Answers
First, find the vertex of the given function, we have
[tex]\begin{gathered} f(x)=-2x^2-8x+1 \\ \\ \text{The coefficients are } \\ a=-2,b=-8,c=1 \\ \\ \text{The x-coordinate of the vertex is at } \\ x=-\frac{b}{2a} \\ x=-\frac{-8}{2(-2)} \\ x=-\frac{-8}{-4} \\ x=-2 \end{gathered}[/tex]Next, substitute x = -2. to the given function and we get
[tex]\begin{gathered} f(x)=-2x^{2}-8x+1 \\ f(-2)=-2(-2)^2-8(-2)+1 \\ f(-2)=-2(4)+16+1 \\ f(-2)=-8+17 \\ f(-2)=9 \end{gathered}[/tex]Therefore, the vertex is at (-2.9).
The axis of symmetry is at x = -2.
The y-intercept at y = 1.
The x-intercepts are the following:
[tex]\begin{gathered} x=\frac{ -b \pm\sqrt{b^2 - 4ac}}{ 2a } \\ x = \frac{ -(-8) \pm \sqrt{(-8)^2 - 4(-2)(1)}}{ 2(-2) } \\ x=\frac{8\pm\sqrt{64-(-8)}}{-4} \\ x = \frac{ 8 \pm \sqrt{72}}{ -4 } \\ x = \frac{ 8 \pm 6\sqrt{2}\, }{ -4 } \\ \text{ Which becomes} \\ \\ x=\frac{8+6\sqrt{2}\,}{-4}\approx−4.12132 \\ x=\frac{8-6\sqrt{2}\,}{-4}\approx0.12132 \end{gathered}[/tex]Graphing the function we get
Related Questions
zachs orange paint is made by mixing 3 cups of red for every 5 cups of yellow. we know that Zach brought 24 cups of red paint. how many cups of yellow paint must he get to make his orange paint mixture?
Answers
For the information given in the statement you have
[tex]\frac{\text{number of cups of red paint}}{\text{ number of cups of yellow paint}}=\frac{3}{5}[/tex]Then
[tex]\frac{3}{5}=\frac{24\text{ cups of red paint}}{\text{ x cups of yellow paint}}[/tex]Solving for x
[tex]\begin{gathered} \frac{3}{5}=\frac{24}{x} \\ \text{Apply cross multiplication} \\ 3\cdot x=24\cdot5 \\ 3x=120 \\ \text{ Divide by 3 into both sides of the equation} \\ \frac{3x}{3}=\frac{120}{3} \\ x=40 \end{gathered}[/tex]Therefore, he must get 40 cups of yellow paint to make his orange paint mixture.
write the following equation in a function form.3x+4y=0
Answers
You have the following equation:
[tex]3x+4y=0[/tex]To write the previous equation in a function form consists in solving for y, just as follow:
3x + 4y = 0 subtract 3x both sides
4y = -3x divide by 4 both sides
y = -3/4 x
Hence, the function for of the given equation is:
y = -3/4 x
a grain silo has a cylindrical shape. its radius is 9ft, and height is 52ft. what is the volume of the silo?use the value of 3.14 for pieround to the nearest whole number
Answers
Given:
Radius = 9 ft
Height = 52 ft
Volume of cylindrical (silo) is:
[tex]\text{Volume}=\pi r^2h[/tex][tex]\begin{gathered} r=9 \\ h=52 \\ \pi=3.14 \end{gathered}[/tex][tex]\begin{gathered} \text{Volume}=\pi r^2h \\ =3.14\times(9)^2\times52 \\ =3.14\times81\times52 \\ =254.34\times52 \\ =13225.68 \end{gathered}[/tex]Nearst whole number is 13226
suppose that you have a 10,000 in a rather risky investment recommend by your financial advisor during the first year your investment decreases by 50% of its original value during the second year your investment at the end of year 1 increases by 60%. Weiser tells you that there must have there must have been a 10% overall increase of your original $10,000 investment. Is your financial advisor using percentages Properly? If Not, what is your actual gain or loss of your original $10,000 investment?
Answers
The financial advisor is NOT using percentages properly, because the 60% increase would multiply the new value after one year, and not the initial value.
So first let's find the investment after one year:
[tex]\begin{gathered} 10000-50\text{\% of 10000} \\ =10000-0.5\cdot10000=10000-5000=5000 \end{gathered}[/tex]Then, we have an increase of 60%, so:
[tex]\begin{gathered} 5000+60\text{\% of 5000} \\ =5000+0.6\cdot5000=5000+3000=8000 \end{gathered}[/tex]The final value is 8000, which is lesser than the original value, so we have a loss.
The percentual loss is:
[tex]\frac{10000-8000}{10000}=\frac{2000}{10000}=0.2=20\text{\%}[/tex]Sort the cards so that each group adds up to 100%
Answers
Answer:
Add the 20%, 0.40 and the 40/100 chart
Add the 1/10, the 0.10, and the 80/100 chart
And finally, add the 6%, the 4/100 chart, and the 90/100
2a + 3b when a=2 and b=4
Answers
Answer:
16
Step-by-step explanation:
[tex]2a+3b \\ \\ =2(2)+3(4) \\ \\ =4+12 \\ \\ =16[/tex]
Answer:
Step-by-step explanation:
2a+3b when a=2 and b=4
2a 2*2 =4
3b 3*4=12
=12+4=16
=2a+3b= 16 :)
If we graph the terms of a factored form of a quadratic equation individually, what type of graphs do you get?
Answers
The factored form of function does not affect the trajectory of the graph.
Given that,
If we graph the terms of a factored form of a quadratic equation individually, what type of graphs do you get is to be discussed?
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
here,
The graph of a quadratic equation is a parabolic structure, when structuring the graph of the factor of the quadratic function it outcome same as the graph of the quadratic function itself.
Thus, the factored form of function does not affect the trajectory of the graph.
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Graph the line with the equation y = 2x - 1.
Answers
A line is uniquely defined by two points.
Since the points (0, -1) and (1, 1) lie on the graph (since they satisfy the equation), you can draw the line through these points.
which is the best estimate of the amount of interest you will save if if you take the 5% of loan instead of the 6% loan?
Answers
For the 5% loan, you will pay a total of:
[tex]219\cdot25=5475[/tex]For the 6% loan, you will pay a total of:
[tex]221\cdot25=5525[/tex]if if you take the 5% of loan instead of the 6% loan you will save:
[tex]5525-5475=50[/tex]Answer:
$50
simplifying with like terms; 3x^2 + 5x - 2x^2
Answers
Simplifying,
[tex]\begin{gathered} 3x^2+5x-2x^2 \\ \rightarrow3x^2-2x^2+5x \\ \rightarrow x^2+5x \end{gathered}[/tex]Can someone help me with this geometry question? I am pretty sure it’s 67
Answers
Solution
Step 1:
The angle at the center is twice the angle at the circumference.
Step 2:
[tex]\begin{gathered} m\angle PMN\text{ = 134} \\ m\angle PON\text{ = ?} \\ m\angle PMN\text{ = 2m}\angle PON \\ 134\text{ = 2m}\angle PON \\ m\angle PON\text{ = }\frac{134}{2} \\ m\angle PON\text{ = 67} \end{gathered}[/tex]Answer
m
Chip Ahoy
The number of chocolate chips in an 18-ounce bag of
Chips Ahoy! chocolate chip cookies is approximately
normally distributed with a mean 1262 chips and a
standard deviation of 118 chips according to a study
by cadets of the U.S. Air Force Academy. (Why are
they studying chocolate chip cookies?}
What percent of bags has between 1026 and 1380 chocolate chips? Write your percent without the percent sign.
What percentage of the 18-ounce bags of chips ahoy! Cookies contains fewer than 1144 chocolate chips? Write the percent without the percent sign.
What percentage of the 18-ounce bags of chips ahoy! Cookies contains more than 1498 chocolate chips? Write the percent without the percent sign.
