The distance from home to second base in a slow pitch softball diamond is approximately 87.68 feet. This calculation is achieved through the use of the Pythagorean theorem, which utilizes the square lengths of the diamond sides to calculate the diagonal path between the bases.
Explanation:The distance from home to second base in a slow pitch softball diamond can be calculated using the Pythagorean theorem, as the path forms a right triangle. The side lengths of the diamond are 62 ft, so we can use these as the legs of our right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, it's a^2 + b^2 = c^2, where c is the distance we want to find.
So, the calculation will be √((62ft)^2 + (62ft)^2). Simplifying this gives √(3844ft^2 + 3844ft^2), which is √7688ft^2. Which gives us approximately 87.68 ft. So, the distance from home to second base is approximately 87.68 feet.
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To find the distance from home to second base on a slow pitch softball diamond, use the Pythagorean theorem to calculate the diagonal of the square. With each side being 62 feet, the distance comes out to approximately 87.7 feet.
How to Find the Distance from Home to Second Base
In a slow pitch softball diamond, the bases form a square with each side measuring 62 feet.
We must compute the diagonal for the square in order to get the distance between home plate and second base.
This can be done using the Pythagorean theorem.
Step-by-Step Solution
Label the sides of the square. Each side is 62 feet.
Recall the Pythagorean theorem formula: a² + b² = c², where 'a' and 'b' are the legs of a right triangle, and 'c' is the hypotenuse (which, in this case, is the diagonal).
Here, both 'a' and 'b' are 62 feet because the square’s sides are equal.
→ Substitute the values into the formula: 62² + 62² = c²
→ Calculate the squares: 3844 + 3844 = c²
→ Combine the values: 7688 = c²
→ Take the square root to find 'c': c = √7688
The diagonal (distance from home to second base) is approximately 87.7 feet.
Therefore, the distance from home to second base is about 87.7 feet.
10. Estimate by rounding -5 2/5+9 8/11-3 5/6
Answer:
0.5
Step-by-step explanation:
-5 2/5=-27/5
9 8/11=107/11
-3 5/6=-23/6
--------------------
-27/5+107/11-23/6
-27/5-23/6+107/11
-162/30-115/30+107/11
-277/30+107/11
-3047/330+3210/330=163/330=0.493=0.5
Urgent!!! Triangle ABC has angles the following angle measures. m<A=2x+7 , m<B=10x+10 and m<C=8x+23. what is the value of x and what is the measure of each angle?
x=
m<A=
m<B=
m<C=
Answer:
The Value of x= 7.
m∠A= 21°
m∠B= 80°
m∠C= 79°
Step-by-step explanation:
Given:
m∠A = 2x+7
m∠B = 10x+10
m∠C = 8x+23
We need to find the value of x and measures of each angle.
Now by angle sum property which states that sum of all angles of a triangle are 180°.
Hence from above statement we can say in ΔABC;
m∠A+m∠B+m∠C=180
Now substituting the given values in above equation we get;
[tex]2x+7+10x+10+8x+23=180\\2x+10x+8x+7+10+23=180\\20x+40=180\\20x=180-40\\20x=140\\\\x=\frac{140}{20} =7[/tex]
Hence value of x is 7.
