The distance from home plate to first base is 90 feet. The distance from first base to second base is 90 feet. If the angle formed by the path from home te
first and first to second is 90°, what is the distance from home plate to second base?

Answer:

Step-by-step explanation:

Given:

To Find:

Solution:

Let's assume :

We know that,

[tex]\: \: \dashrightarrow\sf \: \: \: Length \times Width = Area_{(Rectangle)} \\ \\ [/tex]

On Substituting the required values, we get:

[tex] \\ \: \: \dashrightarrow\sf \: \: \:(2x+ 4)(x) = 126 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2 {x}^{2} + 4x = 126 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2 {x}^{2} + 4x - 126 =0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2( {x}^{2} + 2x - 63) = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: {x}^{2} + 2x - 63 = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: {x}^{2} - 7x + 9x - 63 = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:x(x - 7) + 9(x - 7) \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:(x - 7)(x + 9) = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: \purple {x = 7 \: or \: - 9} \\ \\ [/tex]

Length of the side of the rectangle can't be negative. So, x = 7

Hence,

Answer:

       length = 18 m

       width  = 7 m

Step-by-step explanation:

       Let the width of the rectangle = w m

                                            Length = ( 2w + 4) m

Area of rectangle = 126 square meters

length * width     = 126

 (2w + 4) * w        = 126

     2w² + 4w       = 126

     2w² + 4w - 126 = 0

Divide the entire equation by 2

        w² + 2w - 63  = 0

        Sum  = 2

    Product = -63

   Factors  =  9 , (-7)        { 9 +(-7) = 2  & 9*(-7) = -63}

w² +  9w - 7w - 63 = 0       {rewrite the middle term using the factors}

w( w + 9) - 7(w + 9) =0

        (w +9)(w - 7)  = 0

{Ignore w +9 = 0, as measurement will not come in negative}

w - 7 = 0

       w = 7

length = 2w + 4

           = 2*7 + 4

           = 14 + 4

            = 18

Answer:

29

Step-by-step explanation:

87 / 3 = 29

If you can use a calculator it shouldn't be on brainly...

Answer:

Algebraic Expressions

This calculator builds algebraic expressions based on word representations of numbers using the four operators and the words that represent them(increased,product,decreased,divided,times) Also known as Mathematical phrases

Factorials

Calculates the following factorial items:

* A factorial of one number such as n!

* A factorial of a numerator divided by a factorial of a denominator such as n!m!/a!b!

* Double Factorials such as n!!

* Stirlings Approximation for n!

Step-by-step explanation:

Ty pa follow narin po brainly and thank you for the points

Answer:

Step-by-step explanation:

#hope it helps!

Answered by ReyvREYV111

Answer:

5) 3x = 135° and x = 45°

6) (8x + 5) = 61° and (3x + 8) = 29°

Step-by-step explanation:

5) supplementary of two angles whose sum is 180°

3x + x = 180 → 4x = 180

4x / 4 = 180 / 4

x = 45

3x = 3(45)

135°

6) complimentary of two angles whose sum is 90°

(8x + 5) + (3x + 8) = 90 → 11x + 13 = 90

11x + 13 - 13 = 90 - 13

11x = 77

11x / 11 = 77 / 11

x = 7

(8x + 5) = 8(7) + 5

56 + 5 = 61

(3x + 8) = 3(7) + 8

21 + 8 = 29

Answer:

f(3)=11

Step-by-step explanation:

f(x) = 2x + 5

to find f(3) we simply plug in 3 where ever x is

So f(3) = 2(3) + 5

==> multiply 2 and 3

f(3) = 6 + 5

==> add 6 and 6

f(3) = 11

Answer:

9

Step-by-step explanation:

Y intercept when x = 0

Y = 9

where m is slope and b is y-intercept

Hence,

Here given equation: y = ½ x + 9

Identify,

slope: ½ and y-intercept: 9

Check the picture below.

[tex]2x+15~~ = ~~\cfrac{(10x+20)-80}{2}\implies 4x+30=10x-60 \\\\\\ 4x+90=10x\implies 90=6x\implies \cfrac{90}{6}=x\implies \boxed{15=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{the whole circle is}}{z + 80 + (10x+20)}~~ = ~~\stackrel{degrees}{360}\implies z+80+[10(15)+20]~~ = ~~360 \\\\\\ z+250=360\implies \blacktriangleright~~ z=110 ~~\blacktriangleleft[/tex]

If the value of x is 15 degrees. Then the measure of the arc z will be 110 degrees.

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

The diagram is shown below.

[tex]\rm 2x + 15 = \dfrac{10x + 20 - 80 }{2}[/tex]

Then the value of x will be

4x + 30 = 10x - 60

       6x = 90

          x = 15

Then the value of (10x + 20) will be

(10x + 20) = 10 × 15 + 20

(10x + 20) = 150 + 20

(10x + 20) = 170

Then the measure of the arc z will be

z + 170 + 80 = 360

z = 110

More about the circle link is given below.

https://brainly.com/question/11833983

#SPJ2

Answer:

A

Step-by-step explanation:

I think it's A hope that helps

Answer:

35

Step-by-step explanation:

it takes 5 weeks to make 100 since 20 x 5 = 100

100 x 7 = 700

5 x 7 = 35

Answer:

It will take 35 weeks.

Answer:

See below

Step-by-step explanation:

The turtle’s distance from his starting point is increasing between 0 and 6

seconds (which means it is getting larger in that time interval)

The turtle’s distance from his starting point is constant between 6 and 8 seconds (which means it is not moving in that time interval!)

The turtle’s distance from his starting point is decreasing between 8 and 12

seconds (which means it is getting smaller in that time interval)

Answer:

0-6, 6-8, 8-12

Step-by-step explanation:

For this, we'll have to use the numbers along the x-axis to measure. The line begins moving in a positive direction (up) from 0 to 6, which at that point, it remains stationary until 8 seconds. It then moves in a negative direction (down) all the way to 12.

If I can explain or elaborate in any way, please let me know.

Hope this helps!

Answer: 6 pieces

Step-by-step explanation:

      He is cutting the board into pieces each measuring [tex]\frac{1}{8}[/tex] of a foot. The original board is [tex]\frac{3}{4}[/tex] of a foot long. This means he is dividing, so we will solve the problem by doing the following.

     [tex]\displaystyle \frac{3}{4}/\frac{1}{8}[/tex]

     [tex]\displaystyle\frac{3}{4}*\frac{8}{1}[/tex]

     [tex]\displaystyle\frac{3*8}{4*1}[/tex]

     [tex]\displaystyle\frac{24}{4}[/tex]

     [tex]\displaystyle6[/tex]

     He can cut the board into 6 pieces, each measuring [tex]\frac{1}{8}[/tex] of a foot.

Answer:

The new points to the triangle will be:
[tex]A(1,4)\\ B(1,1)\\ C(-1,1)[/tex]

Step-by-step explanation:

Because the reflection point is at [tex]x=2[/tex], all x values will subtract their distances from [tex]x=2[/tex] to get their new values. The y values remain the same.

The starting values are:

[tex]A(3,4)\\ B(3,1)\\ C(5 ,1)[/tex]

Point [tex]A[/tex] is 1 unit away from [tex]x=2[/tex], so we'll subtract 1 from 2 to get the new x value: [tex]2 - 1 = 1[/tex], so [tex]A(1,4)[/tex].

 

Point [tex]B[/tex] is also 1 unit away from [tex]x=2[/tex], so we'll subtract 1 from 2 to get the new x value: [tex]2 - 1 = 1[/tex], so [tex]B(1,1)[/tex].

Point [tex]C[/tex] is 3 units away from [tex]x=2[/tex], so we'll subtract 3 from 2 to get the new x value: [tex]2 - 3 = -1[/tex], so [tex]C(-1,1)[/tex].

Answer:

The string contains 6 ones and 8 zeros, thus 14 bits in total.

Step-by-step explanation:

Hope this helps.

Answer:

The total is 130 apples.

Step-by-step explanation:

If the ratio of green to red apples is 2:3 and there is a total of 78 red apples, we can divide 78/3 which is 26. Since this is 1/3 of 78 we can multiply that by 2 to get 52 which is 2/3 of 78 which is the total amount of green apples. We dont stop here however. The question askes for the total amount of apples so we att 52 and 78 to get 130 which is the total amount of apples.

78/3 = 26

26*2 = 52

52+78 = 130

a. The number of square cm of paper that would be used to make 4 caps is 3154.56 cm².

b. For the cake to have the required dimensions, they should order 1 kg of cake.

a.

The number of square cm of paper that would be used to make 4 caps is 3154.56 cm².

To find the number of square cm paper would be used to make 4 caps, we need to find the area of a cone.

The area of a cone, A = πr² + πr[√(h² + r²)] where

Now given that the base circumference of the cone is C = 44 cm. So,

C = 2πr where r = radius of base

So, r = C/2π = 44 cm/2π = 22 cm/3.142 = 7 cm

The height of the cone, h = 24 cm

So, A = πr² + πr[√(h² + r²)]

A = π(7 cm)² + π(7 cm)[√((24 cm)² + (7 cm)²)]

A = π(7 cm)² + π(7 cm)(7)[√((4 cm)² + (1 cm)²)]

A = 49π cm² + 49π cm[√(16 cm² + 1 cm²)]

A = 49π cm² + 49π cm[√(17 cm²)]

A = 49π [1 cm² + 4.123 cm²)]

A = 49π [5.123 cm²)]

A = 251.032π

A = 788.64 cm²

Since the area of one cap is A = 788.64 cm²,

the area of 4 caps is A' = 4A

= 4 × 788.64 cm²

= 3154.56 cm²

So, the number of square cm of paper that would be used to make 4 caps is 3154.56 cm².

b.

For the cake to have the required dimensions, they should order 1 kg of cake.

To find the amount of cake to be ordered, we need to find the volume of a cake since it is the volume of a cylinder.

The volume of a cylinder is V = πd²h/4 where

Substituting the values of the variables into the equation, we have

V = πd²h/4

V = π(24 cm)²(14 cm)/4

V = π(576 cm)²(14 cm)/4

V = 8064π cm³/4

V = 2016π cm³

V = 6333.45 cm³

So the volume of the cake is 6333.45 cm³

Since 650 cm³ equals 100 g, 6333.45 cm³ = 6333.45 cm³ × 100 g/650 cm =  974.4 g = 0.974 kg ≅ 1 kg.

So, for the cake to have the required dimensions, they should order 1 kg of cake.

Learn more about volume of a cake here:

https://brainly.com/question/27570775

#SPJ1

If the function is y = 4.5x. Then the rate of change of the function expressed as a unit rate will be 4.5.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A bike rental company charges a fee per hour.

The charge, in dollars, is the same each hour.

The ordered pairs (3, 13.50) and (5, 22.50) represent the corresponding hours, x, and cost, y.

Then the linear equation is given as

[tex]\begin{aligned} \rm y - 22.5 &= \rm \dfrac{22.5 - 13.5}{5 - 3} (x- 5)\\\\\rm y - 22.5 &= \rm 4.5x - 22.5\\\\\rm y &= \rm 4.5x \end[/tex]

Then the rate of change of the function expressed as a unit rate will be

[tex]\rm \dfrac{dy}{dx} = \dfrac{d}{dx} (4.5x )\\\\\dfrac{dy}{dx} = 4.5[/tex]

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ1

Answer:

1/2

Step-by-step explanation:

First square area = 4cm^2, thus the side length is 2cm

Second square area = 16cm^2, thus the side length is 4cm

This gives a ratio of 2/4, simplifying yields 1/2

From the figure, the value of tan j is 13/9

The tangent of an angle is calculated using:

tan(j) = opposite/adjacent

From the figure, we have:

opposite = 13

adjacent = 9

So, we have:

tan(j) = 13/9

Hence, the value of tan j is 13/9

Read more about tangent function at:

https://brainly.com/question/8120556

#SPJ1

Answer:  The answer is 30 inches.

