Answer:
[tex]D=14.56[/tex]
Step-by-step explanation:
We know that the diameter of a circle is twice the radius.
Calculate the radius of the circle with the formula for calculate the distance between two points:
[tex]d=r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Where "r" is the radius.
Knowing that the center of the circle is at point (3, 1) and the circle passes through the point (1, -6), we can substitute values into the formula to find the radius:
[tex]r=\sqrt{(3-1)^2+(1-(-6))^2}=\sqrt{53}[/tex]
Then the diameter of the circle is:
[tex]D=2r\\D=2\sqrt{53}[/tex]
[tex]D=14.56[/tex]
Jefferson High School is looking to expand its student parking lot by expanding the existing lot as
shown below.
(Picture Attached)
The size of the new parking lot will be twice the size of the old parking lot. How many feet, x, was the
old parking lot expanded by?
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This was already answered.
Answer:
The value of x is 60 ft.
Step-by-step explanation:
The area of a rectangle is
[tex]A=length \times width[/tex]
The area of school is
[tex]A=165\times 300=49500[/tex]
The area of old lot with school is
[tex]A=(165+75)(300+75)=90000[/tex]
The area of old lot without school is
[tex]A_1=90000-49500=40500[/tex]
The area of new lot with school is
[tex]A=(165+75+x)(300+75+x)=x^2 + 615 x + 90000[/tex]
The area of old lot without school is
[tex]A_2=x^2 + 615 x + 90000-49500=x^2 + 615 x + 40500[/tex]
It is given that the area of new parking lot will be twice the size of the old parking lot.
[tex]2A_1=A_2[/tex]
[tex]2(40500)=x^2 + 615 x + 40500[/tex]
[tex]0=x^2 + 615 x -40500[/tex]
[tex]0 = (x - 60) (x + 675)[/tex]
[tex]x=60,-675[/tex]
The value of x can not be negative. Therefore the value of x is 60 ft.
What is 265,200 rounded to the nearest hundred thousand
265,000
Hope this helps!
Because the number in the ten thousands place is over 4, it’s going to turn the 2 in the hundred thousands place into a 3, making the answer 300,000
which of the following statements is true about the question ?
Answer:
second one :p
Second one I think ;-;
Tim mails two boxes of cookies to friends. One box weighs 1 3/4 pounds, and the other weighs 2 2/3 pounds. What is the total weight of the two boxes?
the answer would be 4 5/12 pounds
The total weight of the two boxes will be 4 and 5/12 pounds.
What is Algebra?Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.
Tim mails two boxes of cookies to friends. One box weighs 1 and 3/4 pounds, and the other weighs 2 and 2/3 pounds.
Then the total weight of the two boxes will be
Total weight = 1 + 3/4 + 2 + 2/3
Total weight = 3 + 17/12
Total weight = 3 + 1 + 5/12
Total weight = 4 + 5/12
The total weight of the two boxes will be 4 and 5/12 pounds.
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what is the solution to 8(y + 7) > 8y + 3
Answer:
y can be any real number
Step-by-step explanation:
8(y + 7) > 8y + 3
Distribute
8y+56 > 8y+3
Subtract 8y from each side
8y-8y +56 > 8y-8y +3
56 > 3
This is always true so the inequality is always true
y can be any real number
need help asap!!!
The probability of winning a game is 75%. How many times should you expect to win if you play 60 times?
(A)15
(B)45
(C)5
(C)30
Answer:
B.) 45
Step-by-step explanation:
All that is needed to solve this problem is .75*60. Whenever there is a percentage, , just move the decimal place up two :).
Kara rotates a square around its horizontal axis of symmetry to make a solid figure. Which of following could be the shape of a horizontal cross section of the solid figure
Answer:
I am pretty sure the answer is square
Which type of sequence is represented by the given table?
x
1
2
3
4
y
4
-9.6
23.04
-55.296
A.
The table represents a geometric sequence because the successive y-values have a common ratio of -2.4.
B.
The table represents an arithmetic sequence because the successive y-values have a common difference of -17.
C.
The table represents a geometric sequence because the successive y-values have a common ratio of 0.4.
D.
The table represents an arithmetic sequence because the successive y-values have a common difference of 4.2.
Answer:
A.
The table represents a geometric sequence because the successive y-values have a common ratio of -2.4.
Step-by-step explanation:
A geometric sequence, with a first term a and common ratio r, is generally represented as;
[tex]a,ar,ar^{2},ar^{3},ar^{4},............ar^{n}[/tex]
The first term refers to the first number that appears in the sequence. The common ratio is the constant that multiplies a preceding value to obtain the successive one. That is, to obtain [tex]ar^{2}[/tex] from [tex]ar[/tex] we multiply [tex]ar[/tex] by the common ratio r.
In the table given the y-values are as follows;
4, -9.6, 23.04, -55.296
To obtain the common ratio we simply divide each value by the preceding one;
(-9.6)/4 = -2.4
23.04/(-9.6) = -2.4
(-55.296)/23.04 = -2.4
Since the sequence of numbers has a common ratio then it qualifies to be a geometric sequence. Thus, the table represents a geometric sequence because the successive y-values have a common ratio of -2.4.
Answer:
The table represents a geometric sequence because the successive y-values have a common ratio of -2.4
Given that (x,y)=(5,10), find r
ANSWER
[tex]r = 5 \sqrt{5 } [/tex]
EXPLANATION
Given that (x,y)=(5,10), we want to find r.
We use the relation:
[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]
We substitute x=5 and y=10 into the formula to get,
[tex]r = \sqrt{ {5}^{2} + {10}^{2} } [/tex]
This implies that,
[tex]r = \sqrt{ 25+ 100 } [/tex]
[tex]r = \sqrt{125} [/tex]
[tex]r = 5 \sqrt{5 } [/tex]
Find the surface area of the composite solid. Round the answer to the nearest hundredth
Answer:
135.39
Step-by-step explanation:
The solid consist of 4 triangles and a 5 rectangles.
Formula to calculate area of triangle is
1/2 (height) (base)
Formula to calculate area of rectangle is
length x width
so
Total surface area of the composite solid is
2( 4(4) + 6(4) + 1/2(√13)(4) + 1/2(2√2)(6) ) + 6(4)
111.39 + 24
135.39
Answer:
Total area = 135 .39 square yard
Step-by-step explanation:
Given : composite figure.
To find : Find the surface area of the composite solid. Round the answer to the nearest hundredth.
Solution : We have given a composite figure with rectangle base and four triangles .
Base of two triangle = 4 yd .
Height of two triangle = √13 yd .
Base of other two triangle = 6 yd .
Height of other two triangle = 2√2 yd .
Area of rectangle = length * width .
Area of rectangle = 6 *4
Area of rectangle = 24 square yard .
Area of all rectangle = 3 *24 = 72 square yard
Area of two square = 2( 4*4) = 32 square yard.
Area of triangle = [tex]\frac{1}{2} base * height[/tex].
Area of triangle= [tex]\frac{1}{2} 4 *√13 [/tex].
Area of triangle = 2√13 .
Area of two triangle = 2 * 2√13 .
Area of two triangle = 4√13 square yard.
Area of other triangle = [tex]\frac{1}{2} 6 * 2√2 [/tex].
Area of other triangle = 3* 2√2
Area of other triangle = 6√2.
Area of other two triangle = 2 *6√2.
Area of other two triangle = 12√2 square yard.
Total area = Area of 3 rectangle + Area of two triangle + Area of other two triangle + area of square
Total area = 72 + 4√13 + 12√2 + 32
Total area = 135 .39 square yard.
Therefore, Total area = 135 .39 square yard.
I need help with this USA TEST PREP question
Answer:
The Answer is C
Step-by-step explanation:
The volume of the cylinder increases by a factor of 25 when the radius is increased by a factor of 5.
The volume of a cylinder is given by the formula:
Volume = π * (radius^2) * height
If the radius is increased by a factor of 5, the new radius is 5 times the original radius. Let's call the original radius "r" and the new radius "5r." The height remains the same.
Now, let's calculate the new volume with the increased radius:
New Volume = π * (5r)^2 * height
New Volume = π * 25r^2 * height
To find the effect on the volume, we can compare the new volume to the original volume:
Effect on Volume = (New Volume) / (Original Volume)
Effect on Volume = (π * 25r^2 * height) / (π * r^2 * height)
The π, height, and r^2 terms cancel out:
Effect on Volume = (25r^2) / (r^2)
Effect on Volume = 25
So, the volume of the cylinder increases by a factor of 25 when the radius is increased by a factor of 5.
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1. To calculate the height of a tree,
Marie measures the angle of elevation
from a point A to be 34º. She then
walks 10 feet directly toward the tree,
and finds the angle of elevation from
the new point B to be 41°. What is the
height of the tree?
Answer:
h ≈ 30.10 ft
Step-by-step explanation:
Marie measures the angle of elevation from a point A to a tree as 34° . She works 10 ft directly towards the tree and discovered the new angle of elevation is 41°. The height of the tree can be computed below.
let
a = distance from point B to the tree
h = height of the tree
The right angle triangle formed from point B, we can use tan to find the height of the tree.
tan 41° = opposite /adjacent
tan 41° = h/a
cross multiply
h = a tan 41°
The right angle formed from point A
tan 34° = opposite/adjacent
tan 34° = h/(a + 10)
(a + 10)tan 34° = h
Therefore,
a tan 41° = (a + 10)tan 34°
0.8692867378
a = 0.6745085168(a + 10)
0.8692867378a = 0.6745085168a + 6.7450851684
collect like terms
0.8692867378a - 0.6745085168a = 6.7450851684
0.194778221a = 6.7450851684
a = 6.7450851684/0.194778221
a = 34. 629565532 ft
height of the tree can be find with
h = a tan 41°
h = 34. 629565532 × 0.8692867378
h = 30.103022053 ft
h = 30.10 ft
9. Which of the following is the representation of a decimal number? A. 1/2 B. 23 C. 33/10 D. .25
Answer:
B because there is a dot in front of the 25 which is also known as a decimal point.
For this case we have that by definition, a decimal number is a number that is composed of a whole part, which can be zero, and by another lower than the unit, separated from the whole part by a point.
Examples:
0.05
1.76
According to the options given, we have:
A. [tex]\frac {1} {2},[/tex] it is a fraction
B. 23, is a whole number
C.[tex]\frac {33} {10}[/tex], it is a fraction
D. 0.25, is a decimal number.
Answer:
Option D
PLS HELP!!!!What are the sine, cosine and tangent ratios of
angle W in the triangle below
Step-by-step explanation:
Remember SOH-CAH-TOA:
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
The side adjacent to W is 4. The side opposite of W is 3. The hypotenuse is 5.
Therefore:
Sine = 3 / 5
Cosine = 4 / 5
Tangent = 3 / 4
what is the inverse of y=cos(x-pi/2)
Answer:
[tex]f^{-1}(x)=\cos^{-1} x+\frac{\pi}{2}[/tex]
Step-by-step explanation:
The given function is
[tex]y=\cos(x-\frac{\pi}{2})[/tex]
To find the inverse of this function, we interchange x and y.
[tex]x=\cos(y-\frac{\pi}{2})[/tex]
Take the inverse cosine of both sides to obtain;
[tex]\cos^{-1} x=y-\frac{\pi}{2}[/tex]
[tex]\cos^{-1} x+\frac{\pi}{2}=y[/tex]
Therefore the inverse of the given cosine function is;
[tex]f^{-1}(x)=\cos^{-1} x+\frac{\pi}{2}[/tex] where [tex]-1\le x\le 1[/tex]
Answer:
the answer is B
y=tanx- pie/2
Solve by using the square root property. Write your answer in simplest radical form.
Answer: X = t or minus 4 square root 3 and X= 4 square root 3 Explanation: add 48 on both sides bring down x squared = 48 take the square root on both sides you get X= t or - 4 square root 3 and X=4 square root 3) Animex yw
Answer:
x = ±4√3
Step-by-step explanation:
Given: x² = 48, find x. Note that we must take the square root of both sides, and that there are 2 roots (solutions) because this is a second order equation.
√x² = ±√48
48 is not a perfect square, but it does factor into 16 (a perfect square) and 3 (not a perfect square).
Thus, x = ±4√3 (the last answer choice)
Ignore the top just answer both of the questions at the bottom plz
Answer:
y = 5x+2 , y=x-6
Step-by-step explanation:
just by looking at the table you can see for the first one 5x + 2 satisfies the table, and x-6 satisfies the right table.
for the first table the equation is:
[tex]x(5) + 2 = y[/tex]
and for the second it's:
[tex]x - 6 = y[/tex]
Consider the net of a triangular prism where each unit on the coordinate plane represents four feet. If a sheet of plywood measures 4 ft x 8 ft, how many sheets of plywood will a carpenter need to build the prism?
A) 3
B) 3.5
C) 4
D) 4.5
Answer:
B) 3.5 ^_^
Step-by-step explanation:
Find the area of each circle, both in terms of pi and to the nearest tenth. use 3.14 for pi
Circle with radius 9 in.
Answer: 254.47
Step-by-step explanation: A=3.14*r to the power of two=3.14*9 squared=254.47
3.14*9^2=254.34 this would be the answer
Two polygons are similar. The perimeter of the smaller polygon is 48 centimeters and the ratio of the corresponding side lengths is 2/3 . Find the perimeter of the other polygon.
Answer:
= 72 cm
Step-by-step explanation:
The ratio of lengths of two similar figures is called the linear scale factor.
In this case, the linear scale factor is 2/3
The linear scale factor is also equivalent to the ratio of the perimeter of two similar figures.
Therefore, 2/3 = 48/x
x = 48 × 3/2
= 72 cm
The perimeter of the other polygon is 72 cm
Answer:
72 cm
Step-by-step explanation:
Given in the question, there are two similar polygons and the ratio of the corresponding side lengths is 2/3.
Perimeter of the smaller polygon = 48 cm
let perimeter of the larger polygon = x cm
We know that if two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.
So,
Perimeter of smaller polygon / Perimeter of larger polygon = 2 / 3
48 / x = 2 / 3
48(3) = 2(x)
144 = 2x
x = 72 cm
What is the domain of the function?
y= sqrt 5x-10
I don't know if this will help but I found this on YAHOO!
Answer: Domain of definition of a function is the set of numbers which the variable attains and for which the function is defined.
Step-by-step explanation:
f(x) = sqrt (5x-10)
Here x can have value equal to any real number >=2 because if x attains value less that 2, 5x-10 becomes negative and sqrt(5x-10) has no real value.
therefore the domain of the function f(x) is (2, infinity) inclusive of 2.
The domain of the above function is (2, ∞) .
What is a Domain ?Let y = f(x) be a function with an independent variable x and a dependent variable y.
If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.
For the given function [tex]y = \sqrt{5x-10[/tex]
The domain will be the value that satisfies the function and produces a value of y
For any value less than 2 , the value of v will be an imaginary number .
As the square root of a negative number will be an imaginary number.
Therefore (2, ∞) is the domain of the above function.
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Which of the following is equal to 4.6?
A. 1.6+(3×4)−2÷2
B. 1.6+3×4−2÷2
C. [1.6+(3×4)]−(2÷2)
D. (1.6+3)×(4−2)÷2
Answer: D
Step-by-step explanation:
PEMDAS.
1.6+3=4.6
4.6x2 = 9.2
9.2/2 = 4.6
Answer:D
Step-by-step explanation:
A standard six-sided number cube is rolled. What is tge probability a 3 or a 5 will land face up?
Answer:
It's 1/3
Step-by-step explanation:
6 possible outcomes, 2 desired.
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
There are 6 different possible numbers the cube can land on. Because it is a standard cube, all of the sides will have equal probability of getting landed on. 3 and 5 make up 2 out of 6 possibilities hence a probability of
[tex]\frac{2}{6}[/tex]
or
[tex]\frac{1}{3}[/tex]
Give some examples of perpendicular lines inside or outside your classroom.
Answer: Well for example two roads that are meeting with each other and they form a right angle,
Step-by-step explanation:
Answer:
1. A Christian cross.
2. Roads that meet at intersections
3. Hospital crosses.
Step-by-step explanation:
Perpendicular lines are lines that touch each other, or are slanted in a way that they will eventually touch each other. The examples I used are all crosses, which are two line that cross.
The basketball team sold t-shirts and hats as a fundraiser they sold a total of 23 items and made a profit of $246 they made a profit of $10 for every t shirt they sold and $12 for every hat they sold dertermine the number of t shirts and the number of hats the basketball team sold
The basketball team sold a total of 23 items (t-shirts and hats) and made $246. By setting up and solving a system of equations, it was determined that they sold 15 t-shirts and 8 hats.
To determine the number of t-shirts and hats sold by a basketball team for a fundraiser, given that they sold a total of 23 items and made a profit of $246, with a profit of $10 per t-shirt and $12 per hat sold. To solve this problem, we can set up a system of linear equations and solve for the two variables representing the number of t-shirts (T) and the number of hats (H).
Let T represent the number of t-shirts and H represent the number of hats.
We know that T + H = 23 (since 23 items were sold in total).
We also know that the profit from t-shirts is $10 per t-shirt, and the profit from hats is $12 per hat. Therefore, 10T + 12H = $246 (total profit).
We can now set up the equations:
T + H = 23
10T + 12H = $246
From the first equation, we can express H in terms of T: H = 23 - T.
Substitute H = 23 - T into the second equation:
10T + 12(23 - T) = $246
Simplify and solve for T:
10T + 276 - 12T = $246
-2T + 276 = $246
-2T = $246 - 276
-2T = -$30
T = 15 (number of t-shirts sold)
Now, we can find the number of hats by substituting T back into H = 23 - T. Since T is 15, H = 23 - 15 = 8 (number of hats sold).
Therefore, the basketball team sold 15 t-shirts and 8 hats.
Which situation allows you to have the most saved?
A) Having a set amount set aside for savings each time you are paid
B) Having a set minimum or percentage for savings whichever is greater
C) Having a percentage set aside for savings
D) Having a percentage set aside for savings when your pay is higher and hours are more
Answer:
having a set minimum or percentage for savings; whichever is greater
Step-by-step explanation:
Most saved situation is,
A) Having a set amount set aside for savings each time you are paid.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
To find Most saved situation.
Now,, We know that;
When, having a set amount set aside for savings each time you are paid- this can be the most possible answer.
And, Technically a person should save 20% to 25% of his income and this amount increases with income.
So, each time when you are paid, set aside the savings amount.
Thus, Most saved situation is,
A) Having a set amount set aside for savings each time you are paid.
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What is the length of YZ
Answer:
D = 48
Step-by-step explanation:
because if AB is 24, YZ is the double, so YZ is 48
A parabola opening upward shifted 7 units rights and 4 units down
Answer:
y + 4 = a(x - 7)^2
Step-by-step explanation:
The standard vertex form of a parabola with vertex at (h, k) is
y - k = a(x - h)^2
and if we start with the simplest case, y = a(x)^2 and translate its graph 7 units to the right and 4 units down, we get y - {-4] = a(x - 7)^2, or
y + 4 = a(x - 7)^2
The answer is y + 4 = a(x - 7)^2.
The standard vertex form of a parabola with vertex at (h, k) is
y - k = a(x - h)^2
And if we start with the simplest case,
y = a(x)^2 and
translate it Into 7 units to the right and 4 units down,
we get
y - {-4] = a(x - 7)^2
then we get the equation is y + 4 = a(x - 7)^2.
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The width of a rectangle is 12 cm less than the length. The area is 64cm^2 find the length and width. Use quadratic equations by factoring.
Answer:
length=16, width=4
Step-by-step explanation:
Use l as length and make an equation:
64 = x*(x-12)
Solve using quadratics, x=16.
Subtract 12 and get 4.
The circle below is centered at the point (5,3) and has a radius of length 4. What is it’s equation
[tex] {x}^{2} + {y}^{2} - 10x - 6y + 18 = 0[/tex]
Answer:
[tex](x-5)^2 + (y-3)^2= 16[/tex] is the equation of a circle
Step-by-step explanation:
The circle below is centered at the point (5,3) and has a radius of length 4
To find the center form of equation, we use formula
[tex](x-h)^2 + (y-k)^2= r^2[/tex]
where (h,k) is the center and 'r' is the radius of the circle
given center is (5,3)
h=5 and k =3
radius r= 4, plug in all the values in the equation
[tex](x-h)^2 + (y-k)^2= r^2[/tex]
[tex](x-5)^2 + (y-3)^2= 4^2[/tex]
[tex](x-5)^2 + (y-3)^2= 16[/tex] is the equation of a circle