What is the volume of this triangular prism?

Answer:

y = x/3 + 10

Step-by-step explanation:

Let y be the number of minutes the flight takes

She can take off 10 minutes later than expected. She will be able to travel at  a speed three times than expected.

Let her expected speed be s, therefore, she can travel at 3s.

x = number of minutes the flight was expected to take.

In terms of distance and speed:

x = d / s ______(1)

where d = total distance traveled

The time for the flight (minus waiting time) is now the division of the distance she traveled and her speed, i.e.:

t = d / 3s

From (1):

=> t = x / 3

The time she spent waiting is 10 minutes.

Therefore, the total time that the flight takes (plus waiting time) is:

y = t + 10

=> y = x/3 + 10

Answer:

£480

Step-by-step explanation:

we can multiply both terms of ratio with same number without changing the ratio.

Example

a:b = ax: bx (here we have multiplied both terms with x)\

Given

Stevie and Michael share their profit in a ratio 3:5

Let the profit for Stevie and Michael be 3x and 5x

Given Stevie gets £120 more than Michael

Profit for Steve = 120 + profit for Michael

3x = 120 + 5x

3x-5x = 120

=> -2x = 120

=> x= -120/2 = -60

As we see profit is negative , hence it cannot be solution.

It can be solved if Stevie and Michael share their profit in a ratio 5:3

(note: in ratio , bigger number should have bigger term in ratio)

Let the profit for Stevie and Michael be 3x and 5x

Given Stevie gets £120 more than Michael

Profit for Steve = 120 + profit for Michael

5x = 120 + 3x

5x-xx = 120

=> 2x = 120

=> x= x120/2 = 60

Profit for stevei = 5x =5*60 = 300

Profit for Michael = 3x = 3*60 = 180

Total profit for them together = 300 + 180 = 480 Answer.

Answer:

The base salary is $1,400

Step-by-step explanation:

Here, we are interested in calculating the base salary.

Now let’s picture his earnings as this, a base salary of let’s say $x and a percentage of y% of total sales as commission.

So let’s move!

For the month of march, his earnings is calculated as follows;

x + (y/100 * 15,800) = 2427

so we have;

x + 158y = 2427 •••••••(i)

For the month of April, we have

x + (y/100 * 21,100) = 2771.5

x + 211y = 2771.5 ••••••(ii)

So we have two equations to solve simultaneously.

We can easily get y by subtracting equation i from ii

That would be ;

(211y-158y) = 2771.5-2427

53y = 344.5

y = 344.5/53

y = 6.5%

So we can now get the base salary by substituting the value of y in any of the equations. Let’s use the first

x + 158(6.5) = 2427

x + 1027 = 2427

x = 2427-1027

x = $1,400

Answer:

According to the pythagorean theorem, a^2 + b^2 =c^2

c signifies the hypotenuse

a and b are the two legs

the sum of the two legs squared measures will equal the measure of the hypotenuse squared.

Step-by-step explanation:

Answer:

A is right.  domain = {112, 120, 128, 136, 144}

Step-by-step explanation:

The range is the y-coordinate while the domain is the x-coordinate

y = x/4

x = 4y

domain = {4(28), 4(30), 4(32), 4(34), 4(36)}

= {112, 120, 128, 136, 144}

Step-by-step explanation:

2x × 3x +(-5×1)=6x-6=o

Answer:  A: x=-3, 5

Step-by-step explanation: Use the quadratic equation or solving system method to get x=-3,5 the other questions are similar!

Answer: x>1/6

Step-by-step explanation:

For this problem, you solve it as if it had an equal sign.

-2(8x-4)<2x+5                        [distribute -2]

-16x+8<2x+5                           [combine like terms by adding and subtracting on both sides]

3<18x                                      [divide both sides by 18]

x>1/6

Answer:

$959.69 per oz

Step-by-step explanation:

A gold alloy is produced from pure gold and alloy.

10 oz of pure gold costs $1,288 per ounce

55 oz of alloy costs $900 per ounce

The first step is to add the cost of both the pure gold and alloy together

= (10 oz × $1288)+(55 oz × $900)

= $12,880+$49,500

= $62,380

Therefore the cost per ounce can be calculated as follows

= $62,380/10 oz + 55 oz

= $62,380/65 oz

= $959.69 per oz.

Hence the cost per ounce of the gold alloy is $959.69 per ounce

Answer:

The FitnessGram Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly but gets faster each minute after you hear this signal bodeboop. A sing lap should be completed every time you hear this sound. ding Remember to run in a straight line and run as long as possible. The second time you fail to complete a lap before the sound, your test is over. The test will begin on the word start. On your mark. Get ready!… Start

Answer:

The answer is option B.

Hope this helps you

Answer:

trapezoids

Step-by-step explanation:

i know i can delete rectangles and square, but rhombuses and parallelogram don't really have in common so the answer is trapezoids.

is quite easy 4th grade math

hope this helped :)

Answer:

3x+4

Step-by-step explanation:

The perimeter is given by

P = 2 ( l+w)

We know the perimeter is  8x+8

8x+8 = 2 ( l+w)

Divide each side by 2

4x+4 = l+w

The width is x

4x+4 = l+x

Subtract x from each side

4x+4-x = l+x-x

3x+4 = l

The length is 3x+4

Answer:

Option (4)

Step-by-step explanation:

Given table in the picture is,

x              y              1st difference

0            -7                     -  

1             -2               -2 - (-7) = 5

2             3                3 - (-2) = 5

3             8                8 - (3) = 5

4             13               13 - 8 = 5

5             18               18 - 13 = 5

There is a common difference of 5 between every consecutive numbers.

Therefore, this table represents a linear function.

Option (4) will be the answer.

The type of function represented in the table is linear.

Given the table in the picture is,

x              y             1st difference

0            -7                     -  

1             -2               -2 - (-7) = 5

2             3                3 - (-2) = 5

3             8                8 - (3) = 5

4             13               13 - 8 = 5

5             18               18 - 13 = 5

There is a common difference of 5 between every consecutive number.

The term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.

Therefore, this table represents a linear function.

Option (4) will be the answer.

To learn more about the linear function visit:

https://brainly.com/question/4025726

#SPJ2

Answer:

4/6 or 66%

Step-by-step explanation:

Odd numbers from 1 to  6 are: 1, 3, 5

Numbers less than 4 are: 1, 2, 3

So there are  4/ 6 possible outcomes.

So the probability is 4/6 or 66%.

Answer:

It's the first one.

hope it helps :)

Step-by-step explanation:

Answer:

65°

Step-by-step explanation:

The missing angle is x°

tan x° = [tex]\frac{opposite }{adjacent}[/tex]

tan x° = [tex]\frac{850}{400\\}[/tex]

tan x° = 2.125

Using a calculator insert

tan^(-1)(2.125) ≈ 65°  (after rouding the the nearest unit)

Answer:

18.027

Step-by-step explanation:

7.264+3.873+6.89

18.027

Answer:

(1)55.5 feet

(2)7.5 feet

Step-by-step explanation:

Question 1

The diagram is attached below.

Using Trigonometric ratio

[tex]\tan 48^\circ = \dfrac{h}{50} \\h=50 \times \tan 48^\circ\\h=55.5$ feet (to the nearest tenth)[/tex]

The height of the house is 55.5 feet to the nearest tenth.

Question 2

In the diagram, we are required to find the distance the bird must fly to be directly above the fish. This has been represented by x.

Using Trigonometric ratio

[tex]\tan 15^\circ = \dfrac{2}{x} \\x \tan 15^\circ=2\\x=2 \div \tan 15^\circ\\x=7.5 $ feet (to the nearest tenth)[/tex]

The distance the bird must fly to be directly above the fish is 7.5 feet.

Answer:

Common ratio, r=-3

Recursive Formula

[tex]f(n)=-3f(n-1),$ $n\geq 2\\f(1)=-\dfrac{1}{9},[/tex]

Step-by-step explanation:

The formula for the geometric sequence: [tex]-\dfrac{1}{9} ,\dfrac{1}{3}, -1,3,-9,\cdots[/tex] is given as:

[tex]f(x)=-\dfrac{1}{9}(-3)^{x-1}[/tex]

Common Ratio

Dividing the next terms by the previous terms, we obtain:

[tex]\dfrac{1}{3} \div -\dfrac{1}{9} = \dfrac{1}{3} \times -9 =-3\\3 \div -1 =-3\\-9 \div 3 =-3[/tex]

Therefore, the common ratio of the sequence, r=-3

Recursive Formula

We observe that the next term, [tex]f(n)[/tex] is obtained by the multiplication of the previous term. f(n-1) by -3.

Therefore, a recursive formula for the sequence is:

[tex]f(n)=-3f(n-1),$ $n\geq 2\\f(1)=-\dfrac{1}{9},[/tex]

Answer:

It is in fact B. −3; f(x + 1) = −3(f(x))

Step-by-step explanation:

If you have this question on Edge, go with this.

Answer:

2

Step-by-step explanation:

sec∅ is equal to 1/cos∅ or (hypotenuse over adjacent).

With that in mind:

sec∅ = 2/1

sec∅ = 2

Answer:

B. 2

Step-by-step explanation:

We need to find the value of secant for this triangle.

Remember the trigonometric functions: secant = hypotenuse / adjacent, where the hypotenuse is the longest side (2 in this case), and the adjacent is the side right next to the labelled angle but is not the hypotenuse (1 in this case).

Plugging the values into the equation yields:

sec(θ) = hypotenuse / adjacent

sec(θ) = 2 / 1 = 2

The answer is thus B.

~ an aesthetics lover

Answer:

x+5

Step-by-step explanation:

so first you would divide by x (which means you would multiply x+2 by -x)

x^2 + 7x + 10

-x^2 - 2x

5x + 10

then you would divide by 5 (which means you would multiply x+2 by -5)

5x + 10

5x +10

0

So then to check it you would multiply x+5 by x+2

(x+5)(x+2)

x^2 + 2x + 5x + 10

then simplify to get

x^2 + 7x + 10

Answer:

(B) It has the same slope and a different y-intercept

Step-by-step explanation:

The table is presented below:

[tex]\left|\begin{array}{c|c}x&y\\----&---\\-\frac{2}{3} &-\frac{3}{4}\\\\-\frac{1}{6}&-\frac{9}{16}\\\\\frac{1}{3}&-\frac{3}{8}\\\\\frac{5}{6}&-\frac{3}{16}\end{array}\right|[/tex]

Gradient

[tex]m=\dfrac{-\frac{3}{8}-(-\frac{3}{4})}{\frac{1}{3}-(-\frac{2}{3})}\\=\dfrac{-\frac{3}{8}+\frac{3}{4}}{\frac{1}{3}+\frac{2}{3}}\\=\frac{3}{8}\div \frac{3}{3}\\m=\frac{3}{8}[/tex]

Next, we determine its y-intercept

Using the pair [tex](-\frac{2}{3},-\frac{3}{4})[/tex] in y=mx+b

[tex]-\frac{3}{4}=(\frac{3}{8})(-\frac{2}{3})+b\\-\frac{3}{4}+\frac{1}{4}=b\\b=-\frac{1}{2}[/tex]

Comparing with the linear function has an x-intercept of 12 and a slope of [tex]\frac{3}{8}[/tex], we find out that It has the same slope and a different y-intercept.

Option B is the correct option.

Answer:

B

It has the same slope and a different y-intercept

Step-by-step explanation:

please rate and ❤️❤️❤️

Answer:  A

Step-by-step explanation:

The standard form of a cosine equation is: y = A cos (Bx - C) + D  where

Plot the points (see graph below).