Answers
Using the normal distribution, it is found that:
81.85% of bags has between 1026 and 1380 chocolate chips.15.87% of the bags contain fewer than 1144 chocolate chips.2.28% of bags contain more than 1498 chocolate chips.Normal Probability DistributionThe z-score of a measure X of a variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the fraction presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of the number of chips are given as follows:
[tex]\mu = 1262, \sigma = 118[/tex]
The proportion of bags that has between 1026 and 1380 chocolate chips is the p-value of Z when X = 1380 subtracted by the p-value of Z when X = 1026, hence:
X = 1380:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1380 - 1262)/118
Z = 1
Z = 1 has a p-value of 0.8413.
X = 1026:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1026 - 1262)/118
Z = -2
Z = -2 has a p-value of 0.0228.
0.8413 - 0.0228 = 0.8185.
Hence the percentage is 81.85%.
The proportion that has fewer than 1144 chips is the p-value of Z when X = 1144, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1144 - 1262)/118
Z = -1
Z = -1 has a p-value of 0.1587.
Hence the percentage is of 15.87%.
The proportion that has more than 1498 chips is one subtracted by the p-value of Z when X = 1498, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1498 - 1262)/118
Z = 2
Z = 2 has a p-value of 0.9772.
1 - 0.9772 = 0.0228
Hence the percentage is of 2.28%.
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Determine a series of transformations that would map Figure F onto Figure G. 12 11 10 9 8 Figure G7 6 4 3 1 2 3 4 5 6 7 8 9 10 11 12 -12-11-10-9-8-7 -6 -5 -4 -3 -2 -1 -2 -3 -4 -6 N . Figure F -8
Answers
To find the series of transformations that would map Figure F onto Figure G
We will choose one side to figure out the transformations
So, Look at the vertical side of the figure F which has the end points (1 , -3) and (1 , -5)
The image of this side will be the horizontal side of figure G with the end points ( -3 , 1 ) and (-5,1)
so, we need to rotate it
So, the series of transformation will be :
Reflection
To find the rule of reflection
Note ( 1 , -3 ) → (-3 , 1)
this mean ( x , y ) → (y,x)
Which mean reflection over y = x
The same can obtained by translation 2 units up then rtation 90 clockwise
See attached pic. I am confused on how to answer A with the correct number of significant figures.
Answers
Recall one of the rules for significant figures
A final zero or trailing zeros in the decimal portion ONLY are significant
24.00 mg has four significant figures
2,4, 0 and 0
24.00 mg when converted to grams is 0.024 g
0.024 only has 2 significant figures, therefore we need to add 2 more zeroes at the end of 4
0.024 g → 0.02400 g
if i walked to my parents house for Thanksgiving and lived 25.6 miles away, and it took me 4 hrs to get there is it true tht my constant speed would be 4.6 mph?
Answers
Distance walked over time
25.6 miles away, are going to walk
lets find if
25.6/ 4 = 4.6?
Then 25.6 = 24 + 1.6 =
so. 25.6/4= 24/4 + 1.6/4 = 6 + 0.4 = 6.4
So its NOT TRUE that constant speed is 4.6 mph
Mena is making a hamster house. She cuts a hole for a window that has side lengths of 5 inches and 3 inches. Which drawing plan shows the correct rectangular opening? On these graphs, each unit represents 1 inch. 10 B(1,8) C (48) A. 6 5 4 3 2 1 A (1,2) D (4.2) 1 2 3 4 5 6 7 8 9 10 F (7.8) 10 9 E (3.8) 8 7 B. N00 1 H (3,2) G (7.2) 1 2 3 4 5 6 7 8 9 10
Answers
We need a rectangle with one side 5 units long and another side 3 units long
The correct option is:
6) Rotate clockwise around the origin 270°270°AYRSх6-2TQ QWhat is the rule? (x,y) → (Q' (_)R' (_)S'(__)T'(___)
Answers
we know that
The rule for a rotation by 270° about the origin is (x,y)→(y,−x)
so
we have
R(-5,0) -------> R'(0,5)
S(-3,0) ------> S'(0,3)
T(-1,-3) ------> T'(-3,1)
Q(-6,-3) ----> Q'(-3,6)
step 2
Graph the image
Plot the ponts of the image
using a graphing tool
please wait a minute to draw the figure
A twelve-foot ladder is leaning against a wall. If the ladder reaches 8 ft. high on the wall, what is the angle the ladder forms with the ground to the nearest degrees?
Answers
Solution
Recall: SOHCAHTOA
[tex]\begin{gathered} sin\theta=\frac{8}{12} \\ \\ \theta=sin^{-1}0.6667 \\ \theta=41.81^0 \\ \end{gathered}[/tex]The final answer
[tex]\theta=42^0[/tex]I can only send this at first. I will send you a picture of the work problem with the choices for the blanks.
Answers
Concept
Area of the shaded part
= Area of the outer square - Area of the inner square
Next,
Area of the outer square = Length x Length = 5 x 5 = 25
Area of the inner sqaure = Length x Length = 2 x 2 = 4
Final answer
The area of the shaded part = 25 - 4
= 21 inches square
two 5 in by 1.5 in and two 2 in by 1.5 in
1.5
2 in and 5 in
Solve x^2-6+58=0 please fast I need help
Answers
Answer:
No real solutions.
Step-by-step explanation:
When solving this equation, you have to figure out if the two sides of an equation equal each other.
Solve.
x^2-6+58 = 0
Answer: No real solutions.
This is due to the fact that x^2-6+58 does not equal 0.
Hope this helps!
Btw, if this is correct, could I have Brainliest? Thanks!
How long will it take for an investment to triple if interest is compounded continuously at 7%
Answers
Step-by-step explanation:
Question:
How long will it take an investment to triple, if the interest is
7
%
and compounded quarterly?
Future Value:
You have to find time that will it take an investment to triple. The amount is compounded quarterly so, n=4. Substitute all values into the formula,
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Answer and Explanation:
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Can you help me with circumference and rotations?A Bicycle tire has a diameter of 62 cm, What is the distance the bicycle travels in 10 revolutions, round your answer to the nearest cm
Answers
Given:
[tex]\begin{gathered} D_{\text{iamteter of the tire}}=62cm \\ N_{\text{umber of revolution}}=10revolutions \end{gathered}[/tex]To Determine: The distance travelled
The distance travel in 1 revolution is the circumference of the tire.
The circumference of a circle is calculated by the formula below
[tex]\begin{gathered} C_{\text{ircumference of a circle }}=2\pi r \\ 2r=d \\ \text{Therefore} \\ C_{\text{ircumference of a circle }}=\pi d \end{gathered}[/tex]Substituting for diameter in the formula to get the distance travelled in 1 revolution as below
[tex]D_{is\tan ce\text{ travelled in 1 revolution}}=\pi\times62cm=62\pi cm[/tex]Therefore the distance in 10 revolution would be
[tex]\begin{gathered} D_{is\tan ce\text{ travelled in 10 revolutions}}=10\times62\pi cm \\ D_{is\tan ce\text{ travelled in 10 revolutions}}=620\pi cm=1947.787cm \\ D_{is\tan ce\text{ travelled in 10 revolutions}}\approx1948cm \end{gathered}[/tex]Hence, the distance travelled by the bicycle in 10 revolutions to the nearest cm is 1948cm
PLS HELP FAST!! Question due in 5 minutes!!!
Answers
Answer:
hypotenuse 3 leg 1 =1 leg2=
PLEASE HELP!! pleaseAlthough she's only in middle school, Tameka loves to drive go-carts! Her favorite place to drive go-carts, Drivers Delight, has 3 circular tracks. Track 1 has a radius of 60 feet. Track 2 has a radius of 85 feet. Track 3 has a radius of 110 feet. A. Compute the circumference of Track 1. B. Compute the circumference of Track 2. C. Compute the circumference of Track 3.D. Driver's Delight is considering building a new track. They have a circular space with a diameter of 150ft. Compute the circumference of the circular space
Answers
A. Circumference of Track 1 = 2π r
= 2 x 3.14 x 60
=376.8 feet
B.Circumeference of track2 = 2π r
= 2 x 3.14 x 85
=533.8 feet
C.Circumference of track3 = 2π r
=2 x 3.14 x 110
=690.8 feet
D.Circumference of the circular space = 2π r
Diameter was given to be 150 ft
but radius(r) is half the diameter. Hence radius = 150ft/2 = 75 ft
Circumference of the circular space = 2x 3.14 x 75
=471 feet
help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
The function notation f(-5) has a value of -6
How to solve the function?From the question, we have the function definition to be f(-5)
Also, we have the graphs to be f(x) and g(x)
The equation of the first graph is illustrated by the blue curve f(x), while the second is illustrated by the red curve
Because the function is f(x), we make use the blue curve
On the blue curve, we have
f(-5) = -6
The interpretation of the above equation is that
When x = -5, the blue curve has a value of -6
This means that the function f(-5) has a value of -6
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Abel owns a dog walking business. He walks12 dogs every day of the week. If Abel walks2.6 miles each day, how many miles does hewalk in one week?
Answers
Abel walks 2.6 miles each day of the week.
The week has 7 days.
So, to calculate how many miles he walks in one week we simply have to multiply the number of miles that he walks per day (2.6) by the number of days in a week (7).
2.6 miles per day x 7 days = 2.6 x 7 = 18.2 miles a week.
given (10,5) and (x,-10), find all x such that the distance between these two points is 17. separate multiple answers with a comma.
Answers
x = (2, 18)
Explanation:Given the points (10, 5) and (x, -10)
The distance between these points is:
[tex]\begin{gathered} D=\sqrt[]{(x-10)^2+(-10-5)^2} \\ \\ =\sqrt[]{(x-10)^2+(-15)^2} \\ \\ =\sqrt[]{(x-10)^2+225} \end{gathered}[/tex]The distance is given to be 17, so
[tex]\begin{gathered} \sqrt[]{(x-10)^2+225}=17 \\ \\ (x-10)^2+225=17^2 \\ (x-10)^2=17^2-225 \\ (x-10)^2=289-225 \\ (x-10)^2=64 \\ x-10=\pm\sqrt[]{64}=8 \\ x=\pm8+10 \\ x=8+10=18 \\ OR \\ x=-8+10=2 \end{gathered}[/tex]x = 2 or x = 18
Hans paid $37.51 Employment Insurance (El) on his monthly income of $2168.21.
What was the El rate?
Answers
The EI rate is 17.3%
How to calculate the EI rate ?The first step is to write out the parameters given in the question
Hans employment insurance is $37.51
Hans monthly income is $2168.21
The EI rate can calculated as follows
37.51/2168.21 × 100
= 0.0173 × 100
= 17.3%
Hence the EI rate is 17.3 %
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4. What is the discount and special sale price of a pair of shoes regularly priced $120 when the store has a 33% off sale /(round to the nearest dollar)? 5.a retailer purchase a $3 toy in as a markup rate of 150%. determine the markup and the regular retail price of the toy. 6. Jody received a 30% Commission on the profit when he sells over 20 cars in a month . if he sold 23 cars in October, resulting in $15000 profit for the dealership , how much did Joe earn in commission ?7.how much would be in an account when you turn 18 if, on the day you were born, 1000 were disposed into the account which returned 6% simple interest, and no longer disposes or withdrawals were made ?
Answers
Let's begin by identifying key information given to us:
Shoe Price = $120
Discount rate = 33% = 0.33
The Discount price of the shoe is calculated below:
[tex]\begin{gathered} DiscountPrice=ShoePrice-(ShoePrice\cdot DiscountRate) \\ DiscountPrice=120-\lbrack120\cdot(0.33)\rbrack=120-39.6 \\ DiscountPrice=80.40 \end{gathered}[/tex]Therefore, the discount price is $80.40
Nikhil sells digital cameras. He bought a DSLR camera for 24,000. He sold the camera for
€25,500.
What is Nikhil's profit per 100?
Answers
Answer:
He makes €100,000
Step-by-step explanation:
First, subtract 25,000- 24,000= 1000
Then, multiply 1000*100
€100,000 is how much he makes
