A map has a scale 1 inches : 10 miles. Use the given map distance to find the actual distance
A.3 in
B.7.5 in
C.1ft

The correct statements of the triangle are; AC = 5 cm; BA = 4 cm; The perimeter of triangle ABC is 12 cm.

As we know that a, b, and c are midpoints of the sides of right triangle that means midpoint divide the side in equal parts.

Now we have to calculate the sides of triangle ABC by using Pythagoras theorem.

Using Pythagoras theorem in ΔACF :

AC² = FA² + CF²

Thus;

AC² = 3² + 4²

AC = √25

AC = 5

Using Pythagoras theorem in ΔDAB, we have;

BA = √(5² - 3²)

BA = 4 cm

Using Pythagoras Theorem, we have;

CB = √(5² - 4²)

CB = 3 cm

Perimeter of ΔABC = Side AB + Side CB+ Side AC

Perimeter of ΔABC = 4 + 3 + 5

Perimeter of ΔABC = 12 cm

Area of ΔABC = (1/2) * 4 * 3 = 6 cm²

Area of ΔDEF = (1/2) * 8 * 6 = 24 cm²

Area of ΔABC =  (6/24) * Area of ΔDEF

Area of ΔABC = (1/4) * Area of ΔDEF

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Given the information provided, we can determine the lengths of the sides of triangle ABC and its perimeter and area.

Given that points A, B, and C are midpoints of the sides of right triangle DEF, we can determine the lengths of the sides using the information provided.

To find the perimeter of triangle ABC, we sum the lengths of all three sides: AB + BC + CA. Substituting the given lengths, AB = BA = 4 cm, BC = 6 cm, and CA = AC = 5 cm, the perimeter is 4 cm + 6 cm + 5 cm = 15 cm.

The area of triangle ABC can be determined using the formula A = bh, where b is the base and h is the height. Triangle ABC and triangle DEF are similar triangles, so their areas are proportional. Since point A is the midpoint of DE, half the base of triangle DEF is equal to the base of triangle ABC. Substituting the given length of DE = 10 cm, the base of triangle ABC is 10 cm / 2 = 5 cm. The height of triangle ABC is equal to the length of AC = 5 cm. Therefore, the area of triangle ABC is A = 5 cm * 5 cm = 25 cm².

Lance invited 36 people to his party.

Step-by-step explanation:

It is given that,

We know that,

The total quarts of lemonade available for the party = 12

Each person in the party consumes = 1/3 quart.

We need to find out how many people did Lance invited to his party.

To find the number of people :

Let us consider 'x' be the number of people invited to the party.

Total lemonade = number of people × lemonade for each person.

⇒ 12 = x × 1/3

⇒ 12×3 = x

⇒ x = 36 people

Therefore, Lance invited 36 people to his party.

Answer:

4m+10mn

Step-by-step explanation:

because we can't simplify any further, we can just multiply 10 by m AND n when you do this, its like multipling 2 variblies, like bxh = bh.

Answer:

4896 ways

Step-by-step explanation:

We have a total of 18 players, and we want to form groups of three, where the order matters, because there are different roles for each player, so this is a permutation problem.

We solve this problem calculating a permutation of 18 choose 3:

P(18,3) = 18! / (18-3)! = 18! / 15! = 18 * 17 * 16 = 4896

So the coach has 4896 ways to choose the left wing, center and right wing.

Answer: There are 4,896 possible ways

Step-by-step explanation: If there are 18 offensive players on the hockey team, and there is a need to make a selection of three players for three different positions, that means each time you choose one player there is an 18 times 17 (18 x 17) other possibilities for the remaining players. If you choose the next player, there would now be a  17 times 16 (17 x 16) other possibilities for the remaining players, hence we need a formula for the arrangement of 3 players to be chosen from a total of 18.

From the first explanation, if we were to make an arrangement to choose all 18 players the permutation would be given as;

P = 18! (18 factorial)

Which is 18 x 17 x 16 x 15 x 14 x... x 1

However the permutation for selecting just 3 out of the 18 players is given as;

P = 18! ÷ 15!

And this results in;

P = 18 x 17 x 16

P= 4896

Therefore there are 4,896 possible ways

**Note that 18! divided by 15! leaves you with the possible arrangement for 3 persons which is explained as 18 x 17 x 16**

Answer:

the answer is B

Step-by-step explanation:

Answer:

A. -34.5>x

Step-by-step explanation:

The area is shaded below -34.5, so we know that x has to be less

Answer:

5 cups and 4 tbsp

Step-by-step explanation:

4 cups and 20 tbsp of flour

There are 16 tablespoons in 1 cup

5 cups and 4 tbsp

Answer:

I think it's C

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

A graph can only be curved when it has an exponential. B and C are slopes so it cannot be that.

Answer:

$31.41!

Step-by-step explanation:

Answer:

y = -7/3 x -5/3

Step-by-step explanation:

We first need to find the slope

m = (y2-y1)/(x2-x1)

   =(-4-3)/(1--2)

   = (-4-3)/(1+2)

   =-7/3

Slope intercept form of a line is

y=mx+b

y = -7/3x +b

Using the point (-2,3)

3 = -7/3(-2)+b

3 = 14/3 +b

Subtract 14/3 from each side

9/3 -14/3 =b

-5/3

y = -7/3 x -5/3

Answer:

[tex]\frac{-7}{3}[/tex]

Step-by-step explanation:

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

plug in the factors given,

[tex]\frac{-4-3}{1--2}[/tex]

then simplify

[tex]\frac{-7}{3}[/tex]

Answer:

y = 3x

Step-by-step explanation:

The standard format of a directly proportional equation goes by the format of y = k × x. The question asks us to write an equation if y = 75 when x = 25 and y varies directly with x.

So we substitute the values y = 75 and x = 25 in the equation y = k × x

K = constant, we have to work this out

75 = k × 25

75 ÷ 25 = k

k = 75 ÷ 25

k = 3

k = 3 So then we put this back into the original y = k × x to find our final equation which is y = 3x

Th fraction that does not belong is 5/4.

This is because it is an improper fraction while the others are proper fractions.

an example of a fraction = [tex]\frac{2}{9}[/tex]

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The requried expression of the given expression which is a product of two binomials is (x - 3)(x - 7).

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial, and trinomial, etc. ax+b is a polynomial.

Here,
Given expression,
x² - 10x + 21 = 0

In order to factor the above expression in two binomial expressions, split the 10x in two where the multiplication of two numbers produces 21 and their difference produces -10x,
So,
y = x² -7x -3x + 21
y= x(x - 7) - 3 (x - 7)
y = (x - 3)(x - 7)

Thus, the requried expression of the given expression which is a product of two binomials is (x - 3)(x - 7).

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Answer:

1/12 of a jug is what is left

Answer:

The Answer is: The first number is 5 and the second one is 8.

please give me brainliest!! :)

Step-by-step explanation:

Let f = first number and s = second number

Twice the first number added to the second number is 18:

2f + s = 18

The second number is equal to 4 times the first number minus 12:

s = 4f - 12

Substitute:

2f + (4f - 12) = 18

6f - 12 = 18

6f = 18 + 12

6f = 30

f = 5, is the first number.

Solve for the 2nd number:

s = 4(5) - 12 = 20 - 12 = 8, is the second number.

Proof:

2f + s = 18

2(5) + 8 = 18

18 = 18

Hope this helps! Have an Awesome Day! :-)

Answer:

y = 8

x = 5

Step-by-step explanation:

This is a system of equations problem

Set up your two conditions:

2x + y = 18

y = 4x - 12

rearrange them to match

y = -2x + 18

y =   4x - 12

combine them by subtracting one equation from the other in such a way that it eliminates one variable. In this case I choose to subtract each value from the second equation from the first one

0 = -6x + 30

solve

6x = 30

x = 5

plug in the x value to solve for y

2(5) + y = 18

10 + y = 18

y = 8

Answer:800

0.31

0.69

4.2

Step-by-step explanation:

Answer:

800

0.31

0.69 (nice)

4.2

Step-by-step explanation:

edgu 2020

Answer:

144

Step-by-step explanation:

multiply 24 times 6

Answer:                                                                                                                   Ms. Campbell's class collected 48 cans in 6 days. The ratio is 8 cans per day.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Days of collection of the recycling project = 3

Number of cans collected in the first 3 days = 24

Students collect the same number of cans each day

2. How many cans did Ms. Campbell's class collect in 6 days?

Let's use the Direct Rule of Three, for answering this question:

Cans     Days

24            3

x              6

3x = 144

x = 144/3

x = 48

Ms. Campbell's class collected 48 cans in 6 days.

