The perpendicular bisector of a chord...

Part A) The rate of speed is 56 miles/ hour and

Part B) The money that waiter receive is $1.92.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Part A:

Distance traveled by Mr.Ford = 224 miles

Time taken by  Mr.Ford = 4 hours

Rate of speed can be found by

[tex]Speed = \frac{Distance}{time}[/tex]

⇒ [tex]Speed = \frac{224}{4}[/tex]

⇒ [tex]Speed = 56[/tex]

Thus the rate of speed is 56 miles/ hour

Part B:

Cost of lunch bought by Mr.Liston = $12.80

Mr.Liston gave the waiter a tip = 15%

⇒ [tex]15\% = 0.15[/tex]

Now, the money that waiter receive is

⇒ [tex]12.80(0.15)[/tex]

⇒ [tex]1.92[/tex]

Thus the money that waiter receive is $1.92.

Hence we conclude that A) the rate of speed is 56 miles/ hour and B) the money that waiter receive is $1.92.

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Answer:

The system has infinitely solutions

Step-by-step explanation:

we have

[tex]-\frac{1}{3}x^{2}=-\frac{5}{6}+\frac{1}{3}y^{2}[/tex]

[tex]\frac{1}{3}x^{2}+\frac{1}{3}y^{2}=\frac{5}{6}[/tex]

Multiply by 3 both sides

[tex]x^{2}+y^{2}=\frac{5}{2}[/tex] ----> equation A

The equation A is a circle centered at origin with radius [tex]r=\sqrt{5/2}\ units[/tex]

and

[tex]5y^{2} =\frac{25}{2}-5x^{2}[/tex]

[tex]5x^{2}+5y^{2} =\frac{25}{2}[/tex]

Divide by 5 both sides

[tex]x^{2}+y^{2} =\frac{5}{2}[/tex] ----> equation B

The equation B is a circle centered at origin with radius [tex]r=\sqrt{5/2}\ units[/tex]

Equation A and Equation B are the same

Therefore

The system has infinitely solutions

Answer:

infinitely many

Step-by-step explanation:

just took the assignment for

Answer:

D

Step-by-step explanation:

The rules we need to simplify this are:

[tex]a^x*a^y=a^{x+y}[/tex]

and

[tex](a^x)^y=a^{xy}[/tex]

Now, let's simplify the problem:

[tex](y^{-7}*y^{-3})^{-1}\\(y^{-10})^{-1}\\y^{10}[/tex]

Answer choice D is y^10, so that's correct.

The formula for circumference of a circle is:

Circumference = PI x diameter.

Diameter is 11 inches.

Circumference = 11 x 3.14 = 34.54 inches.

.54 is greater then .5, so you would round up.

The answer would be 35 inches.

Answer:

5/16.

Step-by-step explanation:

The probability of getting a correct answer on one question is 1/2 and the probability of getting it wrong is  1 - 1/2 = 1/2.

The probability of the first 2 being correct and the next 3 wrong = (1/2)^5 = 1/32.

There are  10  possible combinations of this ( first wrong the 2nd and third right and last  2 wrong,  etc).

So the  required probability is 10 * 1 /32

= 10/32

= 5/16.

The magnitude of a vector is found by applying the Pythagorean theorem to the horizontal and vertical changes. The formula to calculate the magnitude is given by A = sqrt(x^2 + y^2) where x and y are the vector’s horizontal and vertical displacements respectively.

The magnitude of a vector is calculated by forming a right triangle using the horizontal (x) and vertical (y) changes as the triangle's legs. The magnitude of the vector is the hypotenuse of this right triangle. This relationship is captured by the Pythagorean Theorem which states that the square of the hypotenuse (i.e. the magnitude of vector A) is equal to the sum of the squares of the other two sides (the vector's components or changes).

So, the formula for finding the magnitude of the vector (A) is:

Where x is the horizontal displacement or change, and y is the vertical displacement or change.

For example, if you have a vector with an x component of 3 and y component of 4, you could compute the magnitude as follows:

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To find the magnitude of a vector with horizontal change x and vertical change y, use the Pythagorean theorem: |v| = sqrt(x^2 + y^2).

To find the magnitude of a vector with horizontal change x and vertical change y, you can use the Pythagorean theorem. The magnitude (|v|) of the vector is given by the square root of the sum of the squares of the horizontal and vertical changes:

|v| = sqrt(x^2 + y^2)

For example, if x = 3 and y = 4, the magnitude of the vector would be:

|v| = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.

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Answer:

=135.53°

Step-by-step explanation:

The bearing that the captain should turn is the angle difference between the two islands from the position of the ship.

Let C be the position of the ship, then

AB is c=160

AC is b=220

BC is a=200

We use the cosine rule as follows:

c²=a²+b²-2ab Cos C

160²=200²+220²-2×200×220 Cos C

25600=88400-88000Cos C

88000 Cos C=88400-25600

88000Cos C=62800

Divide both sides by 88000.

Cos C=62800/88000

=0.7136

C=44.47°

He should turn (180°-44.47°)=135.53°

Answer:

135.53

Step-by-step explanation:

I got it correct on founders edtell

Answer:

all numbers greater than or equal to -1

Step-by-step explanation:

Let's find the vertex.

Since the function is in factored form, I'm going to find the zeros.

The average of the zeros will give me the x-coordinate of the vertex.

I can then find the y-coordinate of the vertex by using the equation

y=(x-4)(x-2).

Also the parabola is open up since the coefficient of x^2 is positive (or 1 in this case).

So the range has something to do with the y's. It is where the function exist for the y-values.

So the range for this one since the parabola is open up will be of the form

[y-coordinate of vertex , infinity).

So let's begin.

The zeros can found by solving (x-4)(x-2)=0.

This means we need to solve both x-4=0 and x-2=0.

x-4=0 gives us x=4

x-2=0 gives us x=2

Now the average of our x-intercepts (or zeros) is (4+2)/2=6/2=3.

So the x-coordinate of the vertex is 3. To find the y-coordinate of the vertex we are going to use y=(x-4)(x-2) where x=3.

Plug in:  y=(3-4)(3-2)=(-1)(1)=-1.

So the range is [tex][-1,\infty)[/tex]

or all numbers greater than or equal to -1

Answer:

all real numbers greater then or equal to -1

Step-by-step explanation:

Answers:

1. 147+13=160

2. -55+(-31)= -55-31=-86

positive number and negative number= -negative number

3. 18+71=89

4. -14+21=7

Positive 7 because 21 is greater than -14

5. 12+(-56)= 12-56=-44

6. -4+18=14

7. -31+(-17)=-31-17=-48

8. 72+(-22)=72-22=50

9. 47+23=70

Answer:

X=-16/3 or 5.33

Step-by-step explanation:

The formula is y=mx+c

Substitute in values for gradient

6=-4×3+c

C=18

Y=3x+18

Substitute to find x

2=3x+18

-16=3x

X=-16/3

The slope of a line is the change in the y values over the corresponding x values.

The value of x, that makes the points a linear function is -16/3

Given that:

[tex]m = 3[/tex]

[tex](x_1,y_1) = (x,2)[/tex]

[tex](x_2,y_2) = (-4,6)[/tex]

The slope (m) of a line is calculated using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

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

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

Cross multiply

[tex]3 \times (-4 -x) = 4[/tex]

Divide by 3

[tex]-4 -x = \frac 43[/tex]

Add 4 to both sides

[tex]-x = \frac 43 + 4[/tex]

Take LCM

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

[tex]-x = \frac{16}3[/tex]

Divide by -1

[tex]x =-\frac{16}3[/tex]

Hence, the value of x is -16/3

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B). 1/2

In this question, it's asking to find the probability of Ethan getting a side of the cube that is less than 4.

In this case, we know that Ethan is rolling a 6 sided number cube, meaning that the numbers on the cube will range from 1-6.

On the cube, we need to get the numbers that are less than 4.

1

2        ← These numbers are less than 4.

3  

___

4

5

6

Knowing how many numbers are less than 4, we can solve the question.

We know that there are 3 numbers less than 4. So that will be our numerator.

There are 6 numbers in total, so that will be our denominator.

We can represent probability as a fraction.

Your fraction should look like this:

[tex]\frac{3}{6}[/tex]

We are not done yet, we would need to simplify the fraction.

To simplify, we would just divide the numerator and denominator by 3.

[tex]\frac{3}{6} \div \frac{3}{3}=\frac{1}{2}[/tex]

Once you're done solving, you should get [tex]\frac{1}{2}[/tex]

This means that answer choice B). 1/2 would be the correct answer.

The probability that Ethan gets a number less than 4 by rolling the dice is 1/2.

The probability of an event is the chance of happening that particular event.

The number of events in the sample space when rolling a dice is = 6.

The number of favorable events in that sample space = Getting a number less than 4 = 3.

Therefore, the probability of this particular event is

= 3/6

= 1/2

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Answer:

b=2

Step-by-step explanation:

we have

9x+12y=21 -----> equation A

6x+8y=7b ----> equation B

we know that

If the system of equations have an infinite number of solutions then the equation A must be equal to the equation B

Multiply equation B by 1.5 both sides

1.5*[6x+8y[=7b*1.5

9x+12y=10.5b ----> equation C

Compare equation A and equation C

9x+12y=21 -----> equation A

9x+12y=10.5b ----> equation C

For the equations to be equal it must be fulfilled that

21=10.5b

solve for b

b=21/10.5

b=2

Add all of the numbers together

2+3.5+2+3.5

5.5+5.5

= 11 cm

Answer is 11cm - second time

Answer:

11 cm

Step-by-step explanation:

The perimeter is equal to

P =2(l+w)

P = 2(2+3.5)

  = 2(5.5)

  = 11 cm

Answer:

[tex]1,800(1.015)^{x}[/tex]

Step-by-step explanation:

we have

[tex]f(x)=1,000(1.015)^{x}[/tex]

[tex]g(x)=800(1.015)^{x}[/tex]

we know that

To find the function that represent the total amount Jack and Suzie will save in x years, adds f(x) and g(x)

so

[tex]f(x)+g(x)=1,000(1.015)^{x}+800(1.015)^{x}[/tex]

[tex]f(x)+g(x)=[1,000+800](1.015)^{x}[/tex]

[tex]f(x)+g(x)=1,800(1.015)^{x}[/tex]

Answer: 1,800(1.015)^{x}

Step-by-step explanation:

we have

f(x)=1,000(1.015)^{x}

g(x)=800(1.015)^{x}

we know that

To find the function that represent the total amount Jack and Suzie will save in x years, adds f(x) and g(x)

so

f(x)+g(x)=1,000(1.015)^{x}+800(1.015)^{x}

f(x)+g(x)=[1,000+800](1.015)^{x}

f(x)+g(x)=1,800(1.015)^{x}

Answer:

3/10

Step-by-step explanation:

P(red) = red marbles / total marbles

We have 30 red marbles

total marbles = (20 white+ 50 blue+ 30 red) = 100 marbles

P(red) = 30/100 = 3/10

Answer:

0.30 or 30%.

Step-by-step explanation:

This = number of re marbles / total number of marbles

= 30 / (30+50+20)

= 30 / 100

= 0.30.

Answer:

Option C. 32°

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

Find the measure of arc AB

we know that

The semi-inscribed angle measures half that of the arc comprising

so

74°=(1/2)[arc AB]

arc AB=(2)(74°)=148°

step 2

Find the measure of arc BCDA

we know that

arc BCDA+arc AB=360°

substitute the given value

arc BCDA+148°=360°

arc BCDA=360°-148°=212°

step 3

find the measure of angle m

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

so

m=(1/2)[arc BCDA-arc AB]

substitute

m=(1/2)[212°-148°]=32°

The dimensions of the rectangle are 24x and 90y.

