The distance between points (x₁, y₁) and (4, 8) is the square root of
(x₁ - 8)² + (₁-4)².
True or False?

Answer:

vertex = ( [tex]\frac{2}{3}[/tex], [tex]\frac{8}{3}[/tex] )

Step-by-step explanation:

given the equation of a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = 3x² - 4x + 3 ← is in standard form

with a = 3 , b = - 4 , then

x = - [tex]\frac{-4}{6}[/tex] = [tex]\frac{2}{3}[/tex]

substitute x = [tex]\frac{2}{3}[/tex] into the equation for corresponding y- coordinate of vertex

y = 3([tex]\frac{2}{3}[/tex] )² - 4([tex]\frac{2}{3}[/tex] ) + 3

  = 3([tex]\frac{4}{9}[/tex] ) - [tex]\frac{8}{3}[/tex] + 3

  = [tex]\frac{4}{3}[/tex] - [tex]\frac{8}{3}[/tex] + [tex]\frac{12}{3}[/tex]

  = [tex]\frac{8}{3}[/tex]

vertex = ( [tex]\frac{2}{3}[/tex], [tex]\frac{8}{3}[/tex] )

Answer:

the leading coefficent is 16 or 16n (leading term)

Step-by-step explanation:

The point slope form of line is y+4 = -4( x+3)

The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.

Given:

m=4

We know the general form is

y - b = -4(x - a)

So, from the graph attached below

b= -4, a= -3

So, y-(-4)= -4(x-(-3))

y+4 = -4( x+3)

Hence,  point slope form of line is y+4 = -4( x+3).

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The two options are R₀ 270 , R₀ 90 , Option C and D .

The complete question is attached in the image.

There are two types of transformations namely , Rigid Transformation and Non- Rigid Transformation

The rigid transformations do not change the shape and size of the preimage .

The non Rigid transformation do not change the shape but change the size of the preimage.

The rule rotating the origin , 270 degree is

(x,y) ----> (y , -x)

as (x,y) is (0,5)

Therefore after 270 degree transformation

(y,-x) is (5 , 0)

So, the clockwise rotation is 90 degree about origin

(x,y) ----> (y , -x)

as (x,y) is (0,5)

Therefore after 90 degree transformation

(y,-x) is (5 , 0)

Therefore the two options are R₀ 270 , R₀ 90 , Option C and D .

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Answer:

A. y < -2x + 6

y≤ x + 2

Step-by-step explanation:

I put it in desmos.

Hope this helps!

If not, I am sorry.

Answer:

y = 10x + 422

Step-by-step explanation:

The expression that gives the perimeter of the rectangle in terms of w is 6w+5 units.

Given that, the length of the rectangle is [tex]\frac{5}{2}[/tex] units greater than twice its width.

We need to determine the expression that gives the perimeter of the rectangle in terms of w.

Given, width = w units, then length= 2w + [tex]\frac{5}{2}[/tex] units.

The perimeter of the rectangle is the sum of all the sides of the rectangle.

That is, perimeter of a rectangle = 2 (length+width).

Now, perimeter of a rectangle = 2 (2w + [tex]\frac{5}{2}[/tex]+w)=6w+5 units.

Hence, the expression that gives the perimeter of the rectangle in terms of w is 6w+5 units.

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All three are possible.

The table tells us that for certain x and y, we have f(x) < f(y) if x < y. There's also no evidence that f(x) = f(y) for some points x ≠ y in the interval, so f(x) could easily be monontonically increasing. (I is true)

If we assume f(x) is strictly increasing (which does not contradict the given table) on the entire interval, we have f'(x) > 0. A positive function can be strictly increasing. (II is true)

A function is concave up on an interval if its derivative is increasing on that interval. This follows from statement (II) if it happens to be true. (III is true)

(E)

Problem 1

Reason:

24 people total with 3 absent. So 24-3 = 21 are present

21/24 = (7*3)/(8*3) = 7/8

==========================================================

Problem 2

Work Shown:

1 hour = 60 min

(5/6)*(1 hour) = (5/6)*(60 min)

5/6 of an hour = 50 min

1 hr + 30 min = 60 min + 30 min = 90 min

The first show is 90 minutes. Add on two more shows that are 50 min each to get 90+50+50 = 190 minutes used up

4 hours = 4*60 = 240 min

240 - 190 = 50 min

There are 50 minutes left on the tape.

==========================================================

Problem 3

Explanation:

1 1/2 = 1 + 1/2 = 1 + 0.5 = 1.5

6/(1.5) = 4

Each 6 meter board is cut into 4 equal pieces each 1.5 meters long

There are 6 boards this applies to which means so far that's 6*4 = 24 pieces

Now to the other 6 boards.

3/4 = 0.75

6/(0.75) = 8

Each of the other 6 boards are cut into 8 equal pieces of 0.75 meters each

That's another 6*8 = 48 pieces

In total there are 24+48 = 72 pieces

When cutting into wood, there always is a small sliver that is discarded. While small, these slivers do add up. So yes there is some waste. Unfortunately, we don't have enough info to calculate. We would need to know the width of the saw blade.

Volume is a three-dimensional scalar quantity. The volume of the triangular prism is 66cm².

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given the length of the triangle is 4cm, while the width of the triangle is 11cm, therefore, the area of the base of the triangle will be,

Area of triangle = 0.5 × 4cm × 11cm

Area of triangle = 22 cm²

Now, the volume of the prism with a base area of 22cm² and a height of 3 cm is,

Volume of the triangular prism = 22cm² × 3cm = 66cm³

Hence, the volume of the triangular prism is 66cm².

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Answer:

x = 26

y = 72°

Step-by-step explanation:

(4x - 16)° = (3x + 10)°

Subtract 3x to both sides

4x - 3x - 16 = 10

x - 16 = 10

Add 16 to both sides

x = 10 + 16

x = 26

(4x - 16)° + y° = 180°

4x - 16 + y = 180

4(26) - 16 + y = 180

104 - 16 + y = 180

88 + y = 180

Subtract 88 to both sides

y = 180 - 88

y = 72°

[tex]\rule[225]{225}{2}[/tex]

By the application of algebraic procedures and logarithm properties, the roots of the logarithmic equation [tex]\log \sqrt{x} + \log \sqrt{x-1} = 1[/tex] are x = 2 and x = -1.

In this question we need to solve a logarithmic equation by means of algebraic procedures and logarithm properties:

[tex]\log \sqrt{x} + \log \sqrt{x-1} = 1[/tex]

[tex]\log \sqrt{x\cdot (x-1)} = 1[/tex]

[tex]\log \sqrt{x^{2}-x} = 1[/tex]

[tex]\frac{1}{2}\cdot \log (x^{2}-x) = 1[/tex]

[tex]\log (x^{2}-x) = 2[/tex]

[tex]x^{2}-x = 2[/tex]

[tex]x \cdot (x-1) = 2[/tex]

[tex]x - 1 = \frac{2}{x}[/tex]

[tex]x - \frac{2}{x} = 1[/tex]

[tex]\frac{x^{2}-2}{x} = 1[/tex]

[tex]x^{2} - 2 = x[/tex]

[tex]x^{2}-x-2 = 0[/tex]

[tex](x-2)\cdot (x + 1) = 0[/tex]

[tex]x = 2 \,\lor \,x= -1[/tex]

By the application of algebraic procedures and logarithm properties, the roots of the logarithmic equation [tex]\log \sqrt{x} + \log \sqrt{x-1} = 1[/tex] are x = 2 and x = -1.

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Mixtures D and E have a ratio of 5:12 and will create the same shade of pink. Options D and E are correct.

A ratio is an ordered pair of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two ratios are specified to be equal.

Given data;

red wax  = 12 ml

white wax = 5 ml

A red wax: white wax = 5:12

B. red wax: white wax=4:1

C red wax white wax = 13: 6

D. red wax: white wax=12:5

E. red wax white wax=12:5

Hence, mixtures D and E have a ratio of 5:12 and will create the same shade of pink.

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Answer: Below is the correct data.

Fraction: [tex]\frac{23}{100}[/tex]

Decimal: 0.23

Percent: 23%

I hope this helps! Pls mark brainliest!! :)

when you subtract a negative number from any platitude number the equation changes to addition so you would add the value of the negative number to 1.

