A vehicle is moving in a straight line. The velocity Vms^-1 at time t seconds after the vehicle starts is given by V = A (t− 0.05t^2) for 0 ≤ t ≤ 15. What is the value of A?

Answer:

The x-coordinate of the point of intersection is -2

Step-by-step explanation:

Here we have a typical system of linear equations whose solution will give us both the x- and the y- coordinates (i.e. the intersection point).

Let us solve the system and find which matches the available options, as follow. Given:

[tex]2x+y=1\\9x+3y=-3[/tex]

Taking the first expression and re arranging to solve for [tex]x[/tex] we have:

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

Plugging in it, in the second expression we then have

[tex]9(\frac{1-y}{2} )+3y=-3\\\\\frac{9}{2}-\frac{9y}{2}+3y=-3\\ \\\frac{9}{2}-\frac{9y}{2}+\frac{6y}{2}=-\frac{6}{2}\\ \\-\frac{9y}{2}+\frac{6y}{2}=-\frac{6}{2}-\frac{9}{2}\\-3y=-15\\y=\frac{-15}{-3}\\ y=5[/tex]

So finally plugging in the y value in Eqn.(1) we have

[tex]x=\frac{1-5}{2} \\x=\frac{-4}{2}\\ x=-2[/tex]

The x-coordinate of the point of intersection is -2

Answer:

457

Step-by-step explanation:

I add all the numbers I could see and got 457.... i need more information hope this helps

Answer:0.2

Step-by-step explanation: 1/10 and 1/10

Simply means this in maths

1/10+1/10

0.1+0.1= 0.2

Answer:

  25

Step-by-step explanation:

Area is the square of the side length, so

  s^2 = 25^2

Matching parts of this expression, we see ...

  s = 25

The length of each side is 25.

The solution of the system of equations is (-7 , 5)

Step-by-step explanation:

The steps of the linear combination method are:

∵ 2x + 3y = 1 ⇒ (1)

∵ y = -2x - 9

- Add 2x to both sides

∴ 2x + y = -9 ⇒ (2)

Multiply equation (2) by -1 to make the coefficients of x opposites

∴ -2x - y = 9 ⇒ (3)

Add equations (1) and (3) to eliminate x

∴ 2y = 10

Divide both sides by 2

∴ y = 5

Substitute the value of y in equation (1) or (2) to find x

∵ 2x + 5 = -9

- Subtract 5 from both sides

∴ 2x = -14

- Divide both sides by 2

∴ x = -7

The solution of the system of equations is (-7 , 5)

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Answer:

z = 65°

y= 105°

Step-by-step explanation:

angle z is adjacent to 115° on a straight line, hence they are supplementary angles, i.e they add up to 180°

hence,

z + 115° = 180°

z = 180° - 115° = 65°  

recall that the sum of angles inside a convex quadrilateral always adds up to 360°

i.e z + y  + 102° + 88° = 360°  (we know z from above)

65 + y +102+88=360

y = 360 -65-102-88 = 105°

The lateral area of the cylinder is approximately [tex]45.24 \, \text{cm}^2\)[/tex] and the volume is approximately [tex]\(45.24 \, \text{cm}^3\)[/tex].

To find the lateral area and volume of a cylinder, you can use the following formulas:

1. Lateral Area [tex](\(A_{\text{Lateral}})\)[/tex]:

[tex]\[ A_{\text{Lateral}} = 2 \pi r h \][/tex]

  where r  is the radius of the base and  h  is the height.

2. Volume (V):

 [tex]\[ V = \pi r^2 h \][/tex]

Given that the diameter (D) is 4 cm, the radius (r) is half of the diameter, so [tex]\( r = \frac{D}{2} = \frac{4}{2} = 2 \)[/tex] cm, and the height (h) is 3.6 cm.

Now, let's calculate:

1. Lateral Area:

 [tex]\[ A_{\text{Lateral}} = 2 \pi \times 2 \times 3.6 \][/tex]

2. Volume:

[tex]\[ V = \pi \times 2^2 \times 3.6 \][/tex]

Calculating these values:

1. Lateral Area:

[tex]\[ A_{\text{Lateral}} \approx 45.24 \, \text{cm}^2 \][/tex]

2. Volume:

[tex]\[ V \approx 45.24 \, \text{cm}^3 \][/tex]

So, the lateral area of the cylinder is approximately [tex]45.24 \, \text{cm}^2\)[/tex] and the volume is approximately [tex]\(45.24 \, \text{cm}^3\)[/tex].

