Answers
The function given is:
[tex]f(x)=-16x^2+60x+16[/tex]PART AThe factorization steps are shown below:
[tex]\begin{gathered} f(x)=-16x^2+60x+16 \\ f(x)=4(-4x^2+15x+4) \\ f(x)=4(-4x^2+16x-x+4) \\ f(x)=4(-4x(x-4)-1(x-4)) \\ f(x)=4(-4x-1)(x-4) \end{gathered}[/tex]PART BTo find the x intercepts, we set f(x) equal to 0 and solve for x:
[tex]\begin{gathered} f(x)=4(-4x-1)(x-4) \\ f(x)=0 \\ 4(-4x-1)(x-4)=0 \\ -4x-1=0--------(1) \\ OR \\ x-4=0---------(2) \end{gathered}[/tex]Solving (1), we have:
[tex]\begin{gathered} -4x-1=0 \\ 4x=-1 \\ x=-\frac{1}{4} \\ x=-0.25 \end{gathered}[/tex]and, solving (2), we have:
[tex]\begin{gathered} x-4=0 \\ x=4 \end{gathered}[/tex]The x-intercepts are
[tex]\begin{gathered} x=-0.25 \\ x=4 \end{gathered}[/tex]PART CThe standard equation of a quadratic is
[tex]f(x)=ax^2+bx+c[/tex]The parabola opens upward when a is positive and opens downward when a is negative
1. When parabola opens upward, the end behavior can be described as:
[tex]\begin{gathered} x\rightarrow\infty \\ y\rightarrow\infty \\ \text{and} \\ x\rightarrow-\infty \\ y\rightarrow\infty \end{gathered}[/tex]2. When parabola opens downward, the end behavior can be described as:
[tex]\begin{gathered} x\rightarrow\infty \\ y\rightarrow-\infty \\ \text{and} \\ x\rightarrow-\infty \\ y\rightarrow-\infty \end{gathered}[/tex]Our equation has an "a" value that is negative! So, the parabola opens downward and the end behvaior can be described as:
As x goes to infinity (gets infinitely large), y goes to negative infinity (gets infinitely small) and as x goes to negative infinity (gets infinitely small), y goes to negative infinity (get infinitely small).
PART D
In Part B, we found the x-intercepts. Those are the x-axis cutting points. We can draw those first.
Then,
Using the end behavior information that we found in Part C, we can draw the parabola. The rough sketch is shown:
The exact graph is shown below, for reference:
Related Questions
Convert: 9 kilogramsmilligrams
Answers
Answer
9,000,000 milligrams
Step-by-step explanation
1 kilogram is equivalent to 1,000,000 milligrams. Using this conversion factor, the equivalence of 9 kilograms is found as follows:
[tex]\begin{gathered} 9\text{ kg }=9\text{ kg}{}\cdot\frac{1,000,000\text{ mg}}{1\text{ kg}} \\ \text{ SImplifying the units:} \\ 9\text{ kg }=9\cdot1,000,000\text{ mg} \\ 9\text{ kg}=9,000,000\text{ mg} \end{gathered}[/tex]what is the pi of 53/17
Answers
One way to calculate pi is by dividing the circunferemce by the diameter. So you just need to calculate the ratio 53/17. Using a calculator you get that
[tex]\frac{53}{17}=3.11764[/tex][tex]5 \times 5[/tex]what is 5 times 5
Answers
5 times 5 = 25
5 x 5 = 25
5 + 5 + 5+ 5 +5 = 25
Answer:
answer is going to be 25
Step-by-step explanation:
so pretend you have 5 bags of 5 apples, this should stand for 5(bags of apples) and 5(apples in each bag), if you add the apples all together it will be 25 in total, or just try adding 5 five times: 5+5+5+5+5
36 unless for feeling nice to answer the 3 of them
Answers
36.
y=3x+2
f(x) can replace y
the answer is y
Solve the equation. (Enter your answers as a comma-separated list.)2b2 − 18 = −9b
Answers
Given
The equation,
[tex]2b^2-18=-9b[/tex]To solve for b.
Explanation:
It is given that,
[tex]2b^2-18=-9b[/tex]That implies,
[tex]\begin{gathered} 2b^2-18=-9b \\ 2b^2+9b-18=0 \\ 2b^2-3b+12b-18=0 \\ b(2b-3)+6(2b-3)=0 \\ (2b-3)(b+6)=0 \\ 2b-3=0,b+6=0 \\ 2b=3,b=-6 \\ b=\frac{3}{2},b=-6 \end{gathered}[/tex]Hence, the answer is 3/2, -6.
Given the function f(x) = 2x2 - 5x + 1. Calculate the following values: f(-2) = f(-1) = f(0) = f(1) = f(2) Question Hon
Answers
Given function is
[tex]f(x)=2x^2-5x+1[/tex]Substitute the value of -2 in the equation we get
[tex]\begin{gathered} f(-2)=2(-2)^2-5\times-2+1_{} \\ =8+10+1 \\ =19 \end{gathered}[/tex]Similarly find other values
[tex]\begin{gathered} f(-1)=2(-1)^2-5\times-1+1_{} \\ =2+5+1 \\ =8 \end{gathered}[/tex]And then similarly f(1)=-2 and f(2)=-1 and f(0)=1
[tex]\begin{gathered} f(0)=2(0)^2-5\times0+1_{} \\ =0+0+1 \\ =1 \end{gathered}[/tex][tex]\begin{gathered} f(0)=2(0)^2-5\times0+1_{} \\ =0+0+1 \\ =1 \end{gathered}[/tex]solve and graph the following inequality: x + 19 > 31
Answers
You have the following inequality:
x + 19 > 31
subtract 19 both sides and simplify:
x > 31 - 19
x > 12
The graph of the previous inequality is:
how do i find the volume to the nearest 1 decimal place?
Answers
Solution:
The volume of a cylinder is expressed as
[tex]\begin{gathered} V=\pi\times r^2\times h \\ where \\ V\Rightarrow volume\text{ of the cylinder} \\ r\Rightarrow radius\text{ of its circular ends} \\ h\Rightarrow height\text{ of the cylinder} \end{gathered}[/tex]Given the cylinder below:
we have
[tex]\begin{gathered} height\text{ of the cylinder = 4 cm} \\ diameter\text{ of the circular end = 2 cm} \end{gathered}[/tex]but
[tex]\begin{gathered} radius=\frac{diameter}{2} \\ \Rightarrow r=\frac{d}{2}=\frac{2cm}{2}=1\text{ cm} \end{gathered}[/tex]Thus, the volume of the cylinder is evaluated by substituting the values of 4 cm and 1 cm for h and r respectively into the volume formula.
[tex]\begin{gathered} V=\pi\times1cm\times1cm\times4cm \\ =12.56637 \\ \approx12.6\text{ cubic centimeters} \end{gathered}[/tex]Hence, the volume of the cylinder, to the nearest 1 decimal place is
[tex]12.6\text{ cubic centimeters}[/tex]help pls 1st blank - Graph A, Graph B, Graph C, Graph D 2nd blank - Yes or No 3rd blank - inside or outside
Answers
SOLUTION
From the question,
Let x represent acres for apple orchard
Let y represent acres for peach orchard
Since the farmer can afford a maximum of 54 acres of land, that means
[tex]x+y\le54[/tex]The apple orchard requires 3000 gallons of water, while the peach requires 800 gallons of water. But the farmers irrigation system can deliver a maximum of 80,000 gallons per day, puting in an equation, we have
[tex]3000x+800y\le80,000[/tex]From his apple orchard, he expects to get a profit of $3,400 per year and from peach, a profit of $1,600 per year.
His expected profit will be determined using the equation
[tex]\begin{gathered} P=3400x+1600y \\ \text{where P is the expected maximum profit } \end{gathered}[/tex]So, we will plot the following points
[tex]\begin{gathered} x+y\le54 \\ 3000x+800y\le80,000 \end{gathered}[/tex]This will help us to get the required region needed to find the expected maximum profit
We can see that this is the same with graph B from the question
Now, we will substitute the following points from the graph into the equation of the maximum expected profit. Which ever that gives us the highest value becomes the answer.
For point (0, 54) we have
[tex]\begin{gathered} P=3400x+1600y \\ P=3400(0)+1600(54) \\ P=0+86,400 \\ P=86,400 \end{gathered}[/tex]For Point (16.727, 37.273), we have
[tex]\begin{gathered} P=3400x+1600y \\ P=3400(16.727)+1600(37.273) \\ P=56,871.8+59,636.8 \\ P=116,508.6 \end{gathered}[/tex]Finally, for point (26.667, 0) we have
[tex]\begin{gathered} P=3400x+1600y \\ P=3400(26.667)+1600(0) \\ P=90,667.8+0 \\ P=90,667.8 \end{gathered}[/tex]We can see that the maximum profit is $116,508.60, from
point (16.727, 37.273)
Hence the division of land that will maximize his expected profit is
16.73 acres of land for apple orchard
37.27 acres of land for peach orchard
Now, looking at the graph, the point (30, 20) lies outside the required region, so the farmer cannot maximize his profit at 30 acres for apple orchard and 20 acres for peach orchard.
Hence the answer is No, because the point (30, 20) lies outside the solution region.
Find the slope-intercept form of the line that satisfies the given conditions.x-intercept 8, y-intercept −3
Answers
Given:
A line satisfies the given conditions.
x-intercept 8, y-intercept −3
The x-intercept is the value of x when y = 0
The y-intercept is the value of y when x = 0
So, the given line passes through the points (8, 0) and (0, -3)
We will find the slope using the following formula:
[tex]$$slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}$$[/tex]Substitute with points:
[tex]m=\frac{-3-0}{0-8}=\frac{-3}{-8}=\frac{3}{8}[/tex]The slope-intercept form is: y = m * x + b
substitute m = 3/8 and b = -3
So, the answer will be, that the equation of the line is as follows:
[tex]y=\frac{3}{8}x-3[/tex]Statement Reason
1. AEEC;BDDC 1. given
2. ∠AEC is a rt. ∠; ∠BDC is a rt. ∠ 2. definition of perpendicular
3. ∠AEC ≅ ∠BDC 3. all right angles are congruent
4. ? 4. reflexive property
5. △AEC ~ △BDC 5. AA similarity theorem
What is the missing statement in step 4?
Answers
The missing Statement is 4. ∠EAC ≅ ∠EAC 4. reflexive property
In △AEC and △BDC
We need to know the missing statement in step 4
Statement Reason
1. AE⊥EC;BD⊥DC 1. given
2. ∠AEC is a rt. ∠; ∠BDC is a rt. ∠ 2. definition of perpendicular
3. ∠AEC ≅ ∠BDC 3. all right angles are congruent
4. ∠EAC ≅ ∠EAC 4. reflexive property
5. △AEC ~ △BDC 5. AA similarity theorem
Therefore, the missing Statement is 4. ∠EAC ≅ ∠EAC 4. reflexive property.
To learn more about similarity properties refer here
https://brainly.com/question/24184322
#SPJ1
Assume that when adults with smartphones are randomly selected, 49% use them in meetings or classes. If 11 adult smartphone users are randomly selected, findthe probability that fewer than 4 of them use their smartphones in meetings or classes.The probability is
Answers
Answer: 12.66%
First, we will solve the probability that 3 adults, 2 adults, 1 adult and no adult use their smartphones in meetings or classes,
To solve for this, we will use the following equation
[tex]11Cn\times0.49^n\times0.51^{11-n}[/tex]*Probability of adults using their phones for meetings or classes are 0.49.
1 - 0.49 = 0.51
*Probability of adults NOT using their phones are 0.51
Now, with the values of n at:
n = 0
n = 1
n = 2
n = 3
[tex]11Cn\times0.49^n\times0.51^{11-n}=11C0\times0.49^0\times0.51^{11-0}=0.0006[/tex][tex]11Cn\times0.49^n\times0.51^{11-n}=11C1\times0.49^1\times0.51^{11-1}=0.0064[/tex][tex]11Cn\times0.49^n\times0.51^{11-n}=11C2\times0.49^2\times0.51^{11-2}=0.0308[/tex][tex]11Cn\times0.49^n\times0.51^{11-n}=11C3\times0.49^3\times0.51^{11-3}=0.0888[/tex]Now, we will add these altogether to get the probability that fewer than 4 of them use their smartphones in meetings or classes.
[tex]0.0006+0.0064+0.0308+0.0888=0.1266=12.66\%[/tex]The answer would be 12.66%.
Shelley has a bag containing three balls: one red, one yellow, and one green. All balls are equally likely to be chosen. Shelley will choose one ball without looking in the bag. What is the probability that Shelley will choose the yellow ball out of the bag? A. 2/3 B. 3/1 C. 3/3 D. 1/3
Answers
Answer:
D. 1/3
Explanation:
In the bag, there are one red, one yellow, and one green ball.
Number of yellow ball = 1
Total number of balls = 3
Thus, the probability that Shelley will choose the yellow ball out of the bag:
[tex]=\frac{1}{3}[/tex]T
Answer: D
Step-by-step explanation: There is 3 balls, lets say that is 3/3, and a yellow ball is 1, which is 1/3
[tex]x2 = 49[/tex]what's the answer
Answers
Solve the equation:
[tex]x^2=49[/tex]The simplest method to solve the equation is to apply the square root on both sides of the equation:
[tex]\sqrt{x^2}=\sqrt{49}[/tex]Since the square and the square root are inverse functions, they cancel out, leaving us with the equation:
[tex]x=\sqrt{49}[/tex]We must find a number such that its square results in 49. That number is 7. But we must recall that there is another number that produces 49 when squared. That number is -7.
This gives us two solutions. It can be written:
[tex]x=\pm7[/tex]The equation has two solutions:
x = 7, x = -7
adrienne earns 98$ for working 8 hours. if she earned 453.25$, how many hours did she work?
Answers
Answer: 37 hours
Step-by-step explanation:
98/8 = 12.25
453.35/12.25 = 37
I need help but not all are boxes are used
Answers
Given:
[tex]y=3x-5\text{ and y=-6x+4}[/tex]Aim:
We need to find the solution to the given system of equations.
Explanation:
Consider the equation y =3x-5.
Substitute y =-6x+4 in the equation y =3x-5.
[tex]-6x+4=3x-5[/tex]Solve for x.
Add 6x to both sides of the equation.
[tex]-6x+4+6x=3x-5+6x[/tex][tex]4=3x-5+6x[/tex][tex]4=9x-5[/tex]Add 5 to both sides of the equation.
[tex]4+5=9x-5+5[/tex][tex]9=9x[/tex]Divide both sides by 9.
[tex]\frac{9}{9}=\frac{9x}{9}[/tex][tex]x=1[/tex]Substitute x =1 in the equation y =3x-5.
[tex]y=3(1)-5[/tex][tex]y=-2[/tex]The solution of the given system of equations is x=1 and y =-2.
Final answer:
[tex](1,-2)[/tex]in an election being held by the associated students organization, there are eight candidates for president, five for five president, five for secretary, and seven for treasurer. How many different possible outcomes are there for this election?
Answers
we have
eight candidates for president
five for secretary
seven for treasurer
therefore
The different possible outcomes is giving by
(8)*(5)*(7)=280 outcomes
the answer is 280 outcomeswhich point on the grid below has coordinates (-9, -2)?
Answers
Answer:
A
Explanation:
Given the point (-9,-2):
[tex]\begin{gathered} (x,y)=(-9,-2) \\ \implies x=-9,y=-2 \end{gathered}[/tex]As seen in the graph, the point on the grid that has the coordinates (-9,-2) is point A.
19. If the cost price of 18 apples is the same as selling price of 16 apples, what is the profit in $ as well as percentage gain?
Answers
Answer
Percent Gain = 12.5%
Explanation
We are told that the
cost price of 18 apples = selling price of 16 apples
Let the cost price of an apple be x dollars
Let the selling price of an apple be y dollars
Buying 18 apples will cost 18 × x = (18x) dollars
Selling 16 apples will bring in 16 × y = (16y) dollars
Recall,
cost price of 18 apples = selling price of 16 apples
18x = 16y
We can rewrite as
16y = 18x
Divide both sides by 16
(16y/16) = (18x/16)
y = 1.125x
Percent gain is calculated as
[tex]\text{Percent Gain = }\frac{(\text{Selling price)-(Cost price)}}{Cost\text{ price}}\times100\text{ percent}[/tex]Selling price = y
Cost price = x
But recall that
y = 1.125x
[tex]\begin{gathered} \text{Percent Gain = }\frac{y-x}{x}\times100\text{ percent} \\ =\frac{1.125x-x}{x}\times100\text{ percent} \\ =\frac{0.125x}{x}\times100\text{ percent} \\ =0.125\times100\text{ percent} \\ =12.5\text{ percent} \end{gathered}[/tex]Hope this Helps!!!
Rewrite each of the following expressions so that they have no division
Answers
Using the law of indices,
[tex]\frac{1}{x^6}[/tex]will be
[tex]\frac{1}{x^6}=x^{-6}[/tex]Margaret and Nathan spent a total of $128 at the state fair last weekend. Nathan spent $2 more than twice the amount that Margaret spent. How much did Nathan spend at the fair?
Answers
Let 'y' represent the amount Margaret spent at the state fair.
Let 'x' represent the amount Nathan spent at the state fair.
In the next statement, Nathan spent $2 more than twice the amount that Margaret spent.
Mathematically,
[tex]x=2+2y\ldots\ldots.1[/tex]And also, we were told that Margaret and Nathan spent a total of $128 at the state fair.
Mathematically,
[tex]x+y=\text{ \$128}\ldots\ldots\ldots2[/tex]Let us substitute 'x'= 2+2y into equation 2 and solve for y.
[tex]\begin{gathered} x+y=128 \\ 2+2y+y=128 \\ 2y+y=128-2 \\ 3y=126 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3y}{3}=\frac{126}{3} \\ y=42 \end{gathered}[/tex]Therefore, the amount of money spent by Nathan will be,
[tex]\begin{gathered} x=2+2y \\ x=2+2(42)=2+84=86 \\ \therefore x=86 \end{gathered}[/tex]Hence, Nathan spent $86 at the fair.
Evaluate 2(x-1), if x= -3
Answers
To evaluate the expression for x = -3, we simply put in -3 whereever we see x in the expression.
Doing this gives us
[tex]2(x-1)\rightarrow2(-3-1)[/tex]We now simplify the expression on the right
[tex]=2(-4)[/tex][tex]=-8[/tex]which is our answer!
You have $10,000 in a savings account. You want to take most of the money out and invest it in stocks and bonds. You decide to invest nine times as much as you leave in the account. You also decide to invest five times as much in stocks as in bonds. How much will you invest in stocks, how much in bonds, and how much will youleave in savings?
Answers
Answer:
7,500 in stocks
1,500 in bonds
1,000 in savings
Explanation:
First, let's call x the quantity that you will leave in saving and y the quantity that you will invest in stocks and z the quantity that you will invest in bonds.
Now, we can formulate the following equations:
x + y + z = 10,000
y + z = 9x
y = 5z
Because you have 10,000 in savings, you decide to invest nine times as much as you leave in the account, and you also decide to invest five times as much in stocks as in bonds.
So, we can rewrite the expressions as:
x + y + z = 10,000
-9x + y + z = 0
y - 5z = 0
Now, we can multiply the second equation by -1 and sum this equation with the first one as:
-9x + y + z = 0
(-9x + y + z)*(-1) = 0*(-1)
9x - y - z = 0
Then, the sum is equal to:
x + y + z = 10,000
9x - y - z = 0
10x - 0 - 0 = 10,000
10x = 10,000
x = 10,000/10
x = 1,000
Replacing x on the second equation, we get:
9x - y - z = 0
9*1,000 - y - z = 0
9,000 - y - z = 0
-y - z = - 9,000
Now, we can add the equation with the third one as:
-y - z = - 9,000
y - 5z = 0
0 - 6z = -9,000
-6z = -9000
z = -9000/(-6)
z = 1,500
Finally, using the third equation, the value of y is equal to:
y = 5z
y = 5*1500
y = 7,500
Therefore, you will invest 7,500 in stocks, 1,500 in bonds and you will leave 1,000 in savings.
Which conjecture is possible to prove?A. All quadrilaterals with at least one side length of 3 are congruent.B. All rectangles with at least one side length of 3 are congruent.C. All rhombuses with at least one side length of 3 are congruent.D. All squares with at least one side length of 3 are congruent.
Answers
All the sides of a square are equal, therefore, if at least one side length is congruent, all of them are.
Thus,
The correct answer is option D.
You roll a six-sided dice.Event A: Roll a 6. Event B: Roll a prime number. Find P(A or B) . Express your answer as a fraction in simplest form.
Answers
The probability of rolling a 6 is:
[tex]P(A)=\frac{1}{6}[/tex]There are 3 prime numbers between 1 and 6: 2, 3 and 5. Therefore, the probability of rolling a prime number is:
[tex]P(B)=\frac{1}{3}[/tex]Therefore, the probability of rolling a 6 or a prime number is:
[tex]P(AorB)=\frac{1}{6}+\frac{1}{3}=\frac{1}{2}[/tex]my name is Emma I'm 9 years old I'm in third grade
Answers
From the question we can deduce that, the squares shaded in red represent the area tomatoes are planted in the garden.
The squares unshaded represents the area corn is planted in the garden.
Observe carefully that the total squares shaded in red are 24 (that is 4 by 6 OR 4 times 6). The unshaded squares total 18 (that is 3 times 6).
Each unit (or each square) is 1 square foot. This means on Nora's garden, she has tomatoes planted on 24 square feet. Also she has corn planted on 18 square feet.
Therefore, the difference between both areas is
Difference = 24 - 18
Difference = 6
ANSWER:
There are 6 more square feet of tomatoes than corn in Nora's garden.
The correct answer is option D
if ZQPS is a right angle and mLQPR = 71 ° . what is mZRPS
Answers
Step 1:
A right angle is 90 degree
Step 2:
angle
angle
angle
Step 3:
Sum of angle QPR and RPS = 90 i.e right angle
angle RPS = 90 - 71
m
A cube is dilated by a factor of 3.5.The volume of the resulting cube is ___ times the volume of the original cube.
Answers
A volume of a cube is given by V=L^3 where L is its side length. If a cube is dilated by a factor of 3.5, it means that its sidelength is increased by a factor of 3.5, i.e. if S is the first length, the new length L satisfies L=3.5*S. Now, the old cube's volume v was v=S^3, after it has expanded to the new sidelength L its new volume V is V=L^3. Using the equation L=3.5*S we can replace L in the equation for V like follows:
V=(3.5*S)^3
Expanding the product we get
V=[(3.5)^3]*(S^3)=42.875*(S^3)
We previously noticed that the prior volume of the cube was v=S^3. Replacing v for S^3 in the previeus equation gives us:
V=42.875v
Thus, the factor by wich the volume of the original cube was scaled up is 42.875
What is the ratio of fish to dinosaurs?3 dinosaurs 10 fish
Answers
Answer
10/3
or 3.33
Solution
[tex]\frac{10\text{ fish}}{3\text{ dinosaurs}}\text{ = }\frac{10}{3}=3.33[/tex]What percentage of the data values falls between the values pf 3 and 24 in the data set shown? 0 5 10 15 20 25 O 25% O 50% O 75% O 100%
Answers
The graph shown in the image is a box and whiskers plot.
The sides of the box are determined by the first and third quartiles of the sample.
The left side corresponds to the first quartile (Q₁), this value separates the bottom 25% of the sample from the top 75%
The right side corresponds to the third quartile (Q₃), this value separates the bottom 75% of the sample from the top 25%
The line inside the box represents the second quartile (Q₂), this value is also known as the Median of the sample and divides the bottom 50% from the top 50%.
The body of the box, i.e. the space between Q₁ and Q₃, is the interquartile range (IQR), this represents the mid 50% of the sample.
The left whisker links the first quartile with the minimum value of the sample.
The right whisker links the third quartile with the maximum