To subtract a negative number from one you will need to set it up like this

1- (-x) x equals the negative number you're talking about

so we use the method KCC (keep change change)

So we KEEP the positive one, CHANGE the subtraction sign in to a plus sign "+" then CHANGE the negative number to a positive

lets say the negative number is 2

1-(-2)

1+ (+2)

1+2 = 3

The expression 2x⁴ + 5x³ - 8x - 20 can be express as follows;

x³(2x + 5) - 4(2x + 5)

2x⁴ + 5x³ - 8x - 20

Therefore,

2x⁴ + 5x³ - 8x - 20

x³(2x + 5) - 4(2x + 5)

Hence, the expression 2x⁴ + 5x³ - 8x - 20 can be express as follows:

2x⁴ + 5x³ - 8x - 20 = x³(2x + 5) - 4(2x + 5)

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Answer:

[tex]\boxed {tan\theta = \frac{2}{3}}[/tex]

Step-by-step explanation:

Let's derive a formula :

⇒ Area (triangle) × 3 = Area (square)

⇒ 1/2(bh) × 3 = a²

∴ But a = h (shown in diagram)

⇒ 3/2(bh) = h²

⇒ h = 3b/2

Now, taking tan θ :

⇒ tan θ = b/h

⇒ tan θ = b/(3b/2)

⇒ tan θ = 2b/3b

⇒ tan θ = 2/3

If the function is f(x) = √(7x – 21). Then the inverse function of the function will be f⁻¹(x) = (1/7) x² + 3.

Let the function will be

f: X → Y

Then the inverse function will be

f⁻¹: Y → X

The function is given below.

f(x) = √(7x – 21)

Then the inverse function will be

x = √[7{f⁻¹(x)} – 21]

x² = 7f⁻¹(x) – 21

7f⁻¹(x) = x² + 21

f⁻¹(x) = (1/7) x² + 3

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Answer:

(49p2–490p) ÷(p–10)

Step-by-step explanation:

Answer:

7:24pm

Step-by-step explanation:

At 50 mph, it will take 195/50 = 3.9 hours to reach London

3.9 hours = 3 .9 * 60 = 3 hours and 54 minutes(54 = 0.9 * 60 )

3:30 + 3:34 ==> 7:24

(one way to do this is to add up the hours and minutes separately so we get 6:84) Since 84 minutes = 1 hour and 24 minutes, just add 1:24 to 6 to get 7:24

Another way to do this is to see that if the distance was 200 miles, then it would take exactly 4 hours (200/50) to reach at 7:30pm But it is short by 5 miles. At the speed of 50mph, the time taken to travel 5 miles = 60/50 * 5 = 6 minutes so deduct 6 minutes from 7:30pm to get 7:24pm

If the train is slower average speed, then the arrival time is delayed beyond 7:24pm

Answer:

[tex]x=-18, y=-44[/tex]

Step-by-step explanation:

[tex]y=3x+10\\y=2x-8\\\\3x+10=y\\2x-8=y\\3x-y=-10\\2x-y=8\\\\-2(3x-y=-10)\\3(2x-y=8)\\\\-6x+2y=20\\6x-3y=24\\-y=44\\y=-44\\-44=3x+10\\-54=3x\\x=\frac{-54}{3} \\x=-18\\\\x=-18, y=-44\\[/tex]

CHECK

[tex]-44=3(-18)+10\\-44=-54+10\\-44=-44\\\\-44=2(-18)-8\\-44=-36-8\\-44=-44[/tex]

Answer:

Step-by-step explanation:

Answer:

Basically find the unit rate by doing 3.99/24 = $0.16625/1oz

1 quart = 32 ounces so 4.8/32 = $0.15/1oz

1 gallon = 153.722 ounces so 11/153.722 = 0.07

49.6/768.61 = 0.06

Step-by-step explanation:
D.

Answer:

TRUE

Step-by-step explanation:

Angle <A and angle <B are complementary, which means their sum must be = 90

Angle <B and angle <C are supplementary which means their sum must be = 180

Now let's see

m∠A=3x+17, m∠B=55−x, and m∠C=67(x/3−1)

first find the sum of A and B

3x + 17 + 55 - x = 90 add like terms

2x + 72 = 90 subtract 72 from both sides

2x = 18 divide both sides by 2

x = 9

TRUE OR FALSE is asked for

m∠A=44, m∠B=46, and m∠C=134

to find that we just replace c with 9 with every expression given for angles

m<A = 3x + 17

m<A = 3*9 + 17 = 44

m<B =  55 - x

m<B = 55 - 9 = 46

m<C = 134, we don't really need to calculate one by one since the angle are complementary and supplementary.

The answer is TRUE

The statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have:

∠A and ∠B are complements, while ∠B and ∠C are supplements.

∠A + ∠B = 90 degree

3x + 17 + 55 - x = 90

2x = 18

x = 9

Angle ∠B and angle ∠C are supplementary:

∠B + ∠C = 180

55 -x + 67(x/3  - 1) = 180

x = 9

Put the value of x and find angles A, B, and C.

m∠A = 44

m∠B = 46

m∠C = 134

∠A + ∠B = 90

∠B + ∠C = 180

The above statement is true.

Thus, the statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.

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The conversion to logarithm function will be that log3 27 = 3.

From the information given, we are to convert the exponential equation to logarithm function. This will be:

log 3 27

This will be log 3 3³

= 3 × log 3^3

= 3 × 1

= 3

Therefore, x = 3.

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Answer:

8 soccer balls

Step-by-step explanation:

Since the ratio of players to soccer balls is 5:2, we can conclude that:

The question asks to find how many soccer balls are needed for 20 players.

Multiply both players and soccer balls by 4, this will get:

Henceforth, 8 soccer balls are needed for 20 players.

The graph which resembles the graph of f(x)=[tex]2^{x}[/tex] but is reflected over the x-axis is g(x)=[tex]2^{x} +1[/tex]

Given Function f(x)=[tex]2^{x}[/tex].

We have to generate a function whose graph is similiar to the given function and is reflected over the x axis.

If we take first function g(x)=2x-1

put the value of x=-1 then the value of function g(x)=2*(-1)-1=-2-1=-3 means the value of y in this function will be negative means the graph will be under x-axis.

Taking second function g(x)=[tex]2^{x} +1[/tex]

for all the negative values of x it posses a positive value of y so the graph will be over the x axis.

Taking third function g(x)=-[tex]2^{x}[/tex]

In the above function for each value of x the function possess a negative value so the graph will be under x axis.

Taking fourth function g(x)=2x-1

For all values of x less than 1 the function becomes negative which takes graph below the x axis. First graph is for [tex]2^{x}[/tex] and the second is for [tex]2^{x} +1[/tex]

Hence the graph similar to [tex]2^{x}[/tex] and reflected over x axis is g(x)=[tex]2^{x} +1[/tex].

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Answer:

C

Step-by-step explanation:

using the rule of exponents

[tex](\frac{a}{b}) ^{m}[/tex] = [tex]\frac{a^{m} }{b^{m} }[/tex] , then

[tex](\frac{-2}{3}) ^{3}[/tex]

= [tex]\frac{(-2)^{3} }{3^3}[/tex]

= [tex]\frac{-8}{27}[/tex]

= - [tex]\frac{8}{27}[/tex]

Definition:

[tex]a^2=a\cdot a\\\\a^3=a\cdot a\cdot a\\\\a^4=a\cdot a\cdot a\cdot a\\\vdots\\a^n=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}[/tex]

also

[tex]a^1=a\\\\a^0=1[/tex]

We have

[tex]\left(-\dfrac{2}{3}\right)^3=\left(-\dfrac{2}{3}\right)\cdot\left(-\dfrac{2}{3}\right)\cdot\left(-\dfrac{2}{3}\right)=-\dfrac{2\cdot2\cdot2}{3\cdot3\cdot3}=-\dfrac{8}{27}[/tex]

[tex]\huge\boxed{C:\ -\dfrac{8}{27}}[/tex]

Since the length of this rectangle is twice its breadth, the length is equal to 40 cm.

Mathematically, the area of a rectangle can be calculated by using this formula:

Area = Length × Width

Based on the information provided, we have:

Substituting the parameters into the formula, we have:

LB + 75 = (L - 5)(B + 5)

2B² + 75 = (2B - 5)(2B + 5)

2B² + 75 = 2B(B + 5) - 5(B + 5)

2B² + 75 = 2B² + 10B - 5B - 25

5B = 75 + 25

5B = 100

B = 100/20

B = 20 cm.

For the length, we have:

L = 2B

L = 2 × 20

L = 40 cm.

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