48. In the parabola, y = 3x ^ 2 + 12x + 11 focus is located at a distance p > 0 from the vertex. Then p=a. 3b. 1/3c. 12d. 1/12e. None of the above
Answers
Given the equation,
[tex]y=3x^2+12x_{}+11[/tex]We are to solve for the vertex first, in order to solve for the vertex.
[tex]3x^2+12x+11=y[/tex]factor all through by 3
[tex]\begin{gathered} \frac{3x^2}{3}+\frac{12x}{3}+\frac{11}{3}=y \\ 3(x^2+4x+\frac{11}{3})=y\ldots\ldots.1 \end{gathered}[/tex][tex]x^2+4x=-\frac{11}{3}\text{ complete the square for the inner expression}[/tex][tex]\begin{gathered} x^2+4x+(\frac{4}{2})^2=-\frac{11}{3}+(\frac{4}{2})^2 \\ (x+2)^2=-\frac{11}{3}+4=\frac{1}{3} \\ =(x+2)^2-\frac{1}{3} \end{gathered}[/tex]Put (x+2)²-1/3 into equation 1
[tex]3((x+2)^2-\frac{1}{3})=y\ldots\ldots2[/tex]The vertex is at (-2,-1)
Note:
[tex]\begin{gathered} \text{vertex}=(h,k) \\ \text{focus}=(h,k+\frac{1}{4a}) \end{gathered}[/tex]P is the distance between the focus and the vertex.
[tex]\begin{gathered} (h-h,k+\frac{1}{4a}-k)=(0,\frac{1}{4a}) \\ \end{gathered}[/tex]where,
[tex]a=3\text{ from equation 2}[/tex]Therefore,
[tex]\begin{gathered} p=(0,\frac{1}{4\times3})=(0,\frac{1}{12}) \\ p=(0,\frac{1}{12}) \end{gathered}[/tex]Hence,
[tex]p=\frac{1}{12}[/tex]The correct answer is 1/12 [option D].
Related Questions
determine if each expression is equivalent to [tex] \frac{ {7}^{6} }{ {7}^{3} } [/tex]
Answers
The question says we are to check the options that are equal
[tex]\frac{7^6}{7^3}[/tex]Using the law of indices
[tex]\frac{7^6}{7^3}=7^{6-3\text{ }}=7^3[/tex]So we will check all the options(applying the laws of indices)
The first option is
[tex]7^9(7^{-6})=7^{9-6}=7^3[/tex]yes, the first option is equivalent
We will move on and check the second option
[tex]\frac{7^{-8}}{7^{-11}}\text{ = }7^{-8+11}=7^3[/tex]Yes the second option is equivalent
We will move on to check the third option
[tex](7^5)(7^3)divideby7^{4\text{ }}=7^{5+3-4\text{ }}=7^4[/tex]No the third option is not eqquivalent to the question
We will move to tthe next option, fourth option
[tex]7^{-3\text{ }}\times7^{6\text{ }}=7^{-3+6}=7^3[/tex]yes this option is equivalent to the fraction
Moving on to the fifth option
[tex](7^3)^{0\text{ }}=7^{3\times0}=7^0=\text{ 1}[/tex]No the fifth option is not equivalent to the question
Use area under the curve to complete probability for continuous probability dentist functionsuse the uniform distribution to compute probabilityfind the mean and standard deviation Love the uniform distribution1.One type of card stock which may be used for the cover of a booklet is uncoated paper with waymark as 65 pounds the standard thickness of 65# of card stuck is 9.5 points (0.0095”). A manufacturer determines that the thickness of 65# of card stuck produced followed a uniform distribution varying between 9.25 points and 9.75 points.A)Sketch the description for this situation.B)compute the mean and standard division of the thickness of the 65# cards stuck producedC)compute the probability that a randomly selected piece of 65# card stark has a thickness of a list 9.4 points.D)Compute the probability that a randomly selected piece of 65# card stock has thickness between 9.75 points.
Answers
If x is uniformly distributed over the interval [ a , b ] then,
[tex]\begin{gathered} f(x)\text{ = }\frac{1}{b-a}\text{ , a }\leq\text{ x }\leq\text{ b} \\ f(x)\text{ = 0 , otherwise} \end{gathered}[/tex]Also ,
[tex]\begin{gathered} \text{Mean = }\frac{a\text{ + b}}{2} \\ \text{Std deviation = }\sqrt[]{\frac{(b-a)^2}{12}} \end{gathered}[/tex]It is given that ,
[tex]\begin{gathered} a\text{ = 9.25} \\ b\text{ = 9.75} \\ b\text{ - a = 9.75 - 9.25 = 0.5} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} f(x)\text{ = }\frac{1}{0.5}\text{ 9.25 }\leq\text{ x }\leq\text{ 9.75} \\ f(x)\text{ = 0 otherwise} \end{gathered}[/tex](a)The distribution is as follows :
(b)The mean is calculated as,
[tex]\begin{gathered} \text{Mean = }\frac{a\text{ + b}}{2} \\ \text{Mean = }\frac{9.25\text{ + 9.75}}{2} \\ \text{Mean = 9.5} \end{gathered}[/tex]Standard deviation is calculated as,
[tex]\begin{gathered} \text{Standard deviation = }\sqrt[]{\frac{(b-a)^2}{12}} \\ \text{Standard deviation = }\sqrt[]{\frac{(0.5)^2}{12}} \\ \text{Standard deviation }\approx\text{ 0.1443} \end{gathered}[/tex](c) The probability is calculated as,
[tex]\begin{gathered} P(\text{ atleast 9.4 points ) = P( x }\ge\text{ 9.4)} \\ P(\text{ atleast 9.4 points ) = }\int ^{9.75}_{9.4}(\frac{1}{0.5})dx \\ P(\text{ atleast 9.4 points ) = }\frac{9.75\text{ - 9.4}}{0.5} \\ P(\text{ atleast 9.4 points ) = 0.7} \end{gathered}[/tex](d) The probability is calculated as,
[tex]\begin{gathered} P(\text{between 9.45 and }9.75\text{ ) = P( 9.45 }\leq\text{ x }\leq\text{ 9.75 )} \\ P(\text{between 9.45 and }9.75\text{ ) = }\int ^{9.75}_{9.45}(\frac{1}{0.5})dx \\ P(\text{between 9.45 and }9.75\text{ ) =}\frac{9.75\text{ - 9.45}}{0.5} \\ P(\text{between 9.45 and }9.75\text{ ) = 0.6} \end{gathered}[/tex]how many km/h equals 880ft/min? Explain how you solved this problem
Answers
The number of kilometers per hour in 880 feet / minute can be found to be 16.09 kilometers per hour
How does km/h relate to ft/ min?Based on the conversion rates between kilometers and feet, the number of feet per minute for each kilometer per hour is 54.6807 feet per minute.
In other words, 1 km / h is equal to 54.6807 feet per minute.
If there are 880 ft / minute therefore, the number of kilometers per hour is:
= Speed in feet per minute / feet per minute per kilometer per hour
= 880 / 54.6807
= 16.09 kilometers per hour
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an airplane flew for one hour and landed 100 miles north and 80 miles east from its origin. what was the distance traveled, speed and angle of direction from its origin?
Answers
The distance traveled by airplane is 180 miles.
The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°
The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.
Then, the total distance traveled by airplane will be:
= 100 miles + 80 miles = 180 miles.
The speed can be defined as the distance traveled by the total time taken.
Speed = distance/time
Speed = 180 miles/ 1 hour
Speed = 180 miles/60 minutes
Speed = 3 miles per minute
The angle of direction from its origin will be:
tan (x) = 100 miles/80 miles
x = tan⁻¹ ( 100/80)
x = tan⁻¹ ( 10/8) = tan⁻¹ ( 5/4)
x = 51.34°
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Create a quadratic function in one of the forms and show how to convert it to the other two forms.
Answers
Create a quadratic function in one of the forms and show how to convert it to the other two forms.
Step-by-step explanation:
1) Standard form: y = ax2 + bx + c where the a,b, and c are just numbers.
[tex]y=ax^2+bx+c[/tex]2) Factored form: y = (ax + c)(bx + d) again the a,b,c, and d are just numbers.
[tex]y=(ax+c)(bx+d)[/tex]3) Vertex form: y = a(x + b)2 + c again the a, b, and c are just numbers.
[tex]y=a(x+b)^2+c[/tex]The vertex of the parabola is written as (h, k) where b is the x - coordinate and c - is the y - coordinate
Triangle HJK has vertices at H(2, 2) J(2, 4) and K(0, 2). What is the midpoint of the longest side of the triangle?