Substituting the value of x in all angles we get;
m∠A=[tex]2x+7=2\times7+7=14+7=21\°[/tex]
m∠B=[tex]10x+10=10\times7+10=70+10=80\°[/tex]
m∠C=[tex]8x+23= 8\times7 +23 = 56+23=79\°[/tex]
Final answer:
To find the value of x and the measure of each angle in triangle ABC, set up an equation using the given angle measures. Solve for x and substitute it back in to find the measures of each angle. Then : m<A = 2(7) + 7 = 21 degrees
m<B = 10(7) + 10 = 80 degrees
m<C = 8(7) + 23 = 79 degrees
Explanation:
To find the value of x and the measure of each angle in triangle ABC, we need to set up an equation using the given angle measures. Since the sum of the angles in a triangle is 180 degrees, we can write the equation as:
m<A + m<B + m<C = 180
Substituting the given angle measures, we have:
(2x + 7) + (10x + 10) + (8x + 23) = 180
Simplifying the equation:
20x + 40 = 180
Subtracting 40 from both sides:
20x = 140
Dividing both sides by 20:
x = 7
Now that we know the value of x, we can find the measure of each angle by substituting x into the respective expressions:
m<A = 2(7) + 7 = 21 degrees
m<B = 10(7) + 10 = 80 degrees
m<C = 8(7) + 23 = 79 degrees
What is the equation of the line that is perpendicular to the y-axis and contains the point (-2,7)
A: y=-x+5
B: x=-2
C: y=x+9
D: y=7
Answer:
y = 7
Step-by-step explanation:
The straight line which is perpendicular to the y-axis will be either x-axis or parallel to the x-axis.
Now, the general equation for all straight line which is either x-axis or parallel to x-axis are given by y = c ........... (1), where c is any constant.
For c = 0 the line will be x -axis. therefore, y = 0, is the equation of x-axis.
Now, if the line (1) passes through the point (-2, 7), then the equation will be y = 7. (Answer)
{Since, the point (-2,7) will satisfy the equation (1) and then c will be equal to 7.}
A scientist measured the wavelength of an X-ray as 0.0000000065 meters. Write the number in scientific notation.
Answer:
[tex]6.5 \times 10^{-9}[/tex]
Step-by-step explanation:
The scientific notation of a number is to express the number in the form [tex]x\times 10^{y}[/tex] where x is the base of ten.
So, if we want to express the number 0.0000000065, then we can write it as
[tex]\frac{6.5}{1000000000} = 6.5 \times 10^{-9}[/tex].
So, we can write 0.0000000065 as [tex]65\times 10^{-10}[/tex] or [tex]0.65 \times 10^{-8}[/tex] but those are not the scientific notation.
Therefore, [tex]6.5 \times 10^{-9}[/tex] is the scientific notation of 0.0000000065. (Answer)
20 pts! A line passes through (3, 7) and (6, 9). Which equation best represents the line?
y = 3 over 2 x + 5
y = 2 over 3 x + 5
y = 3x + 2
y = 2 over 3 x + 2
Answer:
y = 2 over 3 x + 5
Step-by-step explanation:
m= y2-y1/x2-x1
m= (9-7)/(6-3)
m=2/3
y=mx+b
y= 2/3x+b
(3,7)
7=2/3(3)+b
7=6/3+b
7=2+b
5=b
b=5
y=2/3x+5
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 350 cubic
centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 cents per square
centimeter. The top will be made of glued paper, costing 0.08 cents per square centimeter. Find the dimensions for
the package that will minimize production cost.
Helpful information:
To minimize the cost of the package:
Radius:
Height:
Minimum
To minimize production cost, we need to find the dimensions of the package that will satisfy the volume equation and minimize the cost equation. Taking the partial derivatives of the cost equation with respect to the variables 'r' and 'h', and setting them equal to zero, we can find the critical points. Solving these equations, we find that the dimensions for the package that will minimize production cost are a height of 7 cm and a radius of 2.5 cm.
Explanation:To find the dimensions of the package that will minimize production cost, we need to consider the cost of the sides and bottom made of styrofoam and the cost of the top made of glued paper. Let's denote the radius of the base of the cylinder as 'r' and the height of the cylinder as 'h'.
The volume of a cylinder is given by the formula V = πr²h. We know that the volume of the package needs to be 350 cubic centimeters, so we can write the equation as πr²h = 350.
The cost of the sides and bottom of the container is given by the formula C1 = 0.03 * (2πrh + πr²), and the cost of the top is given by the formula C2 = 0.08 * πr².
To minimize the cost, we need to find the values of 'r' and 'h' that satisfy the volume equation and minimize the cost equation.
Since this is a calculus problem, we will differentiate the cost equation with respect to 'r' and 'h', and set the derivatives equal to zero to find the critical points.
Taking the partial derivatives of C1 and C2 with respect to 'r' and 'h', we get:
∂C1/∂r = 0.03 * (2πh + 2πr) = 0∂C1/∂h = 0.03 * (2πr) = 0∂C2/∂r = 0.08 * (2πr) = 0∂C2/∂h = 0Solving these equations, we find that h = 7 cm and r = 2.5 cm. Therefore, the dimensions for the package that will minimize production cost are a height of 7 cm and a radius of 2.5 cm.
how do you write six times the quantity two x plus three y with numbers??
Answer:
12x + 18y
Step-by-step explanation:
Lets first write the quantity "two x plus three y", this means, that we have x and y as unknowns. x is 2 times, so we have 2x; and y is 3 times, so he have 3y:
2x + 3y
Additionally we have that this quantity is six times, what means that it is multiplied by a number 6:
6(2x +3y)
If you like, we can apply the distributive property that means that given any three numbers a, b, c we have that a(b+c)=ab + ac. In our case a is 6, b is 2x and c is 3y. Thus, operating:
6(2x +3y) = 6*2x + 6*3y = 12x + 18y
So, "six times the quantity two x plus three y" is 12x + 18y
Find the exact volume of a cone 6yd height 5yd base
Answer:
The exact volume of a cone is 10 yd³.
Step-by-step explanation:
Given:
Height of cone (h) is 6 yd and base (b) is 5 yd.
Now, to get the volume we need to find the radius.
So, to find radius we put the formula of base:
Let the radius be [tex]r[/tex]
Base=[tex]\pi r^2[/tex]
[tex]b=\pi\times r^{2}[/tex]
[tex]5=\pi\times r^{2}[/tex]
Dividing both sides by π and using square root on both the sides:
[tex]5\div \pi=(\pi \times r^{2}) \div \pi[/tex]
[tex]\frac{5}{\pi}=r^{2}[/tex]
[tex]\frac{5}{\pi}=r^{2}[/tex]
[tex]r^{2}=\frac{5}{\pi}-----1[/tex]
Now, putting the formula for getting the volume (v) of cone:
Volume = [tex]\pi r^2\frac{h}{3}[/tex]
[tex]v=\pi\times r^{2}\times \frac{6}{3}[/tex]
[tex]v=\pi\times r^{2}\times 2[/tex]
Substituting the value of [tex]r^2[/tex] from equation (1), we get:
[tex]v=\pi\times \frac{5}{\pi}\times 2[/tex]
[tex]v=10[/tex] yd³
Volume of cone is 10 yd³
Therefore, the exact volume of a cone is 10 yd³.
How can I factor 24 + 32x
Answer:
8(3+4x)
Step-by-step explanation:
it it can be pulled out of both 24 and 32.
Find the Slope and Y-Intercer
1) y = x+3
slope =
y-intercept =
What’s the slope
Answer:
slope is 1 and y-intercept is 3
Step-by-step explanation:
equation is in the format y=mx+c
c = y-intercept
m = slope
if there is no number in front of x it is assumed that 1 is in front of x
Answer:
The slope is 1 and the y-intercept is 3
Step-by-step explanation:
y = x+3 has the form y = mx + b. If we compare these two equations, it becomes readily apparent that m = 1 and b = 3.
The slope is 1 and the y-intercept is 3 (or (0, 3) )
Maura runs 5 miles in 1.25 hours. Ava runs 3 miles in 0.83 hours. Who runs faster?
Answer:
Maura runs faster
Step-by-step explanation:
To avoid decimals ,multiply all by 100
Maura 500 mi/125h = 4 mi/h
Ava 300 mi /83 h =3.61445.....mi/h
Answer:
still from 2019
wsp my dude
Step-by-step explanation:
Need help with this math problem
Answer:
[tex]x=16[/tex]
Lenght of the equal sides: [tex]71\ units[/tex]
Step-by-step explanation:
You can observe in the picture that the triangle have two angles that have equal measure; therefore, it is an Isosceles triangle.
