The answer is 5 hope this helps
Answer:
5
Step-by-step explanation:
abs(a + b) + abs(c)
abs(-3 + 7) + abs(1)
abs(4) + abs(1)
4 + 1
5
Given 12x^2-4x=0, which values of x will satisfy the equation?
Answer:
0, 1/3
Step-by-step explanation:
The equation can be factored as ...
4x(3x -1) = 0
The values of x that will satisfy this equation are the values of x that make the factors be 0.
x = 0 . . . . . . when x=0
3x -1 = 0 . . . when x = 1/3
The values of x that will satisfy the equation are 0 and 1/3.
Answer:
0, 1/3
Step-by-step explanation:
The equation can be factored as ...
4x(3x -1) = 0
The values of x that will satisfy this equation are the values of x that make the factors be 0.
x = 0 . . . . . . when x=0
3x -1 = 0 . . . when x = 1/3
The values of x that will satisfy the equation are 0 and 1/3
The measure of a vertex angle of an isosceles triangle is 120°, the length of a leg is 8 cm. Find the length of a diameter of the circle circumscribed about this triangle.
Answer:
16 cm
Step-by-step explanation:
Consider isosceles triangle ABC with vertex angle ACB of 120° and legs AC=CB=8 cm.
CD is the median of the triangle ABC. Since triangle ABC is isosceles triangle, then median CD is also angle ACB bisector and is the height drawn to the base AB. Thus,
∠DCB=60°
Consider triangle OBC. This triangle is isoscels triangle, because OC=OB=R of the circumscribed about triangle ABC circle. Thus,
∠OCB=∠OBC=60°
So, ∠COB=180°-60°-60°=60°.
Therefore, triangle OCB is equilateral triangle.
This gives that
OC+OB=BC=8 cm.
The diameter of the circumscribed circle is 16 cm.
Answer:
16 cm
Step-by-step explanation:
The point (-7,4) is reflected over the line x=-3. Then the resulting point is reflected over the line y=x. Where is the point located after both reflections
Answer:
(4, 1)
Step-by-step explanation:
Since the first reflection is over the vertical line x=-3, the y-coordinate remains the same. The x-coordinate of A' will make the point (-3, 4) on the line of reflection be the midpoint between A and A':
(-3, 4) = (A +A')/2
2(-3, 4) -A = A' = (-6-(-7), 8 -4) = (1, 4)
The reflection over the line y=x simply interchanges the two coordinate values:
A'' = (4, 1)
The point (-7,4) upon reflection over the lines x = -3 and y = x would be at point; (4,1).
According to the question;
We are required to determine where the point is located after both reflections.For the first reflection;
The first reflection is over the vertical line defined at, x=-3. Consequently, the y-coordinate remains constant.However, the x-coordinate of P' will make the point (-3, 4) on the line of reflection be the midpoint between A and A':
(-3, 4) = (P +P')/2 2(-3, 4) -P = P' = (-6-(-7), 8 -4) = (1, 4)For the second reflection;
The reflection over the line y=x simply interchanges the x- and y- coordinate values:Ultimately, the point P'' = (4, 1)
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What is the volume of this triangular prism?
Answer:
5676.16 cm^3
Step-by-step explanation:
The volume of any prism is given by the formula ...
V = Bh
where B is the area of one of the parallel bases and h is the perpendicular distance between them. Here, the base is a triangle, so its area will be ...
B = 1/2·bh
where the b and h in this formula are the base and height of the triangle, 28 cm and 22.4 cm.
Then the volume is ...
V = (1/2·(28 cm)(22.4 cm))·(18.1 cm) = 5676.16 cm^3
_____
You will note that this is half the product of the three dimensions, so is half the volume of a cuboid with those dimensions. Perhaps you can see that if you took another such prism and placed the faces having the largest area against each other, you would have a cuboid of the dimensions shown.
Answer:
[tex]V=5,676.16\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the triangular prism is equal to
[tex]V=BL[/tex]
where
B is the area of the triangular face
L is the length of the triangular prism
Find the area of the triangular face B
[tex]B=\frac{1}{2}(28*22.4)= 313.6\ cm^{2}[/tex]
we have
[tex]L=18.1\ cm[/tex]
substitute the values
[tex]V=313.6*18.1=5,676.16\ cm^{3}[/tex]
When plucked, the high E string on a guitar has a frequency of 330 cycles per second. What sine function represents this note when it is graphed with an amplitude of 1.5 units? Let x represent the number of seconds. Enter your exact answer in the box.
Let's analyse the function
[tex]y = f(x) = A\sin(\omega x)[/tex]
The amplitude is A, so we want A=1.5
Now, we start at x=0, and we have [tex]1.5\sin(0)=0[/tex]
After one second, i.e. x=1, we want this sine function to make 330 cycles, i.e. the argument must be [tex]330\cdot 2\pi[/tex]
So, we have
[tex]f(1)=1.5\sin(\omega) = 1.5\sin(660\pi)[/tex]
so, the function is
[tex]f(x) = 1.5\sin(660\pi x)[/tex]
Answer:
f(x) = 1.5\sin(660\pi x)
Step-by-step explanation:
Edith has nine children at regular intervals of 15 months. If the oldest is now six times as old as the youngest, how old is the youngest child?
MANY POINTS PLEASE QUICK
Answer:
20 years
Step-by-step explanation:
9=x
8=x+15
7=x+15+15
6=x+15+15+15
5=x+15+15+15+15
4=x+15+15+15+15+15
3=x+15+15+15+15+15+15
2=x+15+15+15+15+15+15+15
1=x+15+15+15+15+15+15+15+15
Xx6=6x
6x=x+15+15+15+15+15+15+15+15
6x=120
divide both sides by 6 to get X as 20
we had written the age of the youngest son as X so the youngest son is 20 years old.
What is the lateral area of the cone to the nearest whole number? The figure is not drawn to scale.
NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!
Answer:
25,133 m^2
Step-by-step explanation:
The lateral area of a cone is found using the slant height (s) and the radius (r) in the formula ...
A = πrs
So, we need to know the radius and the slant height.
The radius is half the diameter, so is (160 m)/2 = 80 m.
The slant height can be found using the Pythagorean theorem:
s^2 = r^2 + (60 m)^2 = (80 m)^2 +(60 m)^2 = (6400 +3600) m^2
s = √(10,000 m^2) = 100 m
Now, we can put these values into the formula to find the lateral area:
A = π(80 m)(100 m) = 8000π m^2 ≈ 25,133 m^2
If $1000 is invested in an account earning 3% compounded monthly, how long will it take the account to grow in value to $1500?
Final answer:
To find out how long it will take for an investment to grow with compound interest, we use the formula A = P(1 + r/n)^(nt). Substitute the given values into the formula and solve for t using logarithms to find the time needed for the investment to reach the desired amount.
Explanation:
To determine how long it will take for $1000 invested in an account earning 3% compounded monthly to grow to $1500, we use the formula for compound interest:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where:
We want to solve for t when A is $1500, P is $1000, r is 0.03 (3%), and n is 12 (since interest is compounded monthly). Substituting these values into the formula we have:
Dividing both sides by $1000 and using algebra, we can solve for t:
[tex]1.5 = (1 + \frac{0.03}{12})^{12t}[/tex]
To solve for t, we take the natural logarithm of both sides:
[tex]ln(1.5) = ln((1 + \frac{0.03}{12})^{12t})[/tex]
[tex]ln(1.5) = 12t * ln(1 + \frac{0.03}{12})[/tex]
[tex]t = \frac{ln(1.5)}{12 * ln(1 + \frac{0.03}{12})}[/tex]
After calculating the above expression using a calculator, you will find the value of t, which is the time in years it will take for the investment to grow to $1500.
Amy makes the following statement:
"There is a 60% chance of snow tomorrow and a 10% chance I will be late for school."
What is the probability that it will snow and Amy will be late for school?
3%
6%
50%
70%
Answer:
The probability that it will snow and Amy will be late for school is 6%
Step-by-step explanation:
The answer is:
The probability that it will snow and Amy will be late for school is 6%
Step-by-step explanation:
I did the question in the quiz and I got it right soo… ^0^
What is the following product?
Answer: Last Option
[tex]4x^5\sqrt[3]{3x}[/tex]
Step-by-step explanation:
To make the product of these expressions you must use the property of multiplication of roots:
[tex]\sqrt[n]{x^m}*\sqrt[n]{x^b} = \sqrt[n]{x^{m+b}}[/tex]
we also know that:
[tex]\sqrt[3]{x^3} = x[/tex]
So
[tex]\sqrt[3]{16x^7}*\sqrt[3]{12x^9}\\\\\sqrt[3]{16x^3x^3x}*\sqrt[3]{12(x^3)^3}\\\\x^2\sqrt[3]{16x}*x^3\sqrt[3]{12}\\\\x^5\sqrt[3]{16x*12}\\\\x^5\sqrt[3]{2^4x*2^2*3}\\\\x^5\sqrt[3]{2^6x*3}\\\\4x^5\sqrt[3]{3x}[/tex]
Find the value of b in the graph of y=3x+b if it is known that the graph goes through the point: N(0,5)
Answer:
I believe b is 5.
Step-by-step explanation:
When you place the points in the values, you get 5=3(0)+b. When you simplify it, you get 5=b. I really hope this is correct, I apologize if it isn't! I hope this helps! :)
I think it’s five too
Two trains 500 miles apart accidentally are on the same track heading toward each other. The passenger train is traveling 80 mph while the freight train is traveling 40 mph. A dispatcher discovers the error and warns them 1 minute before they were to collide. How far apart, in miles, were they when they were warned?
Answer:
2 miles
Step-by-step explanation:
Their combined speed (speed of closure) is 80 mph + 40 mph = 120 mph.
120 mi/h = 120 mi/(60 min) = 2 mi/min
The distance between the trains at the 1-minute mark is ...
(1 min) · (2 mi/min) = 2 mi
They were warned when two miles apart.
Describe how the graph of g(x) is related to the parent function f(x). f(x) = 4^x g(x) = 4^x – 2
Answer:
g(x) is translated down 2 units from f(x)
Step-by-step explanation:
Adding -2 to the function value moves it down 2 units.
Answer:
The graph of f(x) is shifted to right by 2 units to get graph of g(x).
Step-by-step explanation:
We have been given two functions [tex]f(x)=4^x[/tex] and [tex]g(x)=4^{x-2}[/tex]. We are asked to find the graph of g(x) is related to the parent function f(x).
Let us recall transformation rules.
[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]
[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]
[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]
[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]
Upon comparing the graph of f(x) to g(x), we can see that [tex]g(x)=f(x-2)[/tex], therefore, the graph of f(x) is shifted to right by 2 units to get graph of g(x).
Write a quadratic function whose zeros are -3 and -4
Answer:
f(x) = (x -(-3))(x -(-4))
Step-by-step explanation:
The function can be written as the product of binomial terms whose values are zero at the given zeros.
(x -(-3)) is one such term
(x -(-4)) is another such term
The product of these is the desired quadratic function. In the form easiest to write, it is ...
f(x) = (x -(-3))(x -(-4))
This can be "simplified" to ...
f(x) = (x +3)(x +4) . . . . simplifying the signs
f(x) = x^2 +7x +12 . . . . multiplying it out
square root of 29-12square root of 5
For this case we have the following expression:
[tex]\sqrt {29-12 \sqrt {5}}[/tex]
The expression can not be simplified, we can write its decimal form.
We have to:
[tex]12 \sqrt {5} = 26.83281572[/tex]
Then, replacing:
[tex]\sqrt {29-26.83281572} =\\\sqrt {2,16718428} =\\1.4721359584[/tex]
If we round up we have:
[tex]\sqrt {29-12 \sqrt {5}} = 1.47[/tex]
ANswer:
[tex]\sqrt {29-12 \sqrt {5}} = 1.47[/tex]
the population of a small country is modeled by the equation y=525.5e^-0.01t
Where y=population (in thousands)
t=the time (in years) with t=0 for the year 2000.
what was the population in the year 2000?
ANSWER
The population in 2000 is 525.5
EXPLANATION
The population is modeled by the equation:
[tex]y=525.5e^{-0.01t}[/tex]
Where y=population (in thousands)
t=the time (in years) with t=0 for the year 2000.
To find the population in the year 2000, we substitite t=0 into the equation to get:
[tex]y=525.5e^{-0.01 \times 0}[/tex]
Perform the multiplication in the exponent:
[tex]y=525.5e^{0}[/tex]
Note that any non-zero number exponent zero is 1.
[tex]y=525.5(1)[/tex]
Any number multiplied by 1 is the same number;
[tex]y=525.5[/tex]
The population in 2000 is 525.5
The equation A = x(x - 7) describes the area, A, of a rectangular flower garden, where x is the width in feet.
What would be the width in feet of the flower garden if the area is 8 square feet?
A. 9
B. 1
C. 8
D. 7
x(x-7)=8
x^2-7x-8=0
(x-8)(x+1)=0
so x=8 (and -1 but width can’t be negative)
So your answer is C. 8
A 32 gram sample of a substance that’s a by-product of fireworks has a k-value of 0.1368. Find the substance’s half-life, in days. Use formula
N=N0e-kt, t= time in days.
HELP PLS
Answer:
t=5.1 days
Step-by-step explanation:
We know that the formula is:
[tex]N = N_0e^{-kt}[/tex]
Where N is the amount of substance after a time t, [tex]N_0[/tex] is the initial amount of substance, k is the rate of decrease, t is the time in days.
[tex]k=0.1368\\N_0 =32[/tex]
We want to find the average life of the substance in days
The half-life of the substance is the time it takes for half the substance to disintegrate.
Then we equal N to 16 gr and solve the equation for t
[tex]16= 32e^{-0.1368t}[/tex]
[tex]0.5= e^{-0.1368t}[/tex]
[tex]ln(0.5)= ln(e^{-0.1368t})[/tex]
[tex]ln(0.5)= -0.1368t[/tex]
[tex]t= \frac{ln(0.5)}{-0.1368}\\\\t=5.1\ days[/tex]
Answer:
5.1
PLATO answer
Step-by-step explanation:
please help to identify these equations. thank you, much appreciated!!
Answer:
the left curve is: y=(x+2)³-1;
the right curve is: y=3(x-2)³-1
When you flip 4 coins, the probability of getting half heads is 0.38. Likewise, the probability is 0.25 of finding that one fourth of the coins is heads. So, with four coins, the most likely outcome (the most probably state) is getting half heads, BUT thechance of getting one head (or one tail and three heads as well) is not all that much smaller, at 0.25. The charts show the probabilities for getting various fractions of heads for flipping four and for flipping eight coins. Describe the differences between the cases of four coins and eight coins with respect to how the probability of getting one-fourth heads compares to one-half heads changes when going from four to eight coins.
Answer:
Step-by-step explanation:
The probability would be twice as large for eight coins I think
The probability distribution of flipping coins changes as the number of coins increases due to the law of large numbers. The probability of getting half heads is the highest when flipping four coins, whereas the probability distribution broadens with eight coins, making specific outcomes less likely.
Explanation:When analyzing the probability of outcomes when flipping coins, we can compare the cases of flipping four coins to flipping eight coins. When flipping four coins, the most likely outcome is two heads, with a probability of 0.38. The probability of getting one head, which is one-fourth of the coins, has a probability of 0.25. However, these probabilities might change when flipping eight coins because as the number of coin flips increases, the distribution of outcomes tends to become more even due to the law of large numbers.
Tossing a fair coin should theoretically result in 50 percent heads over the long term, as demonstrated by Karl Pearson's experiment which approximated the theoretical probability after 24,000 coin tosses. When moving to eight coins, the probability distribution for getting different fractions of heads will widen, meaning that it's less likely to get a specific outcome (in terms of fractions of heads) because there are more possible combinations (microstates).
Overall, while the exact probabilities for eight coins are not provided, we can expect that the probability of getting exactly half heads will decrease since there are more total combinations possible, and the probability for one-fourth heads will also change but without specific numbers, we cannot determine the precise probabilities.
A baseball is thrown upward and its height after t seconds can be described by formula h(t)=−16t2+50t+5. Find the maximum height the ball will reach.
h(t) = -16t² + 50t + 5
The maximum height is the y vertex of this parabola.
Vertex = (-b/2a, -Δ/4a)
The y vertex is -Δ/4a
So,
The maxium height is -Δ/4a
Δ = b² - 4.a.c
Δ = 50² - 4.(-16).5
Δ = 2500 + 320
Δ = 2820
H = -2820/4.(-16)
H = -2820/-64
H = 2820/64
H = 44.0625
So, the maxium height the ball will reach is 44.0625
The maximum height the ball will reach is 81.25 feet.
Explanation:To find the maximum height the ball will reach, we can use the formula h(t) = -16t² + 50t + 5, where t represents time in seconds. The maximum height occurs at the vertex of the parabolic equation, which can be found using the formula t = -b/2a. In this case, a = -16 and b = 50. Plugging in these values, we get t = -50/(2*(-16)) = 1.5625 seconds.
Now, we can substitute this value of t back into the original equation to find the maximum height. h(1.5625) = -16(1.5625)² + 50(1.5625) + 5 = 81.25 feet. Therefore, the maximum height the ball will reach is 81.25 feet.
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PLZ HELP I BEGGG 20 POINTS!!!!!!!
Answer:
i belive its 100
Step-by-step explanation:
Answer:
hes right its 100
Step-by-step explanation:
For ΔABC, ∠A = 4x + 7, ∠B = 2x + 3, and ∠C = 6x - 10. If ΔABC undergoes a dilation by a scale factor of 2 to create ΔA'B'C' with ∠A' = 5x - 8, ∠B' = 3x - 12, and ∠C' = 7x - 25, which confirms that ΔABC∼ΔA'B'C by the AA criterion?
Final answer:
To establish that ΔABC is similar to ΔA'B'C' by the AA criterion, we need to verify that two pairs of angles are congruent. The sum of angles in each triangle should be equal to 180 degrees. However, the dilation scale factor does not affect angles, so both triangles are similar by AA criterion.
Explanation:
The question involves determining whether two triangles are similar by the AA (Angle-Angle) criterion. The original triangle ΔABC has angles ∠A = 4x + 7, ∠B = 2x + 3, and ∠C = 6x - 10. Similarly, the dilated triangle ΔA'B'C' has angles ∠A' = 5x - 8, ∠B' = 3x - 12, and ∠C' = 7x - 25. To confirm the similarity using the AA criterion, we need to prove that at least two angles of ΔABC are congruent to two angles of ΔA'B'C'.
However, upon examination of the provided angles, it's clear that there is an inconsistency. The angles of the original triangle ΔABC must add up to 180 degrees, as must the angles of the dilated triangle ΔA'B'C'. This gives us two equations to solve for x, 4x + 7 + 2x + 3 + 6x - 10 = 180 for ΔABC and 5x - 8 + 3x - 12 + 7x - 25 = 180 for ΔA'B'C'. Solving these would give us the values of x that we could use to find the angles. But the actual correspondence of angles and the fact that the sum of angles in both triangles must be equal indicates that the scale factor of dilation does not change the angles, which means ΔABC should be similar to ΔA'B'C' by AA criterion regardless of the values of x.
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. y = 8x − x2 x = 0 y = 16
Completing the square gives
[tex]y=8x-x^2=16-(x-4)^2[/tex]
and
[tex]16=16-(x-4)^2\implies(x-4)^2=0\implies x=4[/tex]
tells us the parabola intersect the line [tex]y=16[/tex] at one point, (4, 16).
Then the volume of the solid obtained by revolving shells about [tex]x=0[/tex] is
[tex]\displaystyle\pi\int_0^4x(16-(8x-x^2))\,\mathrm dx=\pi\int_0^4(x-4)^2\,\mathrm dx[/tex]
[tex]=\pi\dfrac{(x-4)^3}3\bigg|_{x=0}^{x=4}=\boxed{\dfrac{64\pi}3}[/tex]
Given: m∠ATB = 63°, arc AB = 115° Find: arc DC
Answer:
The measure of arc DC is [tex]11\°[/tex]
Step-by-step explanation:
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
[tex]m\angle ATB=\frac{1}{2}[arc\ AB+arc\ DC][/tex]
substitute the given values
[tex]63\°=\frac{1}{2}[115\°+arc\ DC][/tex]
[tex]126\°=[115\°+arc\ DC][/tex]
[tex]arc\ DC=126\°-115\°=11\°[/tex]
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite. Then the arc DC will be 11°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
∠ATB = 1/2 [arc AB + arc DC]
63° = 1/2 [115° + arc DC]
arc DC = 11°
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Two cars simultaneously left Points A and B and headed towards each other, and met after 2 hours and 45 minutes. The distance between points A and B is 264 miles. What is the speeds of the cars, if one of the cars travels 14 mph faster than the other?
The answer is:
[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]
Why?To calculate the speed of the cars, we need to write two equations in order to create a relation between the two speeds and be able to isolate one in function of the other.
So, let be the first car speed "x" and the second car speed "y", writing the equations we have:
For the first car:
[tex]x_{FirstCar}=x_o+v*t[/tex]
For the second car:
We know that the speed of the second car is the speed of the first car plus 14 mph, so:
[tex]x_{SecondCar}=x_o+(v+14mph)*t[/tex]
Now, we already know that both cars met after 2 hours and 45 minutes, meaning that positions will be the same at that moment, and the distance between A and B is 264 miles, so, we can calculate the relative speed between them.
If the cars are moving towards each other the relative speed will be:
[tex]RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph[/tex]
Then, since from the statement we know that the cars covered a combined distance which is equal to 264 miles of distance in 2 hours + 45 minutes, we have:
[tex]2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours[/tex]
Writing the equation, we have:
[tex]264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph[/tex]
So, we have that the speed of the first car is equal to 41 mph.
Now, substituting the speed of the first car in the second equation, we have:
[tex]SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph[/tex]
Hence, we have that:
[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]
Have a nice day!
14. Factor the polynomial by grouping, if possible.
3v2w – 21vw – 3v2 + 21v
A. 3vw(v – 7) – 3(w – 1)
B. 3v(v – 7)(w – 1)
C. It can't be factored.
D. 3v(v – 7)(v + 1)
Answer:
3 v (v - 7) (w - 1) thus the answer is B:
Step-by-step explanation:
Factor the following:
3 v^2 w - 21 v w - 3 v^2 + 21 v
Factor 3 v out of 3 v^2 w - 21 v w - 3 v^2 + 21 v:
3 v (v w - 7 w - v + 7)
Factor terms by grouping. v w - 7 w - v + 7 = (v w - 7 w) + (7 - v) = w (v - 7) - (v - 7):
3 v w (v - 7) - (v - 7)
Factor v - 7 from w (v - 7) - (v - 7):
Answer: 3 v (v - 7) (w - 1)
I’ve been confused on this question! Does anyone know?
Answer:
I think it is A. But i'm not 100% sure.
Step-by-step explanation:
Hope my answer has helped you!
A triangle is 20 in tall and 5 in wide. If it is
reduced to a width of 1 in then how tall will
it be?
Answer:
The triangle should be 4 inches tall
Step-by-step explanation:
We can write a proportion to solve. Put the height over the width
20 x
------- = -----------
5 1
Using cross products
20*1 = 5*x
20 = 5x
Divide by 5
20/5 = 5x/5
4 =x
The triangle should be 4 inches tall
To find the new height when the width of a triangle is reduced, you can use the concept of similar triangles and ratios.
Explanation:To determine the new height of the triangle, we can use the concept of similar triangles. Similar triangles have proportional sides. So, if the width of the triangle is reduced from 5 in to 1 in, the height will also be reduced proportionally. Using the ratio of the new width to the original width, we can find the new height:
New height = (new width / original width) * original height = (1 / 5) * 20 = 4 in
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An art student wishes to create a clay sphere as part of a sculpture. If the clay’s density is approximately 88 pounds per cubic foot and the sphere’s radius is 2 feet, what is the weight of the sphere to the nearest pound? Use 3.14 for pi, and enter the number only.
Answer:
The weight of the sphere = 2947 pounds
Step-by-step explanation:
* Lets revise the volume of the sphere
- The volume of the sphere is 4/3 π r³, where r is the radius of
the sphere
- Density = mass ÷ volume
- Mass is the weight and volume is the size, so density is weight
divided through size
- Density = weight ÷ volume
* Now lets solve the problem
∵ The clay's density ≅ 88 pounds/cubic foot
∵ The radius of the sphere is 2 feet
∵ The volume of the sphere = 4/3 π r³
∴ The volume of the sphere = 4/3 π (2)³ = 32/3 π feet³
∵ Density = weight/volume ⇒ by using cross multiply
∴ Weight = density × volume
∵ Density = 88 pounds/foot³
∵ Volume = 32/3 π feet³
∵ π = 3.14
∴ The weight of the sphere = 88 × 32/3 × 3.14 = 2947 pounds