Complete Question:

Janeel has a 10 inch by 12 inch photograph. She wants to scan the photograph, then reduce the results by the same amount in each dimension to post on her Web site. Janeel wants the area of the image to be one eight of the original photograph. Write an equation to represent the area of the reduced image. Find the dimensions of the reduced image.

Correct Answer:

A) [tex](10-x)(12-x)=15[/tex]

B) Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch

Step-by-step explanation:

a. Write an equation to represent the area of the reduced image.

Let the reduced dimensions is by x , So the new dimensions are

[tex]length=10-x\\breadth=12-x[/tex]

According to question , Area of new image is :

⇒ [tex]Area = \frac{1}{8}Length(breadth)[/tex]

⇒ [tex]Area = \frac{1}{8}(10)(12)[/tex]

⇒ [tex]Area = 15[/tex]

So the equation will be :

⇒ [tex](10-x)(12-x)=15[/tex]

b. Find the dimensions of the reduced image

Let's solve :  [tex](10-x)(12-x)=15[/tex]

⇒ [tex]120-10x-12x+x^2=15[/tex]

⇒ [tex]120-22x+x^2=15[/tex]

⇒ [tex]x^2-22x+105=0[/tex]

By Quadratic formula :

⇒ [tex]x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]

⇒ [tex]x = \frac{22 \pm8 }{2}[/tex]

⇒ [tex]x = \frac{22 +8 }{2} , x = \frac{22 -8 }{2}[/tex]

⇒ [tex]x = 15 , x =7[/tex]

x = 15 is rejected ! as 15 > 10 ! Side can't be negative

⇒ [tex]x =7[/tex]

Therefore, Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch

Answer:

y = x - 3

Step-by-step explanation:

Basically, if the lines are parallel, they have the same slope, right? So that part is already complete

And to get the rest of the equation, plug in the points -2 and 1 into the equation for the x values. Then set the equation to solve for b

After you do that you should get b = -3

The slope is 1 and the y-int is -3

Thank me later ;)

Answer: C. 2^63

second part: greater than

Step-by-step explanation:

The number of pennies on square 64 is 2^63

A square is a quadrilateral, that have its four sides to be equal, and all its angles to be right-angles

From the question, the number of pennies on a square is:

[tex]T_n = 2^{n-1[/tex]

So, we have:

[tex]T_{64} = 2^{64 - 1}[/tex]

Evaluate the difference

[tex]T_{64} = 2^{63[/tex]

Hence, the number of pennies on square 64 is 2^63

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Answer:

Step-by-step explanation:

180-110=70

90+70=160

180-160=20

Answer:

20°

Step-by-step explanation:

We know that the exterior angle of a triangle is equal to the sum of interior opposite angles.

<B + <A = <C

90° + <A = 110°

<A = 110° - 90°

<A = 20°

Answer:

x=2

Step-by-step explanation:

shdhvejsjheuhchsjcyhejc7738

Answer:

11

Step-by-step explanation:

divide 5 and 15.25

then multiply by 33.55

Final answer:

The correct method to find Wilson's and Mary's ages with the given equations is to solve the equation m + 6 = 5m - 10 by substitution, which will give you the value of Mary's age (m). After finding m, you can then solve for Wilson's age (w).

Explanation:

Among the provided methods to find Wilson's and Mary's ages based on the given equations w = m + 6 and w = 5m - 10, the correct approach is to solve m + 6 = 5m - 10 to find the value of m, Mary's age. This is due to the fact that by substituting the expression for w from the first equation into the second, we isolate m and solve for it directly. Here is how you'd solve it step by step:

First, substitute w from the first equation into the second equation, resulting in m + 6 = 5m - 10.

Next, rearrange the terms to get all the m terms on one side: 5m - m = 10 + 6.

Then, simplify to find that 4m = 16.

Last, divide both sides by 4 to get m = 4.

Once you have m, substitute it back into either of the original equations to find w. In this case, w = 4 + 6 = 10.

Graphical solutions involving the x or y axis do not apply directly to solving the system of equations and are therefore not correct methods for this particular problem.

