Answer:
B gains 100 yards every minute. So, after 10 minutes, B has lapped A once.
C gains 100 yards on B every minute, so after 10 minutes C has lapped B.
Thus, after 10 minutes, A has gone 7 laps, B has gone 8 laps, C has gone 9 laps, and all are even again.
The incorrect work of a student to solve an equation 2(y + 4) = 4y is shown below: Step 1: 2(y + 4) = 4y Step 2: 2y + 6 = 4y Step 3: 2y = 6 Step 4: y = 3 Which of the following explains how to correct Step 2 and shows the correct value of y? The equation should be y + 4 = 4y after division by 2; y = 5 The equation should be y + 4 = 4y after division by 2; y = 2 2 should be distributed as 2y + 8; y = 4 2 should be distributed as 2y + 8; y = 2
Answer:
2 should be distributed as 2y + 8; y = 4
Step-by-step explanation:
Step 2 is wrong.
2(y + 4) = 4y
The step to solve is to expand brackets or distribute 2, not divide both sides by 2.
2y + 8 = 4y
Subtract both sides by 2y.
8 = 2y
Divide both sides by 2.
4 = y
volume please 20* points
Answer:
1800cm^3
Step-by-step explanation:
l=10cm
w=10cm
h=18cm
V=l.w.h
V=10cmx10cmx18cm
V=100cm^2x18cm
V=1800cm^3
Hope this helps. ❤❤❤
Answer:
600 cm³
Step-by-step explanation:
Volume of a square-based pyramid = a² × h/3
a = 10
h = 18
10² × 18/3
100 × 6
= 600
Write a rule for the linear function in the table.
f(x) = 4x + 3
f(x) = -4x - 3
1
f(x) = x + 3
Answer:
I guess that you want to know the transformations:
We start with:
f(x) = y = 4*x + 3
a)the transformed function is:
f(x) = y = -4*x - 3
So the sign changed.
This means that we go from (x, y) to (x, - y)
This is a reflection over the x-axis which changes the sin of the y component.
b) Now we go to f(x) = 4*x + 3
So the coefficient in the leading term changed.
This is a horizontal contraction:
A horizontal contraction of factor K for the function g(x) is: g(K*x)
In our case, we have:
f(K*x) = 4*(k*x) + 3 = x + 3
4*k*x = x
4*k = 1
k = 1/4
Then the transformation is an horizontal contraction of scale factor 1/4.
an orphanage bought 119 1/4 m of cloth to stitch dresses for kids. The dress for one kid requires 2 1/4m of cloth. How many dresses of the size can be stitched
Answer:53 dresses
Step-by-step explanation:
First of all..if one kid required 2 1/4m of cloth,what about 119 1/4m of cloth?
So u take 119 1/4m of cloth and divide it by 2 1/4m of cloth.
Then change the mixed numbers into improper fractions.
So the question will be 477/4 m divided by 9/4 m.
The second improper fraction (9/4)m will be reciprocated to be (4/9)m.
Afterwards,take 477/4 m and multiply it by 4/9 m.
The result will be 53 dresses.
Find the surface area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest radical form.
Answer:
84 squared units.
Step-by-step explanation:
In order to find the surface area of the pyramid, you use the following formula:
[tex]S=b^2+\frac{1}{2}ps[/tex] (1)
b: base of the pyramid = 6
p: perimeter of the base = 6*4 = 24
s: slant height
Then, you first calculate the slant height, by using the Pythagoras' theorem:
[tex]s=\sqrt{(5)^2-(\frac{6}{2})^2}=4[/tex]
Thus, you replace the values of b, p and s in the equation (1):
[tex]S=(6)^2+\frac{1}{2}(24)(4)=84[/tex]
The surface area of the pyramid is 84 squared units.
Answer:
Step-by-step explanation:
wrong
David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15 : 1 15:1.He currently has 40 grams of the spice blend, and he can go buy more if necessary. He wants to make 10 servings, where each serving has 75 grams of rice. Overall, David spends 4.50 dollars on rice. What is the price of rice per gram?
Answer: Price of rice per gram = $ 0.006 per gram or 0.6 cents per gram .
