6) =0[/tex]

This gives two solutions,

[tex]x = - 10[/tex]

[tex]x = - 6[/tex]

Substitute x = - 10 in (ii);

[tex]x + y = - 16[/tex]

[tex]- 10 + y = - 16\\y = - 16 + 10\\y = - 6[/tex]

Substitute x = - 6 in (ii);

[tex]x + y = - 16[/tex]

[tex]-6 + y = - 16\\y = - 16 + 6\\y = - 10[/tex]

Therefore, both the numbers are - 10 and - 6.

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Answer:

-1,048,572

Step-by-step explanation:

Please mark brainliest :)

Answer:

49.13 in

Step-by-step explanation:

circle circumference: 25.13

rectangle perimeter: 24

total: 49.13

The perimeter of the figure to the nearest hundredth. is 28.56 in.

To find the find the perimeter of the figure we'll add the sides of square and the circumference.

Perimeter of figure = 2 × Perimeter of semicircle + 2 × side of square + 2 × side length after excluding semicircle

Radius of semicircle = 4/2 = 2 in.

Perimeter of semicircle

= π r

= 3.14 × 2

= 6.28 in.

Side of square = 6 in.

Side length after excluding semicircle = 6 - 4 = 2 in.

Perimeter of figure

= 2 × Perimeter of semicircle + 2 × side of square + 2 × side length after excluding semicircle

= 2 × 6.28 + 2 × 6 + 2 × 2

= 12.56 + 12 + 4

= 28.56 in.

Answer:

6/81

there are 9 marbles and 3 are green so 3/9 and 2 are red so2/9 then times to get 6/81

Answer:

C =75.36 m

A =452.16 m^2

Step-by-step explanation:

The circumference is found by  where r is the radius and pi = 3.14

C = 2 * pi *r

C = 2 * 3.14 * 12

C =75.36 m

The area is found by

A = pi r^2

A = 3.14 * 12^2

A =452.16 m^2

Answer:

Circumference: 12.56 m

Area: 452.16 m²

Step-by-step explanation:

Circumference:

2 × 3.14 × 12

12.56 m

Area:

3.14 × 12²

452.16 m²

Answer: 9 weeks

Step-by-step explanation:

First, we would have to set up an equation.

468 - 9w = 18 + 66w

The variable w stands for weeks.

We need to figure out when their bank account will become equal.

So, we need to solve for w.

First, let’s combine like terms. I will move 9w to the other side.

468 = 18 + 66w + 9w

Then simplify:

464 = 18 + 55w

Then, do the same as you did before, just move the 18 to the other side. Keep in mind that when a number switches sides, it’s switches signs (from negative to positive or positive to negative)

464 + 18 = 55w

482 = 55w

To isolate the variable, you would have to divided 55w by 55. Keep in mind, what you do to one side of an equation you must do to the other.

482/55 = 55w/55

8.76 = w

When you round to the nearest whole number, it will be 9 weeks.

Therefore, it will take 9 weeks for them to have the same amount of money in the bank.

A) center: (-3, 2)

B) radius: √65

C) equation: (x +3)² +(y -2)² = 65

Answer:

100; 14400

Step-by-step explanation:

Volume = base * height

a) Base = 4 * 2.5/2 = 5

Height = 20

That makes volume  = 5 * 20 = 100

b) Base = 36 * 16/2 = 288

Height = 50

That makes the volume = 288 * 50 = 14400

Answer:

100, 14400

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

A = P (1 + r) ^t

A is the amount in the account

P is the principle or the amount invested

r is the interest rate

t is the time

A = 5000 (1 + .055)^15

     5000(2.23247)

Rounding to 2 decimals since we round to the nearest penny

      11162.38

Answer: A

Step-by-step explanation:

XD

The teacher can choose four students to present the project out of seven in 35 different ways. This is calculated using the combination formula in combinatorics, a concept in mathematics.

The question involves the concept of combinatorics in mathematics, specifically the combination formula. The combination formula is used when the order of selection does not matter. In this case, the teacher is selecting 4 students out of 7 to present the project, and the order in which the students are chosen is irrelevant.

