Ethan and Leo start riding their bikes at the opposite ends of a 65-mile bike path. After Ethan has ridden 1.5 hours and Leo has ridden 2 hours, they meet on the path. Ethan’s speed is 6 miles per hour faster than Leo’s speed. Find the speed of the two bikers

15√2

area = s² = 450 ← s is length of side

to find s take the square root of both sides

s = [tex]\sqrt{450}[/tex] = [tex]\sqrt{2(9)(25)}[/tex]

  = √2 × √9 × √25 = √2 × 3 × 5 = 15√2

15√2 represents a side length of a square that has an area of 450 square inches.

The answer is option A.

The area of any quadrilateral can be determined by multiplying the length of its base by its height.

area = s² = 450 ← s is length of side

to find s take the square root of both sides

s =  √450 = √2(9)(25)

= √2 × √9 × √25 = √2 × 3 × 5 = 15√2

Since we know the shape here is square, we know that all sides are of equal length. From this, we can work backward by taking the square root of the area to find the length of one side.

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Answer: Option C) Raj forgot the negative when substituting -15+9x for y.

Solution:

(1) 9x-y=15

(2) 2x+8y=28

Isolating y in the first equation. Subtracting 9x both sides of the equation:

(1) 9x-y-9x=15-9x

Subtracting:

(1) -y=15-9x

Multiplying both sides of the equation by -1:

(1) (-1)(-y)=(-1)(15-9x)

(1) y=-15+9x

Then Raj found the value of y. It's not option D.

Substitutng y by -15+9x in the second equation:

(2) 2x+8(-15+9x)=28

Then option C) is the answer: Raj forgot the negative when substituting -15+9x for y.

Eliminating the parentheses applying the distributive property in the multiplication:

(2) 2x-120+72x=28

Adding similar terms:

(2) 74x-120=28

Solving for x. Adding 120 both sides of the equation:

(2) 74x-120+120=28+120

Adding:

(2) 74x=148

Dividing both sides of the equation by 74:

(2) 74x/74=148/74

Dividing:

(2) x=2

Solving for y: Replacing x by 2 in the first equation:

(1) y=-15+9x

(1) y=-15+9(2)

Multiplying:

(1) y=-15+18

Subtracting:

(1) y=3  

10 1/2 golf balls to get it

Hello!

To find the equation of the line with a y-intercept of (0, -3) and a x-intercept of (-4.5, 0), we need to use the slope formula.

The slope formula is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

With that, we substitute the given ordered pairs into the formula, and solve.

[tex]\frac{0 - (-3)}{-4.5 - 0} = \frac{3}{-4.5} =\frac{3}{-\frac{9}{2} } = -\frac{2}{3}[/tex]

The slope of this line is -2/3 or -0.667 repeated (doesn't specify).

Therefore, the equation of the line is y = -2/3x - 3. (I also included the graph!) :-)

This is a cubic form. I am assuming this should be factored.

With cubics like this it's worthwhile trying to find one root by simply guessing. My guess that worked out is x=-2

To verify:

3(-2)^3+7(-2)^2+(-2)-2 = 0   -> so -2 is a root and we get the first factor: (x+2)

Next we divide the cubic by the factor (x+2). I let you do the division. Here is the result

(3x^3 +7x^2 +x -2):(x+2) = (3 x^2 + x - 1)

(3 x^2 + x - 1) is a quadratic form and you can use the quadratic formula to get the two other roots. I got  [tex]\frac{-1\pm \sqrt{13}}{6}[/tex].

So the entire cubic is now factored as follows:

[tex](x+2) \cdot (x+ \frac{-1+ \sqrt{13}}{6}) \cdot (x+ \frac{-1- \sqrt{13}}{6})[/tex]

the 2 equations given are vertical angles which mean they would equal the same.

Set the two equations to equal each other to solve for x:

6(x-2) = 3x+30

Simplify the left side:

6x-12 = 3x+30

Add 12 to eac side:

6x = 3x+42

Subtract 3x from each side"

3x = 42

Divide both sides by 3:

X = 42/3

X = 14

Now you know X, replace x with 14 in the equation for DHG:

DHG = 6(x-2)

6(14-2)

Simplify:

6(12)

Multiply:

72

Angle DHG is 72 degrees.

We can say that nearly all of the students got between a 54 and a 96, that 95% got between a 61 and an 89, and about two-thirds got between a 68 and an 82, but there may be other conclusions one may wish to draw.

Answer:

B. y = 2x + 29

Step-by-step explanation:

The given graph has a slope of 2 (a rise of 10 for a run of 5), so the last two chioices are not viable. Clearly a parallel line through the given point will have a positve y-intercept, so the first choice is not viable.

The appropriate choice is the second one:

... B. y = 2x + 29

Hence the line parallel to this is  y = 2x + 29.

Hence, option B is correct.

A straight group of points that stretch in opposing directions is what is known as a line. It is endless in both directions and lacks any ends. It is not thick. It only has one dimension.

In the given graph,

The line is passing through (0, 15) and (10, 35).

Therefore the slope of this lien is,

m  = (35-15)/(10-0)

    = 2

Now the parallel line to this line will have same slope.

Which passes through (3, 35),

Hence the line be ,

y - 35 = 2(x - 3)

y - 35 = 2x - 6

       y = 2x + 29

Hence the line is  y = 2x + 29.

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First to answer this take note of how much he spends and how much it cost,

456 is the total cost and it is 3 a gallon

To figure how many gallons he got divide 456 by 3

456/3=152

Alright, so let's make 2 3/5 into an improper fraction.

2 x 5 = 10 + 3 = 13

So 13/5 / 11/25.

Keep, change, flip rule: 13/5 x 25/11.

Now you multiple the numerator and denominator from both fractions. (I'm not going to do the math for you. Hope this helped and sorry if my explanation is...yeah.)

The division of 2 3/5 by 1 1/25 is equal to 2.5.

To perform the division, convert the mixed numbers to improper fractions. 2 3/5 becomes 13/5, and 1 1/25 is 26/25. Now divide the fractions: (13/5) ÷ (26/25) = 13/5 * 25/26 = 325/130 = 2.5.

54 nickels and 27 dimes

1 dime = 10 cents = $0.1

1 nickel = 5 cents = $0.05

setting up 2 equations

let n = amount of nickels and d = amount of dimes, then

n + d = 81 → (1)

0.05n + 0.1d = 5.4 → (2)

multiply (2 ) by 10

0.5n + d = 54 → (3)

subtract (3) from (1) to eliminate d

0.5n = 27 ( divide both sides by 0.5 )

n = [tex]\frac{27}{0.5}[/tex] = 54

substitute n = 54 in (1)

54 + d = 81 ( subtract 54 from both sides )

d = 27

Mary has 54 nickels and 27 dimes

Answer:

C. -1/2

Step-by-step explanation:

7π/6 radians is equivalent to (7π/6)(180°/π) = 210°, a 3rd-quadrant angle whose reference angle is 30°. The sine of angles in the 3rd quadrant is negative.

sin(30°) = 1/2

sin(210°) = -sin(30°) = -1/2

_____

In radians mode, your calculator can tell you this result directly.

C - [tex]\frac{1}{2}[/tex]

sin(7π / 6 )

note 7π\6 is in the third quadrant where sin is negative

the related acute angle to 7π/6 is 7π/6 - π = π/6

sin (7π/6) = - sin(π/6) = - [tex]\frac{1}{2}[/tex]

The odds in favor of picking a white marble from a bag with 4 green and 5 white marbles are 5 to 4.

This is calculated by comparing the number of white marbles to the number of green marbles.

To determine the odds in favor of picking a white marble from a bag containing 4 green marbles and 5 white marbles, we need to calculate the ratio of the number of successful outcomes (picking a white marble) to the number of unsuccessful outcomes (not picking a white marble).

In this case, the successful outcomes are the 5 white marbles, and the unsuccessful outcomes are the non-white marbles, i.e., the 4 green marbles.

The odds in favor are therefore 5 to 4, or simply, 5:4.

Here's how to calculate odds using a probability example:

So, the odds in favor of picking a white marble are 5 to 4.

x ≠ - 4, 3

the denominator of the fraction cannot equal zero as this would make the fraction undefined. Equating the denominator to zero and solving gives the values that x cannot be

solve x² + x - 12 = 0

(x + 4)(x - 3) = 0

equate each factor to zero abd solve for x

x + 4 = 0 ⇒ x = - 4

x - 3 = 0 ⇒ x = 3

restrictions on x are : x ≠ - 4, 3

the equation of a line in slope- intercept form is

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

y = 2x + 10 is in this form

To express in functional notation replace y by f(x), thus

f(x) = 2x + 10

f(x+h)-f(x) / h

f(x) = 2x^2-3x-4

Replace X with (x+h):

2(x+h)^2 - 3(x+h) -4

Simplify:

2x^2 + 4hx +2h^2 -3x -3h -4

Now you have:

(2x^2 + 4hx +2h^2 -3x -3h -4 - 2x^2-3x-4) / h

Simplify to get 4x +2h-3

The answer is C.

In this case we do not know for how long have they worked. But lets assume that they both will fix the car in an hour.

Case 1: Lets talk about Abe first.

Abe will charge $70.00 per hour plus a part which costs $130.00.

Now, the total cost to be paid to Abe to fix the car is [tex]70+130=200[/tex] dollars.

So we will have to pay $200.00 to Abe to fix the car.

Case 2: Lets talk about Gabe now,

Gabe can fix it for $80 an hour and finds the part just for $60.

Now, the total cost to be paid to Gabe to fix the car is [tex]80+40=120[/tex] dollars.

So we will have to pay $120.00 to Gabe.

Considering the two cases above we can ask Gabe to fix our car but there is another case.

Case 3: What if Abe finds a part for $60.00 rather $130.00

In that case, we will have to pay [tex]70+60=130[/tex] dollars in total to Abe.

