Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards. Pete walks directly from point A to point C, without passing through point B. What is the direct distance from A to C?



How far would Pete walk if he went from A to B to C? yards

The direct distance from A to C is more than yards.

The inequality w < represents the distance, w, that Pete might save by taking the direct path.

The table of values for the comparison of a function and its inverse function is shown in the image attached below.

An inverse function refers to a type of function that is obtained by reversing the operation of a given function (f(x)).

In Mathematics, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x. By applying this property to the table (see attachment), we have:

Read more on inverse function here: https://brainly.com/question/15635761

#SPJ1

The correct option of the function is C. (f+g)(x)= 6x^3 - 2x^2 + 4x - 8.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

f(x)= 3x^2 + 4x - 6

g(x)= 6x^3 - 5x^2 - 2

So,

(f + g)(x) = (3x^2 + 4x - 6) + (6x^3 - 5x^2 -2)

(f + g)(x) = 3x^2 + 4x - 6 + 6x^3 - 5x^2 - 2

Now, like terms and in order of exponent

(f + g)(x) = 6x^3 - 2x^2 + 4x - 8

Therefore, the correct option is C. (f+g)(x)= 6x^3 - 2x^2 + 4x - 8.

Learn more about function addition ;

https://brainly.com/question/14438192

#SPJ1

Answer:

Eight thousand eighty five, 8000 + 80 + 5

Explanation:
Five ones, thirty-eight tens, twenty-seven hundreds, and five thousands equal to:

5 + 380 + 2700 + 5000

This is 8085 when added or eight thousand eighty-five in word form. This is also 8000 + 80 + 5 in expanded form.

A ratio shows how many times one number contains another.

Hence, the sand is in the ratio [tex]\frac{1}{6}[/tex] of the mixture is

[tex]\frac{1}{6}[/tex]×[tex]1800=300kg[/tex]

The Gravel is in the ratio [tex]\frac{2}{6}[/tex]×[tex]1800=600kg[/tex]

And the cement is in ratio [tex]\frac{3}{6}[/tex]×[tex]1800=900kg[/tex]

What is the ratio ?

A ratio is an ordered pair of numbers [tex]a[/tex] and [tex]b[/tex], written [tex]\frac{a}{b}[/tex] where [tex]b[/tex] does not equal [tex]0[/tex]. A proportion is an equation in which two ratios are set equal to each other.

Here the given ratio is [tex]1:2:3[/tex].

Here given that,

The dry concrete is   [tex]1800kg[/tex].

And the multiplication of the ratio is [tex]1[/tex]×[tex]2[/tex]×[tex]3=6[/tex]

Hence, the sand is in the ratio [tex]\frac{1}{6}[/tex] of the mixture is

[tex]\frac{1}{6}[/tex]×[tex]1800=300kg[/tex]

The Gravel is in the ratio [tex]\frac{2}{6}[/tex]×[tex]1800=600kg[/tex]

And the cement is in ratio [tex]\frac{3}{6}[/tex]×[tex]1800=900kg[/tex]

To know more about the ratio

https://brainly.com/question/23499990

#SPJ2

Based on the amount of cash that Elias Rubio brings, we can calculate that his total cash deposit is $1,323

This can be found as:

= (75 x 1) + (78 x 5) + (83 x 10) + (80 x 0.25) + (32 x 0.10 or 10 cents) + (95 x 0.05 or 5 cents) + (5 x 0.01 or 1 cent)

Solving gives:

= 75 + 390 + 830 + 20 + 3.20 + 4.75 + 0.05

= $1,323

Remaining part of the question:

How much did he deposit in cash?

Find out more on cash deposits at https://brainly.com/question/25803059.

#SPJ1

The Keith will spend $16 to rent 1 movie and 2 video games from the store.

Let's assume the rental fee for each movie is "m" and the rental fee for each game is "g".

From the given information, we can form the following system of equations:

3m + 2g = 25 (Calvin's rental)

2m + g = 14.75 (Samantha's rental)

We can solve for "m" and "g" by using elimination or substitution method. Here, we will use substitution method.

From the second equation, we can solve for "g" in terms of "m":

g = 14.75 - 2m

Substituting this into the first equation, we get:

3m + 2(14.75 - 2m) = 25

Simplifying this, we get:

3m + 29.5 - 4m = 25

-m + 29.5 = 25

-m = -4.5

m = 4.5

Now that we know the rental fee for each movie is $4.50, we can find the rental fee for each game by substituting "m" into either of the original equations:

2(4.5) + g = 14.75

g = 14.75 - 9 = 5.75

So the rental fee for each game is $5.75.

To find how much Keith will spend to rent 1 movie and 2 video games, we can simply add up the rental fees:

1(4.5) + 2(5.75) = 16

Therefore, Keith will spend $16 to rent 1 movie and 2 video games from the store.

To know more about Equation visit:

brainly.com/question/28243079

#SPJ1

If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal is 4.7

We have given that,

Bilquis wants to ride her bicycle 47.6 miles this week. She has already ridden 8 miles.

