Answer:
Distribution property method
Simplify the following expression.(3x – 5)(4 – 9x) + (2x + 1)(6x2 + 5)O12.3 – 21.12 - 671 - 15O12 x3 – 21–2 + 671 - 1512r 3 + 21,2 – 675 + 15O12 x3 + 21x2 + 67x + 15Submit
The Solution:
Given the expression below:
[tex]\mleft(3x-5\mright)\mleft(4-9x\mright)+\mleft(2x+1\mright)\mleft(6x^2+5\mright)[/tex]We are required to simplify the above expression.
[tex]\begin{gathered} \mleft(3x-5\mright)\mleft(4-9x\mright)+\mleft(2x+1\mright)\mleft(6x^2+5\mright) \\ 3x(4-9x)-5(4-9x)+2x(6x^2+5)+1(6x^2+5) \end{gathered}[/tex]Clearing the brackets, we get
[tex]\begin{gathered} 12x-27x^2-20+45x+12x^3+10x+6x^2+5 \\ 12x^3+6x^2-27x^2+12x+45x+10x-20+5 \end{gathered}[/tex][tex]12x^3-21x^2+67x-15[/tex]Therefore, the correct answer is
[tex]12x^3-21x^2+67x-15[/tex]Barney and Robin went shopping at H&M. The store was having a sale on all shirts and pants. Barney spent $70 on 3 shirts and 2 pairs of pants and Robin bought 1 shirt and 4 pairs of pants for $90. d) Use a graphing calculator, to graph your equations in parts a and b. What is the coordinate point where these two lines intersect? How does this compare to your response in part c?
Barney spent $70 on 3 shirts and 2 pairs of pants
Robin bought 1 shirt and 4 pairs of pants for $90
Let x be the cost for each shirt
Let y be the cost for each pair of pants
3x+2y=70 (1)
x+4y=90 (2)
Having this system of equations, we can graph on the graph calculator:
The solution of two linear equations corresponds to the intersection of the two lines because the coordinate pair naming every point on a graph is a solution to its corresponding equation:
In this case the solution is: (10, 20) and corresponds to the cost of the shirt and pant.
Shirt: $10
Pant:$20
How do I do I calculate the curve of best fit with the following data points given?
To determine the curve of best fit, let's look at the x-intercepts of the curve.
Based on the graph, the x-intercepts are at x = -7 and x = -1.
Since -7 and -1 are the x-intercepts, we can say that the factors of this curve are:
[tex](x+7)(x+1)[/tex]Now, we can also see that the graph is opening downward, therefore, the leading coefficient of the equation of this graph must be negative. For this, we will multiply the factors above by -1.
[tex]-(x+7)(x+1)[/tex]All we have to do now is multiply the factors above in order to get the curve of best fit.
[tex]-(x^2+x+7x+7)[/tex]Combine similar terms like x and 7x.
[tex]-(x^2+8x+7)[/tex]Then, distribute the negative sign.
[tex]-x^2-8x-7[/tex]Therefore, the curve of best fit is y = -x² - 8x - 7.
need help with question 4
need answer in cubic feet
Answer: 140cubic feet
Step-by-step explanation:
14Cubic feet x 10cubic feet is 140cubic
Determine the end behavior for each function below. Place the letter(s) of the appropriatestatement(s) on the line provided. A. As x approaches ∞o, y approaches ∞oB. As x approaches -œo, y approaches œC. As x approaches ∞o, y approaches -∞0D. As x approaches -c0, y approaches -00
Solution:
From the given graphs,
The first graph is the absolute function graph.