To calculate the number of ways the teacher can choose four students out of seven, we use the combination formula which is C(n, r) = n! / [(n-r)!r!], where:

Applying this to our scenario, n = 7 (total number of students), and r = 4 (students to be chosen to present). Plugging the values into the formula gives us C(7, 4) = 7! / [(7-4)!4!] = 35. So, there are 35 ways the teacher can choose four students to present the project.

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The teacher can choose 4 students to present the project in 35 ways.

The teacher needs to choose 4 students out of a group of 7 to present the project.

To find the number of ways to choose 4 students from a group of 7, we use the combination formula.

The formula for combinations is C(n, r) = n! / (r! * (n-r)!), where

n is the total number of students and

r is the number of students to be chosen.

Substituting n = 7 and r = 4 into the formula, we get

C(7, 4) = 7! / (4! * (7-4)!) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / (4 * 3 * 2 * 1 * 3 * 2 * 1) = 35.

Therefore, there are 35 ways for the teacher to choose 4 students to present the project.

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Answer:

Slope = 0

Step-by-step explanation:

The slope is zero because it is a straight horizontal line. If it is a straight vertical line, the slope is undefined.

hope this helps :)

The required circumference of circle up to 1 decimal place is 70.4.

Radius = 11.2 cm
π = 3.142
The circumference of the circle is to be determined.

The circumference of object is its boundary measure.

Here, Circumference of circle = [tex]2\pi r[/tex]
                                              = 2 x 3.142 x 11.2
                                              = 70.4

Thus, the required circumference up to 1 decimal place is 70.4.

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Answer:

-19/248

Step-by-step explanation:

There are 720 different ways for 7 students to sit at a circular table for a debate, calculated using permutation principles by fixing one seat and arranging the remaining six students (6!).

The question asks about the number of different ways 7 students can sit at a circular table for a debate, which involves a mathematical concept called permutations. Since a circular arrangement means that the starting point is not fixed, we have to consider one position as fixed to avoid repeating identical seating arrangements caused by rotation. Therefore, with one student fixed, we have 6 seats left to arrange the remaining 6 students. This scenario is a permutation problem without repetition and can be calculated using the factorial operation (6!).

So, the calculation would be:

Therefore, there are 720 different ways the 7 students can sit at the table for the debate.

Answer:

358,000,000 BTU's.

Step-by-step explanation:

Given that the radius is equal to 5 ft. and we need to find the volume of sphere~we can use the following formula. Additionally, we will use 3.14159 to be more accurate in this case...

[tex]V =\frac{4}{3} \pi r^3\\V=\frac{4}{3} (3.14159)5^3\\V=4.18878667(125)\\V=523.6[/tex]

So the volume is 523.6 cubic ft!

To convert this to gallons...

[tex]\\1 ft^3 = 7.48052 gal\\523.6 ft^3 = 3916.8 gallons[/tex]

The final step is to multiply this amount by the original 91,500 BTU, when we do this we get...

[tex]3916.8*91500=358387200[/tex]

The nearest million from this number is 358,000,000!

Final answer:

To determine the number of BTUs a spherical storage tank provides, find the tank's volume in gallons by converting from cubic feet, then multiply by 91,500 BTU per gallon and round to the nearest million BTUs.

Explanation:

To calculate the number of BTUs a spherical storage tank can provide, given in gallons, we first need to know the tank volume in cubic feet. Let's assume the student provides this volume. Since 1 cubic foot is equivalent to approximately 7.48 gallons of liquid, we divide the volume in cubic feet by 7.48 to find the number of gallons of propane the tank can hold. Each gallon of propane yields approximately 91,500 BTU.

To find the total BTUs, we use the following steps:

Calculate the number of gallons in the tank by multiplying the volume in cubic feet by 7.48.

Multiply the number of gallons by 91,500 BTU per gallon to get the total BTUs in the tank.

Round the result to the nearest million BTUs, as the question asks.

For example, if a spherical storage tank has a volume of 100 cubic feet, the number of gallons it can hold would be 100 cubic feet * 7.48 gallons/cubic foot = 748 gallons. Then, the total BTUs would be 748 gallons * 91,500 BTU/gallon = approximately 68,442,000 BTU, which would then be rounded to 68 million BTUs.