The area of a rectangle is represented by the expression 24x6y15. To determine the dimensions of the rectangle, we need to factorize the expression. Factoring out the common factors, we have:

24x6y15 = 2 × 2 × 2 × 3 × x × (2 × 3) × y × (5 × 3)

From this, we can see that the dimensions of the rectangle are:

Length = 2 × 2 × 2 × x × 3 = 24x

Width = 2 × y × 3 × (5 × 3) = 90y

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y< x^{2} -3[/tex]

The solution of the inequality is the shaded area below the dotted line of the quadratic equation [tex]y=x^{2} -3[/tex]

using a graphing tool

see the attached figure

The graph of the given function y < x² - 3 is attached below.

we have inequality that is a mathematical statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠).

Since we are given the inequality as;

y < x² - 3

We can write as;

y = x² - 3

These are used to describe relationships between quantities or to express constraints or conditions.

Therefore, the solution to the inequality is the shaded area below the dotted line of the quadratic equation.

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Answer:

the IQR is 41 because 62-21=41

Answer: The midpoint of segment PQ is the number 2.5

note: 2.5 as a fraction is 5/2; as a mixed number 2.5 converts to 2&1/2

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

Explanation:

Apply the midpoint formula to get the midpoint of -8 and 6

We simply add up the values and divide by 2 and we get (-8+6)/2 = -2/2 = -1

So point Q is at -1 on the number line, which is exactly halfway from R to P

Focus on just points P and Q now. Apply the midpoint formula again

Q = -1

P = 6

(Q+P)/2 = (-1+6)/2 = 5/2 = 2.5

So the midpoint of segment PQ is 2.5

The decimal 2.5 can be written as the mixed number 2&1/2, showing that this new point is exactly halfway between 2 and 3.

Answer:

32,292,000

Step-by-step explanation:

In your question, it asks how many license plate combinations we could make WITHOUT repeats.

We need some prior knowledge to answer this question.

We know that:

With the information we know above, we can solve the question.

Since we CAN'T have repeats, we would be excluding a letter or number for each license plate.

We're going to need to multiply each "section" in order to find how many combinations of license plates we can make.

We decrease by one letter and one number in each section since we can't have repeats.

Now, we can solve.

Work:

[tex]26*25*24*23*10*9 = 32,292,000[/tex]

When you're done multiplying, you should get 32,292,000.

This means that there could be 32,292,000 different combinations of license plates.

[tex]10\cdot9\cdot26\cdot25\cdot24\cdot23=32292000[/tex]

[tex]\bf \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 2\log_2(x)+\log_2(x+5)\implies \log_2(x^2)+\log_2(x+5) \\\\\\ \log_2[x^2(x+5)]\implies \log_2(x^3+5x^2)[/tex]

The expression 2log2x + log2(x + 5) can be simplified to a single term, log2[x² × (x + 5)], by using properties of logarithms.

The subject of this question is the simplification of a logarithmic expression. In the mentioned expression, we have 2log2x + log2(x + 5), and we'll use the properties of logarithms to simplify it.

First remember that in terms of logarithms, mlogₐ(b) = log_a(b^m). So we can take the coefficient of the first term and use it as an exponent, which transforms '2log2x' into 'log2(x²)'.

Next, note the law that states logₐ(b) + log(c) ₐ= logₐ(bc). This means that we can combine the two terms under a singular logarithm to give us a single term: log2[x² × (x + 5)]. So, the simplified form of the expression 2log2x + log2(x + 5) is log2[x² × (x + 5)].

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Answer:

The answer is C. x=2, x=-5

Step-by-step explanation:

Edge 2021

The solutions are 2 and -5.

Option C is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

[tex]12^{x^2 + 5x - 4}[/tex] = [tex]12^{2x + 6}[/tex]

This means,

Since both sides' base is the same.

x² + 5x - 4 = 2x + 6

x² + 5x - 2x - 4 - 6 = 0

x² + 3x - 10 = 0

Solve for x.

x² + 3x - 10 = 0

x² + (5 - 2)x - 10 = 0

x² + 5x - 2x - 10 = 0

x(x + 5) - 2(x + 5) = 0

(x + 5)(x - 2) = 0

x - 2 = 0 and x + 5 = 0

x = 2 and x = -5

Now,

The solutions are 2 and -5.

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Hey there!

Answer:

X = 12

Step-by-step explanation:

Given,

X - 17 = - 5

X = -5 + 17

X = 12

Answer:

(-6,-3)

Step-by-step explanation:

The explanation is in the picture. I really feel like the picture does a better job of explaining it then I could with words.

Answer:

C (-6,-3)

Step-by-step explanation:

A(2,5),B(2,-3), and D(-6,5)

AB  has a length of  8  since the x coordinate is the same , we only worry about the y

5--3 = 5+3 = 8

AD has a length of 8 since the y coordinate is the same, we only worry about the x

2 --6 = 2+6 =8

Notice a pattern.

A and B have the same X

A and D have the same Y

B and C will need the same Y for it to be a square

C and D will need the same x

B has a y coordinate of -3  

D has an x coordinate of -6

C will have coordinates of (-6,-3)

If we look at the attached graph of the 3 points, we see that to make the square, we need to add a point at (-6,-3)

In a game, the odds against Carl winning are 7:5. For every 7 games he loses, there are 5 games he wins. Therefore, the probability of Carl winning is 5 divided by the total of possible outcomes (5+7), which equals to 5/12.

The subject of this question is Mathematics, specifically probability. The odds against Carl beating his friend in a round of golf are 7:5. To calculate the probability of Carl winning, we have to understand that the odds of an event occurring are the ratio of the possibility of the event happening to the possibility of the event not happening. If the odds are 7:5 against Carl winning, that means for every 7 games Carl loses, there are 5 games he wins.

To calculate the probability of Carl winning, we take the number of wins and divide it by the total number of outcomes. So the probability that Carl will beat his friend would be 5/(7+5) = 5/12.

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[tex]\bf -8=2(x+9)^2\implies -8=2(\stackrel{\mathbb{F~O~I~L}}{x^2+18x+81})\implies \cfrac{-8}{2}=x^2+18x+81 \\\\\\ -4=x^2+18x+81\implies 0=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+18}x\stackrel{\stackrel{c}{\downarrow }}{\boxed{+85}}[/tex]

Answer:

D.  x^2 + 8x + 12.

Step-by-step explanation:

The zeroes of the graph ( the x -intercepts) are -2 and -6  so we can write the function as (x + 2)(x + 6) = x^2 + 8x + 12.

The function y = x² + 8x + 12​ describes this graph. This is obtained by using equation of parabola at the origin and transforming the graph to the required position as in the question by using rules of transformation of linear function.

Rules of transformation of linear function are

Equation of parabola at the origin is y = x²

By the transformation we can rewrite the function in f(x+b) form;

that is ⇒ y = (x+4)² ⇒ y = x² + 8x +16

By the transformation we can rewrite the function in f(x)-b form;

that is ⇒ y = x² + 8x +16 - 4 ⇒ y = x² + 8x +12

This is the required function.

Hence the function y = x² + 8x + 12​ describes this graph.

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Answer:

1.6 < x < 9.6.

Step-by-step explanation:

Now x cannot be less than  5.6 - 4.0 = 1.6 as a triangle  could not be formed if it were.

In fact x must be greater than 1.6.

Also x must be less than the sum of the other 2 sides.

So x  must be less than 4.0 + 5.6 = 9.6.

Answer:

1.6 < x < 9.6

Step-by-step explanation:

The range of possible sizes for side x is 1.6 < x < 9.6.

Answer:

[tex]\large\boxed{y=2(x-8)^2-72}\\\boxed{minimum\ is\ -72\ for\ x=8}[/tex]

Step-by-step explanation:

[tex]y=a(x-h)^2+k[/tex]

It's the vertex form of a quadratic equation of [tex]y=ax^2+bx+c[/tex]

The vertex is at (h, k).

k is minimum or maximum for value of h.

[tex]h=\dfrac{-b}{2a}[/tex]

k - its value of y for x = h.

We have

[tex]y=2x^2-32x+56\\\\a=2,\ b=-32,\ c=56[/tex]

[tex]h=\dfrac{-(-32)}{2(2)}=\dfrac{32}{4}=8[/tex]

[tex]k=2(8^2)-32(8)+56=2(64)-256+56=128-256+56=-72[/tex