In baseball, the lengths of the paths between consecutive bases are 90 feet, and the paths form right angles. The player on first base tries to steal second base. How far does the ball need to travel from home plate to second base to get the player out? round your answer to the nearest tenth.

I gotchu :)

So, the base equation is: ax+by=c

x int is c/a

y int is c/b

and the slope is -a/b

So basically, what I wrote above is how to get each aspect of the line using the standard form formula.

The "nonzero" part means that each integer (the A, B, AND C in the formula above) cannot be 0, as that would mean that everything will end up equaling to 0, which does not create the line. So basically, the answer would be:

x int is c/a

y int is c/b

and the slope is -a/b

^ if you apply these to any standard form, you will get the thing I stated next to it. For example, if the standard form equation is:

5x+6y=5

if you want to find the slope, you will do -a/b, and that will give you -5/6, which is your slope

Hope this helps :)

Answer:

3w - 2j

Step-by-step explanation:

twice the length j less of three times the width

Answer:

95%

Step-by-step explanation:

The measure of ∠C using sine rule formula and as shown in the triangle is 39.8°.

The sine rule formula gives the ratio of the sides and angles of a triangle. The sine rule can be explained using the expression, a/sinA = b/sinB = c/sinC,

From the diagram, to calculate the measure of the ∠C, we use the sine rule formula.

From the diagram,

Given:

Substitute these values into equation 1 and solve for angle C

Hence, ∠C is 39.8°.

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Answer:  a)  y - 4 = 2/3(x) - 2

b)  y - 4 = -3/2(x) -2

Step-by-step explanation:

equation of original line:  y = 2/3x -5

point on a line parallel to original line:  (3,4)

The slope of a line parallel to a given line has the same slope, so the equation of the parallel line (in point-slope form) is:

(y - y1) = 2/3(x - x1)

point (x1, y1) is (3, 4)

plug (3,4) into the equation:

y - 4 = 2/3(x - 3)

y - 4 = 2/3(x) - 2

rewrite in slope-intercept form:  y = 2/3(x) + 2

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the first line:  - 1/m

Therefore, the slope of the perpendicular line = -3/2

Equation for the perpendicular line is:

y - 4 = -3/2(x) -2

A different combination of models and colors available is 18.

Combination:

the act of combining or the state of being combined. a number of things combined: a combination of ideas. something formed by combining: A chord is a combination of notes. an alliance of persons or parties: a combination in restraint of trade.

Here it is given 6 different colors. Harley Davidson offers 3 different motorcycle models.

We have to find the number of different combinations of models and colors available.

Based on the above-given data we get the:

Different combination = 3 × 6

= 18

Therefore the number of combinations is 18.

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The required slope of the given line is 1 which is shown in the graph.

The slope of the line is represented as the rise of the line.

Slope m = (y₂ - y₁)/(x₂ -x₁  )

Grab two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

We take the two points (4, 10) and (9, 22)

Let

x₁ = 0, y₁ = 1

x₂ = 8, y₂ = 9

∵ Slope m = (y₂ - y₁)/(x₂ -x₁  )

Substitute values in the formula

m = (9 - 1) / (8 - 0)

m = (8)/(8)

m = 1

Thus, the required slope of the given line is 1 which is shown in the graph.

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The measure of the obtuse angle is 128 degrees

From the question, we have the following statement that can be used in our computation:

Acute angle = 52  degrees

The measure of the obtuse angle is calculated as

Obtuse angle = 180 - Acute angle

Substitute the known values in the above equation So, we have the following equation

Obtuse angle = 180 - 52

Evaluate

Obtuse angle = 128

Hence, the angle is 128 degrees

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Answer: D. 16/25

Step-by-step explanation:

Abe jogs 1. 8 miles on Monday, 1. 3 miles on Tuesday, and 1. 2 miles on Wednesday.

Beth will jog 8.6 miles, if she jogs twice as far as Abe.

The answer provided below has been developed in a clear step by step manner.

Step: 1

Given that,

Abe jogs 1.8 miles on Monday, 1.3 miles on Tuesday and 1.2 miles on Wednesday.

So,

Total miles jog by Abe =1.8+1.3+1.2

Step: 2

Adding, we get,

Total miles jog by Abe = 4.3 miles

To find :-

The number of miles Beth jogged.