Complete Question: Find the lateral area and volume of the cylinder whose diameter is 4 cm and height= 3.6cm.

Answer:

[tex]10 {x}^{2} + 4x[/tex]

Step-by-step explanation:

[tex] \frac{20 {x}^{2} + 8x }{2} = \frac{20x}{2} + \frac{8x}{2} = 10 {x }^{2} + 4x[/tex]

To find the length of the train and its speed, we can use the formula Length = Speed x Time. By setting up and solving equations, we can find that the length of the train is 200 meters and the speed of the train is 20 m/s.

To find the length of the train, we can use the formula:

Length = Speed x Time

Given that the train takes 10 seconds to pass you and 30 seconds to pass the bridge, we can calculate:

Length of train = Speed of train x Time taken to pass you = Speed x 10

Length of train + Length of bridge = Speed of train x Time taken to pass the bridge = Speed x 30

Substituting the values, we have:

Speed x 10 + 100 = Speed x 30

Simplifying the equation, we get:

Speed = 400/20 = 20 m/s

Substituting the value of speed back into the first equation, we have:

Length of train = 20 x 10 = 200 meters

Therefore, the length of the train is 200 meters and the speed of the train is 20 m/s.

Answer:

The difference in finishing time between the 2nd and 3rd places is the shortest and it is 0.07 seconds.

Step-by-step explanation:

The first positioned swimmer took 55.98 seconds and the second positioned swimmer took 56.87 seconds to complete the race.

So, the difference is (56.87 - 55.98) = 0.89 seconds.

The second positioned swimmer took 56.87 seconds and the third positioned swimmer took 56.94 seconds to complete the race.

So, the difference is (56.94 - 56.87) = 0.07 seconds.

The third positioned swimmer took 56.94 seconds and the fourth positioned swimmer took 57.17 seconds to complete the race.

So, the difference is (57.17 - 56.94) = 0.23 seconds.

The fourth positioned swimmer took 57.17 seconds and the fifth positioned swimmer took 57.27 seconds to complete the race.

So, the difference is (57.27 - 57.17) = 0.10 seconds.

The fifth positioned swimmer took 57.27 seconds and the sixth positioned swimmer took 57.35 seconds to complete the race.

So, the difference is (57.27 - 57.35) = 0.08 seconds.

Therefore, the difference in finishing time between the 2nd and 3rd places is the shortest and it is 0.07 seconds. (Answer)

Answer:

Between which two places is the difference in finishing times the shortest?

2 & 3

What is the difference in those times?

0.07

Step-by-step explanation:

i do

Answer:

Its true.A rectangle is never a rhombus.

Answer:

This is actually false according to most accepted definitions - a rectangle that has equal sides would be a square, and thus also a rhombus.

Step-by-step explanation:

The definition of a rhombus is that it has 4 equal sides.

Also, the definition of a rectangle is that it has two pairs or equal sides, and all angles are 90 degrees.

So a square is a special case of a rectangle. And a square is also a special case of a rhombus.

Meaning that a square is both a rhombus and a rectangle, so any rectangle with equal sides would also be a rhombus.

The simple interest rate was: 1.25%

Step-by-step explanation:

Simple interest is given by:

[tex]A = Prt\\Here\\A => Interest\\P=>Principal\ Amount\\r => Rate\\t => Time\ in\ years[/tex]

Given

Principal amount =$3000

Time = t = 2 years

Interest amount = A = $75

putting the values in the formula

[tex]75 = 3000 * r * 2\\75 = 6000r[/tex]

Dividing both sides by 6000

[tex]\frac{6000r}{6000} = \frac{75}{6000}\\r = 0.0125\\[/tex]

So,

The rate is:

0.0125 * 100 = 1.25%

Hence,

the simple interest rate was: 1.25%

Keywords: Simple interest, percentage

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Answer:30

Step-by-step explanation:

Answer:

I think the correct answer is

A- 40

B- 40

Answer:

Volume of metal piece  = 3680 mm³

Step-by-step explanation:

volume of horizontal cuboid:

V =  l * b * h

= 30 * 8 * 8 = 1920 mm³

Volume of vertical cuboid:

breadth = 10 mm

Length = 14+8 = 22 mm

Height = 8 mm

V = 22 * 10 * 8

=  1760 mm³

Volume of metal piece = 1920 + 1760

   = 3680 mm³

Answer:

3680  

i got  100 on test

150 grams of zinc is present

Solution:

Given that, ratio of zinc to copper is 3 to 13

A jar of the chemical contains 650 grams of copper

From given information,

zinc : copper = 3 : 13

Let the zinc present be 3x

Let the copper present be 13x

Given that, jar contains 650 grams of copper

13x = 650

x = 50

Substitute x = 50 in 3x

Zinc present = 3x = 3(50) = 150

Thus it contains 150 grams of zinc

Answer:

1.5

Step-by-step explanation:

Answer:

The person above is right.

Its: T = A^ 1.5

Step-by-step explanation:

Graph the planet data, shown right, using the regression calculator. When you are done, click “Resize window to fit data.”

Mercury and Venus are

✔ closer to

the sun than Earth is.

So, their orbital periods are

✔ shorter

than Earth's orbit.

The further a planet is from the sun, the

✔ longer

its orbit is.

A power regression equation for this data is:

T = A^

1.5

I took it and got it right.

The x intercept is [tex](\frac{18}{5} , 0)[/tex]

The y intercept is (0, -2)

Solution:

Given equation is:

-5x + 9y = -18

We have to find the y intercept and x intercept

The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.

The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero

To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'.

Substitute y = 0 in given equation

[tex]-5x + 9(0) = -18\\\\-5x = -18\\\\x = \frac{18}{5}[/tex]

[tex]\text{Thus the x - intercept is } (\frac{18}{5}, 0)[/tex]

To find the y-intercept, plug 0 in for 'x' and solve for 'y'

Substitute x = 0 in given equation

[tex]-5(0) + 9y = -18\\\\9y = -18\\\\y = -2[/tex]

Thus the y intercept is (0, -2)

Answer: r ~= 24.50986

Step-by-step explanation:

This question is done by simply looking at the circumference formula for a circle (2pi r)

154= 2*pi*r

154/(2*pi) = r

r ~= 24.50986

Answer:

Step-by-step explanation:

[tex]circumference=2\pi*r\\\\2\pi*r=154\\\\2*\frac{22}{7}*r=154\\\\r=\frac{154*7}{2*22}\\\\r=\frac{49}{2}=24.5 cm[/tex]

Answer:

The equations system has multiple solutions for x, y.

Step-by-step explanation:

Let's solve for x and y this equations system:

We can observe that the second equation is a simplification of the first (divided by 2) and therefore, the system has multiple solutions for x and this way:

x           y

-27/5    -5

-21/5    -4

-3         -3

-9/5      -2

-3/5      -1

3/5       0

9/5        1

3           2

21/5      3

27/5     4

33/5     5

Answer:

Up

Step-by-step explanation:

Shifting a graph a number of units up is a vertical translation. So, in a vertical translation, we shift the graph up by adding a constant at the end of the function.

In any function [tex]f(x)[/tex]. If we add the constant [tex]d[/tex] at the end of the function, then this will shift graph of the function [tex]d[/tex] units up.

Answer: 0.5

Step-by-step explanation:

Let the number be x , then

42% of x = 0.21

0.42x = 0.21

divide through by 0.42

x = 0.21/0.42

x = 0.5

Therefore : 42% of 0.5 = 0.21

Answer:

.5

Step-by-step explanation:

.42/1 * x = .21

x = .21/.42

x = .5 or 1/2

Answer:

Step-by-step explanation:

Total cost for trip = 290 + 50 + 95*5 =290+50+ 475 = $ 815

Savings = $143

Money needed = 815 - 143 = $ 672

No. of driveways = 672/48 = 14

14 driveways must she shovel to have enough money to pay for the trip.

Sneha needs to calculate the total cost of her vacation which is $815. After taking into account her savings, she requires an additional $672. As she earns $48 shoveling each driveway, she would need to shovel 15 driveways.