Which can be expressed in the form
[tex]y=-|x|[/tex]Since the leading coefficient is negative,
The end behavior of the graph is
[tex]As\text{ x}\rightarrow\infty,y\rightarrow-\infty\text{ and as x}\rightarrow-\infty,y\rightarrow-\infty[/tex]Hence, the answers are C and D
The second graph is a quadratic graph of the form
[tex]y=x^2[/tex]Since the leading coefficient is positive
The end behavior will be
[tex]As\text{ x}\rightarrow\infty,y\rightarrow\infty\text{ and as x}\rightarrow-\infty,y\rightarrow\infty[/tex]Hence, the answers are A and B
The third graph is a cubic function that can be expressed in the form
[tex]y=-x^3[/tex]The leading coefficient is negative.
The end behavior will be
[tex]As\text{ x}\rightarrow\infty,y\rightarrow-\infty\text{ and as x}\rightarrow-\infty,y\rightarrow\infty[/tex]Hence, the answers are C and B
How many solutions does this equation have? Solve on paper and enter your answer on Zearn.
1/5(25+15x) = 3x+5
No solutions
One solution
Infinitely many solutions
Answer: Infinity many solutions
Step-by-step explanation:
1/5(25+15x) = 3x+5 (Multiply 1/5 with the parentheses)
5+3x=3x+5
^ Both sides are the same, meaning that any number can be plugged into x.
We can also simplify it by subtracting 3x and 5 from both sides:
5+3x=3x+5
3x-3x=5-5
0=0
what are the coordinates for the location of the center of the merry-go-round?
Given the coordinates of the following locations
[tex]\begin{gathered} Q(4,-2) \\ R(2,-4) \\ S(0,2) \end{gathered}[/tex]From the question we have that the distance of the point are equal so we will have;
[tex](x-4)^2+(y+2)^2=(x-2)^2+(y+4)^2=(x-0)^2+(y-2)^2[/tex]Solving equation 1 and 3 simultaneously we will have
[tex]\begin{gathered} x^2-8x+16+y^2+4y+4=x^2+y^2-4y+4_{} \\ -8x+8y=-16 \\ \text{Divide through by 8} \\ -x+y=-2 \\ x=y+2 \end{gathered}[/tex]Solving equation 2 and 3 simultaneously we will have
[tex]\begin{gathered} x^2-4x+4+y^2+8y+16=x^2+y^2-4y+4 \\ -4x+12y=-16 \\ \text{Divide through by 4} \\ -x+3y=-4 \\ x=3y+4 \end{gathered}[/tex]Thus , to solve for y we have;
[tex]\begin{gathered} y+2=3y+4 \\ 2-4=3y-y \\ -2=2y \\ y=\frac{-2}{2}=-1 \end{gathered}[/tex]Substitute y to find x
[tex]\begin{gathered} x=y+2 \\ x=-1+2=1 \end{gathered}[/tex]Hence the coordinates of the center of the merry-go-round is ( 1, - 1)
The second option is the correct option
Anna rolls a die and then flips a coin. Identify the tree diagram which displays the outcomes correctly.
Let:
1 = Get a 1
2 = Get a 2
3 = Get a 3
4 = Get a 4
5 = Get a 5
6 = Get a 6
H = Get heads
T = Get tails
The set of all possible outcomes of the experiment is:
[tex]\begin{gathered} S=\mleft\lbrace(1,H\mright),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),\ldots \\ \ldots(5,H),(5,T),(6,H),(6,T)\} \end{gathered}[/tex]Therefore, the only tree diagram which displays the outcomes correctly is the one in the option A.
2xy^2-x^2Evaluate where x=2 and y=5is that first step correct and what would be the order of operations from there
To evaluate this , replace the terms with the numbers as
2 xy^2 - x^2
[tex]2xy^2-x^2[/tex][tex]2\cdot2\cdot5^2-2^2[/tex][tex]4\cdot5^2-4[/tex][tex]4\cdot25\text{ - 4}[/tex][tex]100-4=96[/tex]It is known that the events ANB are mutually exclusive that p(a)=0.60 and p(b)=0.16
The probability of two mutually exclusive events to happen simultaniously can be described as below:
[tex]P(A\text{ and }B)=P(A)\cdot P(B)[/tex]We can replace the terms above with the probabilities to determine the answer for this problem.
[tex]P(A\text{ and }B)=0.6\cdot0.16=0.096[/tex]The probability of both events happening simultaneously is 0.096.
I need to know if this is the correct answer
Answer:
Correct
Explanation:
Given the function:
[tex]5x+3y=15[/tex]To confirm if the graph is correct, find the x and y-intercepts of the function.
x-intercept
When y=0
[tex]\begin{gathered} 5x+3(0)=15 \\ 5x=15 \\ x=\frac{15}{5}=3 \end{gathered}[/tex]• The x-intercept is (3,0).
y-intercept
When x=0
[tex]\begin{gathered} 5(0)+3y=15 \\ 3y=15 \\ y=\frac{15}{3}=5 \end{gathered}[/tex]• The y-intercept is (0,5)
These are the intercepts on the shown graph.
Your graph is correct.
Determine if it is a true proportion. Please choose the correct letter
Given the equation:
[tex]\frac{\frac{3}{5}}{\frac{14}{2}}=\frac{\frac{1}{2}}{\frac{35}{6}}[/tex]Let's determine if the proportion is a true proportion.
If the proportionis true, it means the ratio on both sides if the equality are equal.
Now, let's find the ratios.
For the first ratio:
[tex]\begin{gathered} \frac{\frac{3}{5}}{\frac{14}{2}} \\ \\ =\frac{3}{5}\div\frac{14}{2} \\ \\ \text{ Flip the fraction on the right and change the division symbol to mutilication:} \\ =\frac{3}{5}\times\frac{2}{14} \\ \\ =\frac{3}{5}\times\frac{1}{7} \\ \\ =\frac{3\times1}{5\times7} \\ \\ =\frac{3}{35} \end{gathered}[/tex]For the second ratio:
[tex]\begin{gathered} \frac{\frac{1}{2}}{\frac{35}{6}} \\ \\ =\frac{1}{2}\div\frac{35}{6} \\ \\ \text{ Flip the fraction on the right and change the division symbol to mutilication:} \\ =\frac{1}{2}\times\frac{6}{35} \\ \\ =\frac{1\times6}{2\times35} \\ \\ =\frac{6}{70} \\ \\ =\frac{3}{35} \end{gathered}[/tex]After simlifying, we have:
[tex]\frac{3}{35}=\frac{3}{35}[/tex]Since the equation is true, we can say the proortion is true because it has a constant ratio.
This is super confused im not the best with graphs
ANSWER
C. The function is negative when x < 0
EXPLANATION
We want to identify the statement that best describes the function graphed.
To do this, we have to study the graph of the function.
The function graphed has both positive and negative values. The positive values of the function are the part of the function that is above the horizontal red line while part of the negative values of the function is the part of the function that is below the horizontal red line.
We notice that the part of the function that is below the horizontal red line occurs when x is less than 0 (the part of the graph to the left of the vertical red line).
Hence, we can conclude that the correct statement that describes the function is:
The function is negative when x < 0. The answer is option C.
In the first episode of a reality show, contestants had to spin two wheels of fate. Spinning the first wheel determined the remote location where contestants would reside for the duration of the season. Spinning the second wheel determined which "bonus survival tool" they would be allowed to bring, along with a few other necessary items. A tent Matches Desert 4 1 Rainforest 3 1 Mountain peak 1 1 What is the probability that a randomly selected participant spun the second wheel and landed on a tent given that the participant spun the first wheel and landed on mountain peak? Simplify any fractions.
Answer:
1/2
Explanation:
Taking into account the table, we know that 2 participants spun the first wheel and it landed on a mountain peak and 1 of those participants spun the second wheel and landed on a tent. So, we can calculate the probability as:
[tex]P=\frac{1}{2}[/tex]Because there are 2 people on a mountain peak and for one of them landed on a tent.
Therefore, the answer is 1/2
Find the area of a triangle ABC when c = 15 m, a = 20 meters, and b = 10 meters.
Recall Heron's Formula to find the area of a triangle with sides a, b and c.
We define a new quantity s given by:
[tex]s=\frac{a+b+c}{2}[/tex]Then, the area of the triangle is given by the formula:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]For a=20, b=10 and c=15 we have:
[tex]s=\frac{20+10+15}{2}=22.5[/tex]Then, the area of the triangle is:
[tex]\begin{gathered} A=\sqrt{22.5(22.5-20)(22.5-10)(22.5-15)} \\ =\sqrt{22.5(2.5)(12.5)(7.5)} \\ =\frac{75\sqrt{15}}{4} \\ =72.61843774... \\ \approx72.6 \end{gathered}[/tex]Therefore, the exact answer is:
[tex]A=\frac{75\sqrt{15}}{4}[/tex]And the approximate area of the triangle ABC when c=15m, a=20m and b=10m is 72.6 m^2.
To solve the rational equation2. 3-x+65X+25how can the expressionX+2be rewritten usingthe least common denominator?
The expression given is:
[tex]\frac{2}{x}+\frac{3-x}{6}[/tex]The Least Common Denominator (L.C.D) of the expression is the product of the denominator:
[tex]6\times x=6x[/tex]Since
[tex]\frac{2}{x}+\frac{3-x}{6}=\frac{5}{x+2}[/tex]Then, we can multiply both the numerator and denominator with the L.C.D of 6x:
[tex]\begin{gathered} \frac{5}{x+2} \\ \\ \frac{5}{x+2}\times\frac{6x}{6x} \\ \\ \frac{30x}{6x(x+2)} \end{gathered}[/tex]Therefore, the final answer is: Option B
Solve the following quadratic function by factoring f(x) = x2 – X – 12 Enter the number that belongs in the green box. x = 4; x = [?] Enter
The given function is
[tex]f(x)=x^2-x-12[/tex]To solve it by factoring, we have to look for two numbers whose product is 12 and whose difference is 1. Those numbers are 4 and 3.
[tex]f(x)=(x-4)(x+3)=0[/tex]Then, we use the zero property
[tex]\begin{gathered} x-4=0\rightarrow x=4 \\ x+3=\rightarrow x=-3 \end{gathered}[/tex]Hence, the answer is -3.A curve has equation x3 - 5x2 + 7x - 2dyDifferentiate the function to obtaindxa) Find the x coordinates of the points where = 0 and hence the coordinates of thed.xturning points on the curve.dyb) With the aid of a table consider the sign of on either side of the turning points,dxdetermine whether the turning points are maximum or minimum points.c) Sketch the curve showing the turning points clearly and label any other points ofinterest.
SOLUTION
Write our the function given
To differentiate the function, we apply the differentiation rule
[tex]y=x^n,\frac{dy}{dx}=nx^{n-1}[/tex]Hence
[tex]\begin{gathered} y=x^3-5x^2+7x-2 \\ \text{Then} \\ \frac{d}{dx}\mleft(x^3-5x^2+7x-2\mright) \end{gathered}[/tex]Then Apply the sum and difference rule for derivative, we have
[tex]\begin{gathered} =\frac{d}{dx}\mleft(x^3\mright)-\frac{d}{dx}\mleft(5x^2\mright)+\frac{d}{dx}\mleft(7x\mright)-\frac{d}{dx}\mleft(2\mright) \\ =3x^2-10x+7-0 \\ =3x^2-10x+7 \end{gathered}[/tex]For dy/dx =0,we have
[tex]3x^2-10x+7=0[/tex]solve quadratic equation, we have
[tex]\begin{gathered} 3x^2-3x-7x+7=0 \\ 3x(x-1)-7(x-1)=0 \\ (3x-7)(x-1)=0 \end{gathered}[/tex]Equation each factor the zero, we have
[tex]\begin{gathered} 3x-7=0,x-1=0 \\ 3x=7,x=1 \\ x=\frac{7}{3},1 \end{gathered}[/tex]Hence
The x coordinates are
x= 7/3 and x=1
To obtain the coordinate of the turning point, we substitute into the equation given
[tex]\begin{gathered} y=x^3-5x^2+7x-2 \\ \text{for x=7/3} \\ y=(\frac{7}{3})^3-5(\frac{7}{3})^2+7(\frac{7}{3})-2 \end{gathered}[/tex]Then by simplification, we have
[tex]y=-\frac{5}{27}[/tex]Then, one of the turning point is
[tex](\frac{7}{3},-\frac{5}{27})[/tex]Then, we substitute the other value of x,
[tex]\begin{gathered} \text{for x=1} \\ y=x^3-5x^2+7x-2 \\ y=(1)^3-5(1)^2+7(1)-2 \\ y=1-5+7-2 \\ y=1 \\ \text{turning point =(1,1)} \end{gathered}[/tex]Therefore the other turning point is (1,1)
The turning point are (7/3, -5/27) and (1,1)
Someone explain I know the answer Reflect the figure at the right across the y-axis. Then rotate theimage 180° around the origin. Draw the image after eachtransformation. What single transformation could you performon the figure to get the same final image?
The single transformation one could per form on the figure to get the final image is a rotation of 270 degrees counterclockwise around the origin.
The original figure cordinates (x,y)
A Reflection of the figure at the right across the y-axis, gives a coordinate(-x, y)
The y axis will remain the same. While the x axis will change sign.
A rotation of 180 degrees around the origin around the origin will have the coordinates (-x, -y)
The x and y axis changes signs.
When we carry out both transformation, the coordinates we get represent a transformation of 270 degrees counterclockwise around the ori
A cyclist rides her bike at a speed of 15 miles per hour. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 5 hours? In your computations, assume that I mile is equal to 1.6 kilometers. Do not round your answers. Speed: Distance traveled in 5 hours:
Given: The cyclist rides her bike at a speed of 15 miles per hour
To Determine: The speed in kilometers per hour and the kilometers cycles in 5 hours
Solution
Please note that 1 miles equal to 1.6kilometers. Let us convert 15miles to kilometers as shown below
[tex]\begin{gathered} 1miles=1.6kilometers \\ 15miles=15\times1.6kilometers \\ 15miles=24kilometers \end{gathered}[/tex]Therefore the speed of 15miles per hour is equivalent to 24kilometers per hour
The kilometers travelled in 5 hours would be
[tex]\begin{gathered} distance=speed\times time \\ speed=24kilometers-per-hour \\ time=5hours \\ distance=24\times5 \\ distance=120kilometers \end{gathered}[/tex]Hence, the speed in kilometers per hour is 24 kilometers per hour,
And the kilometers travelled in 5 hours is 120 kilometers
Write the equation of the line that passes through the points (-2,-2) and (8,0)
Considering the expression of a line, the equation of the line that passes through the points (-2,-2) and (8,0) is y= -1/5x + 8/5.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷ (x₂ -x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the "b" can be obtained.
Equation of the line in this case
Being (x₁, y₁)= (-2, 2) and (x₂, y₂)= (8, 0), the slope m can be calculated as:
m= (0 - 2)÷ (8 -(-2))
m= (0 - 2)÷ (8 +2)
m= (-2)÷ (10)
m= -1/5
Considering point 1 and the slope m, you obtain:
2= (-1/5)×(-2) + b
2= 2/5 +b
2 -2/5= b
8/5= b
Finally, the equation of the line is y= -1/5x + 8/5.
Learn more about the equation of a line having 2 points:
brainly.com/question/12851029
brainly.com/question/19496333
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Patrick is buying rabbits. This graph shows how the total cost depends on the number of rabbits purchased.
Using the graph provided, we must find how many rabbits correspond to a cost of $20.
To find the number of rabbits, we look for the value $20 on the vertical axis, then we follow a horizontal line to the curve, and then we go down vertically to the horizontal axis. We find that the number of rabbits is 5.
We see that we have a linear relationship between the number of rabbits and its cost. If 5 rabbits cost $20, each rabbit costs $20/5 = $4 (we can also find this value looking at the graph).
Using the cost of each rabbit, we have that:
• 5 rabbits cost $4 * 5 = $20,
,• 8 rabbits cost $4 * 8 = $32,
,• 12 rabbIts cost $4 * 12 = $48.
Answer
5 rabbits cost $20,
8 rabbits cost $32,
12 rabbIts cost $48.
2. 2. How many rectangles similar to this one 1 Is possible from the figure below? Ans = A.) 24 B) 25 C) 20
Similar triangles are triangles with corresponding angles and corresponding sides. They don't necessarily mean triangles of the same size(congruent).
From the diagram attached
If you pay Php 38,500.00 at the end of 3 years and 3 months to settle an obligation of Php 35,800. What simple interest rate was used?
Solve 15 - 8x > 3 - 2x and write the solution in interval notation.O Interval notation solution:O No solution
Add 8x to both sides
[tex]\begin{gathered} 15-8x+8x>3-2x+8x \\ 15>3+6x \end{gathered}[/tex]Subtract 3 from both sides
[tex]\begin{gathered} 15-3>3-3+6x \\ 12>6x \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{12}{6}>\frac{6x}{6} \\ 2>x \\ x<2 \end{gathered}[/tex]Interval notation solution: x < 2
Help me out with details
Answer:
The numbers are proportional with each other. If you were to divide the length on the table by the corresponding width, you'd get the same answer each time(0.6)
Find the area ofa cirde with a circumference of 50.24 units,
Step 1
Find radius r , from circumference
circumference = 50.24
[tex]\begin{gathered} \text{Circumference = 2 }\pi\text{ r} \\ \pi\text{ = 3.142} \\ 50.24\text{ = 2 x 3.142r} \\ 50.24\text{ = 6.284r} \\ r\text{ = }\frac{50.24}{6.284} \\ r\text{ = 7.99} \end{gathered}[/tex][tex]\begin{gathered} \text{Area = }\pi r^2 \\ =3.142\text{ x 7.99 x 7.99} \\ =\text{ 200.58} \end{gathered}[/tex]ABOUT HOW MANY NO RESPONCES COULD YOU EXPECT FROM A POPULATION OF 500 WITH 15 OUT OF 60 YES RESPONSES FROM A SAMPLE. A. 15B. 45C. 125D.375 NOT A TEST.
Total population = 500
15 out of 60 gives a YES response
This implies
Probability of getting a YES response is
[tex]\frac{15}{60}[/tex]Out of the 500 population
The number of YES responses will be
[tex]500\times\frac{15}{60}[/tex]Simplifying this gives
[tex]\begin{gathered} 500\times\frac{15}{60} \\ =500\times\frac{1}{4} \\ =125 \end{gathered}[/tex]Hence out of 500 population 125 responses will be YES
Therefore, the number of NO responses is
[tex]500-125=375[/tex]Therefore, the number of NO responses is 375
the table below gives the side lengths and surface areas of different cubes.
Given
Relationship between sides and surface areas
Find
Conclusion from the table
Explanation
From the table we can see that sides double in 1st, 2nd and 4th case
So comparing them
When side =1 then Surface area = 6 cm sq
When side = 2 then Surface area = 24 cm sq
Here we can see that when the side doubles, the surface area quadruples
Similar result is obtained when in relation of side = 2 and side 4
Final Answer
When the side doubles, the surface area quadruples
option (a) is correct
Mr. Jones owned his car for 12 years. The car has 169,344 miles recordedon the odometer. What is the average number of miles driven per year?
total distance travelled by the car is 169344 miles, for 12 years,
the distance travelled in 1 year is
[tex]=\frac{169344}{12}=14112[/tex]so the average number of miles der