Now, we need to pay $130.00 to Abe to fix the car.

Still we can see that we need to pay $10.00 less to Gabe so will ask Gabe to fix the car  (since [tex]130-120=10[/tex]).

(-x³ +3x +4) -(2x³ +7x² -9) = -x³ +3x +4 -2x³ -7x² +9 . . . . eliminate parentheses

= x³(-1-2) +x²(-7) +x(3) +(4+9)

= -3x³ -7x² +3x +13 . . . matches the second choice.

∠Y = 64°

since the triangles are similar

∠Y = ∠C

∠C = 180° - (73 + 43 )° = 64° = ∠Y

Yes. For example, the shape I will use is the circle.

No matter how you rotate the circle, it will always look the same. If you reflect the circle over any drawen line in which it passes through the middle, the two halves created would be congruent.

~Rise Above the Ordinary, Senpai

Answer:

a = 12 units

Step-by-step explanation:

Equation given is [tex]a^2 + 16^2 = 20^2[/tex]

First we have to evaluate the powers.

[tex]16^{2}[/tex] = [tex]16*16[/tex]=[tex]256[/tex]

[tex]20^{2}[/tex] = [tex]20*20[/tex]=[tex]400[/tex]

So we can now write the equation again as:

[tex]a^2 +256  =400[/tex]

Now we have to undo the addition,

[tex]a^2=400-256 [/tex]

[tex]a^2=144 [/tex]

Now we have to find the square root of [tex]a^2[/tex] to get the value of [tex]a[/tex]

[tex]\sqrt{a^{2}} = \sqrt{144}[/tex]

[tex]a=12[/tex]  or [tex]a=-12[/tex]

But the length of a leg cannot be a negative value, so we can take the +12.

a = 12 units

Answer:

a = 12 units

Step-by-step explanation:

Multiply each term in the parentheses by 10x.  (This is the Distributive Law).:-

10x*6x^2 +10x*7x + 10x*9

= 60x^3 + 70x^2 + 90x    

12600 x  to the power of 2 + 37887 x + 40829

your answer would be 9h

Answer:

  E.) △ABC with midpoints M and N.

Step-by-step explanation:

You want a related given statement to the scenario "in a triangle a segment joining the midpoints of two sides is one-half the length of the third side."

The scenario describes a triangle ABC with midpoints designated on two of the sides. There is no "plane R", angles 1 and 2, line l, point P. In triangle ABC, point B will not be between A and C.

These considerations eliminate choices A–D, leaving choice E:

  E.) △ABC with midpoints M and N

Note that both numbers are multiple of 3: you can simplify the ratio as follows

[tex] \dfrac{6}{603} = \dfrac{3\cdot 2}{3\cdot 201} = \dfrac{2}{201} [/tex]

The ratio can't be further simplified because 2 and 201 are coprime. So, the only thing you could do is write down the decimal expansion of the number.

For the record, its period is 33 digits long, and it is

[tex] 0.009950248756218905472636815920398 [/tex]

Answer:

0.00995025

Step-by-step explanation:

to determine the nature of the solutions use the discriminant

Given a quadratic equation in standard form : ax² + bx + c = 0

then the discriminant is b² - 4ac

• If b² - 4ac > 0 , then there are 2 real and distinct solutions

• If b² - 4ac = 0, there are 2 real and equal roots

• If b² - 4ac < 0 , there are no real solutions

for x² - 3x + 8 = 0 with a = 1, b= - 3 and c = 8

b² - 4ac = (- 3)² - (4 × 1 × 8 ) = 9 - 32 = - 23

Hence there are no real solutions to the equation

If you were to think of this diagram as a map of intersecting roads, corresponding angles are the ones on the same corner:

NW corner: ∠1 and ∠3

NE corner: ∠5 and ∠7

SE corner: ∠6 and ∠8

SW corner: ∠2 and ∠4

The choices in bold font above are the only pairs of corresponding angles that are in your answer list:

Answer:

∠1 and ∠3  , ∠6 and ∠8  , ∠5 and ∠7  are corresponding angles

Step-by-step explanation:

Corresponding Angles are angles which occupy same relative position at intersection when a line intersects two lines.

In pair of corresponding angles, one angle is interior angle and other one is exterior angle.

Option 1:

∠1 is exterior angle and ∠3  is interior angle. Also Both are at relatively same position.

Thus they are Corresponding angles.

Option 2:

∠6 is interior angle and ∠8  is exterior angle. Also Both are at relatively same position.

Thus they are Corresponding angles.

Option 3:

∠2 and ∠8  both are exterior angle.

Thus they are not Corresponding angles.

Option 4:

∠5 is interior angle and ∠7 is exterior angle. Also Both are at relatively same position.

Thus they are Corresponding angles.

Option 5:

∠2 and ∠7 both are exterior angles.

Thus they are not corresponding angles.

Option 6:

∠3 and ∠6 both are interior angles.

Thus they are not corresponding angles.

Answer:

1

Step-by-step explanation: