Answer:
The centroid is located at (3,3)
Step-by-step explanation:
Centroid Of A Triangle
The centroid of a triangle is the point where its three medians intersect. It is also the center of gravity of the triangle. The medians are lines that go from each vertex to the midpoint of the opposite side.
Given A(ax,by), B(bx,by), C(cx,cy) the points of the vertices, then the coordinates of the centroid [tex]P(x_c,y_c)[/tex] are
[tex]\displaystyle x_c=\frac{ax+bx+cx}{3}[/tex]
[tex]\displaystyle y_c=\frac{ay+by+cy}{3}[/tex]
The vertices are (0,1) (2,6) (7,2), thus
[tex]\displaystyle x_c=\frac{0+2+7}{3}=3[/tex]
[tex]\displaystyle y_c=\frac{1+6+2}{3}=3[/tex]
The centroid is located at (3,3)
The coordinates of centroid are (3,3)
Step-by-step explanation:
The coordinates of centroid of a triangle are calculated by finding average of x-coordinates of vertices and the average of y-coordinates of vertices.
Given vertices are:
(0,1) (2,6) (7,2)
So,
x-coordinate of centroid:
[tex]x = \frac{0+2+7}{3}\\=\frac{9}{3}\\= 3[/tex]
y-coordinate of centroid:
[tex]y = \frac{1+6+2}{3}\\=\frac{9}{3}\\= 3[/tex]
Hence,
The coordinates of centroid are (3,3)
Keywords: Triangle, centroid
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The perimeter of a rectangle is 40 inches the width is 8 inches shorter than the length find the dimensions of the rectangle
Answer:
p=40
w=l-8
40=w+l
40=2(l-8)+2l
40=2l-16+2l
40=4l-16
56=4l
14=l
length=14
w=14-8=6
l=14
w=6
Main equation:
2L + 2w = 40
We know that
w = L - 8
Substitute in known value
2L + 2(L - 8) = 40
Solve
2L + 2L - 16 = 40
4L = 24
L = 6
Length = 6 inches
Width = 14 inches
Hope this helps :)
The population of a town in 2014 was 78,918 people with an annual rate of increase of about 1.7%. Which type of function can represent this situation?
A) Linear
B) Exponential
Answer:
B. Exponential.
Step-by-step explanation:
Each year you can find the estimated population for the following year by multiplying by 1 + 1.7% = 1.017.
The population estimate in x years time = 78,918 (1.017)^x.
Answer: The answer is B
Step-by-step explanation:
a radio station had 192 tickets to a concert. they gave away 5 times as many tickets to listeners as to the employees. how many tickets did they give away to employees?
A. 32
B.6
C.37
D.5
Answer: OPTION A.
Step-by-step explanation:
Let be "e" the number of tickets that the radio station gave away to employees and "l" the number of tickets that the radio station gave away to listeners.
Based on the data given in the exercise, you can set up the following System of equations:
[tex]\left \{ {{e+l=192 } \atop {l=5e}} \right.[/tex]
Finally you must apply the Substitution Method to solve the System of equations.
To apply it, you must substitute the second equation into the first one and then you must for the variable "e".
Through this precedure you get the following value of "e":
[tex]e+l=192\\\\e+(5e)=192\\\\6e=192\\\\e=\frac{192}{6}\\\\e=32[/tex]
What are the solutions to the equation x2 − 1 = 399?
A. X=20 and x=-20
B. X=200 and x=-200
C. X=400 and x=-400
D. X=398 squared and x=-398 squared
Good evening ,
Answer :
A.
x = ±20
Step-by-step explanation:
x² − 1 = 399 ⇔ x²= 400 ⇌ x² = 20² ⇌ x² − 20² = 0 ⇌ (x-20)(x+20) = 0
⇌ x = 20 or x = -20.
:)
X=20 and x=-20 are the solutions to the equation [tex]x^{2} -1 = 399[/tex]
What is a Quadratic equation?A quadratic equation exists as an algebraic equation of the second degree in x. The quadratic equation in its standard form exists [tex]ax^{2} + bx + c = 0[/tex], where a and b exist as the coefficients, x is the variable, and c stands as the constant term.
Given,
[tex]x^{2} -1 = 399[/tex]
To find,
The solutions to the equation.
