Answer:
The new area of the triangle is (1 / 9) th of the original area.
That is to say the original area of the triangle is decreased to (1/9) th of its value.
Step-by-step explanation:
The area of a triangle is given by, Area = 1/2 [tex]\times[/tex] base [tex]\times[/tex] height
If each side of a triangle is cut to 1/3 of its original size then the base will also become one third and the height will also become one third.
Therefore the new area will be given by = 1/2 [tex]\times[/tex] (1/3 [tex]\times[/tex] base) [tex]\times[/tex] (1/3 [tex]\times[/tex] height)
= 1/9 [tex]\times[/tex] 1/2 [tex]\times[/tex] base [tex]\times[/tex] height
= 1/9 [tex]\times[/tex] Area.
The new area of the triangle is 1 / 9 th of the original area.
When the sides of a triangle are reduced to 1/3 of their original size, the area of the triangle becomes 1/9 of its original area.
When the length of each side of a triangle is cut to 1/3 of its original size, the area of the triangle is affected by the square of the scale factor applied to the sides.
Let's use some mathematics to understand why this happens. The area of a triangle is given by the formula:
A = 1/2 * base * height, where 'base' represents the base of the triangle and 'height' represents the height of the triangle.
If each side of the triangle is reduced to 1/3 of its original size, both the base and the height will become 1/3 of their respective original sizes.
The new area (A') can be calculated as follows:
New base = 1/3 of original baseNew height = 1/3 of original heightA' = 1/2 * (1/3 * base) * (1/3 * height)Simplifying this:
A' = 1/2 * (base * height) * (1/3 * 1/3)
A' = 1/2 * base * height * 1/9
A' = (1/2 * base * height) * 1/9
A' = A * 1/9
Therefore, the area of the triangle becomes 1/9 of its original area.
The fact family model represents 3 + 14 = 17.
A triangle. 17 is in the top corner. 3 is in the bottom left corner. 14 is in the bottom right corner.
How does 17 compare to 3?
14 is 17 less than 3.
3 is 14 less than 17.
3 is 17 greater than 14.
3 is 14 greater than 17. ANSWER PLEASE 100 POINS
Answer:
3 is 14 less than 17
Step-by-step explanation:
17-3=14
Answer:
the answer is B 3 is 14 less than 17
hope it helps!
A sphere intersects a plane that is 6 units away from its center; the intersection is a circle of radius 8. What is the radius of the sphere?
Answer:
10
Step-by-step explanation:
Consider the triangle consisting of the segment from the center of the sphere to the center of the circle, a radius of the circle, and the radius of the sphere to the other end of the radius of the circle. The given leg dimensions of that right triangle are 6 and 8, so the Pythagorean theorem tells you the hypotenuse (radius of the sphere) is ...
√(6²+8²) = √(36+64) = √100 = 10
The radius of the sphere is 10 units.
_____
You may recognize this as a 3-4-5 right triangle scaled by a factor of 2.
In this case, the radius of the sphere is 10 units.
The distance from the center of the sphere to the plane is given as 6 units.
According to the Pythagorean theorem, we have:
[tex]\[ r^2 = d^2 + r'^2 \][/tex]
[tex]\[ r^2 = 6^2 + 8^2 \][/tex]
[tex]\[ r^2 = 100 \][/tex]
Taking the square root
[tex]\[ r = \sqrt{100} \][/tex]
r = 10
The radius of the sphere is 10 units.
plz ans a,b,c and d.
Answer:
a.i) 1 piece = 20 days
1 day= 1/20 piece =0.05 of a piece
a.ii) 0.05*5 =0.25
a.iii) 0.05*10 =0.5 done.
so if the total is 1, 0.5 is half, so he has 0.5 work left
b.i)1 piece=12 days
4 days = 1/3 = 0.3333333333 of his work
b.ii)1/4=0.25
so 12*0.25 = 3 days
c.i)1/3 = 6 days
1 (work)= 6*3 = 18 days
c.ii) 1/18 = 1 day = 0.05555555555
c.iii) 0.5 since 9/18 = 1/2 = 0.5
d.i) 1 hour= 60 mins
whole tank = 60 mins
20 mins = 60/20 = 1/3 of a tank
if capacity = 1500L
1500 = 60 mins
1500/3 = 20 mins
=500 Liters
Please help. I’ll mark you as brainliest if correct
Answer:
527, no mistakes this time
Step-by-step explanation:
Norachai traveled to the recycling plant and back. The trip back took 5 hours. He averaged 9mph faster on the trip there than on the return trip. What was norachai average speed on the outbound trip?
