What term do you use to describe the amount of three-dimensional space
inside a solid?
A. Volume
B. Perimeter
C. Surface area
D. Lateral area

Answer:

Murray can swim 3/4 km downstream

Step-by-step explanation:

Since the current adds to his speed and

then subtracts the same amount, you can

disregard the current

d=r*t

Convert 15 min to hrs ( time to swim downstream )

15(1/60)=1/4 hours

d=3(1/4)

d=3/4 km downstream.

Hence Murray can swim 3/4 km downstream....

Final answer:

Murray swam 0.417 km downstream before turning around and swimming back upstream. The calculation involves solving a simple algebraic equation using Murray's swimming speed and the river's flow rate, within the total time frame of 30 minutes.

Explanation:

The student is asking about a problem involving rates and time, which is a common topic in algebra and physics. In this scenario, Murray is able to swim at a speed of 3 km/h in still water, and the river flow adds an extra 2 km/h when swimming downstream, making his effective downstream speed 5 km/h. When swimming upstream, Murray has to work against the river flow, reducing his effective speed to 1 km/h (3 km/h - 2 km/h). Given that the total time spent swimming is 30 minutes (0.5 hours), we need to determine the distance Murray swam downstream before turning back.

Let the distance Murray swam downstream be d kilometers. The time to swim downstream at 5 km/h is d/5 hours, and the time to swim back upstream at 1 km/h is d hours. The sum of these times equals the total time Murray was swimming:

d/5 + d = 0.5

By solving the equation, we find that d = 0.417 km. Therefore, Murray swam 0.417 kilometers downstream before turning around and swimming back upstream.

Answer:

D:456.2 units²

Step-by-step explanation:

Step 1: Area of all 4 sides of cuboid

Area of rectangle = 4 x length x breadth

Area of rectangle = 4 x 10 x 5

Area of rectangle = 200

Step 2: Calculate bottom of cuboid

Area = length x breadth

Area = 10 x 10

Area = 100

Step 3: Calculate slant height of pyramid

c² = a² + b²

c² is hypotenuse

a² is the base which is half of w (10/2 = 5)

b² is y which is 6

c² = a² + b²

c² = 5² + 6²

c = √61

Step 4: Calculate area of one face of the pyramid

Area of triangle = 1/2 x base x height

Area of triangle = 1/2 x 10 x √61

Area of triangle = 5√61

Step 5: Calculate areas of all 4 faces of the pyramid

4 x 5√61 = 20√61

Step 6: Calculate the total surface area

Total surface area = 200 + 100 + 20√61

Total surface area = 456.2

The surface area of the figure is 456.2 units²

Option D is correct.

!!

Answer:

y = - x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x + 2 ← is in slope- intercept form

with slope m = 1

Given a line with slope m then the slope of a perpendicular line is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{1}[/tex] = - 1, hence

y = - x + c ← is the partial equation of the perpendicular line

To find c substitute (4, - 1) into the partial equation

- 1 = - 4 + c ⇒ c = - 1 + 4 = 3

y = - x + 3 ← equation of perpendicular line

Answer:

x=8

Step-by-step explanation:

(x+4) = (x+8)

------     -------

3            4

Multiply each side by 12 to get rid of the fraction

      (x+4) = (x+8)

12 *------     ------- *12

       3            4

4*(x+4) = (x+8)*3

Distribute

​4x+16 = 3x+24

Subtract 3x from each side

4x-3x+16 = 3x-3x+24

x+16 = 24

Subtract 16 from each side

x+16-16 = 24-16

x = 8

Solutions are denoted by index. Most of the equations you listed has 2 solutions.

Number one cannot be factored using whole numbers.

Number two.

[tex]

4x^2+25=0\Longrightarrow(2x+5)(2x-5)=0 \\

x_1\Longleftrightarrow\boxed{2x+5=0\Longrightarrow x=-\dfrac{5}{2}} \\

x_2\Longleftrightarrow\boxed{2x-5=0\Longrightarrow x=\dfrac{5}{2}}

[/tex]

Number three.

[tex]

x^2+121=0\Longrightarrow(x+11)(x-11)=0 \\

x_1\Longleftrightarrow\boxed{x+11=0\Longrightarrow x=-11} \\

x_2\Longleftrightarrow\boxed{x-11=0\Longrightarrow x=11}

[/tex]

Hope this helps.

Check the picture for the correct answer:                                          

[tex]x^3-3x^2+81x-243=\\x^2(x-3)+81(x-3)=\\(x^2+81)(x-3)=\\(x-3)(x-9i)(x+9i)[/tex]

Answer:

y = 3

Step-by-step explanation:

The y-coordinate of all points on the graph is 3.

The equation is y = 3

Answer:

y = 3

Step-by-step explanation:

The equation of a horizontal line parallel to the x- axis is

y = c

Where c is the value of the y- coordinates the line passes through.

In this case the line passes through points with a y- coordinate of 3, hence

Equation of horizontal line is y = 3

Answer:

[tex]a_n=7 \cdot (-3)^{n-1}[/tex]

Step-by-step explanation:

The explicit form for a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1}[/tex] where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio.

We have the following given:

[tex]a_2=-21[/tex]

[tex]a_5=567[/tex].

We also know that [tex]a_2=a_1 \cdot r[/tex] while [tex]a_5=a_1 \cdot r_4[/tex].

So if we do 5th term divided by second term we get:

[tex]\frac{a_1 \cdot r_4}{a_1 \cdot r}=\frac{567}{-21}[/tex]

Simplifying both sides:

[tex]r^3=-27[/tex]

Cube root both sides:

[tex]r=-3[/tex]

The common ratio, r, is -3.

Now we need to find the first term.

That shouldn't be too hard here since we know the second term which is -21.

We know that first term times the common ratio will give us the second term.

So we are solving the equation:

[tex]a_1 \cdot r=a_2[/tex].

[tex]a_1 \cdot (-3)=-21[/tex]

Dividing both sides by -3 gives us [tex]a_1=7[/tex].

So the equation is in it's explicit form is:

[tex]a_n=7 \cdot (-3)^{n-1}[/tex]

Check it!

Plugging in 2 should gives us a result of -21.

[tex]a_2=7 \cdot (-3)^{2-1}[/tex]

[tex]a_2=7 \cdot (-3)^1[/tex]

[tex]a_2=7 \cdot (-3)[/tex]

[tex]a_2=-21[/tex]

That checks out!

Plugging in 5 should give us a result of 567.

[tex]a_5=7 \cdot (-3)^{5-1}[/tex]

[tex]a_5=7 \cdot (-3)^4[/tex]

[tex]a_5=7 \cdot 81[/tex]

[tex]a_5=567[/tex]

The checks out!

Our equation works!

Final answer:

To find the nth term formula of a geometric sequence with given terms, divide one term by the other to find the common ratio, and then solve for the first term. For this sequence, the nth term is [tex]a_{n}= 7 (-3)^{n-1}[/tex].

Explanation:

To find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively, we must determine the common ratio (r) and the first term (a1) of the sequence. For a geometric sequence, the nth term is given by the formula [tex]a_{n}= a_{1} (r)^{n-1}[/tex].

Since the second term a2 is -21 and the fifth term a5 is 567, we can set up the following equations using the geometric sequence formula:

[tex]a_{2}[/tex] =  [tex]a_{1}[/tex] x r = -21

[tex]a_{5}[/tex] =  [tex]a_{1}[/tex] x [tex]r_{4}[/tex] = 567

Dividing the second equation by the first gives us:

[tex]r_{3}[/tex] = 567 / -21 = -27

Thus, the common ratio r is -3. Now using [tex]a_{2} =a_{1} r[/tex] , we find that [tex]a_{1}[/tex] = -21 / (-3) = 7. Therefore, the nth term of the sequence is:

[tex]a_{n}= 7 (-3)^{n-1}[/tex]

Answer:

see explanation

Step-by-step explanation:

We require to rationalise the denominator by multiplying the numerator and denominator by the complex conjugate of the denominator.

The conjugate of 5 + 3i is 5 - 3i

noting that i² = - 1, hence

[tex]\frac{(9-6i)(5-3i)}{(5+3i)(5-3i)}[/tex] ← expand factors

= [tex]\frac{45-57i+18i^2}{25-9i^2}[/tex]

= [tex]\frac{45-57i-18}{25+9}[/tex]

= [tex]\frac{27-57i}{34}[/tex]

= [tex]\frac{27}{34}[/tex] - [tex]\frac{57}{34}[/tex] i ← quotient

Final answer:

To find the quotient of 9-6i and 5+3i, multiply both the numerator and the denominator by the conjugate of the denominator 5-3i. Simplify by using the distributive property and knowing that i^2 equals -1. The final quotient is 27/34 - 57i/34.