Step-by-step explanation:
Given: David wants to make 10 servings, where each serving has 75 grams of rice.
Total quantity of rice required = 10 x 75 = 750 grams
Overall, David spends 4.50 dollars on rice.
i.e. cost of 750 grams of rice = 4.50 dollars
Price of rice per gram =(cost of 750 grams of rice ) ÷ 750
= (4.50 dollars ) ÷ 750
= $ 0.006 per gram.
Price of rice per gram = $ 0.006 per gram.
Answer:
0.006
Step-by-step explanation:
ehgfdcgmkmvnnrebsbhbnjrfjgnjkae
HELPP PLEASE
2. At Math Camp, students can either pack their own lunch every day or buy lunch at camp. If they want to buy lunch there are 3 options: Option A: they pay an initial fee of $30 and lunches cost $2 each Option B: shown on the graph Option C: they pay a flat fee of $70 which includes all lunches Write an equation for each option. (3 marks) Option A: Option B: Option C: b) Describe under what conditions, a student should choose each option. (Hint: you may want to graph all 3 lines on the same axes) (4 marks) Choose Option A if: Choose Option B if: Choose Option C if: 3. 4. A Campbell’s Soup can is 15cm tall and has a radius of 5 cm. How much paper is needed to make the label (think about what the label covers)? (3 marks) How much soup can this hold? (1 cm3 = 1 mL) (3 marks)
Answer:
3.
A. Y = 2x + 30 (red line)
B. Y=5x (blue line)
C. Y=70 (green line)
From 0 to 10 days, choose option B (shown on graph)
From 10 to 20 days, choose option A (first option)
From 20 days and more, choose option C.
4.
surface area of label = 471.2 cm^2
Step-by-step explanation:
Q1718436 Math Camp
2. At Math Camp, students can either pack their own lunch every day or buy lunch at camp. If they want to buy lunch there are 3 options:
Option A: they pay an initial fee of $30 and lunches cost $2 each
Option B: shown on the graph
Option C: they pay a flat fee of $70 which includes all lunches
Write an equation for each option. (3 marks) Option A: Option B: Option C:
A. Y = 2x + 30 (red line)
B. Y=5x (blue line)
C. Y=70 (green line)
b) Describe under what conditions, a student should choose each option. (Hint: you may want to graph all 3 lines on the same axes) (4 marks)
Choose Option A if: Choose Option B if: Choose Option C if:
Least cost is what is below the lowest possible line for the number of days stayed.
From 0 to 10 days, choose option B (shown on graph)
From 10 to 20 days, choose option A (first option)
From 20 days and more, choose option C.
Note that for days 10 and 20, there are two choices each.
3.
4. A Campbell’s Soup can is 15cm tall and has a radius of 5 cm. How much paper is needed to make the label (think about what the label covers)? (3 marks) How much soup can this hold? (1 cm3 = 1 mL) (3 marks)
The label only covers the curved surface.
Curved surface area
= 2 pi * r * h
= 2 pi (5) * 15
= 150 pi
= 471.2 cm^2
Which statement is correct about the system of linear equations graphed below? A.The system of equations has one solution because the lines will eventually intersect. B.The system of equations has one solution because the lines will never intersect. C.The system of equations does not have one solution because the lines will eventually intersect. D.The system of equations does not have one solution because the lines will never intersect.
Answer: A
Step-by-step explanation:
They have one solution because as you look at the lines they have different slopes and different y intercepts which means it has one solution.It is not parallel to each other to have no solutions. They seems to be going to one direction and eventually they will intersect.
Algebra 2 help needed
Answer:
D
Step-by-step explanation:
From the graph, the y-intercept of f(x) is 2 and since the y-intercept is when x = 0, it would fall into the x ≤ 1 category so the y-intercept of g(x) is 0 - 4 = -4. Since 2 > -4, the answer is D.
Antonio's toy boat is bobbing in the water next to a dock. Antonio starts his stopwatch, and measures the vertical distance from the dock to the height of the boat's mast, which varies in a periodic way that can be modeled approximately by a trigonometric function. The vertical distance from the dock to the boat's mast reaches its highest value of -27 \text{ cm}−27 cmminus, 27, space, c, m every 333 seconds. The first time it reaches its highest point is after 1.31.31, point, 3 seconds. Its lowest value is -44\text{ cm}−44 cmminus, 44, space, c, m. Find the formula of the trigonometric function that models the vertical height HHH between the dock and the boat's mast ttt seconds after Antonio starts his stopwatch. Define the function using radians.
Answer:
Step-by-step explanation:
Since we're given a time at which the height is maximum, we can use a cosine function for the model.
The amplitude is half the difference between the maximum and minimum: (-27 -(-44))/2 = 8.5 cm.
The mean value of the height is the average of the maximum and minimum: (-27 -44)/2 = -35.5 cm.
The period is given as 3 seconds, and the right shift is given as 1.31 seconds.
This gives us enough information to write the function as ...
H(t) = (amplitude)×cos(2π(t -right shift)/period) + (mean height)
H(t) = 8.5cos(2π(t -1.31)/3) -35.5 . . . . cm
Which of the following are identities? Check all that apply.
Answer:
The true answers:
A
B
C
Step-by-step explanation:
A P E X
I'm going to mark whoever gets it right as brainliest Fred's coffee shop sells two blends of beans at the following prices. a) House Blend ($3.50/lb) b) Exotic Blend ($4.00/lb). House blend is 1/2 Costa Rican beans and 1/2 Ethiopian beans. Exotic blend is 1/4 Costa Rican beans and 3/4 Ethiopian beans. Every day Fred receives 200 lbs of Costa Rican Beans and 330 lbs of Ethiopian beans. Which inequality is a constraint? * 1/2x+1/4y or = to 530 x < or = 200
Answer:
(1/2)x + (1/4)y <= 200
Step-by-step explanation:
If
x = # of lbs of House blend he makes/sells a day
y = # of lbs of Exotic blend he makes/sells a day
then constraints are
(1/2)x + (1/4)y <= 200 ....................(1)
x+y <= 530 .....................................(2)
The exact answer choices are not very clear from the question, but either (or both) (1) or (2) must be one of them. If not, please edit question or add a comment to show the answer choices.
Mr. Sanchez's students were asked to add two positive integers. Juan subtracted by mistake and got 2. Maria mistakenly multiplied and got 120. What was the correct answer?
Answer:
22
Step-by-step explanation:
Given
From Juan's calculation,
Difference of two positive integers = 2
From Maria's calculation,
Product of same integers = 120
Required
Find the sum of the two numbers
Let the two integers be represented by a and b
a - b = 2 ------- (1)
a * b = 120 ------- (2)
Make a the subject of formula in (1)
a = 2 + b
Substitute 2 + b for a in (2)
(2 + b) * b = 120
Open bracket
2 * b + b * b = 120
2b + b² = 120
Rearrange
b² + 2b = 120
Subtract 120 from both sides
b² + 2b - 120 = 120 - 120
b² + 2b - 120 = 0
At this point, we have a quadratic equation.
We start by expanding the expression
b² + 12b - 10b - 120 = 0
Factorize
b(b + 12) - 10(b + 12) = 0
(b - 10)(b + 12) = 0
This implies that
b - 10 = 0 or b + 12 = 0
Make b the subject of formula in both cases
b = 10 or b = -12
From the question, we understand that both numbers are positive.
This means that
b = -12 will be discarded.
Hence, b = 10
Recall that a = 2 + b
Substitute 10 for b
a = 2 + 10
a = 12
This implies that the two numbers are 12 and 10.
Their sum = 12 + 10
Sum = 22
The correct answer is 22
please help me :) Which of these numbers is the greatest? A. 3,213,213 B. 7.8 x 10 to the 5 power C. 6.3 x 10 to the 6 power D. 11,014,114
Answer:
Choice C : [tex]6.3*10^{6}[/tex]
Step-by-step explanation:
Choice A won't be it because it's only 3 million.
Choice B won't work because it's 83 million.
Choice C WILL WORK because it's 98 million.
Choice D won't work because it's only 11 million.
Which movie had the audience with the younger median ?