Step 1
[tex]x^{2} -1 = 399[/tex]
Move terms to the left side
[tex]&x^{2}-1=399 \\[/tex]
[tex]&x^{2}-1-399=0[/tex]
Subtract the numbers
[tex]&x^{2}-1-399=0 \\[/tex]
[tex]&x^{2}-400=0[/tex]
Use the quadratic formula
[tex]$$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$[/tex]
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic equation.
[tex]&x^{2}-400=0 \\[/tex]
a=1
b=0
c=-400
[tex]&x=\frac{-0 \pm \sqrt{0^{2}-4 \cdot 1(-400)}}{2 \cdot 1}[/tex]
[tex]&x=\frac{-0 \pm \sqrt{(0^{}-1600)}}{2 }[/tex]
[tex]$x=\frac{\pm 40}{2}$[/tex]
[tex]$x=\frac{40}{2}$[/tex]
[tex]$x=\frac{-40}{2}$[/tex]
Hence,
[tex]$x=20$[/tex]
[tex]$x=-20$[/tex]
Thus, Option A. X=20 and x=-20 are the solutions to the equation [tex]x^{2} -1 = 399[/tex]
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22
alue of the expression below.
7 + (30 – 2) = 7 * 23
Hey Kim! :)
Glad to see you on Brainly.
Look below and watch how we solve this problem.
Ask any questions if you need it! I'll respond when you need it!
[tex]Remove \\parentheses. \\7+30-2=7 * 3\\\\7 + 30 - 2 = 161\\37 - 2 = 161\\\\35 = 161\\ \\ No solution.[/tex]
15. Marteen wants to paint 2/3 of her room today. She wants to paint 1/4
of that before lunch. How much of her room will she paint
today before lunch?
Answer:
1/6
Step-by-step explanation:
2/3 x 1/4 is 2/12, which simplified is 1/6.
Answer: Marteen will paint 1/6 of her room today.
Step-by-step explanation:
In order to solve this equation, all you have to do is multiply how much of her room Marteen wants to paint today (2/3) by how much of that amount she wants to paint before lunch (1/4). because she wants to paint 1/4 of 2/3 of her room before lunch, you have to multiply 2/3 and 1/4. SO...
Multiply: 1/4 x 2/3 = 2/12
Simplify: 2/12 = 1/6
Answer: 1/6
Hope this helps!
√47 rounded to the hundredth place
Answer:
6.855
Step-by-step explanation:
I don't know how to explain that, you can use a calculator.
Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 24 kilometers. If the two airplanes are 30 kilometers apart, how far has the eastbound airplane traveled?
18 km
Step-by-step explanation:
The vector appears as shown in the attached illustration. This is tantamount to finding the ? side of the right-angled triangle. The formulae is;
a² + b² = c²
24² + x² = 30²
x² = 30² – 24²
= 900 - 576
x² = 324
x = 18
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Final answer:
By using the Pythagorean theorem on the right triangle formed by the paths of the two airplanes, it is determined that the eastbound airplane has traveled 18 kilometers.
Explanation:
The question involves a geometrical problem that can be solved using the Pythagorean theorem. We are given that two airplanes leave the same airport, one heading north and the other heading east. After a certain time, the northbound airplane has traveled 24 kilometers. We are asked to find out how far the eastbound airplane has traveled, given that the two airplanes are now 30 kilometers apart.
To solve this, we can consider the path of the two airplanes as two sides of a right triangle, with the distance between the two airplanes being the hypotenuse. Using the Pythagorean theorem which states that in a right triangle the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), or a2 + b2 = c2, we have:
Let x be the distance traveled by the eastbound airplane.
242 + x2 = 302
x2 = 302 - 242
x2 = 900 - 576
x2 = 324
x = √324
x = 18 kilometers
The eastbound airplane has traveled 18 kilometers.
Jonah has a recipe that uses 1 1/2 cups of brown sugar and 2 1/3 cups of flour. Jonah wants to use all of his flour to make as many muffins as possible using this recipe.
Exactly how many cups of brown sugar will Jonah use if he uses all 7 cups of flour?
Answer:
4 1/2
Step-by-step explanation:
Answer:
4 1/2
Step-by-step explanation:
He made the recipe 3 times. 1 1/2*3=4 1/2
A store is having a sale with 10% off everything
Write an equation to show the ale price s of any item given its regular price r
Answer:
Step-by-step explanation:
Since the sale price is always less than the original, we take the original and subtract from it the percent off to give us the sale price. Putting that into equation form:
s = r - .10r
which says, in words, that the sale price is equal to the regular price minus 10% of the regular price.
does anyone have the answers for the rest of this or know the answers ?
Answer:
4.
a) [tex]4x^4-4x^3-16x^2+16x[/tex]
b) [tex]4x^4-4x^3-16x^2+16x[/tex]
5. Yes
Step-by-step explanation:
The distributive property is:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]
It can be extended to a lot of terms as well.
We will use this to multiply both of the probelms shown.
4 a)
[tex](4x^2-4x)(x^2-4)=(4x^2)(x^2)-(4)(4x^2)-(4x)(x^2)+(4x)(4)=4x^4-16x^2-4x^3+16x=4x^4-4x^3-16x^2+16x[/tex]
The answer is [tex]4x^4-4x^3-16x^2+16x[/tex]
4 b)
[tex](x^2+x-2)(4x^2-8x)=(x^2)(4x^2)-(8x)(x^2)+(x)(4x^2)-(8x)(x)-(2)(4x^2)+(2)(8x)=4x^4-8x^3+4x^3-8x^2-8x^2+16x=4x^4-4x^3-16x^2+16x[/tex]
The answer is [tex]4x^4-4x^3-16x^2+16x[/tex]
5. Yes
f(t) = -(t - 2)(t – 15)
1) What are the zeros of the function?
Write the smaller t first, and the larger t second.
Answer:
Smaller t = 2
Larger t = 5
Step-by-step explanation:
Given:
The given function is.
[tex]f(t)=-(t-2)(t-5)[/tex]
Find the zeros of the function.
Solution:
[tex]f(t)=-(t-2)(t-5)[/tex]
Simplify the equation above equation.
[tex]f(t)=-(t^{2}-5t-2t+10)[/tex]
[tex]f(t)=-(t^{2}-7t+10)[/tex]
[tex]f(t)=-t^{2}+7t-10[/tex]
Now, we first find the root of the above equation.
Use quadratic formula with [tex]a=-1, b=7, c=-10[/tex].
[tex]t=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}[/tex]
Put a, b and c value in above equation.
[tex]t=\frac{-7\pm \sqrt{(7)^{2}-4(-1)(-10)}}{2(-1)}[/tex]
[tex]t=\frac{-7\pm \sqrt{49-4\times 10}}{-2}[/tex]
[tex]t=\frac{-7\pm \sqrt{49-40}}{-2}[/tex]
[tex]t=\frac{-7\pm \sqrt{9}}{-2}[/tex]
[tex]t=\frac{-7\pm 3}{-2}[/tex]
For positive sign
[tex]t=\frac{-7 + 3}{-2}[/tex]
[tex]t=\frac{-4}{-2}[/tex]
t = 2
For negative sign
[tex]t=\frac{-7 - 3}{-2}[/tex]
[tex]t=\frac{-10}{-2}[/tex]
t = 5
Put t = 2 in given function.
[tex]f(t)=-(2-2)(2-5)=0[/tex]
Put t = 5 in given function.
[tex]f(t)=-(5-2)(5-5)=0[/tex]
So, the zeros of the function is t = 2 or 5
Therefore, the smaller value of t = 2 and larger value of t = 5.
What is the value of the expression below?
3/8 +-4/5+-3/8+5/4
Answer:
The value of the expression is [tex]\frac{9}{20}[/tex]
Step-by-step explanation:
In order to sum or subtract these fractions we need to find their LCM.
The overall LCM is 20.
Thus:
4/5=16/205/4=25/20The we get:
= -16/20+25/20
Which gives:
=9/20
Find the minimum value of P=5x+6y subject to the following constraints.
Please help me!!
Answer:
The maximum value of P is 34 and the minimum value of P is 0
Step-by-step explanation:
we have the following constraints
[tex]x+y \leq 6[/tex] ----> constraint A
[tex]2x+3y \leq 16[/tex] ----> constraint B
[tex]x\geq 0[/tex] ----> constraint C
[tex]y\geq 0[/tex] ----> constraint D
Solve the feasible region by graphing
Using a graphing tool
The vertices of the feasible region are
(0,0),(0,5.33),(2,4),(6,0)
see the attached figure
To find out the maximum and minimum value of the objective function P, substitute the value of x and the value of y for each of the vertices in the objective function P, and then compare the results
we have
[tex]P=5x+6y[/tex]
For (0,0) ----> [tex]P=5(0)+6(0)=0[/tex]
For (0,5.33) ----> [tex]P=5(0)+6(5.33)=31.98[/tex]
For (2,4) ----> [tex]P=5(2)+6(4)=34[/tex]
For (6,0) ----> [tex]P=5(6)+6(0)=30[/tex]
therefore
The maximum value of P is 34 and the minimum value of P is 0
Three pairs of shoes are priced at $39.95 each.
Estimate the total cost for the all 3 pairs of
shoes.
Answer:
39.95 × 3 = $119.85
Estimated at $40 each
3 pairs total $120
The product of a nonzero rational number and an irrational number is always rational.
True
False
Answer:
Step-by-step explanation:True
A candidate took a phone poll of 110 people. Of the 110 people polled, 87 said they would vote for the other person. There are 9570 people in the district. About how many people are going to vote for the other candidate?
A. 7400 people
B. 7569 people
C. 7069 people
D. 7900 people
Option B
7569 number of people are going to vote for the other candidate
Solution:
Given that candidate took a phone poll of 110 people
Of the 110 people polled, 87 said they would vote for the other person
There are 9570 people in the district
You can set up this problem like a proportion
Let "x" be the number of people who would vote for the other candidate
[tex]\frac{87}{110} = \frac{x}{9570}[/tex]
To solve proportions, you cross-multiply. This means you multiply the numerator by the other denominator, and the denominator by the other numerator
[tex]87 \times 9570 = 110 \times x[/tex]
832590 = 110x
x = 7569
Thus 7569 number of people are going to vote for the other candidate
Answer:
Your answer is B. 7569 people hopefully this helps!
-3x + 2 = -7 what is the x
Answer: x = 3
Step-by-step explanation: To solve for x in this equation, we must first isolate the term containing x which in this problem is -3x. Since 2 is being added to -3x, we subtract 2 from both sides of the equation to isolate the -3x.
On the left, the +2 and -2 cancel out and on the right -7 - 2 is -9 so we have -3x = -9. Now we can finish things off by just dividing both sides of the equation by -3. On the left the -3's cancel and on the right, -9 divided by -3 simplifies to 3. So we have x = 3.
Is triangles congruent?explain why or why not
Answer:
Step-by-step explanation:
Incomplete question.
Find the slope of the line through each pair of points. Pls help and explain if you cann!!
Answer:
1) The slope for the given points (6,7) and (-10,4) is [tex]m=\frac{3}{16}[/tex]
2) The slope for the given points (17,4) and (13,20) is [tex]m=-4[/tex]
3) The slope for the given points (12,19) and (14,18) is [tex]m=-\frac{1}{2}[/tex]
4) The slope for the given points (-11,0) and (18,13) is [tex]m=\frac{13}{29}[/tex]
5) The slope for the given points (3,6) and (-8,20) is [tex]m=-\frac{14}{11}[/tex]
6) The slope for the given points (-16,-20) and (12,5) is [tex]m=\frac{25}{28}[/tex]
7) The slope for the given points (13,20) and (14,-14) is [tex]m=-34[/tex]
8) The slope for the given points (18,15) and (3,0) is [tex]m=1[/tex]
Step-by-step explanation:
To find the slope of the line through each pair of points:
1) Given points are (6,7) and (-10,4)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (6,7) and (-10,4) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{4-7}{-10-6}[/tex]
[tex]m=\frac{-3}{-16}[/tex]
[tex]m=\frac{3}{16}[/tex]
Therefore the slope for the given points (6,7) and (-10,4) is [tex]m=\frac{3}{16}[/tex]
2) Given points are (17,4) and (13,20)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (17,4) and (13,20) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{20-4}{13-17}[/tex]
[tex]m=\frac{16}{-4}[/tex]
[tex]m=-4[/tex]
Therefore the slope for the given points (17,4) and (13,20) is [tex]m=-4[/tex]
3) Given points are (12,19) and (14,18)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (12,19) and (14,18) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{18-19}{14-12}[/tex]
[tex]m=\frac{-1}{2}[/tex]
Therefore the slope for the given points (12,19) and (14,18) is [tex]m=-\frac{1}{2}[/tex]
4) Given points are (-11,0) and (18,13)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (-11,0) and (18,13) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{13-0}{18-(-11)}[/tex]
