Answer:
Step-by-step explanation:
Step-by-step explanation: As shown in the attached figure, the prism-shaped roof has equilateral triangular bases, one of which is ΔABC. We need to create an equation that models the height of one of the roof's triangular bases in terms of its sides. Let ii be AD.
See the figure attached herewith, ΔABC forms an equilateral triangle, in which AD is the height. So, D will be the mid-point of BC and ∠ADB = ∠ADC = 90°.
Now, in ΔADB, we have
AD^2=AB^2-BD^2
AD^2=AB^2-(1/2AB^2)^2
AD=√3/4AB^2
we can find the height of any one of the roof's triangular bases.
2.1. Check picture 1. Let the one side of the triangle be a, drop one perpendicular, CD. Then triangle ADB is a right triangle, with hypothenuse a and one side equal to 1/2a. By the Pythagorean theorem, as shown in the picture, the height is √3/2a
2. if a=25 ft, then the height is √3/2a=√3/2*25=1.732/2*25=21.7(ft)
3. consider picture 2. Let the length of the roof be l feet.
one side of the prism (the roof) is a rectangle with dimensions a and l, so the area of one side is a*l
the lateral Area of the roof is 3a*l
the area of the equilateral surfaces is 2*(1/2*a*√3/2a)=√3/2a^2
so the total area of the roof is
4. The total area was the 2 triangular surfaces + the 3 equal lateral rectangular surfaces. Now instead of 3 lateral triangular surfaces, we have 2.
So the total area found previously will be decreased by al
5. so the area now is √3/2a^2 + 2al
6. now a=25 and l=2a=50
Area= √3/2a^2+2al=√3/2*25^2+2*25*50=25^2(√3/2+4)=625*4.866
=3041.3 (ft squared)
Write the equation of the line that is perpendicular to y=2x-7 and passes through the point (6, 5)
A. y=2x-2
B.y= -1/2x+8
C.y=-1/2x-8
D.y=2x=2
Answer:
B
Step-by-step explanation:
we are given a equation of a line
we want to figure out the equation of the perpendicular line passes through the (6,5) points
in order to do so
recall that,
[tex] \displaystyle m_{ \text{perpendicular}} = - \frac{1}{m} [/tex]
we got from our given equation that m=2
because equation of a line is y=mx+b
thus
[tex] \displaystyle m_{ \text{perpendicular}} = - \frac{1}{2} [/tex]
remember that, when we want to figure out perpendicular line or parallel line we should the formula given by
[tex] \displaystyle y - y_{1} = m(x - x_{1})[/tex]
since we got our perpendicular m is -½, [tex]x_1=6[/tex] and [tex]y_1=5[/tex], substitute
[tex] \displaystyle y - 5 = - \frac{1}{2} (x - 6)[/tex]
to get the perpendicular equation you should simplify the above equation to y=mx+b form
distribute -½:
[tex] \displaystyle y - 5 = - \frac{1}{2} x + 3[/tex]
add 5 to both sides:
[tex] \displaystyle y = - \frac{1}{2} x + 8[/tex]
hence,
our answer choice is B
Find the value of x need help fast
Answer:
x = 30
Step-by-step explanation:
2x + x + 90 = 180
3x + 90 = 180
3x = 90
x = 30
What is the range of possible sizes for x?
Answer:
9.0 - 15.0
Step-by-step explanation:
Give Brainllest
How many triangles can be made with only 60 centimeters, 100 centimeters, and 40 centimeters?
GUYS SOMEONE SMARTER THAN ME, HELP!!! 100 POINTS TO YOU SMART PEOPLE!!
Answer:
6) yes
7) no
Step-by-step explanation:
can you help me pleaseeeeeee
Answer:
It's called proportion.
Step-by-step explanation:
The equality of ratios are proportional because like for example 2:3 and 4:9 these two ratios are the same. If you break down 4:9 you will get 2:3. So That's how the term proportional is applied. If we apply these ratio on a triangle they would look the same but just one is small and one is large and we can get it bigger by increasing the ratios. But the difference bwtween the ratios would be same so they are all proportional
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!
The percentage of American men who say they would marry the same woman if theyhad it to do all over again is 80%. The percentage of American women who say they would marry the same man again is 50%.
A) What is the probability that in a group of 10 married men, at least 7 will claim that they
would marry the same woman again?
B) what is the probability that less than half will say this?
C) what is the probability that in a group of 10 married woman, at least seven would claim that they would marry the same man again?
D) what is the probability that less than half will say this?
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.
1/3 divided by 6 with explanation!
Answer:
Step-by-step explanation:
In mathematics, every integer is a rational number, hence a whole number 6 can be written as 6/1. 1/3 ÷ 6 = 1/18 in fraction form. 1/3 ÷ 6 = 0.0556 in decimal form.
Answer:
1/18 or 18 is your answer.
Step-by-step explanation:
Since 1/3 is already in fraction form, we will now turn 6 into fraction form. Which is 1/6. Now we will put it into the equation 1/3 x 1/6 = 1/18. The fraction 1/18 can also be 18. Therefore, 18 or 1/18 is our answer.
hii please help asap ill give brainliest thanks
Answer:
robes were embroidered with strands of gold.
Step-by-step explanation:
based on archeological evidence
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.
For more details regarding quadratic function, visit:
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what are the measures of three angles with ratios of 1:2:3 and sum is 180
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
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.
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
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]
I need this answer, please?
Answer:
4.23
Step-by-step explanation:
3.68 + 0.21 + 0.25 + 0.01 + 0.08 = 4.23
Help again please........
Answer:
D
Step-by-step explanation:
-7 cubed = -343
-3 squared = -9
-343 - (-9) = -334
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
You can complete
to keep. ALL TESTS ARE DUE ON MONDAY, MAY 3rd! This will count as
grade.
MATH
NATION
A square has sides of length s. A rectangle is 6 inches shorter than the square and 1 inch longer.
Which of the following expressions represents the perimeter of the rectangle?
Answer:
Step-by-step explanation:
Length of rectangle: s +1
Width of rectangle: S -6
Perimeter of rectangle:2(s+1+s-6)=2(2s-5)=4s-10
Can someone help me
the answer is 9 because
3x9=27
and 27-18=9
mark brainliest plz
Solve the equations with variable on both sides: 8x=10x + 20 A. X= -10 B. X= -35 C. X= -23 D. X= -40
The correct answer is A
A) [tex]8(-10)=10(-10)+20[/tex] becomes [tex]-80 = -80[/tex]
B) [tex]8(-35)=10(-35)+20[/tex] becomes [tex]-280 \neq -330[/tex]
C) [tex]8(-23)=10(-23)+20[/tex] becomes [tex]-184 \neq -210[/tex]
D) [tex]8(-40)=10(-40)+20[/tex] becomes [tex]-320\neq -380[/tex]
What is 10 plus 9 plus 5047
Answer:
5066
Step-by-step explanation:
10 + 9 + 5047 = 5066
The answer is 5066
Answer:
5066
Step-by-step explanation:
(10 + 9) + 5047
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.
Estimate the number of fish eaten by the dolphins.
Answer:
so take 354 and add 210 simple u will get 564
Answer:
The correct answer is 564
but a Estimate would be 561.
Your welcome.
Step-by-step explanation:
Triangle ABC is isosceles with AB=CB. Circle M is inscribed in Triangle ABC such that it is tangent at points D, E, and F. If the length of BF is twice the length of CF and the perimeter of Triangle ABC is 32 inches, then determine the length of side BC in inches.
Answer:
The answer is "12 inches".
Step-by-step explanation:
Please find the image file of the graph.
We know [tex]AE = CF \ and \ EB = FB[/tex] so because the triangle is isosceles.
[tex]EB = 2x, FB = 2x,\ and \ CF = x[/tex] when [tex]AE[/tex] is called by [tex]x[/tex].
We know that [tex]AE = AD = x[/tex] since E and D are tangent points to a circle.
They have [tex]CD = CF = x[/tex] since D and F are tangent points only to circle.
Thus, if the perimeter is 32, the following is the result:
[tex]\to AE + EB + BF + FC + CD + DA = 32\\\\\to x + 2x + 2x + x + x + x = 32\\\\\to 8x = 32\\\\\to x = 4[/tex]
Therefore the length of [tex]BC = BF + FC = 2x + x = 3x = 12\ inches[/tex]
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])
Marco has $1.31 in his coin bank. He spends 87c to buy a pen. After he buys the pen,How much does he has left?
Answer: $0.44
Step-by-step explanation:
Since Marco has $1.31 in his coin bank and he spends 87c to buy a pen, the amount taht will be left with him after he buys the pen will be gotten by subtracting 87cents from $1.31.
Note that 100 cents = $1
Therefore, $1.31 will be = 100 × 1.31 = 131 cents.
Therefore, 131 cents - 87 cents = 44 cents or $0.44
He has $0.44 left