Answer:
[tex]His\ average\ speed\ to\ trip\ there\ =45\ mph\\\\His\ average\ speed\ in\ return\ trip=45-9=36\ mph\\\\His\ average\ speed\ during\ whole\ trip=40\ mph[/tex]
Step-by-step explanation:
[tex]Let\ distance\ from\ one\ side=d[/tex]
Trip:
[tex]Let\ speed\ when\ he\ was\ going=x\ mph\\\\Time\ taken=4\ hours\\\\distance=d\\\\distance=speed\times time\\\\d=x\times 4\\\\d=4x\ ...................................eq(1)[/tex]
Return Trip:
[tex]Speed=x-9\ \ \ \ \ (as\ it\ is\ 9\ mph\ slower)\\\\Time\ taken=5\ hours\\\\Distance=d\\\\Distance=speed\times time\\\\Distance=5\times (x-9)\\\\d=5x-45\ ........................................eq(2)[/tex]
[tex]from\ eq(1)\ and\ eq(2)\\\\5x-45=4x\\\\5x-4x=45\\\\x=45\ mph\\\\from\ eq(1)\\\\d=4\times 45=180\ miles[/tex]
[tex]Average\ speed\ during\ whole\ trip=\frac{total\ distance}{total\ time}=\frac{2\times 180}{5+4}=\frac{360}{9}=40\ mph[/tex]
[tex]His\ average\ speed\ to\ trip\ there\ =45\ mph\\\\His\ average\ speed\ in\ return\ trip=45-9=36\ mph\\\\His\ average\ speed\ during\ whole\ trip=40\ mph[/tex]
Factor 18p-3618p−3618, p, minus, 36 to identify the equivalent expressions. Choose 2 answers: Choose 2 answers:
Answer:
18(p-2) and 2(9-18)
Step-by-step explanation:
Dracula ate 70 fries in 14 minutes. Find his fry-eating rate in fries per
minute.
Answer
5 fries per minute
Step-by-step explanation:
To work out this question, you would need to divide 70 by 14. This would give you the rate of fries he eats per minute as 14 divided by 14 = 1.
Dracula's fry-eating rate is 5 fries per minute.
The subject of this question is Dracula's fry-eating rate. In mathematics, we often deal with rates, which are a measure of how something changes over time.
In this case, we are being asked to find how many fries Dracula eats per minute. This can be found by dividing the total number of fries he ate by the total time he took.
Given, Dracula ate 70 fries in 14 minutes.
To find the fry-eating rate, we need to divide the total fries by the total minutes. That is, fry-eating rate = total fries / total time.
So, the fry-eating rate = 70 fries / 14 minutes = 5 fries per minute. Therefore, Dracula's fry-eating rate is 5 fries per minute.
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If f(x) = 2x^2+x find f(x+1)
Answer:
f(x+ 1) = 2x^2 + 5x + 3.
Step-by-step explanation:
We replace the x in the expression for f(x) by x+1:
f(x+1) = 2(x + 1)^2 + x + 1
= 2(x^2 + 2x + 1) + x + 1
= 2x^2 + 4x + 2 + x + 1
= 2x^2 + 5x + 3.
Solve S= 2HW + 2HL + 2WL for L.
To solve for L, you need to isolate/get the variable "L" by itself in the equation:
S = 2HW + 2HL + 2WL Subtract 2HW on both sides
S - 2HW = 2HW - 2HW + 2HL + 2WL
S - 2HW = 2HL + 2WL Take out the "L" in 2HL and 2WL
S - 2HW = L(2H + 2W) Now divide (2H + 2W) to get "L" by itself
[tex]\frac{S-2HW}{2H +2W} =\frac{L(2H+2W)}{2H+2W}[/tex]
[tex]\frac{S-2HW}{2H+2W} =L[/tex]
I think you can stop here, but if you need or want to simplify:
[tex]\frac{S}{2H+2W} -\frac{HW}{H+W} =L[/tex] which looks longer so I don't know if you need to do this
To solve for 'L' in the given equation, we subtract 2HW and 2WL from each side, then divide each side by 2H. The solution is L = (S - 2HW - 2WL) / 2H.
Explanation:We are given the equation S= 2HW + 2HL + 2WL and we are asked to solve for L. To do this, we will need to isolate L on one side of the equation. Here are the steps:
Subtract 2HW and 2WL from both sides of the equation. We are left with: S - 2HW - 2WL = 2HL Divide each side of the equation by 2H to solve for L. Our final solution is: L = (S - 2HW - 2WL) / 2H
So the value of L in terms of the other variables in the equation is (S - 2HW - 2WL) / 2H.
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What is the answer for the question
r = 16/2 = 8 cm
C = 2π·r = 2×3.14×8 = 50.24 cm
You start at (6, 7). You move up 2 units. Where do you end?
NW u ovo
0
1
2
3
4
5
6
7
8
9 10
If you start at (6, 7) and you move up 2 units, you will end at point (6, 9) as shown in the image attached below.
In Mathematics and Euclidean Geometry, the translation a geometric figure upward means adding a digit to the value on the positive y-axis of the pre-image;
g(x) = f(x) + k
In this exercise, we would apply a translation of 2 units up to the point (6, 7), in order to determine the coordinates of its image as follows;
(x, y) → (x, y + 2)
A (6, 7) → (6, 7 + 2) = (6, 9).
So, if you start at (6, 7) and you move up 2 units, you will end at point (6, 9) as shown in the image attached below.
v(t)=659,500(0.91)
find the initial value of the house
Answer: 659,500 is the initial value
Step-by-step explanation:
50 apple's cost $25. How much would 75 apples cost?
Answer:
$37.5
Step-by-step explanation:
(25/50) x 75 = 37.5
$25/50 .... each apple cost $0.5
0.5 x 75 = 37.5
The correct answer is 75 apples would cost $37.50.
To solve this problem, we first need to determine the cost per apple when 50 apples cost $25. We can calculate this by dividing the total cost by the number of apples:
Cost per apple = Total cost / Number of apples
Cost per apple = $25 / 50 apples
Cost per apple = $0.50 per apple
Now that we know the cost per apple is $0.50, we can calculate the cost for 75 apples by multiplying the cost per apple by the number of apples:
Cost for 75 apples = Cost per apple * Number of apples
Cost for 75 apples = $0.50 * 75
Cost for 75 apples = $37.50
Therefore, 75 apples would cost $37.50.
Which one of these graphs matches the function below?
Answer:
The lower right graph.
Step-by-step explanation:
Can someone help me with these and can give a explanation on how to do these thank you!
Answer:
x = 2 and x = 2
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
[tex]log_{x}[/tex] 8 = 3 ⇒ 8 = x³
Note 8 = 2³ = x³ ⇒ x = 2
Given
[tex]log_{5}[/tex] 25 = x ⇒ 25 = [tex]5^{x}[/tex]
25 = 5² = [tex]5^{x}[/tex] ⇒ x = 2
converting to standard form y=3x-8
Standard form for a linear equation is Ax+By=C.
Problem: Write #y=3x-8 in standard form.
Subtract 3x from both sides of the equation.
−3x+y=−8
Multiply both sides by −1.
answer ==> 3x−y=8
1) The table shows the height in centimeters, that a weight bouncing from a spring would achieve if there were no friction, for a given number of seconds.
From it's resting position, how long does it take the weight to bounce one direction, then the other, and then back to it's resting position?