Given:

Given that the coordinates are (3.9, 5.9), (–1.1, 5.9), (–4.1, 3.9), (–4.1, –2.1)

We need to determine domain and range and also find whether the relation is a function.

Domain:

The domain is the set of all independent x - values.

Thus, we have;

[tex]Domain=\{3.9,-1.1,-4.1\}[/tex]

Thus, the domain is {3.9,-1.1,-4.1}

Range:

The range is the set of all dependent y - values.

Thus, we have;

[tex]Range=\{5.9,3.9,-2.1\}[/tex]

Thus, the range is {5.9,3.9,-2.1}

Function:

We need to determine whether the given relation is a function.

For a relation is said to be a function, if every value of x has only one image in the y - coordinate.

After plotting the graph, it is obvious that the x - value -4.1 has two images 3.9 and 2.1

Hence, the given relation is not a function.

Answer:

[5 2.6 8 2]

Step-by-step explanation:

For this we simply add the digits

A+ B

[3+2 2+.6 0+8 -1+3]

[ 5 2.6 8 2]

Answer:

The test contains 10 three-point questions and 14 five-point questions.

Step-by-step explanation:

x + y = 24

3x + 5y = 100

Try elimination.

-3x - 3y = - 72

2y = 28

y = 14

Then x = 10

So, we have 10  3-point problems  and 14 5-point problems.

Answer:

720

I think..i hope it helps

The number of ways that 6 friends can sit together in a row of six empty seats is 720.

Permutation is defined as the calculation of a set such that it defines the number of ways that something can be arranged.

Given that,

Six friends go to a movie theater.

They have to be arranged in 6 different positions.

6 friends can be arranged in 6 different positions as 8P₈ ways.

Number of ways = 8P₈

                           = 8! / (8 - 8)!

                           = 8! / 0!

                           = 8!

                           = 720

Hence the number of ways that 6 friends can be arranged is 720 ways.

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Answer:

The population will reach 39,400 after 17 years.

Step-by-step explanation:

Given that, The population grows at a rate 4%. The population of the town is 20,000 at a certain time.

Exponential function:

[tex]y(t)=y_0(1+r)^t[/tex]

y(t) = The population after t years

[tex]y_0[/tex] = Initial population.

r = Rate of grow

t = Time.

y(t)= 39400, [tex]y_0[/tex] = 20,000, r= 4%=0.04, t=?

[tex]39400=20000(1+0.04)^t[/tex]

[tex]\Rightarrow \frac{39400}{20000}=(1.04)^t[/tex]

[tex]\Rightarrow \frac{197}{100}=(1.04)^t[/tex]

Taking ln both sides

[tex]\Rightarrow ln|\frac{197}{100}|=ln|(1.04)^t|[/tex]

[tex]\Rightarrow ln|\frac{197}{100}|=t\ ln|(1.04)|[/tex]

[tex]\Rightarrow t= \frac{ln|\frac{197}{100}|}{ln|(1.04)|}[/tex]

[tex]\Rightarrow t\approx 17[/tex]

The population will reach 39,400 after 17 years.

Final answer:

To find the time it takes for a town's population to grow from 20,000 to 39,400 at a 4% annual growth rate, the exponential growth formula is used. After rearranging the equation and taking natural logarithms, it's found that it will take approximately 18 years for the population to reach 39,400.

Explanation:

Population Growth Calculation

To calculate how long it will take for a town's population of 20,000 to grow to 39,400 with an annual growth rate of 4%, we can use the formula for exponential growth:

P(t) = P_0 × (1 + r)^t

where:

P(t) is the future population

P_0 is the initial population

r is the growth rate (expressed as a decimal)

t is the time period in years

Starting with 20,000 people and wanting to get to 39,400:

39400 = 20000 × (1 + 0.04)^t

To solve for t, we need to:

Rewrite the equation as: (1 + 0.04)^t = 39400 / 20000

Take the natural logarithm of both sides: ln((1 + 0.04)^t) = ln(39400 / 20000)

Simplify: t × ln(1 + 0.04) = ln(1.97)

Divide by ln(1 + 0.04) to isolate t: t = ln(1.97) / ln(1.04)

Use a calculator to find the numerical value for t.

When calculated, t is approximately 18 years. Therefore, it will take roughly 18 years for the town's population to grow from 20,000 to 39,400.