Answer:

36

Step-by-step explantion:
1 x 1 = 1 so each cube is 1 square inch

2 x 6= 12

12 x 3 = 36

Hi Student!

The first step that we need to take when approaching this problem is to extract the important information that was given in the problem statement.  Reading through it, we can see that we are given a circumference of a pipe being 9.24 centimeters.  After that, they are asking for us to determine what the diameter of the pipe is and tell us to use 3.14 instead of π.

Now that we have completed the information gathering, we can move onto the part of plugging in our values and solving for the unknown.

Plug in the values

Divide both sides by 3.14

Therefore, after solving for our unknown being the diameter we were able to determine that it is around 2.942675 centimeters using the Circumference formula.

Hope this helps, so sorry if I am wrong!

Answer:

A ≈ 1313.19

Step-by-step explanation:

By using the formula [tex]A = 2 \pi r h + 2 \pi r^{2}[/tex] we can just fill in the information with what we know, which is Diameter = 22, Radius = Diameter/2 = 11. The height is 8. So in doing so we get [tex]A = 2\pi (11)(8)+2\pi (11)^{2}[/tex], which
equals ≈ [tex]1313.18573[/tex].

Answer:

y-intercept, when x = 0, y = -6

x-intercept, when y = 0, x = 6

Step-by-step explanation:

y-intercept, when x = 0, y = -6

x-intercept, when y = 0, x = 6

Answer:

First choice.

Step-by-step explanation:

The third side cannot be 26 or greater ( as 11 + 15 = 26).

Answer:

it is A i think

Step-by-step explanation:

Answer:

(3x + 5)(9x^2 - 15x + 25)

Step-by-step explanation:

27x^3 + 125

= (3x)^3 + 5^3

= (3x + 5) ((3x)^2 - (3x)(5) + 5^2)

= (3x + 5)(9x^2 - 15x + 25)

FYI: a³ + b³ = (a + b)(a² – ab + b²)

Answer:

(3x + 5)(9x² - 15x + 25)

Step-by-step explanation:

This is given in the form : a³ + b³

Identity :

Solving :

Answer:

Option #4: [tex]4\left(x+8\right)-10\ge 42[/tex]

Step-by-step explanation:

[tex]4\left(x+8\right)-10\ge 42[/tex]

x ≥ 5

Answer:

4th option

Step-by-step explanation:

the inequality shows x ≥ 5

solving the inequalities

- 7(3x - 7) + 21 ≥ 50

- 21x + 49 + 21 ≥ 50

- 21x + 70 ≥ 50 ( subtract 70 from both sides )

- 21x ≥ - 20

divide both sides by - 21 reversing the symbol as a result of dividing by a negative quantity , then

x ≤ [tex]\frac{20}{21}[/tex] ← not the required solution

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

- 4(- x + 8) - 10 ≤ 8

4x - 32 - 10 ≤ 8

4x - 42 ≤ 8 ( add 42 to both sides )

4x ≤ 50 ( divide both sides by 4 )

x ≤ 12.5 ← not the required solution

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

- 7(3x - 7) + 21x ≥ - 50

- 21x + 49 + 21x ≥ - 50 ( subtract 49 from both sides )

0 ≥ - 99 ← not the required solution

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

4(x + 8) - 10 ≥ 42

4x + 32 - 10 ≥ 42

4x + 22 ≥ 42 ( subtract 22 from both sides )

4x ≥ 20 ( divide both sides by 4 )

x ≥ 5 ← Required solution

Answer:

a) mean = 1.42 occupant/car

b) standard deviation = 0.89 occupants

c) median = 1 occupant

d) The proportion of cars had more than the mean number of occupants is 0.24

e) The proportion of cars with the number of occupants more than one

standard deviation greater than the mean is 0.11

f) The proportion of cars with the number of occupants within one standard

deviation of the mean is 0.89

Step-by-step explanation:

Attached work:

Answer:

option A is the answer of given question 12 less than its greater than 48