Answers
The coordinates of the vertices of triangle are given as H(2,2), (J(2, 4), K(0,2)
We would determine the longest side by applying the formula for finding the distance between two points which is expressed as
[tex]\begin{gathered} \text{Distance = }\sqrt[]{x2-x1)^2+(y2-y1)^2} \\ \text{For HJ, x1 = 2, y1 = 2, x2 = 2, y2 = 4} \\ \text{Distance = }\sqrt[]{(2-2)^2+(4-2)^2}\text{ = }\sqrt[]{2^2}\text{ = 2} \\ \text{For JK, x1 = 2, y1 = 4, x2 = 0, y2 = 2} \\ \text{Distance = }\sqrt[]{(0-2)^2+(2-4)^2}=\sqrt[]{(4+4)}=\text{ }2.83 \\ \text{For HK, x1 = 2, y1 = 2, x2 = 0, y2 = 2} \\ \text{Distance = }\sqrt[]{0-2)^2+(2-2)^2}=\text{ }\sqrt[]{4}\text{ = 2} \end{gathered}[/tex]Thus, the longest side is JK. The formula for finding midpoint is
Midpoint = (x1 + x2)/2, (y1 + y2)/2
Midpoint = (2 + 0)/2, (4 + 2)/2
Midpoint = 2/2, 6/2
Midpoint = 1, 3
Choose the left side that makes a True statement, and shows at the sum of the given complex numbers is 10Choose the left side that makes a true statement, and shows that the product of the given complex numbers is 40
Answers
For statement one:
We need to add up to complex numbers and their sum must give us equal to 10.
Also, we need to use the complex numbers:
5+i√15 and 5-i√15.
Then, we can use:
(5+i√15)+( 5-i√15) =
5+i√15+5-i√15 =
5+5+ i√15-i√15 =
= 10 + 0
= 10
For the second statement:
We need to show the product of complex numbers:
Then, we use:
(5+i√15)(5-i√15))=
5*5 - 5*i√15) +5*i√15) +√15*√15=
25 + 0 + 15=
40
divide fraction2*1/3 / 7*3/8 =
Answers
Step-by-step explanation:
3.999 is the correct answer
X+27+32 = 8
X+ 3y +32 = 10
X + 2y +42 = 9
Answers
Value of x and y are -51 and 8 respectively
What is Algebra?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.
Let,
X+27+32 = 8
X+ 3y +32 = 10
X + 2y +42 = 9
Be, equation 1, 2 and 3 respectively
X+27+32 = 8 -----(1)
X+ 3y +32 = 10 -----(2)
X + 2y +42 = 9 -----(3)
From equation we can find the value of x
X+27+32 = 8
X + 59 = 8
X = 8 - 59
X = - 51
Substituting the value of x in equation 3
X + 2y +42 = 9
(-51) + 2y + 42 = 9
-51 + 42 + 2y = 9
-9 + 2y = 9
2y = 9 + 9
2y = 18
y = 18/2
y = 9
Hence, the value of x = -51 and y = 9
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h(x) = x2 + 1 k(x) = x-2 (h - k)(3) = DONE
Answers
We are given two functions:
h(x) = x^2 + 1
and k(x) = x - 2
We are asked to find the value of:
(h - k) (3) (the value of the difference of the two functions at the point x = 3
So we performe the difference of the two functions:
(h - k) (x) = x^2 + 1 - (x - 2) = x^2 + 1 - x + 2 = x^2 - x + 3
So, this expression evaluated at 3 gives:
(h-k)(3) = 3^2 - 3 + 3 = 9
One could also evaluate what was asked by evaluating each function independently and subtracting the results of such evaluation:
h(3) = 3^2 + 1 = 10
k(3) = 3 - 2 = 1
Then, the difference is : h(3) - k(3) = 10 - 1 = 9
So use whatever method feels more comfortable for you.
what number need to be changed to make a linear function? And what does it have to turn into?
Answers
In order to have a linear function, the rate of change needs to be the same in each point
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For
(-18,2)=(x1,y1)
(-14,4)=(x2,y2)
[tex]m=\frac{4-2}{-14+18}=\frac{1}{2}[/tex]for
(-14,4)=(x1,y1)
(-12,5)=(x2,y2)
[tex]m=\frac{5-4}{-12+14}=\frac{1}{2}[/tex]for
(-12,5)=(x1,y1)
(0,12)=(x2,y2)
[tex]m=\frac{12-5}{0+12}=\frac{7}{12}[/tex]as we can see here are the two numbers so we will obtain the equation in order to know the number that needs to be change
[tex]y=\frac{1}{2}x+11[/tex]therefore if x=0
[tex]y=\frac{1}{2}(0)+11=11[/tex]the number we need to change is 12 and need to be changed for 11
(0,11)
a. The number that needs to be changed in order to create a linear function is 12
b. That number needs to be changed to 11 in order for the function to be linear
If $2,000 is invested at 6% compounded monthly, what is the amount after 5 years?
Answers
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is the number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$2,000
t=5 years
r=6%=6/100=0.06
n=12
substitute the given values in the above formula
[tex]\begin{gathered} A=2,000(1+\frac{0.06}{12})^{12*5} \\ \\ A=\$2,697.70 \end{gathered}[/tex]therefore
The answer is $2,697.70Find the AreaA. 314.2 IN2B. 1256.6 IN2C. 31.4 IN2D. 62.8 IN2
Answers
Given:
Diameter = 20 in
Find-:
Area of circle
Explanation-:
The area of circle is:
[tex]A=\pi r^2[/tex]The radius of circle is:
[tex]r=\frac{D}{2}[/tex]Where,
[tex]\begin{gathered} r=\text{ Radius} \\ \\ D=\text{ Diameter} \end{gathered}[/tex]So the radius of given circle is:
[tex]\begin{gathered} D=20\text{ in} \\ \\ r=\frac{D}{2}\text{ in} \\ \\ r=\frac{20}{2}\text{ in} \\ \\ r=10\text{ in} \end{gathered}[/tex]The area of circle is:
[tex]\begin{gathered} A=\pi r^2 \\ \\ A=\pi(10)^2 \\ \\ A=100\pi \\ \\ A=314.159 \\ \\ A=314.2\text{ in}^2 \end{gathered}[/tex]So, the area of a circle is 314.2
Kaitlin races her bicycle for 98 m. A wheel of her bicycle turns 49 times as the bicycle travels this distance. What is the diameter of the wheel? Use the value 3.14 for n. Round your answer to the nearest tenth
Answers
Answer:
0.6m
Explanation:
Given the following
Total distance covered = 98m
pi = 3.14
Circumference of the wheel is the distance travelled in one rotation. Hence;
distance travelled in one rotation = \pi d
d is the diamter of the wheel
distance travelled in 49 rotation = 49*\pi d
Since distance travelled in 49 rotation = 98m, then;
98 = 49*\pi d
Divide both sides by 49
98/49 = \pi d
2 = 3.14d
d = 2/3.14
d = 0.6m
Hence the diameter of the wheel is 0.6m
The expression secθ - ((tan^2)(θ)/(sec)(θ)) simplifies to what expression?−tan θ−cot θcos θsec θ
Answers
Given the expression
[tex]sec(\theta)-\frac{tan^2(\theta)}{sec(\theta)}[/tex]express in sen and cos terms
[tex]\frac{1}{cos(\theta)}-\frac{\frac{sin^2(\theta)}{cos^2(\theta)}}{\frac{1}{cos(\theta)}}[/tex][tex]\frac{1}{cos(\theta)}-\frac{sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{1-sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{cos^2(\theta)}{cos^(\theta)}[/tex][tex]cos^(\theta[/tex]then the correct answer is option C
Cos (angle)
3. The sum of two consecutive odd integersis 168. What are the integers?
Answers
Integers are numbers such as
[tex]N=\text{ }.\ldots\text{-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9}\ldots.[/tex]And odd numbers are
[tex]1\text{ 3 5 7 9 11 13 }\ldots[/tex]10. A $152,000 home has an assessment rate of 52% and a tax rateof $48 per $1,000. Use the effective tax method to calculate theproperty tax .Hint: When you determine the effective tax rate, round the rateto three places.
Answers
Given
$152,000
52% assessment rate
$48 per $1,000
Procedure
First, let's calculate the assessment rate.
[tex]152000\cdot0.52=79040.0[/tex]Now let's calculate the taxes
[tex]79040.0\cdot\frac{48}{1000}=3793.92[/tex]Property taxes are equal to $3,793.92.
14 pointsWhich are the coefficients of the terms in the algebraic expression, x2 - 3x?O and -31 and -3O and 351 and 36
Answers
Answer:
The coefficients of the terms in the algebraic expression are 1 and -3
[tex]1\text{ }and-3[/tex]Explanation:
The coefficients are the number that multiplies an algebraic term in an algebraic expression.
for example; the coefficient of 3x is 3.
[tex]3x=3\times x[/tex]For the question;
given the expression;
[tex]x^2-3x[/tex]The coefficient of x^2 is 1
[tex]x^2=1\times x^2[/tex]while the coefficient of x is -3
[tex]-3x=-3\times x[/tex]Therefore, the coefficients of the terms in the algebraic expression are 1 and -3
[tex]1\text{ }and-3[/tex]need help asap look at attachment
Answers
Answer: Width =14, Length = 18
Step-by-step explanation:
L = W + 4
2W + 2L = 64
W+ L = 32
2W+ 4 = 32
2W = 28
W = 14
You use substitution to solve a system of equations and after simplifying end with a statement that says 7=7 discrible what this statement means about the number of solutions and about the graph of the system
Answers
Hence there are infinite solutions and the graphs of the system are concurrent.
If the system used straight lines then they would be on top of each other.
4. Identify the properties that are always true for the given quadrilateral by placing an X in the appropriate box. Property Parallelogram Rectangle Rhombus Square Isosceles Trapezoid Kite a. Opposite sides are parallel. b. Only one pair of opposite sides is parallel C. Opposite sides are congruent Side Relationships d. Only one pair of opposite sides is congruent e. All sides are congruent. f. 2 pairs of consecutive sides are congruent.
Answers
There is quadrilateral, means it has 4 lines
Is a rhombus
Find the present value that will grow to $6000 if the annual interest rate is 9.5% compounded quarterly for 9 yr.The present value is $(Round to the nearest cent as needed)
Answers
We need to know how to calculate compound interest to solve this problem. The present value is $2577.32
Compound interest is the interest that is earned on interest. Inorder to calculate the compound interest we need to know the principal amount, the rate of interest, the time period and how many times the interest is applied in per time period. In this question we know the amount after 9 years and the rate of interest is 9.5% and the interest is compounded quarterly. We will use the formula for compound interest get the principal value.
A=P[tex](1+\frac{r}{n}) ^{nt}[/tex]
where A= amount, P= principal, t=time period, n= number of times interest applied per time period, r=rate of interest
A=$6000
r=9.5%
t=9 yrs
n=4
6000=P[tex](1+\frac{9.5}{400} )^{36}[/tex]
6000= P x 2.328
P=6000/2.328=2577.32
Therefore the present value that will grow to $6000 in 9 years is $2577.32
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use your theorem from 2-37 about the angles in a triangle to find in the diagram below. show all work.
Answers
We have that, for any triangle, the sum of all its angles equals 180. In this case, we have the following:
[tex]96+2x+(x+12)=180[/tex]Now we solve for x to get the following:
[tex]\begin{gathered} 96+2x+x+12=180 \\ \Rightarrow2x+x=180-96-12 \\ \Rightarrow3x=72 \\ \Rightarrow x=\frac{72}{3}=24 \\ x=24 \end{gathered}[/tex]We have that x = 24, now to find the angles, we substitute this value on each expression:
[tex]\begin{gathered} 2x \\ x=24 \\ \Rightarrow2(24)=48 \\ x+12 \\ \Rightarrow24+12=36 \end{gathered}[/tex]therefore, the remaining angles are 48° and 36°
13. Puppies have 28 teeth and most adult dogs have 42 teeth. Find the primefactorization of each number. Write the result using exponents. (Example 5)
Answers
To solve our question, first we need to know that a prime factorization is a way to represent a number by a sequence of prime numbers that multiplied together gives us the original number.
So let's calculate our first prime factorization:
As we can see, we divide our number by the smallest prime number and then the factor we follow the same rule until we get "1" (for all divisions we just have integers).
Now, for the second number we have:
And both prime factorizations are our final answers.
5)Which of the following is a critical number of the inequality x^2+5x-6<0 ?
Answers
Answer:
B. 1
Explanation:
Given the inequality:
[tex]x^2+5x-6<0[/tex]To find the critical number, first, change the inequality sign to the equality sign :
[tex]x^2+5x-6=0[/tex]Next, solve for x:
[tex]\begin{gathered} x^2+6x-x-6=0 \\ x(x+6)-1(x+6)=0 \\ (x-1)(x+6)=0 \\ x-1=0\text{ or }x+6=0 \\ x=1\text{ or }x=-6 \end{gathered}[/tex]Therefore, from the options, 1 is the critical number.
The correct option is B.
30 randomly selected students took the statistics final. If the sample mean was 84, and the standard deviation was 12.2, construct a 99% confidence interval for the mean score of all students
Answers
The confidence interval for the mean score of the 30 randomly selected students is: 99% CI {78.26, 89.73}
What is confidence interval?Confidence interval is the range of values for which which is expected to have the values at a certain percentage of the times.
How to construct a 99% confidence intervalGiven data form the question
99% confidence interval
30 randomly selected students
mean sample = 84
Standard deviation = 12.2
Definition of variables
confidence level, CI = 99%
mean sample, X = 84
standard deviation, SD = 12.2
Z score, z = 2.576
from z table z score of 99%confidence interval = 2.576sample size, n = 30
The formula for the confidence interval is given by
[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex] OR [tex]CI=X-Z\frac{SD}{\sqrt{n} }[/tex]
[tex]=84+2.576\frac{12.2}{\sqrt{30} }[/tex]
=[tex]=84+2.576*2.2274[/tex]
= 84 + 5.7378 OR 84 - 5.7378
= 89.7378 OR 78.2622
= 89.73 to 78.26
The confidence interval for the mean score of all students is 78.26 to 89.78
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*You will use the following scenario forquestions 1-4*On the Wechsler Adult IntelligenceScale a mean IQ is 100 with a standarddeviation of 15. You may assume thatIQ scores follow a normal distribution.What percent of people have an IQscore less than 90?*Write your answer as a percent andround to 2 decimal places*
Answers
The Solution:
Given:
[tex]\begin{gathered} x=90 \\ \mu=100 \\ \sigma=15 \end{gathered}[/tex]By formula,
[tex]Z=\frac{x-\mu}{\sigma}=\frac{90-100}{15}=\frac{-10}{15}=-0.6667[/tex]From the z-score tables:
[tex]P(Z\leq90)=0.25248[/tex]Convert to percent by multiplying with 100.
[tex]0.25248\times100=25.248\approx25.25\text{\%}[/tex]Thus, the number of people that have an IQ score less than 90 is 25.25%
Therefore, the correct answer si 25.25%
Solve fort 30 on t =(Type (Type an integer or a simplified fraction)
Answers
Multiply both sides by t:
[tex]\frac{12t}{10}=30[/tex]Multiply both sides by 10:
[tex]12t=300[/tex]Divide both sides by 12:
[tex]\begin{gathered} t=\frac{300}{12} \\ t=25 \end{gathered}[/tex]I need help with the problem!
Answers
a)The vertex of the function is (3, -1)
b)The line of symmetry is x= 3
c) The maximum is no maximum and minimum is (3, -1)
a) What is the vertex of the function of the parabola ?
[tex]f(x) = x^{2} -6x+8[/tex]
Transforming the function in the vertex form,
[tex]f(x) = a(x-h)^{2} +k[/tex]
[tex]f(x)=(x-3)^{2} -1[/tex]
The vertex of the function is given by,
(h, k) = (3, -1)
So ,the vertex of the function of the parabola is (3, -1)
b) What is the line of symmetry in the function?
In a parabola , the axis of symmetry is x = h.
Here, x = 3
So, the line of symmetry of the function of the parabola is x= 3
c) What is the maximum and minimum?
There is no maximum for the function because, the parabola opens upward. (Refer image for graph)The minimum for the function is the vertex (h, k) = (3, -1)What is a function of a parabola?
A parabola is the shape of a quadratic function's graph. Although the width or steepness of a parabola can vary as well as its direction of opening, they share the same fundamental U form. Regarding a line known as the axis of symmetry, all parabolas are symmetric. The vertex of a parabola is the location where the axis of symmetry of the curve crosses.To learn more about function of a parabola , refer:
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This is Calculus 1 Linear Optimization Problem! MUST SHOW ALL THE JUSTIFICATION!!!
Answers
Given:
Required:
We need to find the value of AB
Explanation:
Here ABC is the right anglr triangle
so
[tex]\begin{gathered} AB^2=BC^2+AC^2=36+36=72 \\ AB=6\sqrt{2} \end{gathered}[/tex]Final answer:
The minimum length of crease is
[tex]6\sqrt{2}[/tex]