Given:
One diagonal of the kite is three times as long as the other diagonal.
The area of the kite is 48 square meters.
To find:
The length of each diagonal.
Solution:
We know that, the area of the kite is:
[tex]A=\dfrac{d_1d_2}{2}[/tex]
Where, [tex]d_1,d_2[/tex] are two diagonals of a kite.
It is given that, one diagonal of the kite is three times as long as the other diagonal.
Let [tex]d_1=3d_2[/tex]. Then the area of the kite is:
[tex]A=\dfrac{3d_2d_2}{2}[/tex]
[tex]A=\dfrac{3d_2^2}{2}[/tex]
The area of the kite is 48 square meters.
[tex]\dfrac{3d_2^2}{2}=48[/tex]
[tex]3d_2^2=2(48)[/tex]
[tex]d_2^2=\dfrac{96}{3}[/tex]
[tex]d_2^2=32[/tex]
Taking square root on both sides, we get
[tex]d_2=\sqrt{32}[/tex] [It is only positive because side length cannot be negative]
[tex]d_2=4\sqrt{2}[/tex]
Now,
[tex]d_1=3d_2[/tex]
[tex]d_1=3(4\sqrt{2})[/tex]
[tex]d_1=12\sqrt{2}[/tex]
Therefore, the diagonals of the kite are [tex]4\sqrt{2}[/tex] units and [tex]12\sqrt{2}[/tex] units.
What is the answer ??
Answer:
23 yards
Step-by-step explanation:
I need this answer, please?
Answer:
4.23
Step-by-step explanation:
3.68 + 0.21 + 0.25 + 0.01 + 0.08 = 4.23
GUYS SOMEONE SMARTER THAN ME, HELP!!! 100 POINTS TO YOU SMART PEOPLE!!
Answer:
6) yes
7) no
Step-by-step explanation:
Please help, I’ll give brainleist and 15 points
pretty sure its y=2^x aka B
Points (3, 2) and (7, 2) are on the graphs of both quadratic functions f and g. The graph of f opens downward, and the graph of g opens upward. Which of these statements are true?
1. The graphs of f and g have the same axis of symmetry.
2. The graphs of f and g have the same x-intercepts.
3. The graph of f has a maximum point, and the graph of g has a minimum point.
4. The graph is a result of a reflection of the graph pf g across the x-axis.
Answer: I and III
Step-by-step explanation:
The graphs of f and g have the same axis of symmetry. The graph of f has a maximum point, and the graph of g has a minimum point. The graph is a result of a reflection of the graph pf g across the x-axis. The correct options are 1, 3, and 4.
What is quadratic function?A quadratic polynomial in mathematics is a polynomial of degree two in one or more variables. The polynomial function defined by a quadratic polynomial is known as a quadratic function.
We can use the fact that the points (3,2) and (7,2) are on the graphs of both functions to find out which of the given statements are true.
Let's start by using the fact that the graphs of the functions f and g pass through the points (3,2) and (7,2).
Since the y-coordinate is the same for both points, we can set the equations of the functions equal to 2 and solve for the unknown coefficients.
For the downward-opening quadratic function f, the equation is of the form:
[tex]f(x) = a(x - h)^2 + k[/tex]
Where (h,k) is the vertex of the parabola. Since f opens downward, the coefficient a is negative.
Using the point (3,2), we get:
[tex]2 = a(3 - h)^2 + k[/tex]
Using the point (7,2), we get:
[tex]2 = a(7 - h)^2 + k[/tex]
Subtracting the second equation from the first, we get:
[tex]0 = a[(3 - h)^2 - (7 - h)^2][/tex]
Simplifying this expression, we get:
0 = a[(3 - h + 7 - h)(3 - h - (7 - h))]
0 = a[-4(h - 5)]
Since a is non-zero (otherwise the parabola is not quadratic), we get:
h = 5
Plugging in h = 5 and using one of the equations above, we can solve for k:
[tex]2 = a(3 - 5)^2 + k[/tex]
2 = 4a + k
k = 2 - 4a
Therefore, the equation of the quadratic function f is:
[tex]f(x) = a(x - 5)^2 + (2 - 4a)[/tex]
Using the same method for the upward-opening quadratic function g, we get:
[tex]g(x) = b(x - 5)^2 + (2 + 4b)[/tex]
Where b is positive.
Now, let's check which of the given statements are true:
The graphs of f and g have the same axis of symmetry.
Since the vertex of f is (5, 2 - 4a) and the vertex of g is (5, 2 + 4b), the x-coordinate of the axis of symmetry for both functions is 5. Therefore, statement 1 is true.
The graphs of f and g have the same x-intercepts.
The x-intercepts of f are given by:
[tex]0 = a(x - 5)^2 + (2 - 4a)\\4a = a(x - 5)^2[/tex]
x - 5 = ±√(4/a)
x = 5 ± 2√(a)
The x-intercepts of g are given by:
[tex]0 = b(x - 5)^2 + (2 + 4b)[/tex]
-4b = [tex]b(x - 5)^2[/tex]
x - 5 = ±√(-4/b)
x = 5 ± 2i√(b)
Thus, since a and b have opposite signs, the x-intercepts of f and g are different. Therefore, statement 2 is false.
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(PLEASE HELP)
Find the area of the given trapezoid.
240 is the answer you're looking for!
Step-by-step explanation:
To find the area, spilt the trapezoid into 3 shapes.
2 triangles (at the ends) and 1 rectangle (the center).
Let's start with the rectangle, the formula for rectangle area is:
[tex]l*w=A[/tex]
The length of the rectangle is 12, the width is 20. Add the numbers in:
[tex]12*20=A[/tex]
Solve:
[tex]12*20=240[/tex]
The area of the rectangle is 240. Now solve for the Triangles.
The formula for finding the area of triangles are is:
[tex](L*W)/2[/tex]
The length of the triangle is 12. To find the width subtract 20 from 30.
L = 12, W = 10. Add in the numbers.
[tex](12*10)/2 = A[/tex]
Use order of operations to solve, start with parenthesis:
[tex]120/2=A[/tex]
Rember to divide it by 2 because a triangle is half of a rectangle.
[tex]60 =A[/tex]
Since there are two identical triangles, you don't need to solve for the other
Now, add the areas together:
[tex]60 + 120+60=A[/tex]
Then solve:
[tex]180+60=A[/tex]
[tex]240=A[/tex]
The correct answer is 240.
HELPPPP PLEASE !!! I will give brainliest!!! THANK YOU
The parabola y = x2 is reflected across the x-axis and then scaled vertically by a factor of 5.
What is the equation of the new parabola?
y =
THANK YOu!!!!!
Answer:
Step-by-step explanation:
something like this Gigi,
y = -5([tex]x^{2}[/tex])
In how many orders can six people line up from left to right for a group photo?
Answer:
720 possible orders
Step-by-step explanation:
To order 6 people in a line, let's imagine them as 6 possible spaces:
( )( )( )( )( )( )
Going from left to right, let's start with space 1.
There are 6 possibilities for space 1 as any of the 6 people could occupy that space in the line.
(6)( )( )( )( )( )
Next, since one person will have already occupied space 1, there are only 5 people left who can occupy space 2, so there are 5 possibilities for space 2:
(6)(5)( )( )( )( )
Continuing in this fashion, there are now only 4 people left so 4 possibilities for space 3 and etc.
(6)(5)(4)(3)(2)(1)
This means we have 6,5,4,3,2 and 1 possibilities for each space respectively.
Multiply them together and we have:
6x5x4x3x2x1 = 720 possible orders.
Hope this helped!
Answer:
We have to arrange 6 people in line
. Now, the number of ways to arrange n items = n!.
Hence, the answer is 6!=
=6×5×4×3×2×1= 720 orders
is the answer a,b,c or d
Answer:
C) SSS
Step-by-step explanation:
SSS stands for "side, side, side" and means that we have two triangles with all three sides equal.
If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
Can someone help me
the answer is 9 because
3x9=27
and 27-18=9
mark brainliest plz
A triangle has sides with lengths of 47 inches, 27 inches, and 36 inches. Is it a right triangle?
Answer:
No because one side would have to be 54 in order for it to work
Step-by-step explanation:
the area is 634 and the perimeter is 128 so that would mean that one side would need to be 54
Write the new equation if the graph of f (x) = –2x2 + 5 is translated down 10
units. (Include f(x) in your answer)
HELPPP
PLEASE NO LINKS JUST WRITE OUT THE ANSWER
Answer:
how would i know the answer
Step-by-step explanation:
The table below shows the cost of different numbers of goldfish at a pet store.
COST OF GOLDFISH
Number of Goldfish Cost
5 $1.50
10 $3.00
15 $4.50
20 $6.00
The cost is a linear function of the number of goldfish. Which statement describes the rate of change of this function?
A. The cost increases $0.30\$ 0.30$0.30 each time 111 goldfish is added.
B. The cost increases $1.50\$ 1.50$1.50 each time 111 goldfish is added.
C. The cost increases $3.00\$ 3.00$3.00 each time 555 goldfish are added.
D. The cost increases $6.00\$ 6.00$6.00 each time 555 goldfish are added.
Answer:
A (I think because i cant tell what the answers are saying)
Step-by-step explanation:
1.5/5= 0.3
3/10=0.3
4.5/15=0.3
6/20=0.3
Next time take a screenshot because i can not really see what the answers are supposed to be. But A is the only one that should be correct
14 yd
Area Formula= base x height
Base = 7 yd X 2yd Height= 14 yd
Volume = Area of base x height
Answer:
The volume is 196 cubic yards
Step-by-step explanation:
Given
[tex]Base\ Area = 7yd * 2yd[/tex]
[tex]Height = 14yd[/tex]
Required
The volume
The volume is given as:
[tex]Volume = Base\ Area * Height[/tex]
Where:
[tex]Base\ Area = 7yd * 2yd[/tex]
[tex]Height = 14yd[/tex]
So, the equation becomes
[tex]Volume = 7yd * 2yd * 14yd[/tex]
[tex]Volume = 196yd^3[/tex]
Jason owns a food truck that sells tacos and burritos. He sells each taco for $4.75 and
each burrito for $7.50. Yesterday Jason made a total of $790 in revenue from all
burrito and taco sales and there were twice as many burritos sold as there were tacos
sold. Write a system of equations that could be used to determine the number of
tacos sold and the number of burritos sold. Define the variables that you use to write
the system.
Answer:
good luck
Step-by-step explanation:
i have no clue but plz r8 5
x is 6 or less and more than – 5
A: – 5 <
x
≤ 6 B: – 5 >
x
≤ 6 C: – 5 ≤
x
≤ 6 D: – 5 <
x
< 6 E: – 5 ≤
x
< 6
Answer:
A
Step-by-step explanation:
X is 6 or less so we can start there x≤6. X is also more than -5 so we can do that. -5<x. If we put those two together we get -5<x≤ 6.
The expression for the statement is option (A) [tex]-5 < x\leq 6[/tex] is the correct answer.
What is an inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is the condition of being unequal.
For the given situation,
The statement of inequality is x is 6 or less and more than – 5
The inequality for x is 6 or less ,
⇒ [tex]x\leq 6[/tex]
The inequality for x is more than – 5
⇒ [tex]x > -5[/tex]
Thus x is 6 or less and more than – 5 can be written as inequality,
⇒ [tex]-5 < x\leq 6[/tex]
Hence we can conclude that the expression for the statement is option (A) [tex]-5 < x\leq 6[/tex] is the correct answer.
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answer this question for 30 points and brainilest
Answer:
Volume of left side cylinder will be less than the volume of right side cylinder.
Step-by-step explanation:
Volume of a cylinder is given by the formula,
Volume = πr²h
Here, r = radius of the circular base
h = Height of the cylinder
Volume of the left hand cylinder = π(b)²a
Volume of the right hand cylinder = π(a)²b
It's given in the question that a > b
Let the value of a = 3 and b = 2
Then the volume of left hand cylinder = π(2)²(3)
= 12π
Similarly, volume of right hand cylinder = π(3)²(2)
= 18π
Therefore, volume of left side cylinder will be less than the volume of right side cylinder.
Find a volumn please help me
Step-by-step explanation:
In cuboid .
Volume
= Length * breadth * height
= 12 m * 6 m * 5 m
= 360 m³
Hope it will help :)❤
Answer:
360 m^3Step-by-step explanation:
To find volume we need to do length × width × height
We know the length is 12, the width is 6 and the height is 5
[tex]12*6=72[/tex]
[tex]72*5=360[/tex]
Once you have multiplied the numbers, you add the form of measurement which in this case is meters/m. So we will add m to the end.
Also since it is volume, we need to add ^3
360 m^3
PLS HELP ME THIS IS Probability (Single event) PLS HELP ME
Answer:
6/7
Step-by-step explanation:
a quadratic function f(x) is graphed in the xy-coordinate plane in which wuadrant eould the vertex of f (x+3)+2
Answer:
The vertex is located on the x-axis between the second and third quadrants
Step-by-step explanation:
Whereby the function is f(x) = (x + 3)², we have;
f(x) = (x + 3)² = x² + 6·x + 9
The vertex, (h, k), of the quadratic function given in general form, a·x² + b·x + c is found as follows;
h = -b/(2·a) and k = f(h)
Therefore by comparison of the given quadratic function and the general form of a quadratic function, we have;
a = 1, b = 6, c = 9
h = -6/(2 × 1) = -3
k = f(-3) = (-3)² + 6 × (-3) + 9 = 0
The vertex (h, k) = (-3, 0)
Therefore, the location of the vertex is on the x-axis axis between the second and the third quadrant.
Find the surface area of the prism? Enter your answer in the box
Step-by-step explanation: it 6
Answer: 252m^2 (squared)
Step-by-step explanation: 2×(6×3 + 6×12 + 3×12) = 252m^2
The sum of the interior angles of a regular 16-gon is
Answer:
The answer should be 2520
hii please help i’ll give brainliest:)
Answer:
They most of the time used the ability to row ships to get to places
Step-by-step explanation:
They were more reliable to row ships to trade with other people because the Mediterranean Sea was critical to how they were able to trade.
Help again please........
Answer:
D
Step-by-step explanation:
-7 cubed = -343
-3 squared = -9
-343 - (-9) = -334
PLEASE ANSWER!
I need asap
Answer:
input sloperelation outputStep-by-step explanation:
very sorry if I'm wrong
Given the figure below, find the values of x and z.
Answer:
x = 9
z = 71
Hope this helps!
Given the function F(x) = x ^ 3 + 2x - 1 , find the value f(- 2)
which expression is equivalent to 2x+x^2+3x|+5x^2-10x?
(A) x
(B) x^2
(C) -5x+6x^2
(D) 15x+6x^2
Consider function h.
What are the values of the function when x = 0 and when x = 4 ?
Answer:
x = 0 -> use the second
2(0)²-3(0)+10
h(0)= 10
x= 4 -> use the 3rd
h(4)=2⁴ = 16
The value of h(0) is 10, and h(4) is 16 because the function is a piecewise function.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a piecewise function shown in the graph:
When x = 0
h(x) = 2x² -3x + 10, 0 ≤ x , 4
h(0) = 2(0)² -3(0) + 10
h(0) = 10
When x = 4
h(x) = 2ˣ
h(4) = 2⁴ = 16
Thus, the value of h(0) is 10, and h(4) is 16 because the function is a piecewise function.
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what are the measures of three angles with ratios of 1:2:3 and sum is 180