Answer:
Slope of the base segment line is zero, hence base segment is horizontal
Slope of the segment that joins the vertex angle to the midpoint of its base is undefined hence the line is vertical
Therefore, angle between base segment line and the segment line from the vertex angle to the midpoint is perpendicular
Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base
Step-by-step explanation:
Here we prove the required relation as follows;
Let the isosceles be ABC
The coordinates of the points are
C = (0, 0) (Vertex)
A = (-a, b)
C = (a, b)
P = (0, b) (Midpoint of base)
Therefore, the gradient or slope of the base AC is presented as follows;
[tex]Slope, m \, of \. base, \, AC= \frac{dy}{dx} = \frac{b - b}{a - (-a)} = \frac{0}{2\cdot a} = 0[/tex]
Hence, segment AC is vertical
[tex]Slope, m \, of \, segment \ CP \, joining \, vertex, \, to \, midpoint, P, on \,AC = \frac{0 - b}{0 - 0} = \frac{-b}{0} = Undifined.[/tex]
Hence, segment CP is vertical
Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base.
In an isosceles triangle with base BC, the segment from vertex A to the midpoint M of BC is vertical, whereas BC is horizontal. Since vertical and horizontal lines are perpendicular by definition, AM is perpendicular to BC.
Let's assign coordinates to the isosceles triangle ABC, where AB = AC and BC is the base. Assume the vertex A is at the origin (0, 0), the base endpoints B and C are at coordinates (-b, c) and (b, c) respectively.
First, find the midpoint M of BC. The coordinates of M will be the average of the x-coordinates and the y-coordinates of B and C. Thus, M = (0, c).Next, determine the slope of line AM (vertex to midpoint). Since A is at (0, 0) and M is at (0, c), the slope is:What is the solution to the inequality -4x < 8?
x < -2
x > -2
x < -24
x > -24
Answer:
x > -2
Step-by-step explanation:
-4x < 8
-8 < 4x
-2 < x
x > -2
what is (a^4/-7b^3)^2 simplified?
Answer:
Step-by-step explanation:
[tex](\frac{a^{4}}{-7b^{3}})^{2}=\frac{(a^{4})^{2}}{(-7b^{3})^[2}}\\\\=\frac{a^{4*2}}{(-7)^{2}b^{3*2}}\\\\=\frac{a^{8}}{49b^{6}}[/tex]
Kayla hit 4 homeruns at batting practice
out of 12 pitches thrown. What is the
experimental probability that Kayla will hit a
homerun at batting practice?
Answer:
[tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given,
Total number of trial = 12
Total number of favorable event = 4
Experimental probability of hitting home run is
[tex]P(home\ run)=\dfrac{Favorable\ event}{Total\ trial}[/tex]
[tex]P(home\ run)=\dfrac{4}{12}[/tex]
[tex]P(home\ run)=\dfrac{1}{3}[/tex]
Answer:1/3
Step-by-step explanation:Answer:
Step-by-step explanation:
Given,
Total number of trial = 12
Total number of favorable event = 4
Experimental probability of hitting home run is
f(x)=4x2−16
find the zeros of the function
Answer:
x=2 x=-2
Step-by-step explanation:
f(x)=4x^2−16
f(x)=4(x^2-4)
f(x)=4(x-2)(x+2)
x=2 x=-2
Hope this helps! Please mark brainliest :)
The zeros of the function f(x) = 4x2 − 16 are found by factoring the quadratic equation, which results in two solutions x = -2 and x = 2.
Explanation:To find the zeros of the function f(x) = 4x2 − 16, we need to set the function equal to zero and solve for x:
0 = 4x2 - 16
To solve this quadratic equation, you can factor out the common factor of 4:
0 = 4(x2 - 4)
We now have a difference of squares, which can be factored further:
0 = 4(x + 2)(x - 2)
Set each factor in the parentheses equal to zero:
x + 2 = 0 → x = -2x - 2 = 0 → x = 2So the zeros of the function are x = -2 and x = 2.
Quadratic formula what is the expression for discriminant
Answer:
b^2-4ac
Step-by-step explanation:
By looking at that part after substituting and calculating, you can tell these things about the solution
When finding the volume of a soup can, Tommy needs to calculate the area of the base. Describe what type of base Tommy’s soup can has and what formula he should use to find its area.
Answer: The base is a circle and you can use the formula (pi)r^2 the find the area of the base
Step-by-step explanation:
a soup can is a cylinder and the base of a cylinder is a circle. you can google "area of a circle calculator" on google to show you the formula
Answer:
Sample response: The soup can has a circular base. The radius measure is needed. If the diameter is given, find the radius, which is half the diameter. Square the radius and multiply that answer by pi for the base area.
Step-by-step explanation:
I just did it on edge
how much space do all three of the soccer balls take up ?
Answer: 2713 cubic centimeter
Step-by-step explanation:
Answer:
339 cubic centimeters
Step-by-step explanation:
The formula for the volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex]. In this case, a ball with the radius of 3 centimeters would have a volume of [tex]\frac{4}{3}\pi \cdot 3^3=113.04[/tex] cubic centimeters. Multiplying this by the three soccer balls, you get about 339 cubic centimeters, or the third option. Hope this helps!
An artist is creating a sculpture where a globe with a diameter of 48 inches sits in a cone like a scoop of ice cream. She wants the cone of her sculpture to be geometrically similar to an actual ice cream cone that has a diameter of 2 1/2 inches and a height of 6 inches. What should be the height of the cone in the artist’s sculpture?
We have been an artist is creating a sculpture where a globe with a diameter of 48 inches sits in a cone like a scoop of ice cream. She wants the cone of her sculpture to be geometrically similar to an actual ice cream cone that has a diameter of 2 1/2 inches and a height of 6 inches.
We will use proportions to solve our given problem.
[tex]2\frac{1}{2}=2.5[/tex]
[tex]\frac{\text{Height of sculpture}}{\text{Diameter of sculpture}}=\frac{\text{Height of cone}}{\text{Diameter of cone}}[/tex]
[tex]\frac{\text{Height of sculpture}}{48}=\frac{6}{2.5}[/tex]
[tex]\frac{\text{Height of sculpture}}{48}\cdot 48=\frac{6}{2.5}\cdot 48[/tex]
[tex]\text{Height of sculpture}=6\cdot 19.2[/tex]
[tex]\text{Height of sculpture}=115.2[/tex]
Therefore, the height of the sculpture should be 115.2 inches.
Answer:
115 1/5
Step-by-step explanation:
This is 100% the answer because I took a test with this question and that was the correct answer
Please mark as brainliest :)~
Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 17 feet by 17 feet by 2 inches for a patio if the concrete costs $64.00 per cubic yard?
Answer:
$114.17
Step-by-step explanation:
First we need to convert cubic yard to cubic feet.
One yard is equivalent to three feet, so one cubic yard is 3^3 = 27 cubic feet.
So the cost of one cubic feet is 64/27 = $2.3704
We also need to convert from inches to feet.
One inch is 1/12 feet, so 2 inches is 2/12 = 1/6 feet
Now we need to find the volume of the slab:
Volume = 17 * 17 * (1/6) = 48.1667 ft3
Now, to find the cost, we can use a rule of three:
1 cubic feet -> $2.3704
48.1667 cubic feet -> X
X = 48.1667 * 2.3704 = $114.1743
1. According to the box and whisker plot below, what was the lower quartile weight of Frank's
classmates?
Weights of Frank's Classmates (in lbs.)
50 75 100 125 150
HHHHHHHHH
a) 65
b) 75
c)
95
d) 125
B
Step-by-step explanation:
I hoped this helped
Based on the provided box and whisker plot, the lower quartile (Q1) represents the 25th percentile of the data, which means 25% of the data points are below this value. To find the lower quartile weight of Frank's classmates, we need to identify the middle value of the lower half of the data.
The box and whisker plot separates the data into four quartiles: the lower whisker, the box (which contains Q1), the median (Q2), and the upper whisker. The box covers the interquartile range (IQR), which contains the middle 50% of the data.
Let's find the lower quartile (Q1) based on the provided data:
Weights of Frank's Classmates (in lbs.): 50, 75, 100, 125, 150
Step 1: Arrange the data in ascending order: 50, 75, 100, 125, 150
Step 2: Find the position of Q1:
Position of Q1 = (25/100) * (Total number of data points + 1)
Position of Q1 = (25/100) * (5 + 1)
Position of Q1 = (25/100) * 6
Position of Q1 = 1.5
Since the position is not a whole number, we need to take the average of the data points at positions 1 and 2.