Explanation:

To find the quotient of the complex numbers 9-6i divided by 5+3i, we must multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of 5+3i is 5-3i. So, the process is as follows:

Thus, the quotient is 27/34 - 57i/34 or approximately 0.7941 - 1.6765i.

Answer:

[tex]x=\frac{5 \pm \sqrt{97}}{12}[/tex]

Step-by-step explanation:

First step is to arrange so it is in the form [tex]ax^2+bx+c=0[/tex].

We have [tex]5x=6x^2-3[/tex].

Add we really need to do is subtract 5x on both sides:

[tex]0=6x^2-5x-3[/tex].

Now let's compare [tex]6x^2-5x-3[/tex] to [tex]ax^2+bx+c[/tex].

We have [tex]a=6,b=-5,c=-3[/tex].

The quadratic formula is [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].

I like to break this into parts:

Part 1:  Find [tex]-b[/tex].

Part 2: Find [tex]b^2-4ac[/tex].

Part 3: Find [tex]2a[/tex].

Answering the parts:

Part 1: [tex]-b=5[/tex] since [tex]b=-5[/tex].

Part 2: [tex]b^2-4ac=(-5)^2-4(6)(-3)=25-24(-3)=25+72=97[/tex].

Part 3: [tex]2a=2(6)=12[/tex].

Now our formula in terms of my parts looks like this:

[tex]x=\frac{\text{Part 1} \pm \sqrt{Part 2}}{Part 3}[/tex]

Our formula with my parts evaluated looks like this:

[tex]x=\frac{5 \pm \sqrt{97}}{12}[/tex].

Answer:

Step-by-step explanation:

[tex]f(x)=x^2-x-2\\\\\text{The zeros are for}\ f(x)=0:\\\\x^2-x-2=0\\\\x^2-2x+x-2=0\\\\x(x-2)+1(x-2)=0\\\\(x-2)(x+1)=0\iff x-2=0\ \vee\ x+1=0\\\\x-2=0\qquad\text{add 2 to both sides}\\x=2\\\\x+1=0\qquad\text{subtract 1 from both sides}\\x=-1[/tex]

Answer:

The correct option is B) [tex]f(x)=-5x+250[/tex].

Step-by-step explanation:

Consider the provided information.

let x represents the number of weeks and y represents the fixed cars.

During week 10 of the recall, the manufacturer fixed 200 cars.

Thus, the ordered pair can be made with the help of the above data is: (10,200).

In week 15, the manufacturer fixed 175 cars.

Thus, the ordered pair can be made with the help of above data is: (15,175)

Now use two point slope formula: [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Substitute the [tex](x_1,y_1)=(10,200)\ \text{and}\ (x_2,y_2)=(15,175)[/tex] in the above formula.

[tex]y-200=\frac{175-200}{15-10}(x-10)[/tex]

[tex]y-200=\frac{-25}{5}(x-10)[/tex]

[tex]y-200=-5(x-10)[/tex]

[tex]y-200=-5x+50[/tex]

[tex]y=-5x+250[/tex]

Which also can be written as:

[tex]f(x)=-5x+250[/tex]

Hence, the correct option is B) [tex]f(x)=-5x+250[/tex].

Answer:

B

Step-by-step explanation:

The x- intercepts are the points on the x- axis where the graph crosses.

That is (- 3, 0), (1, 0) and (2, 0) → set B

Answer:

D. (1,0), (2,0), (-3,0), and (0,6)

Step-by-step explanation:

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

[tex]\huge\bold{{32 = [4(2 + 5) - 2\times6]}}[/tex]

[tex]\text{[4(2 + 5) - 2} \ \times \ 6][/tex]

[tex]\text{Do PEMDAS}\downarrow[/tex]

[tex]\huge\text{Parentheses}\\\huge\text{Exponents}\\\huge\text{Multiplication}[/tex] [tex]\huge\text{Division}\\\huge\text{Addition}\\\huge\text{Substraction}[/tex]

[tex]\huge\text{First, we do PARENTHESES}[/tex]

[tex]\huge\text{2 + 5 which equals 7}[/tex]

[tex]\huge\text{4(7) - 2(6)}[/tex]

[tex]\huge\text{Next step is multiplication since we don't have}[/tex] [tex]\huge\text{exponents}[/tex]

[tex]\huge\text{4(7) = 28}\\\\\huge{\text{2(6) = 12 }[/tex]

[tex]\huge\text{Thirdly, we have to do subtraction since}[/tex] [tex]\huge\text{we don't have have any division or addition}[/tex]

[tex]\huge\text{28 - 12 = 16}[/tex]

[tex]\boxed{\boxed{\huge\bf{Answer: 32\neq16\ so,\ it \ is \ FALSE}}}\checkmark[/tex]

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

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

Answer:

x > -3

Step-by-step explanation:

We are given the following inequality that we are to solve:

[tex]3(x+2)>x[/tex]

Applying the distributive property of multiplication on the left side of the inequality to get:

[tex] 3 x + 6 > x [/tex]

Rearranging the inequality:

[tex] 3 x - x > - 6 [/tex]

[tex] 2 x > - 6 [/tex]

[tex] x > \frac { - 6 } { 2 } [/tex]

x > -3

Answer:

[tex]\large\boxed{x>-3\to\{x\ |\ x>-3\}\to x\in(-3,\ \infty)}[/tex]

Step-by-step explanation:

[tex]3(x+2)>x\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(3)(x)+(3)(2)>x\\\\3x+6>x\qquad\text{subtract 6 from both sides}\\\\3x+6-6>x-6\\\\3x>x-6\qquad\text{subtract x from both sides}\\\\3x-x>x-x-6\\\\2x>-6\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}>\dfrac{-6}{2}\\\\x>-3[/tex]

Answer:

64 : 1

Step-by-step explanation:

Given 2 similar cylinders with linear ratio = a : b then

volume ratio = a³ : b³

Here the height ratio = 4 : 1, hence

volume ratio = 4³ : 1³ = 64 : 1

Answer: Step 3

Step-by-step explanation:

He should have divided 8 by 2 and then added it to 49.

In the third step, Rahul made his first mistake. Simplification is to be done using the BODMAS rule.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

Rahul simplified an expression. His work is shown below.

The expression is given below.

7 (8.5 - 1.5) + 8 / 2

Step 1. 7 (7) + 8 / 2

Step 2. 49 + 8 / 2

Step 3. 49 + 4

Step 4. 53

In the third step, Rahul made his first mistake.

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Answer:

= 1/59049 ....

Step-by-step explanation:

9 to the 2 = 9^2 = 9*9 = 81

9 to the 7 = 9^7= 9*9*9*9*9*9*9 = 4782969

Now simplify the values by table of 9

=81/ 4782969

=9/531441

=1/59049 ....

Step-by-step explanation:

9 to the 2ND power is 81

9 to the 7th power is 4,782,969

81 divided by 81 is 1

4,782,969 divided by 81 is 59,049

so the final answer is 1

59,049

Answer:

140°

Step-by-step explanation:

<3 = 40 because they are vertical angles

<3 +<4 = 180 because they are same side interior angles

40 + <4 = 180

Subtract 40 from each side

40-40 + <4 = 180-40

<4 = 140

Answer:

[tex]l=\frac{P}{2}-w[/tex].

Step-by-step explanation:

The perimeter of a rectangle is the sum of it's side lengths.

A rectangle has 4 sides where it's opposite sides are congruent.

So if one side has measurement w, then there is another side that has measurement w.

If there is one side that has measurement l, then there is another side that has measurement l.

So if you add w+w+l+l you get 2w+2l.

They are giving us that the perimeter is P, so P=2w+2l.

we are being asking to solve for l.

P=2w+2l

First step: Isolate term that contains the l, so get 2l by itself first.

We are going to subtract 2w on both sides giving us:

P-2w=2l

2l=P-2w

Now that we have 2l by itself it is time to perform the last step in getting l by itself.

Second step: Divide both sides by 2.

This gives us:

l=(P-2w)/2

You may separate the fraction like so:

[tex]l=\frac{P-2w}{2}=\frac{P}{2}-\frac{2w}{2}=\frac{P}{2}-w[/tex].

I don't know your options but I have solve for l in terms of P and w

and got [tex]l=\frac{P}{2}-w[/tex].

Please let me know if you have further questions with this problem.

Answer:

C

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 5 =  - 3(x + 2) ← is in point- slope form

with slope m = - 3

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]

and (a, b) = (6, - 1), hence

y - (- 1) = [tex]\frac{1}{3}[/tex](x - 6), that is

y + 1 = [tex]\frac{1}{3}[/tex](x - 6) → C

Answer:

if she would sell it for what it is worth now she would make $36.50

Step-by-step explanation:

0.75 x 83 = 62.5

62.5 + 8.75 = 71

71 is how much it is worth now

71 - 34.5 = 36.5

36.50 is how much she would make

Answer:

$36,50

Step-by-step explanation:

That is correct to me. You do those exact steps to arrive at that answer.