By definition, Isosceles triangles have two equal angles and two equal sides.
Based on this, you can write the following equation:
[tex]9x-73=3x+23[/tex]
Solving for "x", you get this value:
[tex]9x-3x=23+73\\\\6x=96\\\\x=\frac{96}{6}\\\\x=16[/tex]
Finally, you can subsitute the value of "x" into any expression to find the lenght of the equal sides:
[tex]3(16)+23=71\ units[/tex]
[tex]3x - 7 = 3x + 1[/tex]
solve for x
Answer:
No Solution.
Step-by-step explanation:
3x-7=3x+1
3x-3x-7=1
0-7=1
-7=1
no solution
The sum of 3 consecutive odd numbers is 183
Answer:
Step-by-step explanation:The sum of three consecutive odd numbers is 183. Find the numbers. 57; 59; 67 59; 61; 63 60; 61; 62 65; 67; 69.
Solve linear equations :
Solve step by step for each one
7. 10n - 11 = 3 + 4n + 6n
8. -8(k + 4) = -96
9. -6(2k + 5) + 7k = -6 + 7k
Answer: 7.) Wrong Question
8.) 8
(9.) - 2
Step-by-step explanation:
7.) 10n - 11 = 3 + 4n + 6n
Collect like terms
10n - 4n - 6n = 3 + 11
10n - 10n = 14
It's not possible to have zero n = 14
8.) -8(k + 4) = - 96
Exland the bracket
-8k - 32 = - 96
Collect like terms
-8k = - 96 + 32
-8k = - 64
Divide through by -8
-8k/-8 = - 64/-8
k = 8
9.) -6(2k + 5) + 7k = -6 + 7k
Open the bracket
-12k - 30 +7k = -6 + 7k
Collect like terms
-12k + 7k - 7k = - 6 + 30
-12k = 24
Divide both sides by -12
-12k/-12 = 24/-12
k = -2
Grant has 2/3
of ice cream in a bowl. He then removes two 1/6
cups of ice cream to share with his little br
amount of ice cream left in Grant's bowl?
Answer: 2/6 or 1/3
Step-by-step explanation:
2/3 = 4/6. 1 /6 Two times is 2/6 so by subtracting you should get 2/6 or 1/3
Solve for y. Then find the values of y that correspond
to the given values of x for the linear function.
7. y + 8x = -2 for x = 0, 1,2-2,
8. 12x + 3y = 15 for x = -1, 0, 1
y - 3x = 9 for x = -2,0, 2
10. 0.4y + 2x = 1.2 for x = -3,0,
7.
y + 8x = -2
f(x) = y = -8x - 2
f(0)=-2, f(1)=-10, f(2)=-18, f(-2)=14
8.
12x + 3y = 15
3y = -12x + 15
f(x) = y = -4x + 5
f(-1)=9, f(0)=5, f(1)=1
9.
y - 3x = 9
f(x) = y = 3x + 9
f(-2)=3, f(0)=9, f(2)=15
10.
0.4y + 2x = 1.2
4y + 20x = 12
4y = -20x + 12
f(x) = y = -5x + 3
f(-3) = 18, f(0)=3
Solve the system by graphing. Write the solution as an ordered pair.
y = –3x + 3
y = 12x – 4
The solution on the graph is the coordinate of the point where both lines intersect
Given the equation of two lines expessed as;
y = -3x + 3 and y = 12 x - 4
Since both expressions ara y values, equating both will give;
-3x + 3 = 12x - 4
-3x - 12x = -4 - 3
-15x = -7
x = 7/15
Substitute x = 7/15 into any of the equatons;
y = -3x + 3
y = -3(7/15) + 3
y = -7/5 + 3
y = 8/5
Hence the solution as an ordered pair is (7/15, 8/15)
The solution on the graph is the coordinate of the point where both lines intersect as shown in the graph below;
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There are 70 students attending summer camp, 21 girls and 49 boys. What is
the ratio of girls to boys at summer camp?
O A. 7:3
O B. 3:7
O 6. 2:1
SUBMIT
five numbers that have 3, 7, and 13 as prime factors
Step-by-step explanation:
(3)(7)(13) = 273
(3)(3)(7)(13) = 819
(3)(7)(7)(13) = 1911
(3)(7)(13)(13) = 3549
(3)(3)(3)(7)(13) = 2457
(3)(7)(7)(7)(13) = 13377
(3)(7)(13)(13)(13) = 46137
....
find the value for x.
Answer: x = -13
=========================
Work Shown:
19 = 38/2
19 & 1/2 = 19 + 1/2
19 & 1/2 = 38/2 + 1/2
19 & 1/2 = (38+1)/2
19 & 1/2 = 39/2
-------
In the original equation, replace the "19 & 1/2" with "39/2" to get
(5/2)x + (1/2)x = 39/2 + (9/2)x
Each term involves a fraction with a denominator of 2. If we multiply both sides by the common denominator, then the fractions will cancel out
For example: 2*(5/2)x = (10/2)x = 5x
So after multiplying both sides by 2, you should have this new equation
5x + 1x = 39 + 9x
--------
Let's solve that latest equation for x
5x + 1x = 39 + 9x
6x = 39 + 9x
6x-9x = 39 + 9x-9x ... subtract 9x from both sides
-3x = 39
-3x/(-3) = 39/(-3) .... divide both sides by -3
x = -13
The height of a skydiver jumping out of an airplane is given by h=16t +3200
Answer:
The answer is yes :)
Step-by-step explanation:
What should the following rate be divided by to convert it to a unit rate?
6 inches
12 hours
Answer:
so if all of the awnsers are whole numbers it is going to be 12/12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Unit rate is a rate that has 1 as denominator.
Given the rate: 6 inches / 12 hours, we have to divide numerator and denominator by 12 to transform the denominator in 1, as follows:
[tex]\frac{6}{12} = \frac{6/12}{12/12} =[/tex] 0.5 inches/hour
The cost of having one pizza delivered is $14. Each additional pizza cost $9 more. Write the explicit and recursive formula to represent the situation.
Answer:
14 +(9×x) = y x being the number of pizzas that are not the first one and y is the amount it all cost
Answer:
See explanation below:
Step-by-step explanation:
Here we want to express the number of pizza delivered. Lets try to understand the case.
If we buy one pizza (p1) the cost is 14 because of the delivery plus 9 for the cost of the pizza. So:
p1 = 14 + 9 = 23
If we buy 2 pizzas (p2) we have to pay 14 for the delivery and 9 for each pizza:
p2 = 14 + 9 + 9 = 14 + 2*9 = 32
If 3 pizzas are bought (p3) the reasoning is the same, 14 for the delivery and 9 for each pizza:
p3 = 14 + 9 + 9 + 9 = 14 + 3*9 = 41
Here we can see a pattern: for any amount of pizzas n the cost will be 14 plus n-times 9, the price of a pizza. It is:
pn = 14 + 9*n
But we can separate the last equation in such a way:
pn = 14 + 9*(n-1) + 9 , as 9*(n-1) + 9 = 9*n
But if our general formula it true, the first to terms on the right are the vost of buying n-1 pizzas, so:
pn = pn-1 + 9
We can keep on separating terms as we did to arrive to this form, this is, separating the 9n in 9*(n-2) + 9*2, 9*(n-3) + 9*3, ..., 9*(n-m) + 9*m for any m < n . Here I will keep pn = pn-1 + 9 as the Recursive Formula, but you could use other formulation with, e.g., pn-2, pn-3, etc, using the above recursion.
Now, the explicit formula is such that gives as the value of any amount, finding all the terms of the sequence with those not depending on previous terms (contrary to the recursive). This formula was showed above and is: pn = 14 + 9*n. This is, given any number of pizzas we can find the cost without knowing the cost of previous values.
So, we have:
Recursive: pn = pn-1 + 9
Explicit: pn = 14 + 9*n
no one helped me with the last question but i got it can someone help me with this
y = 2x
Step-by-step explanation:
The linear functions are given by:
y = mx+b
To find the slope, we have to find the change in x and y
The change in x is:
[tex]-14-(42) =-14+42 =28\\14+14= 28[/tex]
The change in y is:
[tex]-28-(-84) = -28+84 = 56\\28-(-28) = 28+28 = 56[/tex]
The slope is:
[tex]Slope = \frac{change\ in\ y}{Change\ in\ x}\\=\frac{56}{28}\\= 2[/tex]
Putting slope in equation of linear function
[tex]y =2x+b[/tex]
To find the value of b, we will put any pair of input and output in the slope-intercept form
So, putting (14,28)
[tex]28 = 2(14) + b\\28 = 28+b\\b = 28-28\\b = 0[/tex]
Hence,
the linear equation for function is:
y = 2x
Keywords: Linear function, slope intercept form
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h/2 + 3 = 3(h/4 - 1)
Answer:
h=24
Step-by-step explanation:
h/2+3=3(h/4-1)
h/2+3=3h/4-3
h/2-3h/4=-3-3
2h/4-3h/4=-6
-h/4=-6
-h=-6*4
-h=-24
h=24
Franklin Construction Company build a sidewalk around two sides of a new library, as shown in the figure. what is the area of the sidewalk.
please help
Answer:
[tex]630.36\ ft^2[/tex]
Step-by-step explanation:
we know that
To find out the area of the sidewalk, multiply the length by the width of the sidewalk
The width of the sidewalk is equal to
[tex]113.4\ ft-110\ ft=3.4\ ft[/tex]
or
[tex]75.4\ ft-72\ ft=3.4\ ft[/tex]
The area is equal to
[tex]113.4(3.4)+72(3.4)\\385.56+244.8\\630.36\ ft^2[/tex]
Bills annual salary is 2/3 of Jen's annual salary.if bills salary is$64,000, what is Jen's salary?
Answer:
$96,000
Step-by-step explanation:
To find Jen's annual salary, divide Bill's annual salary of $64,000 by 2/3, resulting in Jen's salary being $96,000.
Explanation:To calculate Jen's annual salary based on the information that Bill's annual salary is 2/3 of Jen's, first express Bill's salary as a fraction of Jen's:
Let J represent Jen's annual salary.According to the problem, we have that Bill's salary equals 2/3 of Jen's, so (2/3)*J = $64,000.To find Jen's salary J, divide Bill's salary by 2/3, so J = $64,000 / (2/3).After calculation, J = $64,000 * (3/2), which simplifies to J = $96,000.Therefore, Jen's annual salary is $96,000.
A local hamburger shop sold a combined total of 500 hamburgers and cheeseburgers on Tuesday. There were 50 fewer cheeseburgers sold than hamburgers.
How many hamburgers were sold on Tuesday?
Answer: 275
Step-by-step explanation:
Let the total number of hamburger be x and the total number of cheeseburgers be y. That is
x + y = 500 ................... equation 1
Since there were 50 fewer cheeseburgers sold than hamburgers, this means that the number of hamburgers sold is more than cheeseburgers by 50 , that is
x - y = 50 ............. equation 2
solving the resulting linear equation by substitution method;
From equation 2 , make x the subject of the formula , that is
x = 50 + y ................ equation 3
substitute equation 3 into equation 1 , we have
50 + y + y = 500
50 + 2y = 500
2y = 500 - 50
2y = 450
y = 450/2
y = 225
substitute y = 225 into equation 3 to find the value of x. we have
x = 50 + y
x = 50 + 225
x = 275
Therefore 275 hamburgers were sold
is y=5-2x and 4x+2y=10 a single solution
Answer:
X= 0
Step-by-step explanation: