Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same point. Alan races around the track in 45 seconds before Brian does and overtakes him every 9 minutes. What are their rates, in meters per minute?

Answer:

1234567890

Step-by-step explanation:

1234567890-zxhjk

A. 0

The slope of a horizontal line is always 0.

Answer:

Step-by-step explanation:

Answer:

The average rate of change of [tex]f(x)=x^2 + 7x + 10[/tex] over the interval [tex]-20\leq x\leq -15[/tex] is -28.

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by this expression:

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

It is a measure of how much the function changed per unit, on average, over that interval.

To find the average rate of change of [tex]f(x)=x^2 + 7x + 10[/tex] over the interval [tex]-20\leq x\leq -15[/tex] you must:

Evaluate x = -15 and x = -20 into the function f(x)

[tex]f(-15)=(-15)^2 + 7(-15) + 10=130\\f(-20)=(-20)^2 + 7(-20) + 10=270[/tex]

Applying the expression for the average rate of change we get

[tex]\frac{f(-15)-f(-20)}{-15+20} \\\\\frac{130-270}{-15+20} \\\\\frac{-140}{5}\\\\-28[/tex]

Shouldn’t it be 180 because that half of a circle (360)

I think this should be it!

Answer:

4

Step-by-step explanation:

move up a units then take a line and move that down 4 units then down four more then back up 8 and you get your answer of

Answer:

1.12 B. sin(s) = cos(u)

1.13 C. showing similar triangles

Step-by-step explanation:

1.12 First of all, it is useful to identify the complementary angles. These are the two acute angles in the same right triangle: (s, u) or (t, v), or the adjacent angles that together make a right ange: (s, t) or (u, v).

Only choices B and D involve complementary angles. Only choice B shows the right relationship between trig functions of those angles.

___

1.13 It helps if you've seen the short, cute proof of the Pythagorean theorem using similar triangles. One of the early steps in the proof is to show the triangles are similar: choice C.

Even if you've never seen that proof, you can still make a good guess as to the correct choice. Choices A and D are just plain incorrect. Choice B might be the end result of the proof of the Pythagorean theorem, but won't be a step in that proof. In any event, the point of the proof is to show AC^2 + BC^2 = AB^2, not the equation of choice B.

That leaves choice C, which is both correct and likely to be a step in the proof.

Answer:

C

Step-by-step explanation:

The equation of a line is given by the formula  [tex]y-y_1=m(x-x_1)[/tex]

Where [tex]x_1[/tex] is the x-coordinate (it is given as 5)

[tex]y_1[/tex] is the y-coordinate (it is given as 1), and

m is the slope (it is given  as -3)

Plugging in all the info into the formula we have:

[tex]y-y_1=m(x-x_1)\\y-1=-3(x-5)[/tex]

From the answer choices, we see that C is the correct answer.

Answer:

c.y-1 = -3(x-5)

Step-by-step explanation:

We have given slope of a line and the point that is passing through the line.

slope  = -3 and (x₁,y₁) = (5,1)

We have to find the equation of line.

y-y₁ = m(x-x₁) is point-slope form of the equation of line where m is slope.

Putting given values in above formula, we have

y-(1) = -3(x-(5))

y-1 = -3(x-5) is the equation of the line through (5,1) with a slope of -3.

The simplified form of the expression is [tex]7c^2d - 7c + 4d - 10[/tex].

To simplify the expression, we first combine like terms:

[tex]5c^2d - 4c + 3d - 3 + 2c^2d - 3c + d - 7[/tex]

Grouping similar terms:

[tex](5c^2d + 2c^2d) + (-4c - 3c) + (3d + d) + (-3 - 7)[/tex]

Simplifying each group:

[tex]7c^2d - 7c + 4d - 10[/tex]

Thus, the simplified form of the expression is [tex]7c^2d - 7c + 4d - 10[/tex]. This result arises from combining the coefficients of like terms. The coefficients of [tex]c^2d[/tex] add up to 7, those of c add up to -7, those of d add up to 4, and the constants add up to -10.

Complete Question:
What is the simplified form of the expression?

[tex]$$5 c^2 d-4 c+3 d-3+2 c^2 d-3 c+d-7$$[/tex]

[tex]a. 3 c^2 d-7 c+2 d-10\\\\b. 3 c^2 d-7 c+4 d-10\\\\c. 7 c^2 d-7 c+2 d-10\\\\d. 7 c^2 d-7 c+4 d-10[/tex]

Answer:

8 inches

Step-by-step explanation:

You want to find the width (w) in inches such that ...

V = LWH

2720 = (2w+4)·w·17 . . . . . . . . . . fill in the given values

80 = (w+2)(w) = w^2 + 2w . . . . . divide by 34

81 = (w +1)^2 . . . . . . . . . . . . . . . . complete the square

9 = w+1 . . . . . . square root (we only care about the positive solution)

8 = w . . . . . . . . subtract 1

The width of the box is 8 inches.

Answer:

8 inches

Step-by-step explanation:

The right choice is (C) A translation that leaves the origin fixed while changing the shape of the curve

A transformation in which the center of rotation is fixed and everything else on the plane rotates about that point by a given angle is called rotation. A rotation is described by the centre of rotation, the angle of rotation, and the direction of the turn. The centre of rotation is the point that a shape rotates around. Each point in the shape must stay an equal distance from the centre of rotation.

Answer: a translation that leaves the origin fixed while not losing the shapes of the curves

Step-by-step explanation:

If the square of a certain quantity must be 16, that quantity must be either 4 or -4.

In fact, in both cases we have [tex]4^2=(-4)^2=16[/tex]

So, we have two possible solutions:

[tex]x+1=4 \iff x=3[/tex]

[tex]x+1=-4 \iff x=-5[/tex]

Answer:

A. x= 3 or -5

Step-by-step explanation:

The solution is x = 3 or -5. The steps for solving the equation are shown.

(x + 1)2 = 16

(x + 1)2

= ±

16

x + 1 = ± 4

x + 1 = 4 or x + 1 = -4

x = 3 or -5

Answer:

9%

Step-by-step explanation:

✯Hello✯

↪  We can formulate an equation to help us solve this

↪  800(x%) = 728 in this case x=91

↪  We do 100-91 meaning that this is a 9% decrease on price

↪  To check that this is correct we can work out 9% of 800 which is 72

When subtracting 72 from 800 it is confirmed that 728 is the right amount

❤Gianna❤

Final answer:

To find the percent of decrease in the TV's price, calculate the difference between the original and the new price, divide by the original price, and multiply by 100, which results in a 9% decrease.

Explanation:

To calculate the percent of decrease when the price of a TV is reduced from $800 to $728, you subtract the new price from the original price and then divide by the original price. Next, you multiply the result by 100 to get the percentage.

Step-by-step calculation:

Find the difference in price: $800 - $728 = $72.

Divide the difference by the original price: $72 ÷ $800 = 0.09.

Multiply by 100 to get the percentage: 0.09 x 100 = 9%.

So, the percent of decrease in the price of the TV is 9%.

Answer:

  196 mm³

Step-by-step explanation:

The ratio of volumes the the cube of the ratio of linear dimensions. Hence the volume of the red solid is ...

   (7/21)³×(5292 mm³) = 196 mm³

Answer:

The graph of the line in the attached figure

Step-by-step explanation:

we have

[tex]y+7=\frac{2}{3}(x+6)[/tex]

This is the equation of a line into point slope form

The slope is [tex]m=\frac{2}{3}[/tex]

The line pass through the point (-6,-7)

To graph the line find the y-intercept

Remember that

The y-intercept of the line is the value of y when the value of x is equal to zero

so

For x=0

[tex]y+7=\frac{2}{3}(0+6)[/tex]

[tex]y+7=\frac{2}{3}(6)[/tex]

[tex]y+7=4[/tex]

[tex]y=4-7=-3[/tex]

The y-intercept is the point (0,-3)

with the point (-6,-7) and (0,-3) plot the line

see the attached figure

Answer:

Step-by-step explanation:

H(x)=0

-2x^2 +4x+16=0

X^2 - 2x - 8 = 0

(X + 2) (x-4) = 0

X + 2 = 0 or x -4 = 0

X= -2 or x=4

Since -2 doesn’t make sense use 4

The ball will hit ground in 4 seconds

Answer:

4 seconds

Step-by-step explanation:

Given : The ball's height (in meters above the ground), x seconds after Antoine threw it, is modeled by: [tex]h(x)=-2x^2+4x+16.[/tex]

To Find: How many seconds after being thrown will the ball hit the ground?

Solution:

We are supposed to find after how much time the ball hits the ground.

So, we are required to substitute h = 0 because when ball hits the ground the height will be 0

So, [tex]0=-2x^2+4x+16[/tex]

[tex]2x^2-4x-16=0[/tex]

[tex]x^2-2x-8=0[/tex]

[tex]x^2-4x+2x-8=0[/tex]

[tex]x(x-4)+2(x-4)=0[/tex]

[tex](x-4)(x+2)=0[/tex]

[tex]x=4,-2[/tex]

Since time cannot be negative .So, neglect -2

Hence A ball will take 4 seconds to hit the ground after being thrown.

Answer:

it is d

Step-by-step explanation:

Answer:

  b.  secants

Step-by-step explanation:

A line that intersects a circle in two places is called a "secant."

___

It is a tangent line if it intersects the circle in one point.

It is a diameter if it is a chord that goes through the center of the circle.

It is a chord if it is a line segment with each endpoint being on the circle. (BE and CD are chords.)

"Cosecant" is the name of the trigonometric function that is the ratio of the hypotenuse of a right triangle to the side opposite the angle of interest.

Answer:

 =705.79

Step-by-step explanation:

F=P(1+i)n  where F is the Future amount P is the Present amount/Capital i is the interest rate n is the number of periods.

In this case you have the given as follows:

    P = $500 i = 9% n = 4 years

Substituting the values to the formula you'll have:

F=500(1+0.09)^4

 =705.79

Answer:

Step-by-step explanation:

To determine the side lengths of a right triangle, use the converse of the Pythagorean Theorem, where c is the longest side, as shown below.

If c2 < a2 + b2, the triangle is acute.

If c2 = a2 + b2, the triangle is right.

If c2 > a2 + b2, the triangle is obtuse.

Check each answer choice, according to the rules above.

This is an acute triangle.

This is an obtuse triangle.

This is an obtuse triangle.

This is a right triangle.

Therefore, 54 in, 72 in, and 90 in are the side lengths of a right triangle.

Correct option is (D) 54 in, 72 in, 90 in

Using the converse of the Pythagorean Theorem, we can determine whether the given sides form a right angled triangle or not

Thus if   '[tex]c^2 < a^2 + b^2[/tex]' then the triangle is acute angled triangle

Similarly if ' [tex]c^2 = a^2 + b^2[/tex] ' then the triangle is right angled triangle  

Similarly if ' [tex]c^2 > a^2 + b^2[/tex] ' then the triangle is obtuse angled triangle

Thus we would be checking for each options

Option(A) :

Given that the sides are 54 in, 72 in, 108 in

[tex]108^{2} =11664[/tex]

[tex]54^2+72^2=2916+5184\\54^2+72^2=8100[/tex]

Thus it can be seen that

[tex]108^2 > 54^2 + 72^2[/tex]

We can say that the given sides form an acute angled triangle

Option(B) :

Given that the sides are 54 in, 81 in, 90 in

[tex]90^{2} =8100[/tex]

[tex]54^2+81^2=2916+6561\\54^2+81^2=9,477[/tex]

Thus it can be seen that,

[tex]90^2 > 54^2 + 81^2[/tex]

We can say that the given sides form an obtuse angled triangle

Option(C) :

Given that the sides are 45 in, 72 in, 90 in

[tex]90^{2} =8100\\45^2+72^2=2025+5184\\45^2+72^2=7209[/tex]

Thus it can be seen that,

[tex]90^2 > 45^2 + 72^2[/tex]

We can say that the given sides form an obtuse angled triangle

Option(D) :

Given that the sides are 54 in, 72 in, 90 in

[tex]90^{2} =8100\\54^2+72^2=2916+5184\\54^2+72^2=8100[/tex]

Thus it can be seen that,

[tex]90^2 =54^2 + 72^2[/tex]

We can say that the given sides form an right angled triangle

Thus, 54 in, 72 in, and 90 in are the side lengths of a right triangle.

Answer:

3/40 = 7.5%

Step-by-step explanation:

3/40 percent error.

3/40 = 7.5%

Answer:

  84.5%

Step-by-step explanation:

The area of the smaller square is ...

  smaller square = (5.98 cm)^2 = 35.7604 cm^2

The area of the larger square is ...

  larger square = (15.2 cm)^2 = 231.04 cm^2

So, the shaded area is ...

  larger square - smaller square = (231.04 -35.7604) cm^2 = 195.2796 cm^2

Then a randomly chosen point will be in the shaded region this fraction of the time:

  (shaded area)/(larger square area) = 195.2796/231.04 ≈ 0.84522 ≈ 84.5%

Answer:

The correct answer is A) x does not equal 8

Step-by-step explanation:

In order to find gaps in the domain, we look for two things. The first we look for is negatives under square roots (which are not an issue here since there are none) and then we look for 0, denominators. So to find the gap, we set the denominator equal to 0 and see what the x value cannot be.

x - 8 = 0

x = 8

Answer:

The measure of the arc PJ is [tex]75\°[/tex]

Step-by-step explanation:

step 1

Find the measure of angle L

we know that

In a inscribed quadrilateral opposite angles are supplementary

so

[tex]m<L+m<J=180\°[/tex]

we have

[tex]m<J=110\°[/tex]

substitute

[tex]m<L+110\°=180\°[/tex]

[tex]m<L=70\°[/tex]

step 2

Find the measure of arc KJ

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m<P=\frac{1}{2}(arc\ LK+arc\ KJ)[/tex]

substitute the values

[tex]95\°=\frac{1}{2}(125\°+arc\ KJ)[/tex]

[tex]190\°=(125\°+arc\ KJ)[/tex]

[tex]arc\ KJ=190\°-125\°=65\°[/tex]

step 3

Find the measure of arc PJ

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m<L=\frac{1}{2}(arc\ PJ+arc\ KJ)[/tex]

substitute the values

[tex]70\°=\frac{1}{2}(65\°+arc\ PJ)[/tex]

[tex]140\°=(65\°+arc\ PJ)[/tex]

[tex]arc\ PJ=140\°-65\°=75\°[/tex]

Answer:

20

Step-by-step explanation:

The number of combinations of 6 points taken 3 at a time is ...

6!/(3!·(6-3)!) = 6·5·4/(3·2·1) = 5·4 = 20

___

If you number the points 1–6, the points of the 20 triangles will be ...

123 124 125 126 134

135 136 145 146 156

234 235 236 245 246

256 345 346 356 456

Answer:

4

Step-by-step explanation:

The distance from B to C is the same as the distance from A to D. Points B and C will both have the same x-value, as do points A and D. Points B and C will have the same difference in y-values (2 -(-2) = 4) that points A and D have.

The distance from B to C is 4 units.

Answer:

  area of the triangle is about 15,183.766

Step-by-step explanation:

The sum of the two shortest sides is 367, which is greater than the longest side, hence these side lengths can form a triangle.*

The perimeter is ...

  p = 240 +127 +281 = 648

so the semi-perimeter is ...

  s = p/2 = 648/2 = 324

Heron's formula tells you the area is ...

  A = √(s(s -a)(s -b)(s -c)) = √(324·84·197·43) = √230,546,736

  A ≈ 15,183.766

The area of the triangle is about 15,183.766 square units.

_____

* The terms s-a, s-b, and s-c are all positive, which is further evidence the side lengths will form a triangle. If one or more of those factors is negative, the side lengths will not form a triangle.

Answer:

(k·j)(x) = -12x^2 -x +6

Step-by-step explanation:

(k·j)(x) = k(x)·j(x) = (4x+3)(-3x+2) . . . . . substitute function definitions

  = 4·(-3)x^2 +(4·2+3(-3))x +3·2 . . . . . multiply using the distributive property

  = -12x^2 -x +6

Answer:

  B.  4

Step-by-step explanation:

When you perform the multiplication, you get ...

  (x +c)(x +4) = x² + (c+4)x +4c = x² + 8x +4c

Then ...

  c + 4 = 8 . . . . coefficients of x must match

  c = 4 . . . . . matches choice B

Answer:

(B)

Step-by-step explanation:

Option (B) is in correct order when talking about the specific ones.

Polygon is the least specific as it can be of many sides.

example: A polygon with 3 sides is a triangle. and the polygon with 4 sides is a quadrilateral.

Hence, quadrilateral is on the second number in least specific group.

Quadrilaterals with 2 sides parallel and equal are known as parallelogram.

Therefore, they are on the 3rd number in specific group.

Parallelograms with opposite sides parallel and equal and all the vertex angles at right angles are known as rectangles.

Therefore, rectangles are the most specific one in the group. The list is given by (option (B):

1) polygons

2) quadrilaterals

3) parallelograms

4) rectangles.

mark brainliest  :)

Answer:

The answer is B!!!!

Step-by-step explanation:

I not that good at explain but i'll try to explain :).Ummmmmmm....I took the same test so thats how I know

Expand the left hand side:

[tex]17f+34+45.99<200[/tex]

Simplify the left hand side:

[tex]17f+79.99<200[/tex]

Subtract 79.99 from both side:

[tex]17f<120.01[/tex]

Divide both sides by 17:

[tex]f<\dfrac{120.01}{17} \approx 7.06[/tex]

So, he must invite less than 7 friend to the party.

Final answer:

To solve the inequality, distribute 17 to f and 2, combine like terms, subtract 79.99 from both sides, and divide both sides by 17. The maximum number of friends that can attend the birthday party is 7.

Explanation:

To solve the inequality 17(f+2) + 45.99 < 200, we first distribute 17 to f and 2: 17f + 34 + 45.99 < 200. Combine like terms: 17f + 79.99 < 200. Next, subtract 79.99 from both sides of the inequality: 17f < 120.01. Finally, divide both sides of the inequality by 17: f < 7.06. So the maximum number of friends that can attend the birthday party is 7.