We have to determine that If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal.

Based on the given conditions, formulate: 8+4x=26

Rearrange unknown terms to the left side of the equation:4x=26-8

Calculate the sum or difference:4x=18

Divide both sides of the equation by the coefficient of the variable:4x/4=18/4

Calculate the product or quotient:x=18/4

We get the result:4.7

To learn more about the equation visit:

https://brainly.ph/question/25003

#SPJ1

Answer: The answer is 6.6

Step-by-step explanation:

d) 5x ≥ 15

Let's solve your inequality step-by-step.

5x≥15

Step 1: Divide both sides by 5.

[tex]\frac{5x}{5} \geq \frac{15}{5}[/tex]

[tex]x\geq 3[/tex]

(Attachment #1)

e) 3(2x + 1) ≤ 15

Let's solve your inequality step-by-step.

3(2x+1)≤15

Step 1: Simplify both sides of the inequality.

6x+3≤15

Step 2: Subtract 3 from both sides.

6x+3−3≤15−3

6x≤12

Step 3: Divide both sides by 6.

[tex]\frac{6x}{6} \leq \frac{12}{6}[/tex]

[tex]x\leq 2[/tex]

(Attachment #2)

Answer:34

Step-by-step explanation:

Giving away all that is not new or fav so 12 fav + 18 new + 4 which are new an favorite = 34

Answer:

22

Step-by-step explanation:

63 is the total

14 are new

8 are fav

14+8=22

Answer: [tex]x=-\frac{5}{4}[/tex] and [tex]x=-2[/tex]

Step-by-step explanation:

To factor an equation in the form of [tex]ax^2+bx+c[/tex] you need to find the value of [tex]ac[/tex]. So first solve for that

[tex](4)(10) = 40[/tex]

Now we need to find two numbers that add up to b and multiply together to make ac. In this case those numbers are 5 and 8 since 5+8=13 and (5)(8)=40

Now split 13x into 5x+8x and solve by grouping

[tex]4x^2+5x+8x+10\\(4x^2+5x)+(8x+10)[/tex]

Factor out the GCF in each quantity

[tex](4x^2+5x)+(8x+10)\\x(4x+5)+2(4x+5)[/tex]

Now group x+2 together

[tex](x+2)(4x+5)[/tex]

Finally, set each factor equal to 0 and solve for x

[tex]x+2=0\\x+2-2=0-2\\x=-2\\\\\\4x+5=0\\4x+5-5=0-5\\4x=-5\\\frac{4x}{4} =\frac{-5}{4} \\x=-\frac{5}{4}[/tex]

Answer:

d

Step-by-step explanation:

- 5 (3x - 7) ← multiply each term in the parenthesis by - 5

= - 15x + 35

Answer: d.) -15x + 35

Given expression:

⇒ -5(3x - 7)

Apply distributive method: a(b + c) = ab + ac

⇒ -5(3x) -5(-7)

multiply the variables

⇒ -15x + 35

[tex]a\cdot b=(7)(4)+(3)(-1)=25\\\\|a|=\sqrt{7^{2}+3^{2}}=\sqrt{58}\\\\|b|=\sqrt{4^{2}+(-1)^{2}}=\sqrt{17}\\\\\cos \theta=\frac{25}{\sqrt{58}\sqrt{17}}\\\\\theta=\cos^{-1} \left(\frac{25}{\sqrt{58}\sqrt{17}} \right) \approx 37.235^{\circ}[/tex]

Answer:

the probability is  10%

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

supplementary because it adds to 180

Answer:C

Step-by-step explanation:

khan

According to the commutative property of multiplication, changing the order of components has no effect on the product. The correct option is B.

According to the commutative property of multiplication, changing the order of components has no effect on the product.

For example: 4 × 8 = 8 × 4 = 32

The equation that correctly shows the Commutative Property of Multiplication is,

5 × 1 3 = 5 × 1 3

Hence, the correct option is B.

Learn more about the Commutative Property of multiplication:

https://brainly.com/question/14391436

#SPJ1

Answer: y= -1 and x=-8

x+8y=-16

x=-8y-16

so x-3y=-5

-8-16-3y=-5

-11y-16=-5

-11y=-5+16

-11y=11

y=-1

x-3y=-5

x+3=-5

x=-8

The real number of the given expression is a=-2.

Given that the expression is [tex]\frac{1}{a^3+7}-7=\frac{-a^3}{a^3+7}[/tex]

Real numbers is known as the union of both rational and irrational numbers. Real numbers can be both positive or negative and are denoted by the symbol “R”.

To compute the value of a.