Step: 3

Since Beth jogs twice as far as Abe, we have,

Number of miles Beth jog = 2×4.3 miles = 8.6 miles

Since Abe jog 4.3 miles in total, Beth will jog (2* 4.3) miles

Hence the answer is, Beth will jog 8.6 miles, if she jogs twice as far as Abe.

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Answer:

y - y = m(x - x)

y + 6 = 2(x + 1)

y + 6 = 2x + 2

y = 2x -4

Answer:

Rule SAS; side angle side

Step-by-step explanation:

Since they give that DM and CM are equal, and BM and AM are equal, you already have two sides. And since you have already marked vertical angles (correct because of intersection), you have 2 sides and 1 angle that are equal. This is enough to prove they are equal so it is the rule SAS or side, angle, side.

The balance of the account after 1 year and after 2 years  16400 and 16820 is respectively.

A bank account starts with a balance, P = $8000

rate of interest = 5%

compound interest for 1 year is :

[tex]CI = P(1 + R/100)^n[/tex]

CI = 8000(1 + 5/100)

CI = 8000(1 + 1/20)

CI = 8000(21/20) = 8400

A = CI + P = 8000 + 8400 = 16400

compound interest for 1 year is :

[tex]CI = P(1 + R/100)^{2n}[/tex]

CI = 8000(1 + 5/100)^2

CI = 8000(1 + 1/20)^2

CI = 8000(21/20)^2 = 8820

A = CI + P = 8000 + 8820 = 16820

The balance of the account after 1 year and after 2 years  16400 and 16820 is respectively.

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Answer:

c = 121

Step-by-step explanation:

Take half of the middle term coefficient: -22/2 = -11

Now square it: (-11)² = 121

c = 121

Answer: 40%

Step-by-step explanation:

100(175-125/125)

Simplify: 100(50/125)

Simplify: 100(0.4)=40

The total number of residents that voted in the town election is 5275 votes

Total number of votes received = 2300 votes

Consider the total number of votes in the town election = x

She received 190 more than 2/5 of the total number of votes

2/5 of the total number of votes = (2/5)x

190 more than 2/5 of the total number of votes = (2/5)x + 190

The equation will be

(2/5)x + 190 = 2300

Move 190 to the right hand side of the equation

(2/5)x = 2300 - 190

(2/5)x = 2110

0.4x = 2110

x = 2110 / 0.4

x = 5275 votes

Hence, the total number of residents that voted in the town election is 5275 votes

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Equation with option B and C has no solution.

What is equation?

When two expressions are connected with the equals sign, a formula known as an equation is created.

Main Body:

A) -3(x+5) = x-15 -2x

⇒ -3x -15 = x-15-2x

⇒ -3x = -x

⇒ -2x= 0

⇒ x = 0, this means it has a solution.

B) -3(x+5) = x- 15 -4x

⇒ -3x -15 = -3x -15

So this equation also has no solution.

as L.H.S cancels out R.H.S completely so this equation has no solution.

C) -3(x+5) = x-10 -4x

⇒ -3x -15 = -3x -10

⇒ -15 ≠ 10

hence the equation with no solution is option b and c.

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The function f(x)=x³-e⁻⁷ˣ is continuous function. That is a continuous function is one whose graph is continuous throughout without any pauses or leaps.

Given that,

The function is f(x)=x³-e⁻⁷ˣ

We have to find the function f(t) is it continuation on 0≤t<8.

We know that,

Take the function f(x)=x³-e⁻⁷ˣ

As the name implies, a continuous function is one whose graph is continuous throughout without any pauses or leaps. To put it another way, we say that a function is continuous if we can draw the curve (graph) of the function without ever picking up the pencil.

Therefore, The function f(x)=x³-e⁻⁷ˣ is continuous function. That is a continuous function is one whose graph is continuous throughout without any pauses or leaps.

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The area of a triangle is 8.

What is the area of a triangle?

Area of a triangle = [s(s - a)(s - b)(s - c)], where s is the triangle's semi-perimeter and a, b, and c are the lengths of the triangle's three sides.

We know that the area of the triangle whose vertices are (x1 ,y1),(x2 ,y2), and (x3, y3) is:

1/2 |x1(y2−y3)+x2(y3−y1)+x3 (y1−y2)|

Area of triangle = 1/2 |-3(5 − 1)+ (-6)(1−1) + 1(1 − 5)|

Area of triangle = 1/2 |-12 + (-4)|

Area of triangle = 8

Hence, the area of a triangle is 8.

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The 12 terms of the series will be -

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

The formula to calculate the nth term of an Arithmetic Sequence is -

a(n) = a + (n - 1)d

a - first term of A.P.

d - Common difference of A.P.

n - position of term

We have -

a[1] = 3

a[12] = 25

Then, using the formula to calculate the nth term, we get -

a(n) = a + (n - 1)d

a[1] = 3

AND

a(12) = 3 + 11 x d

25 = 3 + 11d

22 = 11d

d = 2

So, the terms of the series will be -

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

Hence, the 12 terms of the series will be -

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

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Answer:

3/10

Step-by-step explanation:

4/5 - ½

The l.c.m of the Denominator is 10

=8-5/10

=3/10

The total number of small boxes is 2.1 and the large boxes is 6.3.

Given;

To build a house, a contractor has to purchase nails. Both small and large boxes of nails are provided. There are 150 nails in each small box and 400 in each large box. The contractor purchased 3 more tiny boxes than large boxes. Totaling 2850 nails.

To calculate the proportion of small and large boxes that were bought,

Let's assume the small boxes as 's' and the big boxes as '3s'.

∴ s(150) + 3s(400) = 2850

  150s + 1200s = 2850

  1350s = 2850

  s = 2850/1350

  s = 2.1

∴ 3s = 2.1 * 3

      = 6.3

Hence, the total number of small boxes is 2.1 and the number of large boxes is 6.3.

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Answer:

The number of small boxes purchased are 3 and the number of large boxes purchased are 6.

Step-by-step explanation:

Let the small boxes bought be x

Therefore the large boxes will be 2x

Total nails bought = 2850

Nails in x small boxes = 150x

Nails in 2x large boxes = 400. 2x = 800x

2850 = 150x + 800x

2850 = 950x

x= 2850/950 =  3

2x = 2x3= 6

[tex]\fbox{3x}[/tex]

Simplify:

[tex]x+y+2x+-y[/tex]

Combine Like Terms:

[tex](x+2x)+(y+-y)[/tex]

[tex]=3x[/tex]

Answer:

3:1

Step-by-step explanation:

bc the lcm is 3

Answer:

the ratio is 3/1

Natasha has left with 4.5 inches of oak boards.

What is a simplification?

The act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining trade processes.

Here, we have

120 inches of oak boards

50.75 inches for shelves, 36 1/4 more inches of oak boards, and she didn’t use 401/2 inches for the top and 60.5 inches for the sides.

We have to find how many inches of oak boards Natasha has left.

We use here simplification, we get

= 120 + 36 1/4 - 50.75 - 40 1/2 - 60.5

= 4.5 inches

Hence, Natasha has left with 4.5 inches of oak boards.

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A(3) = 185mg

Formula for exponential growth/decay is

A(t) = A0 * e^(xt)

Where A0 is your initial amount

x is your percentage

t is the time

A(3) = 250 * e^(-0.1*3)

A(3) = 185.2mg

Key point x is negative in this case as it's a decaying function. If it was growth it would be positive

Any number apart from 3 can be used to replace the ? to create a function.

In a function, the inputs do not repeat that is the input in all cases should be unique in nature.

The inputs are assigned to exactly one output for each.

Three is one of the options to create a non function as three is already an input in the given function.

Replacing the ? with 3 would create the a function would be to replace it with any number but 3.

(3,5) (2, 4) (9, 0) (3,6)

Any number apart from 3 can be used to replace the ? to create a function.

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The width of the tent is twice the width of one side which is 10.5 feet.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, Brothers Bob and Tom Katz buy a tent that has a center pole 6.25 feet high and the sides of the tent make a 50° angle with the ground.

Here the opposite is the height with the reference angle of 50° and we have to determine the adjacent which is the width of the tent.

∴ tan50° = Height of the pole/width.

1.19 = 6.25/width.

width = 6.25/1.19.

width = 5.25 feet.

But the total width of the tent will be twice as we have obtained only one side width.

∴ Total width is (2×5.25) = 10.5 feet.

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