[tex]m=\frac{13}{29}[/tex]
Therefore the slope for the given points (-11,0) and (18,13) is [tex]m=\frac{13}{29}[/tex]
5) Given points are (3,6) and (-8,20)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (3,6) and (-8,20) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{20-6}{-8-3}[/tex]
[tex]m=\frac{14}{-11}[/tex]
[tex]m=-\frac{14}{11}[/tex]
Therefore the slope for the given points (3,6) and (-8,20) is [tex]m=-\frac{14}{11}[/tex]
6) Given points are (-16,-20) and (12,5)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (-16,-20) and (12,5) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{5-(-20)}{12-(-16)}[/tex]
[tex]m=\frac{5+20}{12+16}[/tex]
[tex]m=\frac{25}{28}[/tex]
Therefore the slope for the given points (-16,-20) and (12,5) is [tex]m=frac{25}{28}[/tex]
7) Given points are (13,20) and (14,-14)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (13,20) and (14,-14) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{-14-20)}{14-13}[/tex]
[tex]m=\frac{-34}{1}[/tex]
[tex]m=-34[/tex]
Therefore the slope for the given points (13,20) and (14,-14) is [tex]m=-34[/tex]
8) Given points are (18,15) and (3,0)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (18,15) and (3,0) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{0-15}{3-18}[/tex]
[tex]m=\frac{-15}{-15}[/tex]
[tex]m=1[/tex]
Therefore the slope for the given points (18,15) and (3,0) is [tex]m=1[/tex]
Part 1: You are playing a game of Russian roulette with me. I put it 2 bullets in consecutive chambers, spin it, and take my turn. I survived the round, and now it's your turn. You can either take the gun as it is, or spin the chamber to make it random again. Which option gives you a better chance of surviving?
Part 2: what would the answer be if there was only 1 bullet instead?
Answer:
1. The option of spinning the chamber to make it random again gives you a probability of surviving of 67% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 60% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again gives you a better chance of surviving.
2. The option of spinning the chamber to make it random again gives you a probability of surviving of 83% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 80% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again also gives you a better chance of surviving with only one bullet.
Step-by-step explanation:
1. Which option gives you a better chance of surviving?
Let's assume the gun has six chambers, so the probabilities are:
Number of bullets remaining/Number of chambers
For the first attempt, probabilities are = 2/6 or 33%
For the second attempt of shooting the gun, the probability of having a bullet in the chamber would be = 2/5 or 40%
On the other hand, if you spin the chamber to make it random again, the probability of having a bullet in the chamber would be = 2/6 or 33%
The option of spinning the chamber to make it random again gives you a probability of surviving of 67% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 60% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again gives you a better chance of surviving.
2. What would the answer be if there was only 1 bullet instead?
Number of bullets remaining/Number of chambers
For the first attempt, probabilities are = 1/6 or 17%
For the second attempt of shooting the gun, the probability of having a bullet in the chamber would be = 1/5 or 20%
On the other hand, if you spin the chamber to make it random again, the probability of having a bullet in the chamber would be = 1/6 or 17%
The option of spinning the chamber to make it random again gives you a probability of surviving of 83% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 80% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again also gives you a better chance of surviving with only one bullet.
While testing a new pesticide, an agricultural scientist uses two functions to predict the yields of two same-sized potato farms that have different soil conditions. The scientist's predicted yield, in tons, of the first farm can be represented by the following function, where x is the liters of pesticide he uses per acre of the farm. His predicted yield, in tons, of the second farm can be represented by the following function, where x is the liters of pesticide he uses per acre of the farm. If the scientist uses the same amount of pesticide on the two farms, select the function that accurately represents the predicted combined yield from both farms.
f(x)= -2.43x^2+10.37x+9 and g(x)= -3.43^2+13x+25
A. h(x)= -5.86x^2 + 23.37x + 34
B. h(x)= -5.86x^2 + 2.63x + 34
C. h(x)= -x^2 + 2.63x + 16
D. h(x)= x^2 + 2.63x - 16
Answer:
A. h(x)= -5.86x^2 + 23.37x + 34
Step-by-step explanation:
If the scientist uses the same amount of pesticide on the two farms then the x's of the functions are the same.
Then, the combined yield [tex]h(x)[/tex] of the two farms is just the yield of the first farm plus the yield of the second farm:
[tex]h(x)=f(x)+g(x)[/tex].
Now, since
[tex]f(x)= -2.43x^2+10.37x+9[/tex]
and
[tex]g(x)= -3.43x^2+13x+25[/tex],
then
[tex]h(x)= (-2.43x^2+10.37x+9)+(-3.43x^2+13x+25)[/tex]
we add the coefficients of the corresponding terms to get:
[tex]h(x)= (-2.43x^2-3.43x^2)+(10.37x+13x)+(9+25)[/tex]
[tex]\boxed {h(x)=-5.86 x^2 + 23.37 x + 34.}[/tex]
Which is choice A.
School administrators collect data on students attending the school. Which of the following variables is quantitative?
the variable qould b and aStep-by-step explanation:
Youssef can either way from his home to his workplace or ride his bicycle. he walks at a pace of 1 block per min, but he can travel 1 block in 20 sec on his bicycle. if it takes youssef 10 min longer to walk to work than to ride his bike, how many blocks away from work does he live ?
Youssef lives 15 blocks away from his work
Solution:
Given that Youssef can either way from his home to his workplace or ride his bicycle
Let "x" be number of blocks away from work Youssef works
Case 1: walking
He walks at a pace of 1 block per min
Therefore,
1 block = 1 minute
Thus to cross "x" blocks he takes "x" minutes
Case 2: Bicycle
He can travel 1 block in 20 sec on his bicycle
We know that,
To convert seconds to minute, divide the time value by 60
[tex]\rightarrow 20 seconds = \frac{20}{60} minutes = \frac{1}{3} minutes[/tex]
Thus he takes 1/3 minutes for 1 block
So to cross "x" blocks he will take [tex]\frac{x}{3}[/tex] minutes
Given that it takes youssef 10 min longer to walk to work than to ride his bike
This means difference between time taken to cross "x" blocks by walking and ride by bicycle is 10 minutes
[tex]\rightarrow x - \frac{x}{3} = 10\\\\\rightarrow \frac{3x - x}{3} = 10\\\\\rightarrow \frac{2x}{3} = 10\\\\\rightarrow x = \frac{30}{2}\\\\\rightarrow x = 15[/tex]
Thus he lives 15 blocks away from his work
Final answer:
Youssef lives 15 blocks away from his workplace, which is determined by solving the equation x = x/3 + 10 after converting his biking speed to 3 blocks per minute.
Explanation:
To solve for how many blocks away Youssef lives from his workplace, we'll set up an equation using the information given. First, let's convert Youssef's bicycling speed to blocks per minute. Since he can travel 1 block in 20 seconds, and there are 3 sets of 20 seconds in a minute, he travels at a speed of 3 blocks per minute on his bicycle.
Let's denote the number of blocks to Youssef's workplace as 'x'. According to the question, walking there takes Youssef 10 minutes longer than biking. If he walks at the pace of 1 block per minute, walking to work takes 'x' minutes. Biking, at 3 blocks per minute, would take 'x/3' minutes. The relationship between the walking time and biking time is therefore 'x = x/3 + 10'.
We can solve the equation by multiplying each term by 3 to get rid of the fraction: '3x = x + 30'. Solving for 'x' gives us '2x = 30', and thus 'x = 15'. Youssef lives 15 blocks away from his workplace.
robert makes 50 litres of green paint by mixing litres of yellow paint and litres of blue paint in the ratio 2:3.
yellow paint is sold in 5 litre tins. each tin costs £26.
blue paint is sold in 10 litre tins. each tin costs £48.
robert sells all the green paint he makes in 10 litre tins. the sells each tin of green paint for £66.96.
work out Roberts percentage profit of each tin of green paint he sells.
Answer:
35%Explanation:
1. Cost of each liter of yellow paint:
Yellow paint is sold in 5 litre tins and ach tin costs £26, thus the cost of one liter is £26 / 5 liters = £5.2 per liter.