Answer:

See below.

Step-by-step explanation:

It decreases in the interval where x  > -2.

In interval notation this is (-2, ∞).

The quadratic function decreasing at x>-2.

A quadratic polynomial is a polynomial of degree two in one or more variables.

Given is a graph,

It decreases in the interval where x  > -2.

In interval notation, this is (-2, ∞).

Hence, the quadratic function decreasing at x>-2.

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b) -4

- 8x +4 =36

First, we subtract 4 from 36 to get 32

36-4=32

-8x=32

Since a negative times a negative equals a positive, then the answer has to be negative because 36 is positive.

32 divided by 8 = 4

B) -4

Answer:

The answer is B, x=-4

Step-by-step explanation:

-8x + 4 = 36

-8x - 4 = 36 - 4

-8x = 32

-8x/-8 = 32/-8

x = -4

Answer:

Part A) Annual [tex]\$66,480.95[/tex]  

Part B) Semiannual [tex]\$66,862.38[/tex]  

Part C) Monthly [tex]\$67,195.44[/tex]  

Part D) Daily [tex]\$67,261.54[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

Part A)

Annual

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=1[/tex]

 substitute in the formula above  

 [tex]A=47,400(1+\frac{0.07}{1})^{1*5} \\A=47,400(1.07)^{5}\\A=\$66,480.95[/tex]

Part B)

Semiannual

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=2[/tex]

 substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{2})^{2*5} \\A=47,400(1.035)^{10}\\A=\$66,862.38[/tex]

 Part C)

Monthly

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=12[/tex]  

substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{12})^{12*5}\\A=47,400(1.0058)^{60}\\A=\$67,195.44[/tex]

 Part D)

Daily

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=365[/tex] 

substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{365})^{365*5}\\A=47,400(1.0002)^{1,825}\\A=\$67,261.54[/tex]

Answer:

19 t-shirts

Step-by-step explanation:

x= number of t-shirts

6x+54=168; now subtract 54 from both sides of the equation

6x=114; now divide both sides by 6 to isolate the "x"

x=19

The full length of one line times the length of the line outside the circle is equal the the other line.

(7+x)*7 = (13 +8) * 8

Simplify:

7x +49 = 21 * 8

7x +49 = 168

Subtract 49 from each side:

7x = 119

Divide both sides by 7:

x = 17

The answer is B. 17

The value of x for the given circle will be 17 so option (B) will be correct.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circle objects for example our bike wheel.

The longest line which can be drawn inside the circle will be the diameter.

Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.

By theorem in circle

( 13 + 8) × 8 = ( x + 7) × 7

21 × 8 =  ( x + 7) × 7

x + 7 = 3 × 8

x = 24 - 7

x = 17

Hence, The value of x for the given circle will be 17.

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Answer:

Angle of elevation of the highest point of the mountain is 77°

Step-by-step explanation:

Lynne is hiking. When she stands at the base of the mountain, the horizontal distance between Lynne and the highest point of the mountain is 588 feet.

Elevation of the mountain is 2610 feet.

We have to calculate the angle of elevation ∠C.

tanC = [tex]\frac{2610}{588}[/tex]

tanC = 4.439

C = [tex]tan^{-1}(4.439)[/tex]

C = 77.30 ≈ 77°

Therefore, angle of elevation of the mountain is 77°

Answer:

The median is 11.

Step-by-step explanation:

First arrange the data in ascending order:

4, 5, 5, 8, 9 , 10, 10, 10, 12, 14, 15, 16, 16, 18, 19, 21

There are 16 numbers so the median is the mean of the middle 2 numbers in the list. That is the  mean of the 8th and ninth number.

Median = 10 + 12 / 2

= 11.

Answer:

answer is 12 ape x

Step-by-step explanation:

i am not sure why tho to be honest if a verified answer is 11

Answer: D

Step-by-step explanation:

They are rectangles when the sides are 90 degrees. :)

A rhombus is a rectangle when all its angles are right angles.

A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

Given is a rhombus.

A rhombus is a rectangle when all its angles are right angles. Due to this, the tilt of the vertical sides of rhombus will become 0 degrees.

Therefore, a rhombus is a rectangle when all its angles are right angles.

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