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.

Answer:

Step-by-step explanation:

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Answer:  [tex]\textsf{y = 4x - 12}[/tex]

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Given: [tex]\textsf{Slope = 4, Point = (2, -4)}[/tex]

Find:  [tex]\textsf{The equation in slope-intercept form}[/tex]

Solution: We need to plug in the values into point-slope form and after simplifying, distributing, and solving for y we will have our equation in slope-intercept form.

Plug in the values

Distribute and simplify

Subtract 4 from both sides

Using the information that was provided in the problem statement we were able to determine that the equation in slope-intercept form was y = 4x - 12.

Answer:

y = 4x - 12

Step-by-step explanation:

Given:

slope of 4, and point (2, -4)

Here, we're being asked to write the equation in Slope-Intercept Form. As we have been given the slope and a point on the line, we can use the Point-Slope Form to be able to find that equation.

First, know the two forms:

⇒ Point-Slope Form: y - y₁ = m(x - x₁)

where: m is the slope, and (x₁, y₁) is the given point

⇒ Slope-Intercept Form: y = mx + b

where: m is the slope, and b is the y-intercept

Now, substitute the given values into the Point-Slope Form:

⇒ y - y₁ = m(x - x₁)

⇒ y - (-4) = 4(x - 2) [simplify]

⇒ y + 4 = 4x - 8

Change to the Slope-Intercept Form:

⇒ y + 4 = 4x - 8 [subtract 4 from both sides]

⇒ y + 4 - 4 = 4x - 8 - 4

⇒ y = 4x - 12

Therefore, the equation of the line in slope-intercept form is: y = 4x - 12

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Answer:

y = 97°

Explanation:

Opposite angles in a quadrilateral inscribed in a circle sum ups to 180°

So following the rule:

A + C = 180°

y + 83° = 180°

y = 180° - 83°

y = 97°

By the binomial theorem,

[tex]\displaystyle \left(x^2 + \frac px\right)^6 = \sum_{n=0}^6 \binom 6n \left(x^2\right)^n \left(\frac px\right)^{6-n} = \sum_{n=0}^6 p^{6-n} \binom 6n x^{3n-6}[/tex]

where

[tex]\dbinom kn = \dfrac{k!}{n!(k-n)!}[/tex]

is the so-called binomial coefficient.

The term that's independent of x is the constant term, which occurs when [tex]3n-6=0[/tex], or [tex]n=2[/tex]. Given that this constant 240, we have

[tex]p^{6-2} \dbinom62 = 240 \implies p^4 = 16 \implies p = \pm2[/tex]

but [tex]p[/tex] must be positive, so [tex]\boxed{p=2}[/tex]

Option third "He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x², –x, –6x, and 6' is correct.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have a quadratic expression to model the area of the rectangle:

= x² – 7x + 6

[tex]\rm =\left(x^2-x\right)+\left(-6x+6\right)[/tex]

[tex]=\rm x\left(x-1\right)-6\left(x-1\right)[/tex]

= (x - 1)(x - 6)

Thus, option third "He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x², –x, –6x, and 6' is correct.

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Answer:

[tex]x = 45 \sqrt{5} [/tex]

Step-by-step explanation:

[tex] {3}^{2 log_{3}(x) + log_{3}(5) } = {3}^{ 4log_{3}(15) } [/tex]

[tex] {3}^{ log_{3}( {x}^{2} ) } {3}^{ log_{3}(5) } = {3}^{ log_{3}( {15}^{4} ) } [/tex]

[tex]5 {x}^{2} = {15}^{4} [/tex]

[tex] {x}^{2} = \frac{ {15}^{4} }{5} [/tex]

[tex]x = \frac{ {15}^{2} }{ \sqrt{5} } ( \frac{ \sqrt{5} }{ \sqrt{5} } )[/tex]

[tex]x = \frac{ {15}^{2} \sqrt{5} }{5} = 45 \sqrt{5} [/tex]

The correct answer is option D which is the function is even because of its symmetry about the y-axis.

The function which remains unchanged when the negative value of the variable is filled in the function is called an even function and this function is symmetric about the y-axis.

Given function:-

f(x) = 3x⁴+2x²

Now put the value x = -x in the function

f(-x) = 3( -x⁴)+2(-x²)

f(-x) = 3x⁴ + 2x²

f(-x) = f(x)

here we can see that when we put the value of negative x the function remains unchanged.

Therefore the correct answer is option D which is the function is even because of its symmetry about the y-axis.

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Answer:

Each given factor written as a polynomial in descending order is;  (7x + 6y)(49x² - 42xy + 36y²)

We are given the polynomial;

343x³ + 216y³

343x³ + 216y³ is a sum of cubes and factors in general as;

a³ + b³ = (a + b)(a² - ab + b²)

Thus;

343x³ + 216y³ = (7x)³ + (6y)³

= (7x + 6y)((7x)² - 7x(6y) + (6y)² )

= (7x + 6y)(49x² - 42xy + 36y²)

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Answer: D

Step-by-step explanation:

We know that the line [tex]y=10[/tex] is shaded below, so it represents [tex]y \leq 10[/tex].

Similarly, the line [tex]y=x+1[/tex] is shaded above, so it represents [tex]y > x+1[/tex].

Answer: [tex]35^{\circ}[/tex]

Step-by-step explanation:

Angles ACB and DCA add to form angle ACB, which is a right angle, so:

So, [tex]m\angle ACB=6(7)-7=\boxed{35^{\circ}}[/tex]

Amount of Tax = (Original Cost)(Tax %) , Option C is the right answer.

The complete question is

Most everyday purchases at the store are labeled with the price of the item before sales tax. Which expression could be used to find the amount of tax? Amount of Tax = Original Price + Total Cost Amount of Tax = (Total Cost)(Original Price) Amount of Tax = (Original Cost)(Tax %) Amount of Tax = (Total Cost)(Tax %)

Tax is the % of the amount taken by the government on the sales or income of a person , There are many kinds of taxes imposed on various sectors.

The amount of tax is taken on the cost of the product ans thus can be represented by

Amount of Tax = (Original Cost)(Tax %) , Option C is the right answer.

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The 15 are women, keeping track of the number of men chosen is Not binomial the trials are not independent.

We have given that,

The given procedure results in a binomial distribution. If not, state the reason why. Choosing 5 people (without replacement) from a group of 58 people, of which 15 are women, keeping track of the number of men chosen.

In samples with replacement, the probability has to be the same for each trial, that is, they are independent.

Hypergeometric distribution

Samples without replacement, as the probabilities depend on the previous outcomes, that is, they are not independent.

In this question

Marbles are chosen without replacement, which means that for each trial the probabilities of choosing a red marble are different, which means that the trials are not independent. So the answer is:

Not binomial the trials are not independent.

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This chart represents a proportional relationship. The rate of change will be 4.

Firstly, there is a proportional relationship.

Two values x  and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.

The constant k is called the constant of proportionality.

Given;

x y

1 4

2 8

3 12

4 16

Here, x = ky

put the first value

k = 1/4

This chart represents a proportional relationship.

So the rate of change will be

[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}\\\\Rate = \dfrac{8 - 4}{2 - 1}\\\\Rate = 4[/tex]

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Answer:

1/2

Step-by-step explanation:

(Is this the question? In the pic above)

Sin of an angle os the side opposite over it divided by the hypotenuse.

Sin = opposite/hypotenuse

Sin = 5/10

Sin = 1/2

The value of t is 6.65

An exponential function is a mathematical function of the following form: f ( x ) = a^x. where x is a variable, and a is a constant called the base of the function.

Given:

A= 210 million

P= A e^(kt)

225 = 210 * e ^ (0.0069t)

225/210=  e ^ (0.0069t)

1.07 =  e ^ (0.0069t)

Taking log on both side

log  1.047 = 0.0069 t log e

[tex]\frac{0.0069t\ln \left(e\right)}{0.0069\ln \left(e\right)}=\frac{\ln \left(1.047\right)}{0.0069\ln \left(e\right)}[/tex]

t= log ( 1.047) / 0.0069

t= 6.65

Hence, value of t is 6.65.

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Answer:

Step-by-step explanation:

Answer:

4:5

girls:boys

16:20

divide both by 4

4:5

The given expression can be simplified as [tex]96x^{9}+3x^{36} +3[/tex].

The given expression is [tex]6x^{9} (7-3).4+3x^{36} +3[/tex].

We need to simplify the given expression.

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.

First, multiply the numbers 6×4=24.

That is, [tex]24x^{9} (7-3)+3x^{36} +3[/tex].

Next, subtract the numbers 7-3=4.

[tex]24x^{9}.4+3x^{36} +3[/tex]

Finally, multiply the numbers 24×4=96.

[tex]96x^{9}+3x^{36} +3[/tex].

Hence, the given expression can be simplified as [tex]96x^{9}+3x^{36} +3[/tex].

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Answer:

-x + 4

Step-by-step explanation:

(4x+5)+(−5x−1)

4x+5−5x−1  [Remove the parentheses]

-x + 4           [Combine Like Terms]

Answer:

-x+4

Step-by-step explanation:

Given:

(4x+5)+(−5x−1)

Solution:

To re-write this in it's simplest terms:

Combine like terms:

Hence the simplest form is -x+4.

Done.

Answer:

from the image above

Triangle ABE = Triangle ADE

AE = AE ( common).

angle AEB = angle AEO ( each 90°)

AB = AD ( given).

by side angle side criteria

so area of ABE = area of ADE

similarly,

BC = DC ( given)

BEC = DEC ( 90°)

EC = EC ( 9m each)

so area of BEC = Area of DEC

Answer:

28

Step-by-step explanation:

similar triangles are proportional

and add all the sides of the bigger triangle

T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)

A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

[tex]\left[\begin{array}{ccc}7&6\\4&5\end{array}\right][/tex]

The inverse of the matrix is

[tex]\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right][/tex]

So, the Inverse Transformation is given by

[tex]T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]

So, no option is correct. And the answer is

[tex]T^{-1}(x,y)=(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]

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Answer:

1/3×22/7×r^2h

Step-by-step explanation:

the volume =1/3 ×22/7×r^2×13.5

Answer:

B

Step-by-step explanation:

using the addition identity for sine

sin(A + B) = sinAcosB + cosAsinB

using the sine and cosine ratios in the right triangle

sinABC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{4}{5}[/tex]

cosABC = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{3}{5}[/tex]

using the exact values

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos60° = [tex]\frac{1}{2}[/tex]

Then

sin(ABC + 60)

= sinABC cos60 + cosABC sin60

= ( [tex]\frac{4}{5}[/tex] × [tex]\frac{1}{2}[/tex] ) + ([tex]\frac{3}{5}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] )

= [tex]\frac{4}{10}[/tex] + [tex]\frac{3}{10}[/tex] [tex]\sqrt{3}[/tex]

= [tex]\frac{2}{5}[/tex] + [tex]\frac{3}{10}[/tex] [tex]\sqrt{3}[/tex]

sin<ABc

cos<ABC

Now

Answer: Option (1)

Step-by-step explanation:

The domain is the set of input values, also known as the set of x-values.

Answer:

Question 4: letter c

Question 3: letter c

Step-by-step explanation:

Answer:

-4/3

Step-by-step explanation:

mtan × mline = -1

mtan× 3/4 = -1

mtan =-4/3

Answer:

1.4y

Step-by-step explanation: