I’m doing the Pythagorean Theron in math class an I’m stuck on this question - the base path of a base ball diamond form a square.if it is 90 feet from home to first how far does the catcher have to through to catch someone stealing second base

Answer:

7.3 repeating

Step-by-step explanation:

58-14

=44

44/6

=7.3 repeating

Answer:

Amount of gas that can be hold by Joe's tank = 16 gallons.

Step-by-step explanation:

Given that Joe's gas tank is 1/4 full. After he buys 6 gallons of gas, it is 5/8 full. Now we need to find about how many gallons can Joe's tank hold.

So let's find change that happened after filling the gas.

Change = (5/8 full) - (1/4 full)

Change = (5/8 - 1/4)  full

Change = (5/8 - 2/8)  full

Change = (5 - 2)/8  full

Change = 3/8  full

So that means 3/8 full happens in 6 gallons

then 1 full will happen in 6/(3/8) gallons = 6*(8/3) gallons = 48/3 gallons = 16 gallons

So the amount of gas that can be hold by Joe's tank = 16 gallons.

Answer:

? = 113

Step-by-step explanation:

The angles are alternate interior angles.  Alternate interior angles are equal if the lines are parallel.  Since the lines are parallel, the angles are equal.

? = 113

Since the two lines are parallel and they are both being bisected by the same line, then the resulting bisected angles are the same.

To solve for x you will set 2x - 3 = 135, since both angle measures are the same.

2x - 3 = 135

2x = 138

x = 69

Answer:

0.8125

Step-by-step explanation:

See picture!

Answer:

Correct answer is option (B)

Step-by-step explanation:

We have been given that area of Maxine's living room is 88 square feet. Further, we are given that length of the room is 3 feet longer than the width.

Let us assume that x be the width of the room, therefore, length of the room will be [tex]x+3[/tex].

We know that area of a rectangle can be found by multiply the measures of length and width, therefore, we can set:

[tex]\text{Area} = \text{length}\times \text{width}\\\text{Area} = (x+3)\times x\\\text{Area} = x^{2}+3x\\[/tex]

Now, since we are given that area is 88 square feet, therefore, we can set this expression for area equal to 88 to get the desired equation:

[tex]x^{2}+3x=88[/tex]

Therefore, correct answer is option (B)

Answer:

-7 = -3x + b

Step-by-step explanation:

i'm guessing because you have not provided a visual so i can not determine the B.

Answer:

2

Step-by-step explanation:

Final answer:

Assuming a square garden with each side being 8 feet, 50% of the space allocated to daisies would be 32 square feet.

Explanation:

Mr. King is dividing his garden evenly for tulips and daisies, meaning each flower type will occupy 50% of the garden's area. The length of the garden is given as 8 feet, but the width is not mentioned. To determine the actual area for daisies, we need both dimensions of the garden. However, if we assume that the width is also provided or the garden is square (8 feet by 8 feet), then the total area of the garden is 64 square feet (8 feet * 8 feet).

Now, to find the space filled with daisies, we calculate 50% of the total area:

0.50 * 64 square feet = 32 square feet.

Therefore, if the garden is a square and the other dimension equals the given length, the space filled with daisies will be 32 square feet.

Answer:

Domain of y=[tex]\sqrt[4]{x-1}[/tex]: is x>=1

Interval notation: [1,∞)

Step-by-step explanation:

We have y=[tex]\sqrt[4]{x-1}[/tex]

1) The domain of a function is the set of x values for which the function is real and defined.

2) So, x-1 should be positive means x-1>=0, because fourth root of any negative value would be a complex number and not a real number.

3) Now we solve the inequality x-1>=0

4) Adding 1 to both sides of the inequality we get,

x-1+1 > = 0+1

5) Cancel out -1 and +1 from the left side

6) We get x>=1

It concludes that for the domain of the given function, the x value must be greater than or equal to 1

Answer:

26.

Step-by-step explanation:

You just have to do 22.10 ÷ 0.85.

Final answer:

By dividing the total cost spent on drinks by the cost of each drink ($22.10 ÷ $0.85), we find that 26 people attended the Lopez family picnic.

