Mr. Ford drove 224 miles in 4 hours. At what rate of speed did he drive?

Mr. Liston bought lunch for $12.80. He gave the waiter a tip of 15%. How much money did the waiter receive?
A: $1.28
B: $1.92
C: $2.56
D: $3.84

PLEASE SHOW WORK!!

Answer:

Step-by-step explanation:

1/5 + 1/5^-2

1/5 + 1/25

1/5 = 5*1 / 5*5

5/25 + 1/25

6/25 which cannot be reduced or changed.

Answer:

2/7

Step-by-step explanation:

If two events A and B are independent, then P(A and B)=P(A)P(B).

So since Q and R are independent, then P(Q and R)=P(Q)P(R).

Let's substitute and evaluate:

[tex]P(Q\text{ and }R)=P(Q)\cdot P(R)=\frac{4}{7} \cdot \frac{1}{2}=\frac{4}{14}[/tex].

Both 2 and 14 are divisible by 2, so to reduce 4/14 we could divide top and bottom by 2:

4/14=(4/2)/(14/2)=2/7

Answer:

√135

Step-by-step explanation:

3^2+b^2=12^2

9+b^2=144

9-9+b^2=144-9

b^2=135

√135=b

Answer:

Step-by-step explanation:

Put a = -0.1 to the first an second equation and find velue of b:

3 = 10a + b

3 = 10(-0.1) + b

3 = -1 + b             add 1 to both sides

4 = b → b = 4

2 = 20a + b

2 = 20(-0.1) + b

2 = -2 + b       add 2 to both sides

4 = b → b = 4

CORRECT

Answer:

The slope is 745 and the y-intercept is 500

The slope means The amount of money increases by $745 per month

The y-intercept means the business opened with initial amount $500

Step-by-step explanation:

* Lets explain how to solve the question

- The graph represents the relation between the number of months

  since the business opened and the total amount of money the

  business has earned

- The x-axis represents the number of month

- The y-axis represents the amount of money

- In the line the slopes from any two points on the line are equal

- The slope of the line whose end-points are (x1 , y1) and (x2 , y2)

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

- The equation of the line is y = mx + c ,where m is the slope of the line

 and c is the y-intercept

* Lets check is the relation between x and y is linear by calculating the

 slopes between each to points

∵ (2 , 1990) , (5 , 4225) , (9 , 7205) are points from the graph

- m1 is the slope of the points (2 , 1990) and (5 , 4225) , m2 is the slope

 of the points (5 , 42250) and (9 , 7205) , m3 is the slope of the points

 (2 , 1990) and (9 , 7205)

∵ [tex]m_{1}=\frac{4225-1990}{5-2}=745[/tex]

∵ [tex]m_{2}=\frac{7205-4225}{9-5}=745[/tex]

∵ [tex]m_{3=\frac{7205-1990}{9-2}}=745[/tex]

∴ m1 = m2 = m3 = 745

∴ The relation between the number of months and the amount of

   money is linear

* The slope is 745

∵ The form of the linear equation is y = mx + c

∵ m = 745

∴ y = 745 x + c

- The y-intercept means the line intersect the y-axis at point (0 , c),

  then to find c substitute x and y of the equation by the coordinates

  of any point on the line

∵ x = 2 , y = 1990

∴ 1990 = 745(2) + c

∴ 1990 = 1490 + c ⇒ subtract 1490 from both sides

∴ c = 500

∵ c is the y-intercept

* The y-intercept is 500

* The slope represents the rate of increasing of money per month

∴ The amount of money increases by $745 per month

* The y-intercept represents the initial amount of money when the

  business opened

∴ The business opened with initial amount $500

Answer:

The slope is 745 and the y-intercept is 500

The slope means The amount of money increases by $745 per month

The y-intercept means the business opened with initial amount $500

Step-by-step explanation:

Answer:

y-int:3

slope:-3

Step-by-step explanation:

6x-2y=-6

change to y=mx+b: -2y=-6x-6

divide by -2

y=3x+3

Answer:

1/12 of a gallon of water in each container

Step-by-step explanation:

Answer = [tex]\frac{Water}{Containers}[/tex] = 1/12

Answer:

Oliver poured [tex]\frac{1}{12}[/tex] gallons of water in each container.