A = 28

[tex]\dfrac{1}{2}P=6\quad \rightarrow \quad P=12\\\\\\P=\dfrac{2\pi}{B}\qquad \rightarrow \qquad 12=\dfrac{2\pi}{B}\qquad \rightarrow \qquad \large\bold{B=\dfrac{\pi}{6}}[/tex]

Phase Shift = 7 = C/B

                      [tex]7=\dfrac{C}{\frac{\pi}{6}}\qquad \rightarrow \qquad \large\bold{C=\dfrac{7\pi}{6}}[/tex]

D = 49

Input the values of A, B, C, and D into the standard form of a cosine equation to get:

[tex]\large\boxed{y=28\cos \bigg(\dfrac{\pi}{6}x-\dfrac{7\pi}{6}\bigg)+49}[/tex]

Answer:

40

Step-by-step explanation:

The angles stay the same but, the position of the triangle changes.

Hope this helps,

kavitha

Answer: A’ = 40ᴼ

Step-by-step explanation:

The angles are congruent and add to equal 180ᴼ

A = 40ᴼ

The measure of A stays the same when the angles are rotated

Answer:

Number common to both sides=6

Step-by-step explanation:

Average of first four numbers=5

4*5=20

Average of the last four numbers=8

4*8=32

Average of all seven numbers=6 4/7

7*6 4/7

Find the number common to both sets of four numbers

Solution

4*5=20

4*8=32

32+20=52

7 * 6 4/7

=7*46/7

=46

Number common to both sides=52-46

=6

Answer:

(3, 4)

Step-by-step explanation:

Midpoint Formula: [tex](\frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]

Just plug in the coordinates as variables to find your answer:

(2 + 4)/2 = 3

(4 + 4)/2 = 4

Answer:

You have to multiply all the sides by 4.

B to C = 2.8*4

2.8 * 4 = 11.2

B to A = 3*4

3*4 = 12

A to C = 2.2*4

2.2*4 = 8.8

Hope this helped!

Answer:

1) 245 x 20 remander2/13 = 4940

2) square root of 58 - 29 + 38

= 8.19

Step-by-step explanation:

245 x 20 remander2/13= 245* 20 2/13

245 x 20 remander2/13= 245 * 262/13

245 x 20 remander2/13= (245*262)/13

245 x 20 remander2/13 =64190/13

245 x 20 remander2/13= 4937.69

245 x 20 remander2/13 = 4940

square root of 58 - 29 + 38

= √(58-29+38)

square root of 58 - 29 + 38

= √(96-29)

square root of 58 - 29 + 38

= √(67)

square root of 58 - 29 + 38

= 8.185

square root of 58 - 29 + 38

= 8.19

Answer:

a) x = 17/8

b) x = 23

c) x = -8/11.

Step-by-step explanation:

a)

-3x + 5 = 5x - 12

Add 3x to both sides:

5 = 8x - 12

Add 12 to both sides:

17 = 8x

Divide both sides by 8:

17/8 = 8x/8

x = 17/8.

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

b)

6(x-3)-4(x+2) = 20

Distribute:

6x - 18 - 4x - 8 = 20

Combine like terms:

2x - 26 = 20

Add 26 to both sides:

2x = 46

Divide both sides by 2:

x = 23.

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

c)

-2/5(x + 3) = 1/3(x - 2)

Distribute:

-2/5x - 6/5 = 1/3x - 2/3

Add 2/5x to both sides by creating a common denominator:

-6/15x - 6/5 = 5/15x - 2/3

-6/5 = 11/15x - 2/3

Add 2/3 to both sides. Create common denominator:

-18/15 = 11/15x - 10/15

-8/15 = 11/15x.

Divide both sides by 11/15:

[tex]\frac{-8}{15}* \frac{15}{11} = \frac{-8}{11} = x[/tex]

x = -8/11.