Explanation:

To determine how many people attended the Lopez family picnic, we need to divide the total cost spent on drinks by the cost of each drink. Since the Lopez family spent $22.10 on drinks and each drink cost $0.85, we perform the following calculation:

Total cost spent on drinks ÷ Cost of each drink = Number of people

$22.10 ÷ $0.85 = 26 people

Therefore, 26 people attended the Lopez family picnic.

Answer:

0

Step-by-step explanation:

[tex]f(x)=\sqrt{x}+12  and g(x)=2\sqrt{x}[/tex]

We need to find (f-g)(144)

(f-g)(144) = f(144) - g(144)

[tex]f(x)=\sqrt{x}+12[/tex]

[tex]f(144)=\sqrt{144}+12=12+12= 24[/tex]

[tex]g(x)=2\sqrt{x}[/tex]

[tex]g(144)=2\sqrt{144}=2(12)= 24[/tex]

(f-g)(144) = f(144) - g(144)= 24-24=0

Answer:

o is correct answer

Step-by-step explanation:

f(x)=[tex]\sqrt{x}[/tex]+12

g(x)=2[tex]\sqrt{x}[/tex]

we will find

(f-g)x=[tex]\sqrt{x}[/tex]+12-2[tex]\sqrt{x}[/tex]

(f-g)x=-[tex]\sqrt{x}[/tex]+12

now we  will find

(f-g)(144)

put x=144

(f-g)(144)=- [tex]\sqrt{144}[/tex]+12

(f-g)(144)=-12+12=0

hence proved

Answer:

the new frame is bigger than the original frame by 10%

Step-by-step explanation:

Let the length of the original frame be l,

then it's width is (10% of l)=[tex]\frac{10}{100}[/tex]×l

                                           =[tex]\frac{l}{10}[/tex]

hence area of original frame=A=length×width

                                               =[tex]\frac{l^{2} }{10}[/tex]

now the length of frame is enlarged by 10%

new lenght of frame=l+10%×l

                                 =l+[tex]\frac{10}{100}[/tex]×l

                                  =[tex]\frac{11}{10}[/tex]×l

width of new frame==[tex]\frac{l}{10}[/tex]

area of new frame=length×width

                              =[tex]\frac{11l^{2} }{100}[/tex]

percent change=((area of new frame-area of old frame)×100)÷area of old frame

=10%

Answer:

9.09091%

Step-by-step explanation:

Answer:

90 meters/second = rate

Step-by-step explanation:

To find out how fast he ran, we use the equation

distance = rate * time

We know the distance = 270 meters

and we know the time = 3 seconds

Substitute these values in

270 meters = rate * 3 seconds

Divide both sides by 3 seconds

270 meters  / 3 seconds = rate

90 meters/second = rate

Answer:

Step-by-step explanation:

you want to find his speed  so your going to divide the distance he ran by the amount of time which is  270/3 and the answer is 90

The ratio of the height of the building to the number of floors is 13 feet/floor, i.e., each floor of the building is approximately 13 feet tall.

Given the information that a single building with 8 floors measures 104 feet in height, we can calculate the ratio of the height of the building to the number of floors as follows:

104 feet / 8 floors = 13 feet/floor

This ratio or unit rate represents the height corresponding to one floor. In plain terms, this means each floor of the building is approximately 13 feet tall.

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Answer:

13 feet/floor

Step-by-step explanation:

Answer: 457.65

Step-by-step explanation:

40,731 / 89 = 457.65

Have a good day :)

The answer to the division of 89 by 40,731 is approximately 0.00218468. This number is so small because you are dividing a small number by a significantly larger one.

The question is asking for the division of 89 by 40,731. In this case, you have to divide the two numbers. Using a calculator, 89 divided into 40,731 yields a very small number, approximately 0.00218468. This is a very small number because you are dividing a smaller number by a significantly larger one.

To better conceptualize this, consider making a pie with 40,731 pieces, and you only took 89 pieces. The proportion you took (or the answer to 89 divided by 40,731) would be very small, just like the number 0.00218468.

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i think it is 0.33...i could be wrong.

Answer:

.33 acre  per lot

Step-by-step explanation:

We want to take 25.08 acres and divide them evenly into 76 lots

25.08 /76 = .33 acre  per lot

Answer:

$25 821.69

Step-by-step explanation:

The formula for the future value (FV) of an investment is

FV =PV(1 + r/n)^nt

FV = 20 000(1 + 0.087/2)^(2×3)

FV = 20 000(1 + 0.0435)⁶

FV = 20 000(1.0435)⁶

FV = 20 000 × 1.291 0847

FV = $25 821.69

Answer:

Motorcycle will complete the 540 mile trip in 11.25 hr.