Step-by-step explanation:

Oliver has the amount of water = 0.5 gallons.

He pours all of the water into 6 containers.

So amount of water in each container will be = [tex]\frac{\text{Total amount of water}}{\text{Number of containers}}[/tex]

= [tex]\frac{0.5}{6}[/tex]

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

= [tex]\frac{1}{12}[/tex] gallons of water.

Therefore, in each container amount of water poured will be [tex]\frac{1}{12}[/tex] gallons.

Answer:

6^ -24

Step-by-step explanation:

We know that a^b^c = a^ (b*c)

(6^-4)^6  = 6^ (-4*6) = 6^ -24

Answer:

b

Step-by-step explanation:

I would use b.

Why?

[tex]2 \csc(2x)[/tex]

[tex]2 \frac{1}{\sin(2x)}[/tex]

[tex]\frac{2}{\sin(2x)}[/tex]

[tex]\frac{2}{2\sin(x)\cos(x)}[/tex]

[tex]\frac{1}{\sin(x)\cos(x)}{/tex]

[tex]\frac{1}{\sin(x)\frac{1}{\cos(x)}[/tex]

[tex]\csc(x) \sec(x)[/tex]

I applied the identity sin(2x)=2sin(x)cos(x) in line 3 to 4.

Answer: OPTION B.

Step-by-step explanation:

It is important to remember these identities:

[tex]csc(x)=\frac{1}{sin(x)}\\\\sec(x)=\frac{1}{cos(x)}[/tex]

Knowing this, we can say that:

[tex]csc(x) sec(x)=\frac{1}{sin(x)}*\frac{1}{cos(x)}=\frac{1}{sin(x)*cos(x)}[/tex]

Now we need to use the following Double angle identity :

[tex]sin(2x)=2sin(x)cos(x)[/tex]

And solve for [tex]sin(x)cos(x)[/tex]:

[tex]\frac{sin(2x)}{2}=sin(x)cos(x)[/tex]

The next step is to make the substitution into [tex]\frac{1}{sin(x)*cos(x)}[/tex] and finally simplify:

[tex]\frac{1}{\frac{sin(2x)}{2}}=\frac{\frac{1}{1}}{\frac{sin(2x)}{2}}=\frac{2}{sin(2x)}=2csc(2x)[/tex]

Answer:

The distance is equal to [tex]3\sqrt{13}\ units[/tex]

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]R(-1,0)\\S(8,6)[/tex]  

substitute the values

[tex]d=\sqrt{(6-0)^{2}+(8+1)^{2}}[/tex]

[tex]d=\sqrt{(6)^{2}+(9)^{2}}[/tex]

[tex]d=\sqrt{36+81}[/tex]

[tex]d=\sqrt{117}\ units[/tex]

Simplify

[tex]d=3\sqrt{13}\ units[/tex]

1st one

Step-by-step explanation:

I have answered ur question

Answer:

A

Step-by-step explanation:

Given

x² - 8x = 3

To complete the square

add (half the coefficient of the x- term)² to both sides

x² + 2(- 4)x + 16 = 3 + 16

(x - 4)² = 19 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{19}[/tex] ( add 4 to both sides )

x = 4 ± [tex]\sqrt{19}[/tex]

Solution set is (4 - [tex]\sqrt{19}[/tex], 4 + [tex]\sqrt{19}[/tex] )

This is a linear equation in standard form [tex]\( Ax + By = C \).[/tex] None of the options provided in the multiple-choice question exactly match this equation in standard form

To find the equation of a line perpendicular to the given line and passing through a specific point, follow these steps:

1. Identify the slope of the original line.

  The line given is [tex]\( y = -10x + 1 \)[/tex]. The slope (m) of this line is -10.