A. Movie A
B. Movie B
C. Both
D. Cannot be determined
How can we tell? Look at the vertical lines inside the box. This is where the median is located. For movie A, the inner vertical line is somewhere between 30 and 40 (perhaps 35 or so). So this is the median for movie A. Meanwhile, the median for movie B is somewhere between 40 and 50. I'd say maybe 46 or 47 as its a bit higher than the halfway point.
-----------
Extra info:
The left edge of the box is the first quartile (Q1).The right edge of the box is the third quartile (Q3).The tip of the left whisker is the min value, assuming there are no outliers to the left.The tip of the right whisker is the max value, assuming there are no outliers to the right.factorise 8a^3+b^3+12a^2b+6ab^2
Answer:
(2a+b)^3
Step-by-step explanation:
8a^3+b^3+12a^2b+6ab^2
(2a)^3 + 3. (2a)^2 b + 3 (2a) b^2 + b^3
the above equation compare to (a+b)^3 = a^3 + 3a^2b+3ab^2 +b^3
when we compare both the equations
our a= 2a and b=b
so, our answer is (2a + b)^3
Can anyone else not see the answers?
Answer: no I cannot it hasn't been working since this late afternoon I believe
Step-by-step explanation:
PLZZZ HELP WILL GIVE BRAINLIEST !!!!! NEED THIS FAST PLZZZ
Answer:
8
Step-by-step explanation:
Let's denote the number of members ordered chicken a, the number of members ordered beef b.
We have:
a + b = 12 (total number of members is 12)
10a + 14b = 136 (the chicken costs 10$, the beef costs 14$)
a + b = 12 => a = 12 - b
Substitute a into second equation, we have:
10(12 - b) + 14b = 136
=> 120 - 10b + 14b = 136
=> 4b = 16
=> b = 4
=> a = 12 - b = 12 - 4 = 8
=> Number of members ordered chicken: a = 8
Jose unlocks his cellphone by placing his right thumb on a square of 1 centimeter by 1 centimeter at the center of the screen. Upon recognizing his thumbprint, the square expands outward. The cellphone unlocks when the perimeter reaches 32 centimeters, taking a total of 2.5 seconds. What is the perimeter of the square after 1.5 seconds?
Answer: 20.8 cm
Step-by-step explanation:
Notice that the corners of the squares form a line.
Set the x-axis to time and the y-axis to length of a side (not perimeter) to create coordinates.
At 0 seconds the side length is 1 --> (0, 1)
At 2.5 seconds the perimeter is 32 (side length is 32/4 = 8) --> (2.5, 8)
First, find the slope between the coordinates using [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Let (x₁, y₁) = (0, 1) and (x₂, y₂) = (2.5, 8)
[tex]m=\dfrac{8-1}{2.5-0}\quad =\dfrac{7}{2.5}\quad =\dfrac{7}{\frac{5}{2}}\quad =\dfrac{14}{5}\quad =2.8[/tex]
Next, use the Point-Slope formula to find the equation of the line:
[tex]y-y_1=m(x-x_1)\\\\y-1=2.8(x-0)\\\\y=2.8x+1[/tex]
Lastly, find the side length (y) when x = 1.5
y = 2.8(1.5)x + 1
= 4.2 + 1
= 5.2
Perimeter of a square = 4 times the side length
P = 4(5.2)
= 20.8
If $f(x)$ is a polynomial of degree 3, and $g(x)$ is a polynomial of degree 5, then what is the degree of polynomial $2f(x) + 4g(x)$?
Answer:
Degree 5
Step-by-step explanation:
Given
Degree of f(x) = 3
Degree of g(x) = 5
Required
Degree of 2f(x) + 4g(x)
Analyzing both polynomialsf(x)2f(x) means 2 * f(x)
Since 2 is a constant
Multiplying f(x) by 2 will result in a polynomial with a degree of 3
Hence 2f(x) has a degree of 3
g(x)4g(x) means 4 * g(x)
Since 4 is also a constant
Multiplying g(x) by 4 will result in a polynomial with a degree of 5
Hence 4g(x) has a degree of 5
Having said that;
When 2 polynomials of different degrees are added together, the degree of the result will be the higher degree of both polynomials;
This means that;
Adding a polynomial of degree 3 and another of degree 5 will result in a polynomial of degree 5
explain briefly. in your own words.
Rational and irrational numbers.
give examples.
exponential equation.
rational numbers are numbers which can be expressed in fraction form whereas irrational is just opposite
Exponential equations are equations in which variables occur as exponents. For example, exponential equations are in the form ax=by .
1+1+2+6+7+9x89x98x45x56/4
Answer:
49453757
Step-by-step explanation:
Answer:
49453757
Step-by-step explanation:
Dont forget to rate and thanks!
5
Write 2 -% as a decimal (not
8
as a
percentage).
Answer: 0.4
Step-by-step explanation:
i think
Jordon will play a triangle at his school’s music program. As its name suggests, the musical instrument is shaped like a triangle. Jordon has customized the dimensions to produce a unique melody, which is played when the shortest side is hanging down, parallel to the ground. Which side of the musical instrument should be parallel to the ground if its dimensions are as shown in the diagram?
Answer:
A. AB
Step-by-step explanation:
Given that the musical instrument has a shape of ∆ABC, we can determine the shortest side that would be parallel to the ground by comparison of the 3 angles of the triangle corresponding to each side that is opposite each of them.
What this means is that, the larger angle would have the largest side opposite it. The medium angle will have medium length side opposite it, while the smallest angle will have the smallest side opposite it.
m < A = 59°
m < C = 57°
m < C = 180 - (59+57) (sum of angles in a triangle)
m < C = 64°
The smallest angle out of the three angles is angle C = 57°.
The side opposite it, is side AB.
Side AB is the shortest side of ∆ABC.
Therefore, AB should be parallel to the ground.
The
side
of the musical instrument that should be parallel to the ground if the
dimensions
are as given is side AB, which is option A.
Given that:
Jordon will play a
triangle
in his school’s music program.
When playing, the shortest side
is hanging down,
parallel
to the ground.
From the figure:
m∠A = 59°
m∠C = 57°
By the
angle sum
property,
m∠A + m∠B + m∠C = 180°
59° + m∠B + 57° = 180°
m∠B + 116° = 180°
m∠B = 180° - 116°
= 64°
The
shortest side
will be the side that is opposite to the smallest angle.
So, the smallest side is the side opposite to C.
So, the side is AB.
Hence, the side is AB, which is option A.
Learn more about
Triangles
here :
https://brainly.com/question/2773823
#SPJ6
Pls answer will make brainlist
Answer:
D. 48 in.^2
Step-by-step explanation:
Sides DE and AB are corresponding, and the triangles are similar.
linear scale factor = k = AB/DE = 12/60 = 1/5
area square factor = k^2 = (1/5)^2 = 1/25
area of ABC = area of DEF * area scale factor = 1200 sq in * 1/25
area of ABC = 48 sq in
Answer: D. 48 in.^2
Trigonometry.... plzzz helllppp
Answer:
Hey there!
We can write this equation:
cosine xyz=6/15, or 0.4
arc cosine 0.4= 66.4
Thus, angle xyz is 66.4 degrees
Hope this helps :)
I have no clue how to do this please help
Answer:
Max = (6,0); min = (-2, 4)
Step-by-step explanation:
1. Summarize the constraints
[tex]\text{Constraints} = \begin{cases}(a)\qquad 2x - y & \leq 12\\(b)\qquad 4x+ 2y & \geq 0\\(c) \qquad x + 2y & \leq 6\\ \end{cases}[/tex]
2. Optimization equation
z = 5x + 2y
3. Graph the constraints to identify the feasible region
See the figure below.
The "TRUE" regions for each graph are the shaded areas to the side of the line indicated by the arrows.
The "feasibility region" is the dark green area where all three areas overlap and all three conditions are satisfied.
5. Determine the points of intersection among the constraints
(i) Constraints (a) and (b)
[tex]\begin{array}{rcr}2x - y & = & 12\\4x + 2y & = & 0\\4x - 2y & = & 24\\8x&=&24\\x & = & \mathbf{3}\\6 - y & = & 12\\-y & = &6\\y & = & \mathbf{-6}\\\end{array}\\[/tex]
The lines intersect at (3,-6).
(ii) Constraints (a) and (c)
[tex]\begin{array}{rcr}2x - y & = & 12\\x + 2y & = & 6\\4x - 2y & = &24\\5x & = & 30\\x & = & \mathbf{6}\\6 + 2y & = & 6\\2y & = &0\\y & = & \mathbf{0}\\\end{array}[/tex]
The lines intersect at (6,0).
(iii) Constraints (b) and (c)
[tex]\begin{array}{rcr}4x+ 2y &= & 0\\x + 2y &=& 6\\3x & = & -6\\x & = & \mathbf{-2}\\-2 +2y & = & 6\\2y & = &8\\y & = & \mathbf{4}\\\end{array}[/tex]
The lines intersect at (-2,4).
6. Determine the x- and y-intercepts of the feasible region
The five black dots at (3,-6), (6,0), and (-2,4) are the vertices of the polygon that represents the feasible region.
Each vertex is a possible maximum or minimum of z.
7. Calculate the maxima and minima
Calculate z at each of the vertices.
(i) At (-2,4)
z = 5x + 2y = 5(-2) + 2(4) = -10 + 8 = 2
(ii) At (3,-6)
z = 5(3) + 2(-6) = 15 - 12 = 3
(iii) At (6,0)
z = 5(6)+ 2(0) = 30 + 0 = 30
The maximum of z occurs at (6,0).
The minimum of z occurs at (-2, 4).
What number on the number line represents ground level?
0
-1
-2
-3
-4
-5
-6
Answer:
0 represents ground level.
Step-by-step explanation:
0 on the number line represents ground level. Based on the photo, the 0 is in between the underground and the space above. The answer cannot be one of the negative numbers because those are all shown to be underground in the photo.
factorize (X + 2 y)square - (2 x minus y) square
Answer:
- (x - 3y)(3x + y)
Step-by-step explanation:
Given
(x + 2y)² - (2x - y)² ← expand both parenthesis using FOIL
= x² + 4xy + 4y² - (4x² - 4xy + y²) ← distribute
= x² + 4xy + 4y² - 4x² + 4xy - y² ← collect like terms
= - 3x² + 8xy + 3y² ← factor out - 1 from each term
= - 1(3x² - 8xy - 3y²) ← factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the coefficient of the y² term which sum to give the coefficient of the xy- term.
product = 3 × - 3 = - 9 and sum = - 8
The factors are - 9 and + 1
Use these factors to split the xy- term
3x² - 9xy + xy - 3y² ( factor the first/second and third/fourth terms )
= 3x(x - 3y) + y(x - 3y) ← factor out (x - 3y) from each term
= (x - 3y)(3x + y)
Thus
(x + 2y)² - (2x - y)² = - (x - 3y)(3x + y)
Of his take-home pay each month, Jerry spends 1/6 on car payment and 1/4 on food. What fraction of his take-home pay is left after paying for these two items?
Answer:
The fraction of Jerry's take-home pay that is left after paying for these two items is 7/12.
Step-by-step explanation:
Consider that the total take-home pay each month Jerry receives is, $x.
It is provided that:
Jerry spends 1/6 on car payment, i.e. Car Payment = [tex]\frac{1}{6}x[/tex].Jerry spends 1/4 on food, i.e. Food = [tex]\frac{1}{4}x[/tex].The remaining amount can be computed by subtracting the amount spent from the total amount.
Compute the amount Jerry has spent so far:
Amount Spent = Car Payment + Food
[tex]=\frac{1}{6}x+\frac{1}{4}x\\\\=[\frac{1}{6}+\frac{1}{4}]x\\\\=[\frac{2+3}{12}]x\\\\=\frac{5}{12}x[/tex]
Compute the remaining amount as follows:
Remaining Amount = Total Amount - Amount Spent
[tex]=x-\frac{5}{12}x\\\\=[1-\frac{5}{12}]x\\\\=[\frac{12-5}{12}]x\\\\=\frac{7}{12}x[/tex]
Thus, the fraction of Jerry's take-home pay that is left after paying for these two items is 7/12.