2. Cost of each liter of blue paint:
Blue paint is sold in 10 litre tins and each tin costs £48, thus the cost of one liter of blue paint is £48 / 10 liters = £4.8 per liter
3. Cost of each liter of green paint.
Green paint is made by mixing yellow paint and blue paint in the ratio 2:3
Thus, 5 liters of green paint will cost:
2 liters yellow paint: 2 liter × £5.2 / liter = £10.4
3 liters blue paint: 3 liter × £4.8 / liter = £14.4
========== ========
5 liters green paint: 5 liter £24.8
Cost of one liter of gree paint: £24.8 / 5 liter = £4.96 / liter
4. Profit
Price of each liter of green paint: £66.96 / 10 liters = £6.696 / liter = £6.70 / liter
Profit per liter = price per liter - cost per liter = £6.70/liter - £4.96 / liter = £1.74 / liter
Percentage profit = profit per liter / cost per liter × 100
Percentage profit = (£1.74 / liter) / (£4.96/liter) × 100 = 35.08% = 35%
Explain how you would simplify the
following:
Answer:
Step-by-step explanation:
185,000[tex]\\\sqrt{x}[/tex]
Answer:
Step-by-step explanation:
∛108c¹⁷ = ∛2*2*3*3*3*3*c¹⁵ *c²
= 3c⁵∛4c²
Hint: c¹⁵ = (c⁵)³ = c⁵ * c⁵ *c⁵
(2-4x^9+3x^3)-(7x + x^3-6 + 12x^4)
Answer:
-4x^9-12x^4+2x^3-7x+8
Answer:
=−4x9−12x4+2x3−7x+8
Step-by-step explanation:
Distribute the Negative Sign:
=2−4x9+3x3+−1(7x+x3−6+12x4)
=2+−4x9+3x3+−1(7x)+−1x3+(−1)(−6)+−1(12x4)
=2+−4x9+3x3+−7x+−x3+6+−12x4
Combine Like Terms:
=2+−4x9+3x3+−7x+−x3+6+−12x4
=(−4x9)+(−12x4)+(3x3+−x3)+(−7x)+(2+6)
=−4x9+−12x4+2x3+−7x+8
a concert venue can hold 200 people. student tickets are 50% less than adult tickets. Adult tickets at $50.00. The venue was sold out and made a revenue of $9125 for one event. How many adults vs. student tickets were sold?
Answer:
The number of adults tickets sold is 165
The number of students tickets sold is 35
Step-by-step explanation:
Given as :
The total people that concert venue hold = 200 people
The price of adults tickets = $50
The price of students tickets = 50% less than adults tickets
I.e The price of students tickets = $50 - 50% of $50
Or, The price of students tickets = $25
The total revenue earn = $9125
Let The number of adults tickets sold = A
The number of students tickets sold = S
Now, According to question
The total people that concert venue hold = 200
Or, A + S = 200 ...........1
The total revenue earn = The number of adults tickets sold × The price of adults tickets + The number of students tickets sold × The price of students tickets
Or, A × $50 + S × $25 = $9125
Or, 50 A + 25 S = 9125 ..........2
Solving both equations
(50 A + 25 S) - 25 × (A +S) = 9125 - 25 × 200
Or, (50 A - 25 A) + (25 S - 25 S) = 9125 - 5000
Or, 25 A + 0 = 4125
∴ A = [tex]\dfrac{4125}{25}[/tex]
I.e A = 165
So, The number of adults tickets sold = A = 165
Put the vale of A in eq 1
I.e A + S = 200
So, S = 200 - A
∴ S = 200 - 165
I.e S = 35
So. The number of students tickets sold = S = 35
Hence The number of adults tickets sold is 165 and
The number of students tickets sold is 35 Answer
Simplify the following expression, 4.2x+4.7=18.6
Answer:
use photomath
Step-by-step explanation:
Help I’m almost out of time
Answer: First option.
Step-by-step explanation:
You can idenfity in the figure that [tex]\angle FCE[/tex] is formed by two secants that intersect outside of the given circle.
It is important to remember that, by definition:
[tex]Angle\ formed\ by\ two\ Secants=\frac{1}{2}( Difference\ of\ intercepted\ Arcs)[/tex]
Knowing this, you can set up the following equation:
[tex]m\angle FCE=\frac{1}{2}(BD-FE)[/tex]
Therefore, you must substitute values into the equation and then evaluate, in order to find the measure of the angle [tex]\angle FCE[/tex].
This is:
[tex]m\angle FCE=\frac{1}{2}(112\°-38\°)\\\\m\angle FCE=37\°[/tex]