In the given expression multiply both sides with (a³+7) as

[tex]\frac{(a^3+7)}{a^3+7}-7=\frac{-a^3(a^3+7)}{a^3+7}[/tex]

Simplify the expression as,

1-7(a³+7)=-a³

Expand out terms of the left hand side

1-7a³-49=-a³

-7a³-48=-a³

Taking out minus common from both sides and cancel them

-(7a³+48)=-(a³)

7a³+48=a³

Add -a³-48 on both sides

7a³+48-a³-48=a³-a³-48

6a³=-48

Divide both sides with 6

(6÷6)a³=(-48÷6)

a³=-8

write -8 in the expansion form which is (-2)×(-2)×(-2)=-8

a³=(-2)³

From above it says that

a=-2

Hence, real number that satisfy [tex]\frac{1}{a^3+7}-7=\frac{-a^3}{a^3+7}[/tex] is a=-2.

Learn about real numbers from here brainly.com/question/10180279

#SPJ4

The two-dimensional net of this pyramid that is surface area will be 34,416 square feet.

Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.

The surface area of the pyramid will be

SA = 2(1/2 × B × K) + 2(1/2 × L × K) + (L × B)

The largest pyramid at Giza is a square pyramid. It has a base of 756 feet and a slant height of 612 feet.

We have

L = W = 27.5 feet

Then the two-dimensional net of this pyramid that is surface area will be

SA = 2(1/2 × B × K) + 2(1/2 × L × K) + (L × B)

SA = 4(1/2 × 27.5 × 612) + 756

SA = 33,660 + 756

SA = 34,416 square feet

More about the surface area of the pyramid link is given below.

https://brainly.com/question/23302816

#SPJ1

Answer:

X

Step-by-step explanation:

The number of seconds it takes for the waste to hit the ground for the given function is: 5 seconds.

We are given the function of height to time as, h(t) = -16t² + initial height, and we have the following:

Plug in the values into the equation of the function

0 = -16t² + 400

Solve for t

0 - 400 = -16t²

-400 = -16t²

-400/-16 = t²

400/16 = t²

√(400/16) = t

20/4 = t

5 = t

t = 5

The number of seconds it takes is: 5 seconds.

Learn more about functions on:

https://brainly.com/question/10439235

#SPJ1

Step-by-step explanation:

no calculator ? or what is the problem ?

I had to use the calculator too.

so, the square root of 0.00053361 is 0.0231.

Answer:

The area is approximately 28.73ft²

Step-by-step explanation:

Given: Circumference = 19 ft

The necessary formula area,

Area: A = πr²

Circumference: C = 2πr

Combine:

A = [tex]\frac{C^{2} }{4\pi }[/tex]

A = [tex]\frac{19^{2} }{4\pi } \\\\ \frac{361 }{4\pi }[/tex]

A = 28.72747

Answer: X = 1

Step-by-step explanation:

25/50 = 4x/8

First, multiply both sides by 8, therefore, the 8 on the right side will be canceled out.

25*8/50 = 4x*8/8

25*8/50 = 4x

25*8 = 200

200 divided by 50 = 4

4 = 4x

After that, you just need to divide 4 on both sides, therefore, the 4 on the right side will cancel out.

4/4 = 4x/4

1 = x

X = 1

Hope I helped! :]

By direct observation on the graph and concept of relative minimum, we conclude that the relative minimum of the graph is contained by the point (x, y) = (3, - 17).

Let be f a function that exists in a interval [a, b], there is a value c such that f(c) < f(x), for x ≠ c and x ∈ [a, b]. In this case, f(c) is the relative minimum of f. By direct observation, we find that the relative minimum of the graph is contained by the point (x, y) = (3, - 17).

To learn on relative minima: https://brainly.com/question/6422517

#SPJ1

Answer:

C

Step-by-step explanation:

1.75n = 7 ( to isolate n divide both sides by 1.75 )

n = [tex]\frac{7}{1.75}[/tex] = 4

Answer:

c.)  Divide by 1.75

Step-by-step explanation:

Given equation:

⇒ 1.75n = 7

Here the coefficient of n which is 1.75 needs to be removed. There is only one way of doing that - by dividing both sides by 1.75.

When done so:

⇒ 1.75n/1.75 = 7/1.75

⇒ n = 4

The probability that a participant successfully catches 3 rainbow trout, given that the participant was a woman is 0.0042.

P(woman) = 12/28

= 3/7

P(men) = 16/28

= 4/7

P(3 trouts) = P(3 trout | women)*P(woman) + P(3 trout | men)*P(man)

= P(3 trout | women)*(3/7) + (15C3 * (0.09^3)*(1-0.09)^(15*3))*(4/7)

= P(3 trout | women)*(3/7) + (0.00476)*(4/7)

P(woman | 3 trout) = P(3 trout | women)*P(woman) / P(3 trouts)

{P(3 trout | women) = p}

p*(3/7) / (p*(3/7) + (0.00476)*(4/7)) = 0.40

p*(3/7)/0.40 = (p*(3/7) + (0.00476)*(4/7))

p*((3/7)/0.40 - (3/7)) = (0.00476)*(4/7)

p = [(0.00476)*(4/7)] / [((3/7)/0.40 - (3/7))]

= 0.0042

Learn more about probability here https://brainly.com/question/24756209

#SPJ4