Step 3: Calculate Q1:
Q1 = (Data at position 1) + [(Position of Q1 - Integer part of Position of Q1) * (Data at position 2 - Data at position 1)]
Q1 = 50 + [(1.5 - 1) * (75 - 50)]
Q1 = 50 + [0.5 * 25]
Q1 = 50 + 12.5
Q1 = 62.5
So, the lower quartile weight of Frank's classmates is 62.5 lbs.
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Enrico buys 3/8 of cheddar cheese and 4/8 pounds of Swiss cheese .How much cheese did Enrico buy in all?
Answer: 7/8 pounds of cheese
Step-by-step explanation:
Add the two numbers.
4/8 + 3/8 = 7/8.
That is your answer.
Analyzing Student Work
Analyze Marika's steps. Which statement is true about
her work?
Marika solved the equation (6x +15)2 + 24 = 0. Her work
is below.
1. (6x + 15)2 = -24
2. V6x +15)2 = -24
In step 2, Marika should have simplified / -24 to be
4-6
3. 6x + 15 = -25
4. 6x = -2.5 - 15
-256-15
5. X=
There are no real solutions to this equation because
the square root of a negative number is not a real
number
There should be two real solutions to this equation
because -24 = +25.
Marika correctly solved this equation.
Answer:B
Step-by-step explanation:
Edge2021
On a game show, a contestant randomly chooses a chip from a bag that contains numbers and strikes. The theoretical probability of choosing a strike is 1/8. The bag contains 7 strikes. How many chips are in the bag?
Answer:
Let x be the number of chips.
\frac{8}{x}=\frac{1}{5}
x = 40
The answer is: There are 40 chips in
Easy Question means Easy points
Topic: Volume
Focus on Scenario 2
Answer:
20,000 cm³
Step-by-step explanation:
The shape is a triangular prism
Base area × height
½ × 20 × 25 × 80
20,000 cm³
Answer:
20,000 cm³
Reason Why I know is because I had to do this very same thing :P
you invest 3200 in an account that pays an interest rate of 7.25% compounded continuosly
HELP 100 POINTS GIVEN 1. An inground non-diving swimming pool has the following dimensions. It is 33 feet long and 14 feet wide. On the
shallow end, it is 3 feet 6 inches deep and slopes gradually to a depth of 5 feet 4 inches. A picture is below. What
shape(s) can be used to estimate the volume of the pool.
2. What volume formula(s) will be used for the shape listed in
number 1
3. The pool has dimensions that are in both feet and inches. Perform unit conversions on this step
4. Apply the dimensions from number 3 to the formula(s) listed in number 1 and calculate the approximate volume of
the pool.
5. Write the answer from number 4 in scientific notation. It can be approximated.
Answer:
14inches farenheight
Step-by-step explanation:
Answer:
14 inches farenheit
Step-by-step explanation:
A machine can scan 12 pages in 3/5 minute. How many pages can be scanned in 1 minute?
Answer:
20 pages
Step-by-step explanation:
Answer:
20 pages
Step-by-step explanation:
3/5 minute =36sec
if 36=12
.·.60= 60×12÷36=20
which prism has a greater volume prism a has 17 more cubic units of volume than prism B prism B has 3 more cubic units of volume than prism a prism B has 8 more cubic units of volume than prism a
Answer:
B
Step-by-step explanation:
I also took a test
The correct answer is that neither prism has a greater volume they must have the same volume.
Let denote the volume of prism A as [tex]\( V_A \)[/tex] and the volume of prism B as [tex]\( V_B \).[/tex] According to the problem statement, we have the following relationships:
1. Prism A has 17 more cubic units of volume than prism B:
[tex]\[ V_A = V_B + 17 \][/tex]
2. Prism B has 3 more cubic units of volume than prism A:
[tex]\[ V_B = V_A + 3 \][/tex]
3. Prism B has 8 more cubic units of volume than prism A:
[tex]\[ V_B = V_A + 8 \][/tex]
However there is a contradiction in the last two statements. Prism B cannot have both 3 more cubic units and 8 more cubic units than prism A. This suggests there might be a typographical error in the problem statement.
Assuming there is a mistake and we only consider the first two statements, we can solve for the volumes by setting the two equations equal to each other since both right-hand sides are equal to [tex]\( V_B \):[/tex]
[tex]\[ V_B + 17 = V_A + 3 \][/tex]
Now, we can solve for [tex]\( V_A \)[/tex]in terms of[tex]\( V_B \)[/tex] using the first equation:
[tex]\[ V_A = V_B + 17 \][/tex]
Substitute \( V_A \) into the second equation:
[tex]\[ V_B = (V_B + 17) + 3 \][/tex]
Simplify the equation
[tex]\[ V_B = V_B + 20 \][/tex]
This simplifies to:
[tex]\[ 0 = 20 \][/tex]
This is not possible, which means our initial assumption that the two statements could be true simultaneously is incorrect. The only logical conclusion, given the contradictory information, is that neither prism has a greater volume; they must have the same volume. This is the only way to satisfy the condition that each prism has more volume than the other by different amounts.
Therefore, the volumes of prism A and prism B are equal:
[tex]\[ V_A = V_B \][/tex]
This resolves the contradiction in the problem statement. The volumes of the two prisms must be the same for the given conditions to hold true.
Find the surface area of this triangular prism.
Your answer would be 900m².
We can find this by finding the area of each of the shapes that make up the surface of this prism.
First there is the bottom of the prism, which would be 11 × 24 = 264m².
Then you have the two triangles on the sides of the prism, which are both (10 × 24)/2 each, which equals 120m² for each triangle. This means that the area for both triangles is 120 × 2 = 240m².
Next we have the area of the back of the prism, which is 11 × 10 = 110m².
Finally we need to find the area of the rectangle on top of the prism, which is 11 × 26 = 286m²
This means your final answer would be the sum of all of these, which is 264 + 240 + 110 + 286 = 900m².
I hope this helps!
Can anybody find the measure of arc KL and arc JK?
click on image for full picture
Answer:
Arc KL = 30°
Arc JK = 90°
Step-by-step explanation:
Arc KL is a connected to a central angle with the measurement of 30°. Because it is a central angle, the arc's measurement will be the same as the central angle's measurement:
Arc KL = 30°
Arc JK is connected to a central angle that has a right angle measurement sign. A right angle = 90°. Because it is a central angle, the arc's measurement will be the same as the central angle's measurement:
Arc JK = 90°
~
Answer:
arc kl= 30
arc jk=90
Step-by-step explanation:
Helllllllppppp ....,.:,:::;;,:()$?;;:/&//&
Answer:
The answer is 41>6t+7
Step-by-step explanation:
It said that he wants to earn "more than" $41 so the inequality sign is more than. Then it says $6 per hour so 6t. Then you add $7
Can you please help me with this?
Answer:
30 ,345,986
Step-by-step explanation:
Sandy plays tennis once every 6 six days. Jim plays once every 8 eight days. If they both played tennis today, in how many days will they play on the same day again?
Answer: 24 days
Step-by-step explanation:
Sandy plays tennis once every 6 six days while Jim plays tennis once every 8 eight days.
To get the number of days they will play on the same day again, we find the lowest common multiple for the numbers.
The lowest common multiple is the smallest positive integer which is evenly divisible by both 6 and 8.
6 = 6, 12, 24, 30
8 = 8, 16, 24, 32
The lowest common multiple is 24.
In 24 days, they will play on the same day again
PLEASE HELP ME
Find the surface area of the sphere. *
We have been given a sphere with radius 8.6 ft. We are asked to find the surface area of the given sphere.
We know that surface area of a sphere is equal to [tex]4\pi r^2[/tex].
[tex]A=4\pi r^2[/tex]
Upon substituting [tex]r=8.6\text{ ft}[/tex] in surface area formula, we will get:
[tex]A=4\pi (8.6\text{ ft})^2[/tex]
[tex]A=4\pi \cdot 73.96\text{ ft}^2[/tex]
[tex]A=295.84\pi\text{ ft}^2[/tex]
[tex]A=929.4087706\text{ ft}^2[/tex]
Upon rounding to nearest hundredth, we will get:
[tex]A\approx 929.41\text{ ft}^2[/tex]
Therefore, the surface of the given sphere would be approximately [tex]929.41\text{ ft}^2[/tex].
Examine the number line and select all the statements that are true.
The sum of B and C is negative.
the product of A and B > the product of A and D
|A| < |D|
A - B = -2 2/3
A + D = B
The quotient of C and B is equivalent to -2/3
Answer:
the sum of B and C is negative
A + D = B
The quotient of C and B is equivelent to -2/3
Step-by-step explanation:
The quotient of C and B is equivalent to -2/3. Therefore, the correct option is option D among all the given options.
What is number line?A picture of numbers along a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it. Just to refresh your memory, a whole number is a collection of numbers that contains all counting numbers.
Comparing numbers is made simpler by writing them on a number line. As seen in the aforementioned graphic, the integers to the left are smaller compared to the integers for the right. As an illustration, the numbers 0 and 1 are less than each other, as are the numbers -1 and -2. The sum of B and C is negative.
Therefore, the correct option is option D.
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Two sides of a rectangular fence are 5 5/8 feet long.The other two sides are 6 1/4 feet long.What is the perimeter?
Answer:
im not sure
Step-by-step explanation:
so sorry i didnt know the answer.
Answer:
the perimeter of the rectangle is 23.75 feet.
Step-by-step explanation:
5 5/8 × 2 = 11 1/4.
6 1/4 × 2 = 12 1/2
11 1/4 + 12 1/2 = 23 3/4 or 23.75
Please help for both of them
Answer:
18 is for the top
6 is for the bottom
Answer:
1. C
2. D
Step-by-step explanation:
The formula in cell B1 is =A$2. Autofill is used by dragging B1's autofill box across to C1, D1, and E1. What formulas will appear in C1, D1, and E1, respectively?
Answer:
=A$2, =A$2, =A$2
Step-by-step explanation:
Autofill is used in excel to fill a series of cells automatically. If the formula in cell B1 is =A$2. On using autofill by dragging B1's autofill box across to C1, D1, and E1, =A$2, =A$2, =A$2 appear in C1, D1, and E1, respectively. Excel tries to guess and insert next values on the basis of selected data.
Answer:
Step-by-step explanation:
A$2 A$3 A$4
houses cost £100000 one year ago
now they cost £________
this is a 25% increase
Final answer:
The new cost of houses after a 25% increase from the original price of £100,000 is £125,000. You calculate this by finding 25% of £100,000, which is £25,000, and then add it to the original price.
Explanation:
The student is asking how to calculate the new cost of houses after a 25% price increase from the previous year when the houses cost
£100,000. To find the new price, we need to calculate 25% of £100,000 and then add that to the original price.
First, find 25% of £100,000:
0.25
(multiplier for 25%)
× £100,000
(original cost)
= £25,000
(the increase).
Next, add the increase to the original cost:
£100,000
+ £25,000
= £125,000.
Therefore, the new cost of the houses after a 25% increase is £125,000.
The height of a right circular cylinder is 1.5 times the radius of the base. What is the ratio of the total surface area to the lateral (curved) surface area of the cylinder?
Let r represent the radius of cylinder.
We have been given that the height of a right circular cylinder is 1.5 times the radius of the base. So the height of the cylinder would be [tex]1.5r[/tex].
We will use lateral surface area of pyramid to solve our given problem.
[tex]LSA=2\pi r h[/tex], where,
LSA = Lateral surface area of pyramid,
r = Radius,
h = height.
Upon substituting our given values in above formula, we will get:
[tex]LSA=2\pi r\cdot (1.5)r[/tex]
Now we will find the total surface area of cylinder.
[tex]TSA=2\pi r(r+h)[/tex]
[tex]TSA=2\pi r(r+1.5r)[/tex]
[tex]TSA=2\pi r(2.5r)[/tex]
[tex]\frac{TSA}{LSA}=\frac{2\pi r(2.5r)}{2\pi r(1.5r)}[/tex]
[tex]\frac{TSA}{LSA}=\frac{2.5r}{1.5r}[/tex]
[tex]\frac{TSA}{LSA}=\frac{25}{15}[/tex]
[tex]\frac{TSA}{LSA}=\frac{5}{3}[/tex]
Therefore, the ratio of total surface area to lateral surface area is [tex]5:3[/tex].