The car will complete it 2.25 hours less, or 9 hours.

The speed of the car therefore is 540/9 = 60 mph.

60t + 48t = 540

108t = 540

t = 5

So they will meet in 5 hours, after which time the motorcycle will have traveled 48*5 = 240 miles

and the car will have traveled 60*5 = 300 miles.

Hope this help

Step-by-step explanation:

Answer:

We have $440 to spend on fliers

Step-by-step explanation:

Budget = supplies + fliers

555 = 115 + fliers

Subtract 115 from each side

555-115 = 115-115 + fliers

440 = fliers

We have $440 to spend on fliers

Answer:

The cell phone took 4.7 seconds to reach the ground.

Step-by-step explanation:

A hang glider dropped his cell phone from a height of 350 feet:

Initial velocity: Vo = 0 ft/s

Height: h = 350 feet = 350 ft

Time to reach the ground: t=?

Gravity's acceleration: g = 32 ft/s^2

h = Vo t + g t^2 / 2

Replacing the known values in the equation above:

350 ft = (0 ft/s) t + (32 ft/s^2) t^2 /2

350 ft = 0 + (16 ft/s^2) t^2

350 ft = (16 ft/s^2) t^2

Solving for t^2: Dividing both sides of the equation by 16 ft/s^2:

(350 ft) / (16 ft/s^2) = (16 ft/s^2) t^2 / (16 ft/s^2)

21.875 s^2 = t^2

Solving for t: Square root both sides of the equation:

sqrt(21.875 s^2) = sqrt(t^2)

4.677071733 s = t

t = 4.677071733 s

Rounding to the nearest tenth:

t = 4.7 s

The cell phone takes about 4.7 seconds to reach the ground

Acceleration is rate of change of velocity.

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem!

Given:

Height = h = 350 feet

Gravitational Acceleration = g = 32.2 feet/s²

Initial Velocity = u = 0 m/s

Unknown:

time taken to reach the ground = t = ?

Solution:

This problem is about Free Fall.

When an object experiences free fall, the acceleration experienced by the object is the same as the acceleration due to gravity which is equal to 9.8 m/s² or 32.2 feet/s²

[tex]h = ut + \frac{1}{2}gt^2[/tex]

[tex]350 = 0t + \frac{1}{2}(32.2)t^2[/tex]

[tex]350 = 0 + 16.1t^2[/tex]

[tex]t^2 = 350 \div 16.1[/tex]

[tex]t \approx 4.7 ~ \text{seconds}[/tex]

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle

[tex]Use\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\dfrac{14ab^2x^3}{2abx^2}=\dfrac{14}{2}\cdot\dfrac{a}{a}\cdot\dfrac{b^2}{b}\cdot\dfrac{x^3}{x^2}=7\cdot1\cdot b^{2-1}\cdot x^{3-2}=\boxed{7bx}[/tex]

Answer:

[tex]7bx[/tex]

Step-by-step explanation:

[tex]\mathrm{Divide\:the\:numbers:}\:\frac{14}{2}=7 =\frac{7ab^2x^3}{abx^2}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:a =\frac{7b^2x^3}{bx^2}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:b =\frac{7bx^3}{x^2}[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}\:=\:x^{a-b}[/tex][tex]\frac{x^3}{x^2}=x^{3-2}=x[/tex]

[tex]=7bx[/tex]

Hope this helps!!!

Answer:

x=2

Step-by-step explanation:

-2(1 - 4x) = 3x + 8

The first step is to distribute the -2

-2*1 -2(-4x) = 3x+8

-2+8x = 3x+8

Subtract 3x from each side.

-2+8x-3x = 3x-3x+8

-2+5x=8

Add 2 to each side

-2+2 +5x=8+2

5x=10

Divide by 5

5x/5 = 10/5

x=2

Number of red blood cells = [tex]4.5*10^{6}[/tex]

Number of white blood cells = 5000 or we can write this as [tex]5*10^{3}[/tex]

We have to find how many times more red blood cells are there than white in the sample. so we will divide the two to get the answer.

[tex]\frac{4.5*10^{6}}{5*10^{3}}[/tex]

= [tex]0.9*10^{3}[/tex]

= [tex]9*10^{2}[/tex] = 9*10*10 = 900

Hence, the red blood cells are 900 times more than white blood cells.

Answer:

Red blood cells are 900 times of white blood cells in the blood sample of Laura.

Step-by-step explanation:

Sample of Laura's blood sample contains number of red plus cells = 4.5[tex]10^{6}[/tex] and number of white blood cells = 5×[tex]10^{3}[/tex]

Now we calculate the ratio of red blood cells and white blood cells

= 4.5×[tex]10^{6}[/tex]÷5[tex]10^{3}[/tex]

= 4.5×[tex]10^{3}[/tex]÷5

= 4500÷5

=900

Now scientific representation of data will be

Test                                  Result              Range

White Blood Cells      5×[tex]10^{3}[/tex]per [tex]mm^{3}[/tex]       5-10

Red Blood Cells       4.5×[tex]10^{3}[/tex] per[tex]mm^{3}[/tex]    4.2-6.11            

Answer:

B

Step-by-step explanation:

• A line sloping upwards from left to right has a positive slope

• A line sloping downwards from left to right has a negative slope

The line shown here slopes downwards from left to right, hence has a negative slope → B

Answer:

16

Step-by-step explanation:

Since Dean bought 8 postcards during 2 days of vacation, then after 4 days, that would be 16 because multiply by 2.

Answer:

16 postcards

Step-by-step explanation:

So Dean's rate of buying is:

8 postcards/2 days = 4 postcards per day.

Thus, we can find out how many postcards he gets after 4 days by multiplying

4 postcards × 4 days, which equals to 16 postcards.

Hope this is helpful!

Final Answer:

The equations of the tangents to the curve[tex]\(x = 9t^2 + 6, y = 6t^3 + 3\)[/tex]that pass through the point (15, 9) are [tex]\(y = 2x - 21\)[/tex] and[tex]\(y = -2x + 51\).[/tex]

Explanation:

To find the equations of the tangents, we first substitute (x = 15) and (y = 9) into the parametric equations[tex]\(x = 9t^2 + 6\)[/tex] and [tex]\(y = 6t^3 + 3\)[/tex]. Solving for (t), we get (t = 1) and (t = -1). These values of (t) correspond to the points of tangency.

Next, we find the slopes of the tangents by taking the derivatives of (x) and (y) with respect to (t), resulting in (dx/dt = 18t) and (dy/dt = 18[tex]t^2[/tex]). At (t = 1), the slope is (18), and at (t = -1), the slope is (-18).

Using the point-slope form of a linear equation [tex]\(y - y_1 = m(x - x_1)\)[/tex], where (m) is the slope and [tex]\((x_1, y_1)\)[/tex] is the point of tangency, we obtain the equations of the tangents: (y - 9 = 18(x - 15)) and (y - 9 = -18(x - 15)). Simplifying these expressions yields (y = 2x - 21) and (y = -2x + 51).

Answer:

(a)

Given expression: 49% of 162

we can write 49% as [tex]\frac{49}{100}[/tex]

then;

[tex]\frac{49}{100} \times 162 = \frac{49 \times 162}{100} = \frac{7938}{100}=79.38[/tex]

Therefore, the estimate of the given expression is, 79.38.

(b)

Using mental math to calculate 49% of 162.

Mental math is used as a way to calculate an estimate quickly.

We can write 49% = 50% -1%

(50%-1%) of 162 = 50% of 162 -1% of 162

so,

50% of 162 = [tex]\frac{50}{100} \times 162 = \frac{1}{2} \times 162 = 81[/tex]

and

1% of 162 = [tex]\frac{1}{100} \times 162 = \frac{162}{100} = 1.62[/tex]

Now, subtract these we get;

81 - 1.62 = 79.38

Therefore, by using mental math 49% of 162 is, 79.38

[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &18800\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ t=\textit{elapsed time}\dotfill &13\\ \end{cases} \\\\\\ A=18800(1-0.12)^{13}\implies A=18800(0.88)^{13}\implies A\approx 3568.0636019[/tex]

Answer:

1.5

Step-by-step explanation:

Answer:

y=-5x+4

Step-by-step explanation:

y-4=-5(x-0)

y-4=-5x

y=-5x+4