Answer:
The graph shows that a consistent time to go from resting position to point A, then back to resting, then to point B, then back to resting, and so on is 0.75 seconds.
To bounce from resting to point A then point B and back to resting is 3 seconds.
The question pertains to the period of oscillation in a simple harmonic motion scenario involving a weight and a spring. The period is calculated using the formula T = 2π√(m/k). The student asks how long it takes for the weight to complete one full oscillation cycle, which can be calculated using mass and spring constant.
Explanation:The students asked about the period of oscillation for a weight attached to a spring. In physics, especially concerning simple harmonic motion (SHM), the period is the time it takes for one full cycle of motion: moving in one direction, reversing, and returning to the starting point. To find the period of a mass-spring system, we use the formula T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. This formula is derived from the motion equations that describe SHM.
For example, if you have a mass of 0.750 kg attached to a spring with a spring constant of 150 N/m, you would calculate the period using the mass (m) and the spring constant (k) from Hooke's Law. Similarly, when a spring exerts an upward force of 2.00 mg at the lowest point, this is due to the spring force being equal to the gravitational force at that point (mg) and also providing the restoring force needed for SHM (another mg).
Understanding SHM and its principles such as spring constant, and force of gravity are critical in solving these types of physics problems. These concepts explain how an attached weight on a spring moves in the absence of friction and other forces, such as air resistance.
Use the table at the right.
a. What is the approximate volume of the small truck?
Volume of the small truck = 554.54 cubic ft
Solution:
Given data:
Length of the small truck = [tex]11\frac{1}{13}[/tex] ft
Width of the small truck = [tex]7\frac{5}{12}[/tex] ft
Height of the small truck = [tex]6\frac{3}{4}[/tex] ft
Volume of the small truck = length × width × height
[tex]$=11\frac{1}{13}\times7\frac{5}{12}\times 6\frac{3}{4}[/tex]
Let us change the mixed fraction into improper fraction.
[tex]$=\frac{11\times 13 + 1}{13}\times\frac{7 \times 12 + 5}{12}\times \frac{6 \times 4 + 3}{4}[/tex]
[tex]$=\frac{144}{13}\times\frac{89}{12}\times \frac{27}{4}[/tex]
[tex]$=\frac{7209}{13}[/tex]
= 554. 54 cubic ft
Volume of the small truck = 554.54 cubic ft
Stacey buys 6 pounds of chicken for $39 days how much will she pay for 11 more pounds of chicken?
Answer:
$110,5
Step-by-step explanation:
If 6 pounds costs $39, then 17 pounds (11+6) will cost $110,5
The solution can be found using famous math rule called "Rule of three".
In this case we have an unknown quantity [tex]\left \{ {{6=39}\atop {17=?}} \right.[/tex] where ? can be found multiplying $39 x 17 (new quantity) and dividing by the first quantity, [tex]? = \frac{39x17}{6}[/tex]
what toolkit function are discontinuous
The functions that are discontinuous are:
Step Function
Absolute Value Function
Dirichlet Function
Piecewise-defined Functions
We have,
Several functions are known to be discontinuous at certain points or intervals.
Here are a few common examples of functions that exhibit discontinuity:
- Step Function:
A step function is a piecewise-defined function that "jumps" from one constant value to another at specific points.
- Absolute Value Function:
The absolute value function, denoted as |x|, is discontinuous at x = 0, where it changes its slope abruptly.
- Dirichlet Function:
The Dirichlet function is defined as follows: D(x) = {1 for rational x, 0 for irrational x}.
This function is discontinuous at all rational numbers and irrational numbers.
- Piecewise-defined Functions:
Functions that are defined using different formulas or rules for different intervals can exhibit discontinuities at the points where the rules change.
Thus,
The functions that are discontinuous are:
Step Function
Absolute Value Function
Dirichlet Function
Piecewise-defined Functions
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Can someone answer this question please answer it correctly and show work please
Answer:
40) D
41) -56.33
Step-by-step explanation:
40)
Equation #1) 1 centimeter = 2.5 meters on the drawing
Equation #2) Length of the cafeteria on the drawing = 12.25 cm
Actual length:
Multiply both sides of equation #1 by 12.25 to get the actual length of the cafeteria
1(12.25) = 2.5(12.25)
12.25 cm = 30.625 meters
D
41)
[tex]\frac{0.5\left(8\ +\ 3.2\right)}{-0.1}+\ \frac{3}{\left(-2.7\ -\ 6.3\right)}[/tex]
Start with multiplication inside the parenthesis
[tex]\frac{4\ +\ 1.6}{-0.1}+\ \frac{3}{\left(-2.7\ -\ 6.3\right)}[/tex]
Add/Subtract
[tex]\frac{5.6}{-0.1}+\ \frac{3}{-9}[/tex]
Simplify
[tex]-56+\left(-0.33\right)[/tex]
[tex]-56 - 0.33[/tex]
[tex]-56.33[/tex]Hope this helps ツ
NEED HELP ON THIS QUESTION ASAP PLEASE
Answer:
the last one
Step-by-step explanation:
There is another option that got cut off, it is
D: -1;the amount of water decreases by 1 gallon per minute
PLEASE ANSWER
Answer:
answer is b
Step-by-step explanation:
look at the picture
What is the value of d + e + fwhen d = 20, e = -4 and f = -2?
0-26
O 14
0-22
18
The value of d + e + f is 14
Solution:
Given that,
d = 20
e = -4
f = -2
We have to find the value of d + e + f
Substitute d = 20 and e = -4 and f = -2
Thus we get,
d + e + f = 20 + (-4) + (-2)
Remove the parenthesis
We know that, when we multiply negative sign with positive sign, we get negative sign as result
d + e + f = 20 - 4 - 2
d + e + f = 20 - 6
d + e + f = 14
Thus value of d + e + f is 14
Decide whether the rates are equivalent.
$16 for 4 pounds
$1 for 4 ounces
Answer:
No i dont think so
Step-by-step explanation:
Because 16:4 isn't an equivilent ratio to 1:4
Jacob earns $8 per hour babysitting. The table below shows the amount of money he earns for hours worked. Which of the following is the independent variable
Answer:
What table below
Step-by-step explanation:
The independent variable is what you change
The dependent variable is what you measure
So the money he earns per hour seems like a constant, and it won't change. Therefore the dependent variable would be the amount of money he earns.
The number of hours he works can be changed, so the independent variable would the number of hours he works/babysits
Find the volume of the pet carrier shown at the right
Answer:
Volume of the pet carrier [tex]=2702.5[/tex] cubic inches
Step-by-step explanation:
The Pet carrier in the image is in the shape of a cuboid
The volume of a cuboid can be found by the formula
volume of cuboid= [tex]Length*Breadth*Height[/tex]
Given:
Length = 20 inches, Breadth=[tex]11\frac{3}{4} =\frac{(11*4)+3}{4}=\frac{47}{4}[/tex] inches,
Height=[tex]11\frac{1}{2}=\frac{23}{2}[/tex] inches
Volume of the pet carrier:
[tex]=20*\frac{47}{4}* \frac{23}{2}\\\\= 5*47*\frac{23}{2} \\\\=5*47*11.5\\[/tex]
[tex]=2702.5[/tex] cubic inches
Volume of the pet carrier [tex]=2702.5[/tex] cubic inches
help pls pls pls
4 x 10
plssss plz plz plzz so hard
Answer:
40
Step-by-step explanation:
4 x 10= 40
PlZ add brainliest.
Answer:
40 is the answer to this question
If the mean of the following distribution is 91 and sum of frequencies is 150 find x and y
Answer:
Step-by-step explanation:
Mean = ∑x/ N
91 = ∑x / 150
∑x = 150 * 91 = 13650
x= 6825 and y = 6825
y × 6 for y = 2/3. what is the y? please help.
Answer:
The answer is Y = 4. Hope this helps.
Answer: y is 2/3, or the answer to the equation is 4
Step-by-step explanation:
it tells you what y is with y=2/3, so you need to plug that into the equation nto get 4, or just use 2/3 as your answer