2. Find the perpendicular slope:

  The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, the perpendicular slope [tex]\( m_{\perp} \) is \( \frac{1}{10} \)[/tex]  because [tex]\( m_{\perp} = -\frac{1}{m} \).[/tex]

3. Use the point-slope form to find the equation:

  The point-slope form is [tex]\( y - y_1 = m_{\perp}(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is the point the line passes through, which is (5,7) in this case.

4. Plug in the point and the perpendicular slope:

  [tex]\( y - 7 = \frac{1}{10}(x - 5) \)[/tex].

5. Simplify the equation to get it into slope-intercept form  [tex](\( y = mx + b \))[/tex]:

  [tex]\( y = \frac{1}{10}x - \frac{1}{10}(5) + 7 \)[/tex].

  [tex]\( y = \frac{1}{10}x - \frac{1}{2} + 7 \)[/tex].

  [tex]\( y = \frac{1}{10}x + \frac{13}{2} \)[/tex] after combining like terms.

The equation in slope-intercept form is [tex]\( y = \frac{1}{10}x + \frac{13}{2} \),[/tex]which corresponds to one of the choices given in the multiple-choice question. Let's identify which one it is.

The equation that represents a line which is perpendicular to the line [tex]\( y = -10x + 1 \)[/tex] , passing through the point (5,7), is:

[tex]\[ y = \frac{1}{10}x + \frac{13}{2} \][/tex]

This can be simplified to:

[tex]\[ 10y = x + 65 \][/tex]

Or:

[tex]\[ x - 10y = -65 \][/tex]

This is a linear equation in standard form \( Ax + By = C \). None of the options provided in the multiple-choice question exactly match this equation in standard form

ANSWER

alternate interior angles theorem

EXPLANATION

According to the alternate interior angles theorem, when two parallel lines are are intercepted by a straight line (transversal) the angles in the interior corners of a Z-shape pattern are congruent.

From the above diagram line r is parallel to line s, therefore

[tex] \angle \: 3 \cong \angle6[/tex]

and

[tex] \angle \: 4\cong \angle5[/tex]

because they are alternate interior angles.

See attachment for how to spot alternate interior angles.

Question:

Given that r||s and q is a transversal, we know that  by the [________].

Answer:

alternate interior angles theorem

Answer:

3                     sqrt(3)

-----------    or  -----------

2 sqrt(3)            2

Step-by-step explanation:

3 sqrt(8)

-----------------

4 sqrt(6)

3 sqrt(4*2)

-----------------

4 sqrt(3*2)

We know that sqrt(ab) = sqrt(a) sqrt(b)

3 sqrt(4) sqrt(2)

------------------------

4 sqrt(3) sqrt(2)

Canceling the sqrt(2) and sqrt(4) is 2

3*2

----------

4 sqrt(3)

3

-----------

2 sqrt(3)

We can simplify the answer be multiplying by sqrt(3)/sqrt(3)

3                 sqrt(3)

----------- * ----------

2 sqrt(3)     sqrt(3)

3 sqrt(3)

-----------

2 *3

sqrt(3)

-----------

2

Answer:

the answer is D

Step-by-step explanation:

if you look on the graph and compare the statements you'll see none of them correlate except for the last one. 7 erasers cost 3.50, since the point on the graph is (7, 3.50)

Answer:

The correct option is D) Seven eraser cost $3.50

Step-by-step explanation:

Consider the provided graph.

The graph shows the relationship between the total cost and the number of erasers bought at the student store.

Here the x-axis represents the number of erasers bought and the y-axis represents the total cost.

Now consider the provided options.

Options (A) Each eraser cost $1.00

This option is incorrect because when x = 1 the value of y = 0.5, that means the cost of each eraser is $0.5

Options (B) Each eraser cost $1.50

This option is incorrect as the cost of each eraser is $0.5

Options (C) Three eraser cost $6

This option is incorrect because when x = 3 the value of y = 1.5, that means the cost of 3 eraser is $1.5

Options (D) Seven eraser cost $3.50

This option is correct because when x = 7 the value of y = 3.5, that means the cost of 7 eraser is $3.5

Answer:

- 3, 9, 25

Step-by-step explanation:

To find the required terms of the sequence substitute n = 2, 5, 9 into the given rule, that is

[tex]a_{2}[/tex] = - 7 + (2 - 1)4  = - 7 + (1 × 4) = - 7 + 4 = - 3

[tex]a_{5}[/tex] = - 7 + (5 - 1)4 = - 7 + (4 × 4) = - 7 + 16 = 9

[tex]a_{9}[/tex] = - 7 + (9 - 1)4 = - 7 + (8 × 4) = - 7 + 32 = 25

The second, fifth, and ninth terms of the sequence are -3, 9, and 25, respectively.

The second, fifth, and ninth terms of the sequence defined by the formula an = -7 + (n - 1) * 4 are -3, 9, and 25, respectively.

To find the second, fifth, and ninth terms of the sequence given by the formula an = -7 + (n - 1) * 4, we can simply plug the corresponding values of n into the formula.

For the second term (a2), where n=2:

a2 = -7 + (2 - 1) * 4

a2 = -7 + 1 * 4

a2 = -7 + 4

a2 = -3

For the fifth term (a5), where n=5:

a5 = -7 + (5 - 1) * 4

a5 = -7 + 4 * 4

a5 = -7 + 16

a5 = 9

For the ninth term (a9), where n=9:

a9 = -7 + (9 - 1) * 4

a9 = -7 + 8 * 4

a9 = -7 + 32

a9 = 25

Therefore, the second, fifth, and ninth terms of the sequence are -3, 9, and 25, respectively.

Answer:

nope its not. You should  count it like this  (8 / 2) * (2 + 2)

Step-by-step explanation:

(8 / 2) * (2 + 2)

4 * 4

16

[tex]\text{Hey there!}[/tex]

[tex]\text{PEMDAS means: Parentheses, Exponents, Multiplication, Division, Addition}\\\text{, \& Subtraction}[/tex]

[tex]\text{\underline{No}, it is \underline{NOT} correct because you had to work with the parentheses first}[/tex]

[tex]\dfrac{8}{2}(2 + 2) = \ ? \\ \\ (2 + 2) = 4 \\ \\ \dfrac{8}{2}(4) = \ ? \\ \\ \dfrac{8}{2}= 4 \\ \\ \text{4(4)\ = 16} \\ \\ \boxed{\boxed{\huge\text{Answer should be: 16 }}}[/tex]

[tex]\text{You had to do what was inside the parentheses first, then}\text{ divsion}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

False.

Step-by-step explanation:

To see if these sides can form a right triangle, all we need to do is see if the following equation holds [tex]a^2+b^2=c^2[/tex] where [tex]c[/tex] is the larger measurement.  [tex]a \text{ and } b[/tex] it doesn't really matter which you assign as 5 or 8.

So I'm choosing the following [tex]a=5,b=8,c=12[/tex].

[tex]c[/tex] has to be 12 because 12 is the largest.

Now we got to see if [tex]a^2+b^2=c^2[/tex] holds.

That is, we need to see if [tex]5^2+8^2=12^2[/tex] holds.

[tex]5^2+8^2=12^2[/tex]

[tex]25+64=144[/tex]

[tex]89=144[/tex]

That's totally false.  89 is definitely not 144 so 5,8, and 12 cannot be put together to form a right triangle.

Answer:

a is the only true one if you meant 6 times 5!

Step-by-step explanation:

Before we being

n!=n*(n-1)*(n-2)*...(3)(2)(1)

Example: 5!=5(4)(3)(2)(1) and 10!=10(9)(8)(7)(6)(5)(4)(3)(2)(1)

Yes that operation is multiplication.

a) Does 6!=6*5!

Let's see

6!=6*5*4*3*2*1

5!=5*4*3*2*1

So 6*5!=6(5*4*3*2*1)=6*5*4*3*2*1=6!

So true!

b) Does 4!+2!=6! ?

4!=4(3)(2)(1)

2!=2(1)

6!=6(5)(4)(3)(2)(1)

Does

4(3)(2)(1)+2(1)=6(5)(4)(3)(2)(1)

24          +2  =720

26=720 (this is not true)

So 4!+2! is not 6!

c) Does 6!/3!=2! ?

6!=6(5)(4)(3)(2)(1)

3!=3(2)(1)

If you divide 6! by 3!, then the factors 3 and 2 and 1 cancel and you are left with 6(5)(4).

So the question becomes is 6(5)(4)=2!

2!=2(1)=2

6(5)(4)=2?

No way! That is saying 120=2 which is not true.

The evaluations of the statements are: (a) false because non-integer factorials are not defined, (b) false because the sum of 4! and 2! does not equal 6!, and (c) false because 6! divided by 3! is 120, not 2!.

Let's evaluate each statement one by one.

This statement is false. The factorial function is defined for non-negative integers. Since there is no definition for non-integer factorial such as 6.5!, this comparison is invalid. A correct statement may involve only integer factorials.

This statement is also false. To show this, let's calculate each factorial:

Adding 4! and 2! gives 24 + 2 = 26, which is not equal to 6! (720). This statement could be corrected by finding two factorials that add up to another factorial, if such a pair exists.

This statement is false. By calculating the factorials, we have:

Therefore, 6!/3! is equal to 720/6, which simplifies to 120, not 2 (which is the value of 2!). The correct statement is 6!/3! = 120.

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Answer:

D

Step-by-step explanation:

Given

9 - 7x = (4x - 3)² + 5 ← expand the squared factor

9 - 7x = 16x² - 24x + 9 + 5, that is

9 - 7x = 16x² - 24x + 14 ( subtract 9 - 7x from both sides )

0 = 16x² - 17x + 5, that is

16x² - 17x + 5 = 0 ← in standard form → D

Answer:

6

Step-by-step explanation:

60% of 40 = 24

25% of 24 = 6

Therefore, 6 girls in  the class wear glasses.

To find the exact value of tan^-1(-sqrt(3)), we first rewrite the equation using the definition of the arctangent function. Next, we use the trigonometric identity sin^2(x) + cos^2(x) = 1 to simplify the equation and solve for sin(x). We find that sin(x) = sqrt(3)/2. By looking at the unit circle, we determine that the angle whose sine is sqrt(3)/2 is pi/3 radians. Therefore, the exact value of tan^-1(-sqrt(3)) in radians is -pi/3 + 2*pi*n, where n is an integer.

To find the exact value of tan^-1(-sqrt(3)), we need to recall the definition of the arctangent function. The arctangent function returns an angle whose tangent is equal to a given number. In this case, we are looking for an angle whose tangent is -sqrt(3). Since tan(x) = sin(x)/cos(x), we can rewrite the equation as -sqrt(3) = sin(x)/cos(x).

Next, we can use the fact that sin^2(x) + cos^2(x) = 1 to rewrite the equation as -sqrt(3) = sin(x)/sqrt(1 - sin^2(x)). Cross-multiplying and rearranging, we get -sqrt(3)*sqrt(1 - sin^2(x)) = sin(x).

Now, we can square both sides and simplify the equation to get -3*(1 - sin^2(x)) = sin^2(x). Expanding and rearranging, we have -3 + 3sin^2(x) = sin^2(x). Combining like terms and isolating sin^2(x), we get sin^2(x) = 3/4. Taking the square root of both sides, we find sin(x) = sqrt(3)/2.

Finally, we can find the angle whose sine is sqrt(3)/2 by looking at the unit circle. The angle is pi/3 in radians. Therefore, the exact value of tan^-1(-sqrt(3)) in radians is -pi/3 + 2*pi*n, where n is an integer.

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The answer is c $92,598

Answer:

$92,598

Step-by-step explanation:

The purchaser pays Ben $20,000 today and then $20,000 every year for the next 4 years.

The interest rate is 4% per annum.

So the net present value of all the payments is :

20000 + 20000/1.04 + 20000/(1.04^2) + 20000/(1.04^3) + 20000/(1.04^4)

= 20000 + 19230.77 + 18491.12 + 17779.73 + 17096.08

= 92597.7

= 92,598 (approx)

So the net present value of all the payments made to Ben is $92,598.

Answer:

Step-by-step explanation:

2(9+4)

According to the BODMAS rule:

B = BRACKET

O = OPEN

D= DIVISION

M = MULTIPLICATION

A = ADDITION

S= SUBTRACTION

First we will solve the bracket:

=2(9+4)

=2(13)

=26....

Answer:

A, B, and C

Step-by-step explanation:

= 2 (9 +4)

= 2 (13)

= 26

A

= 2(9) + 2 (4)

= 18 + 8

= 26

B

= 2(13)

= 26

C

= 18 + 8

= 26

D

= 22

D does not apply because it does not equal 26

Answer:

1 3/4 t -7/2

Step-by-step explanation:

t + 3/4t - 7/2

Get a common denominator for the t terms, which is 4

4/4t + 3/4t - 7/2

7/4 t -7/2

This is an improper fraction so change it to a mixed number

1 3/4 t -7/2

Answer:

It can be written as 825/1000. You can simplify this to get the simplest form which would be 33/40. All decimals are out of one, they are a part. When you first get a decimal, put the numbers such as 825 on top. The last number is in the thousandths place, so it is out of 1000. 1000 is your denominator. Your fraction is then 825/1000. From here you can simplify if possible.

Hope this helps ^-^

ANSWER

(0, 1), (1, 3), (2, 9), (3, 27)

EXPLANATION

The first and third options are completely out because the y-value of an exponential function is never zero.

For the second option the y-values has no geometric pattern or common ratio.

For the last option, we can observe the following pattern

[tex]1 = {3}^{0} [/tex]

[tex] {3}^{1} = 3[/tex]

[tex] {3}^{2} = 9[/tex]

[tex] {3}^{3} = 27[/tex]

:

:

[tex] {3}^{x} = y [/tex]

The correct choice is the last option

Answer:

D

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

Given:

Center of circle = (h,k)= (3,8)

Radius = r = 5

The standard form of equation of circle with center and radius is:

[tex](x-h)^2+(y-k)^2=r^2\\Putting\ the\ values\\(x-3)^2+(y-8)^2=(5)^2\\Simplifying\\x^2+9-6x+y^2+64-16y=25\\x^2+y^2-6x-16y+9+64=25\\x^2+y^2-6x-16y+73=25\\x^2+y^2-6x-16y+73-25=0\\x^2+y^2-6x-16y+48=0[/tex]

Therefore, the general form of the equation of circle given is:

[tex]x^2+y^2-6x-16y+48=0[/tex]

Hence, option A is correct ..

Answer:

$225,000

Step-by-step explanation:

To calculate the percentage change we will apply the formula:

p= N-O/O *100

p is the increased percentage

N is the current value

O is the old value.

Substitute the values in the formula:

36 = 306,000 - O/O *100

Divide both the sides by 100

36/100 = 306,000 - O/O *100/100

36/100 = 306,000 - O/O

Now multiply O at both sides

36/100 * O = 306,000-O/O * O

At R.H.S O will be cancelled by O

At L.H.S 36/ 100 = 0.36

0.36 O= 306,000-O

Combine the like terms:

0.36 O+O =306,000

1.36 O = 306,000

Divide both the terms by 1.36

1.36 O/ 1.36 = 306,000/1.36

O= $225,000

Therefore  when the house was purchased its value was $225,000....

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=5x+2&(1)\\3x=-y+10&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\3x=-(5x+2)+10\\3x=-5x-2+10\qquad\text{add 5x to both sides}\\8x=8\qquad\text{divide both sides by 8}\\x=1\\\\\text{put the value of x to (1):}\\\\y=5(1)+2\\y=5+2\\y=7[/tex]