This is a question of basic algebra and problem solving. Sneha needs to calculate the total cost of her vacation first. She will spend $50 on transportation, $290 on food, and $95 per night for the hotel for 5 nights, or $475 ($95 x 5) for the hotel total.

Adding these amounts together, Sneha's vacation will cost $815 ($50 + $290 + $475). She currently has $143 in savings, meaning she needs $672 more dollars ($815 - $143).

As Sneha earns $48 for each driveway she shovels, we divide the total she needs by the earning for each driveway. That gives us 14 driveways. As Sneha can't shovel a fraction of a driveway, she will need to shovel 15 driveways in total.

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Answer:

1/2 is equivalent to 50%

Step-by-step explanation:

In order to convert a fraction to a percentage you divide the numerator (Top number of a fraction) by the denominator (Bottom number of a fraction), multiply by 100, and add a percentage sign.

So lets try that with our first answer option A) 1/2:

1 divided by 2 = 0.5

0.5 x 100 = 50

50%

So we know that 1/2 is equivalent to 50%

Answer: $1,624

Step-by-step explanation:

The amount after x-years is given as :

9[tex]x^{2}[/tex] + 50x + 1000

Since x represents number of years , this means that after 6 years , the amount will be :

9([tex]6^{2}[/tex] ) + 50(6) + 1000

⇒9(36) + 300 + 1000

⇒324 + 300 + 1000 =

Therefore, the amount after 6 years will be $1,624

Answer:

1.3

Step-by-step explanation:

Radius is half of a diameter so you just need to divide 3.6 by 2

Answer:

1.8

Step-by-step explanation:

The formula for diameter and radius is 2r = d, if we solve this equation we get 2r = 3.6 So, divide 3.6 by 2 and you got your answer!

Answer:

the eight pound bag is better because you would have to pay $10.76 if you buy two of the 4 pound bags so you are saving $3.36

Step-by-step explanation:

Answer:

the 8 pound buy

Step-by-step explanation:

Answer:

540

Step-by-step explanation:

4×4×15×6×6=540

Explanation:

hope it helps

The volume of the solid rectangular prism with a hole is 444 mm³.

The correct answer is option A.

To find the volume of the solid rectangular prism with a hole, we calculate the volume of the outer rectangular prism and subtract the volume of the inner rectangular prism.

Volume of the Outer Rectangular Prism:

The outer rectangular prism has dimensions 15 mm (length) × 6 mm (width) × 6 mm (height). The volume (V_outer) is given by:

Volume_outer = length × width × height = 15 × 6 × 6 = 540 mm³.

Volume of the Inner Rectangular Prism:

The inner rectangular prism has dimensions 4 mm (length) × 4 mm (width) × the height of the outer prism (6 mm). The volume (V_inner) is given by:

Volume_inner = length × width × height = 4 × 4 × 6 = 96 mm³.

Volume of the Solid Rectangular Prism with Hole:

Subtracting the volume of the inner prism from the volume of the outer prism gives the volume of the solid:

Volume_solid = V_outer - V_inner = 540 - 96 = 444 mm³.

Therefore, the correct volume of the solid rectangular prism with a hole is 444 mm³.

The question probable may be:

The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic millimeters.

A. 444

B.300

C.540

D.780

Answer:

(144.9;145.5) so from 144.9 to 145.5lbs

6.9 for X and -0.55 for X and 1 for Y

Step-by-step explanation:

The numerical Coefficient is said to be the fixed number that is in multiple with the variable. If the number is not with the variable then it is not taken into account.

STEP 1:

6.9 is the coefficient for X

STEP 2:

-0.55 is the coefficient for x

STEP 3:

1 is the coefficient for y

STEP 4:

343 a 2.65 not considered as the don't have the variables.

Answer:

The difference between a median and altitude of a triangle is given below :

Altitude is the perpendicular line drawn from a vertex of a triangle to its opposite side .But a median of a triangle is a segment connecting a vertex to the midpoint of its opposite side.

Step-by-step explanation:

The difference between a median and altitude of a triangle is given below :

Altitude is the perpendicular line drawn from a vertex of a triangle to its opposite side .But a median of a triangle is a segment connecting a vertex to the midpoint of its opposite side.