Answers
The equation of the parabola in the vertex form with vertex (6,-6) and passing through (8,6) is y = 3(x - 6)² - 6 , the correct option is (b) .
In the question ,
it is given that ,
the parabola passes through the point (8,6) .
the vertex of the parabola = (6,-6) .
We know that the equation of parabola in the vertex form with vertex (h,k) is
(y - k) = C.(x - h)²
we substitute the vertex and the point passing ,
we get ,
6 - (-6) = C.(8 - 6)²
6 + 6 = C(2)²
12 = 4C
C = 12/4
C = 3
So , the equation is (y - (-6)) = 3.(x - 6)²
y + 6 = 3(x - 6)²
y = 3(x - 6)² - 6
Therefore , The equation of the parabola in the vertex form with vertex (6,-6) and passing through (8,6) is y = 3(x - 6)² - 6 , the correct option is (b) .
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Related Questions
Use the compound interest formula to determine the final value of the following amount. $1900 at 10.4% compounded monthly for 4.5 years . What is the final value of the amount?
Answers
Answer:
$3027.80
Explanation:
The compound interest formula is the following.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A = final amount
P = principle amount
r = interest rate / 100
n = number of compounds per interval
t = time interval
Now in our case,
A = unknown
P = $1900
r = 10.4/100
n = 12 months / year ( because the interest is compounded monthly)
t = 4.5 yrs
Therefore, the compound interest formula gives
[tex]A=1900(1+\frac{10.4/100}{12})^{12*4.5}[/tex]Using a calculator, we evaluate the above to get
[tex]\boxed{A=\$3027.80}[/tex]which is our answer!
Hi can you help me with this problem?Formulate a system of equations for the situation below and solve.The total number of passengers riding a certain city bus during the morning shift is 1300. If the child's fare is $0.50, the adult fare is $1.50, and the total revenue from the fares in the morning shift is $1550, how many children and how many adults rode the bus during the morning shift?children=adults=
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Let "A" represent the number of adults that ride the bus and "C" represents the number of children that ride the bus.
On a certain morning shift 1300 people rode the bus, this means that the number of adults and the number of children add up to 1300. You can express the total number of passengers on that shift as follows:
[tex]A+C=1300[/tex]The child's fare is $0.50, so if C children ride the bus a total of 0.50C will be paid.
The adult's fee is $1.50, so if A adult rides the bus, the total earned will be 1.50A.
If you add both fares, you will determine the total fares for the shift, which was $1550
[tex]1.50A+\text{0}.50C=1550[/tex]Using both equations you have determined the number of adults and children that rode the bus:
-First, write the first expression for one of the variables, for example, write it for A:
[tex]\begin{gathered} A+C=1300 \\ A=1300-C \end{gathered}[/tex]-Second, replace the expression obtained in the second equation
[tex]\begin{gathered} 1.50A+0.50C=1550 \\ 1.50(1300-C)+0.50C=1550 \end{gathered}[/tex]Now you have to solve for C
→ Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} 1.50\cdot1300-1.50\cdot C+0.50C=1550 \\ 1950-1.50C+0.50C=1550 \end{gathered}[/tex]→Simplify the like terms
[tex]\begin{gathered} 1950+(-1.50C+0.50C)=1550 \\ 1950+-C=1550 \\ 1950-C=1550 \end{gathered}[/tex]→Subtract 1950
[tex]\begin{gathered} 1950-1950-C=1550-1950 \\ -C=-400 \end{gathered}[/tex]→ Multiply both sides by -1 to invert the sign:
[tex]\begin{gathered} (-1)(-C)=(-1)(-400) \\ C=400 \end{gathered}[/tex]Finally, once you have determined the value of C, you can calculate the value of A as follows:
[tex]\begin{gathered} A=1300-C \\ A=1300-400 \\ A=900 \end{gathered}[/tex]So, 400 children and 900 adults rode the bus.
Is the system of equations consistent and independent, consistent and dependent, or inconsistent? Y=-3x+1 y=-6x+2
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Reason:
The equations are y = -3x+1 and y = -6x+2
The slopes of each equation are -3 and -6. Compare the equations to the form y = mx+b to determine the slope m.
Since the slopes are different, it means the lines aren't parallel and intersect at exactly one location. This immediately tells the reader the system is consistent and independent.
-----------------------------
Extra info:
parallel lines have equal slopes, but different y intercepts.consistent = system has at least one solution. When written with "independent" it leads to "exactly one solution".independent = neither equation is a scaled version of one another, i.e. they produce different lines. In contrast a dependent system is where two lines perfectly overlap to produce infinitely many solutions all along that line.inconsistent = the lines are parallel and never intersect; leading to no solutions.how many terms the expression x^3+4x^2+2x^-9
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How many terms the expression
x^3+4x^2+2x^-9? 3 TERMS
If angle AOB and angle BOC are complementary angles, and m angle AOB = x°, what is the measure of the supplement of angle BOC?
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Complementary angles are angles whose sum is 90 degrees.
If angle AOB and angle BOC are complementary and angle AOB is x degrees, it means that angle BOC is (90 - x) degrees
Supplementary angles are angles whose sum is 180 degrees. If angle BOC is (90 - x) degrees, then the measure of its supplement would be
180 - (90 - x)
= 180 - 90 + x
= 90 + x
the measure of the supplement of angle BOC is (90 + x) degrees
I don’t know if my answer is correct I got 28
Answers
1) Consider that in 2 days she took 7 bottles each one with 16oz of water:
So we can write out the following:
[tex]undefined[/tex]1.BhEvaluate the formula V =3O 9.6 in.³O 288 in. 3332 in.O 96 in.3for B = 9 in.² and h = 32 in.
Answers
Given -
B = 9 in²
h = 32 in
To Find -
Evaluate the formula (V) =?
Step-by-Step Explanation -
As we are given
[tex]V\text{ = }\frac{Bh}{3}[/tex]Simply putting the values in the above formula:
[tex]V\text{ = }\frac{9\times32}{3}\text{ = 3}\times32\text{ = 96 in}^3[/tex]Final Answer -
Option D. 96 in³
Pat is 20 years older than his son Patrick. In 2 years, the sum of their ages will be 90. How old are they now?Patrick is years old, and Pat is ?years old.
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Let "x" be the age of Patrick.
Pat is 20 years older than his son Patrick so we can represent this as "x+20".
In two years, the age of patrick will be x+2 and the age of Pat will be x+22.
Since in 2 years, the sum of their ages will be 90, we can write:
[tex]\begin{gathered} x+2+x+22=90 \\ 2x+24=90 \\ 2x=66 \\ x=33 \end{gathered}[/tex]And, the age of Pat is x+20 which is 53.
Therefore, Patrick is 33 years old, and Pat is 53 years old.
The systolic blood pressure of women is normally distributed with a mean of 150 mmHg. and a standard deviation of 10 mmHg. What percentage of a 50-year-old women have a systolic blood pressure between 130 mmHg. and 170 mmHg.?
Answers
The required percentage of a 50-year-old woman have a systolic blood pressure between 130 mmHg. and 170 mmHg is 95.44%.
Given that,
The systolic blood pressure of women is normally distributed with a mean of 150 mmHg. and a standard deviation of 10 mmHg.
What is probability?
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
z = [ x - μ]/σ
Accoding to the question,
= p[z < (170-150)/10] - p[z < 130-150/10]
= p [z <2] - p [z < -2]
= 0.9772 - 0.0228
= 95.44%
Thus, the required percentage of a 50-year-old woman have a systolic blood pressure between 130 mmHg. and 170 mmHg is 95.44%.
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The graph shows the profit, y, of a community fundraiser, with respect to the number of tickets sold, x.Use the graph to complete each statement.Drag and drop the answers into the boxes. The y-intercept is Response area.The y-intercept represents Response area.
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Answer:
The y-intercept is -700
The y-intercept represents the initial amount of expenses.
Explanation:
The y-intercept of the graph is the point where the graph crosses the vertical axis. In this case, it is also the value of the profit when the number of tickets sold is 0.
Therefore, the answers are:
The y-intercept is -700
The y-intercept represents the initial amount of expenses.
write the following division expression using a division symbol and as a fraction 7 divided by x
Answers
We are asked to write the following division expression using a division symbol and as a fraction.
7 divided by x
Using a division symbol:
Here you need to write the dividend (7) then the division sign and finally the divisor (x)
[tex]\begin{gathered} dividend\: \div\: divisor \\ 7\: \div\: x \end{gathered}[/tex]As a fraction:
Here you need to write the dividend (7) in the numerator (top) and the divisor (x) in the denominator (bottom)
[tex]\begin{gathered} \frac{dividend}{divisor} \\ \frac{7}{x} \end{gathered}[/tex]Therefore, the division expression using a division symbol is
[tex]7\: \div\: x[/tex]Therefore, the division expression as a fraction is
[tex]\frac{7}{x}[/tex]Suppose you invest $2200 at an annual interest rate of 5.3% compounded continuously. How much will you have after 7 years?
Answers
Answer:
$3188.20
Explanation:
From the information given:
• Principal, P = $2200
,• Interest Rate, r=5.3% = 0.053
,• Time, t=7 years
For a principal compounded continuously, we use the formula to determine the amount in the account:
[tex]A(t)=Pe^{rt}[/tex]Substituting the given values, we have:
[tex]\begin{gathered} A(t)=2200\times e^{0.053\times7} \\ =\$3188.20 \end{gathered}[/tex]You will have $3188.20 after 7 years.
Can you help me with this problem 5^3 x 5^1 then it says select one Add, Subtract, Multiply
Answers
Fractions and exponents
5^3 x 5^1
FIRST ADD 3+1 = 4
THEN MULTIPLY 4 times 5^4= 5x5x5x5= 625
write an explicit formula for an nth term of the sequence 7, 35, 175,....
Answers
hello
to write an explicit formula, we have to determine what type of sequence is it
7, 35, 17
this is clearly a geometric progression with values of
first term = 7
common ratio = 5
the explicit formula of a geometric progression is given as
[tex]\begin{gathered} a_n=a\cdot r^{(n-1)}^{} \\ n=\text{nth term} \\ a=\text{first term} \\ r=\text{common ratio} \end{gathered}[/tex]now let's substitute the variables into the equation
[tex]\begin{gathered} a_n=a\cdot r^{(n-1)} \\ a_n=7\cdot5^{(n-1)} \\ a_n=35^{(n-1)} \end{gathered}[/tex]the equation above is the explicit formula for the sequence
x/4 (this part is division)
x/4 + 3 = 3
What does x equal?
Answers
To isolate the x, you need to first subtract 3 on both sides.
x/4 + 3 - 3 = 3 - 3
=
x/4 = 0
Then you need to multiply (4) on both sides to because it is the bottom of the fraction x/4.
x/4 (4) = 0 (4)
x = 0
Answer:x=0
Step-by-step explanation:
Find the area of the shaded region. Use 3.14 for π as necessary.The circle centered on point A, and has a radius of 5 cm, is shaded. BC is a diameter of the circle. Point D is on the cicle, such that line AD is perpendicular to line BC. Triangle BCD is not shaded.A. 132 cm²B. 53.5 cm²C. 26.8 cm²D. 17.1 cm²
Answers
Given
radius = 5 cm
To get the area of the shaded region, get the difference between the area of the circle, and the area of the triangle
We have the following
[tex]\begin{gathered} A_{\text{circle}}=\pi r^2 \\ A_{\text{circle}}=(3.14)(5\text{ cm})^2 \\ A_{\text{circle}}=(3.14)(25\text{ cm}^2) \\ A_{\text{circle}}=78.5\text{ cm}^2 \\ \\ A_{\text{triangle}}=\frac{1}{2}bh \\ A_{\text{triangle}}=\frac{1}{2}(10\text{ cm})(5\text{ cm})\text{ *the base is twice the radius} \\ A_{\text{triangle}}=25\text{ cm}^2 \\ \\ A_{\text{shaded area}}=A_{\text{circle}}-A_{\text{triangle}} \\ A_{\text{shaded area}}=78.5\text{ cm}^2-25\text{ cm}^2 \\ A_{\text{shaded area}}=53.5\text{ cm}^2 \end{gathered}[/tex]Therefore, the area of the shaded region is 53.5 cm².
Find the difference: (−1−5i)−(5−7i)
Answers
To determine the difference between complex number:
[tex](-1-5i)-(5-7i_{})[/tex]Step 1: Remove the bracket and find the difference
[tex]\begin{gathered} (-1-5i)-(5-7i_{}) \\ -1-5i-(5-7i_{}) \\ -1-5i-5+7i_{} \end{gathered}[/tex]Step2: Collect like terms
[tex]\begin{gathered} (-1-5i)-(5+7i_{}) \\ (-1-5i)-(5+7i_{} \\ -1-5-5i+7i \\ -6+2i \\ 2i-6 \end{gathered}[/tex]Hence the final answer is 2i - 6
Which of the following is the median of the data set? 15 20 20 25 30 35 40 40 45 50 55(1) 28(2) 30(3) 32(4) 34
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Median: The media is the middle number in a list of values. If there is an even number of values (so there is no middle number) then average the middle two values together.
so:
[tex]set\colon\mleft\lbrace15,20,20,25,30,35,40,40,45,50,55\mright\rbrace[/tex]From the data set, we can conclude that the middle number (median) is:
[tex]35[/tex]5] Great America has a season pass that costs $45 plus $7 each time you attend thepark, or you can pay $12 each time you go. How many times do you have to go beforeyou pay the exact same amount?
Answers
Let the number of time he attend the park be represented with n.
So that,
C = 45 + 7n ....eqn(1)
C = 12n ..........eqn(2)
Equating both equations, we have,
[tex]\begin{gathered} 12n=45+7n \\ \text{Collecting like terms, we get} \\ 12n-7n=45 \\ 5n=45 \\ \text{Dividing both sides by 5, we get} \\ n=\frac{45}{5}=9 \end{gathered}[/tex]He has to attend the park 9 times before he can pay exactly the same amount.
So, the correct answer is 9.
Write an equation in point-slope form for the line through the given point with the given slope (9,-1); m =4/3 A . Y-1=4/3(x-9)B. Y-9=4/3(x+1) C. Y+1=4/3(x-9)D. Y-1=4/3(x+9
Answers
Step 1: List the given data
[tex]\begin{gathered} m\text{ = }\frac{4}{3} \\ \text{Coordinates (x}_{1\text{ , }}y_1)\text{ = ( 9, -1 )} \end{gathered}[/tex]Step 2: Write the equation of a line formula in a point-slope form
[tex]y-y_1=m(x-x_1\text{ )}[/tex]Step 3: Substitute all values in the point-slope form equation.
[tex]\begin{gathered} y\text{ - (-1) = }\frac{4}{3}(x\text{ - 9)} \\ y\text{ + 1 = }\frac{4}{3}(x\text{ - 9)} \end{gathered}[/tex]Step 4: Final answer
[tex]y\text{ + 1 = }\frac{4}{3}(\text{ x - 9) Option C}[/tex]- Your shipping staff of 15 employees must pack an order of 240 case today. In order for each person to do an equal share of the work How many cases does each staff member need to pack to the order?
Answers
Divide the 240 cases into the 15 employees:
Then, each staff member need to pack 16 cases.please find the slopes and lengths then fill in the words that best describes the type of quadrilateral.
Answers
We can find the slopes using the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]And the lengths using the following formulas:
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Therefore:
[tex]m_{QR}=\frac{5-2}{-1-(-9)}=\frac{3}{8}[/tex][tex]m_{RS}=\frac{9-5}{1-(-1)}=\frac{4}{2}=2[/tex][tex]m_{ST}=\frac{6-3}{-7-1}=\frac{3}{8}[/tex][tex]m_{TQ}=\frac{6-2}{-7-(-9)}=\frac{4}{2}=2[/tex][tex]\begin{gathered} L_{QR}=\sqrt[]{(-1-(-9))^2+(5-2)^2} \\ L_{QR}=\sqrt[]{73} \end{gathered}[/tex][tex]\begin{gathered} L_{RS}=\sqrt[]{(1-(-1))^2+(9-5)^2} \\ L_{RS}=2\sqrt[]{5} \end{gathered}[/tex][tex]\begin{gathered} L_{ST}=\sqrt[]{(6-9)^2+(-7-1)^2} \\ L_{ST}=\sqrt[]{73} \end{gathered}[/tex][tex]\begin{gathered} L_{TQ}=\sqrt[]{(6-2)^2+(-7-(-9))^2}_{} \\ L_{TQ}=2\sqrt[]{5} \end{gathered}[/tex]Since:
[tex]\begin{gathered} m_{RS}=m_{TQ}\to m_{RS}\parallel m_{TQ} \\ m_{QR}=m_{ST}\to m_{QR}\parallel m_{ST} \end{gathered}[/tex]And:
[tex]\begin{gathered} L_{QR}=L_{ST} \\ L_{RS}=L_{QT} \end{gathered}[/tex]According to this, we can conclude it is a parallelogram
simplify the expression 6w + 2/3 + 3w
Answers
we have
6w + 2/3 + 3w
step 1
Combine like terms
(6w+3w)+2/3
9w+2/3Match each measurement on the left with an equal measurement on the right. Some answer options on the right will not be used.31/2 yards66 inches2 miles21/2 miles51/2 feet10,560 feet101/2 feet91/2 feet12,300 feet13,200 feet
Answers
Solution
Recall
1 yard is 3feet
1 foot is 12inches
1 mile is 5,280 feet
[tex]3\frac{1}{2}\text{yards =10}\frac{1}{2}\text{ ft}[/tex][tex]66\text{inches =5}\frac{1}{2}ft[/tex][tex]\begin{gathered} 1\text{ miles = 5280 ft} \\ 2\text{miles = 10,560ft} \end{gathered}[/tex][tex]\begin{gathered} 1\text{mile = 5280 ft} \\ 2\frac{1}{2}\text{miles =}13,200ft \end{gathered}[/tex]Jen L cut out the following figures on the solid lines and folded them on the third lines which figure formed a rectangle prism
Answers
A rectangular prism is a figure that has the following shape:
When the figure is unfolded the shape it has is the following:
Therefore, the right answer is the bottom right shape.
6 Ms. Carson drove 96 miles in 15 hoursWhat was her speed in miles per hour!48 miles per hourB.54 miles per hourС64 miles per hourD. 144 miles per hour
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10 + 8x + 2 = 4x + 36
Answers
we have
10 + 8x + 2 = 4x + 36
solve for x
step 1
Combine like terms left side
12+8x=4x+36
step 2
subtract 12 both sides
8x=4x+36-12
8x=4x+24
step 3
subtract 4x both sides
4x=24
step 4
Divide by 4 both sides
x=6
the answer is x=6identify two different types of optional deductions that an employer may subtract from a paycheck
Answers
Two possible deductibles can be the social care or the medical care
6) Raul received a score of 74 on a history test for which the class mean was 70 with a standard deviation of 3. He received a score of 70 on a biology test for which the class mean was 70 with standard deviation 7. On which test did he do better relative to the rest of the class?a)biology testb)history test c)the same
Answers
Solution:
The z score value is expressed as
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ where \\ x\text{ is the sample score} \\ \mu\text{ is the mean score} \\ \sigma\text{ is the standard deviation of the score} \end{gathered}[/tex]Given that
[tex]\begin{gathered} History: \\ x=74 \\ \mu=70 \\ \sigma=3 \\ Biology: \\ x=70 \\ \mu=70 \\ \sigma=7 \end{gathered}[/tex]To determine which test Raul did better,
step 1: Determine the z score value for the history test.
Thus,
[tex]\begin{gathered} z_{history}=\frac{74-70}{3}=1.333333333 \\ \end{gathered}[/tex]step 2: Determine the z score value for the biology test.
[tex]z_{biology}=\frac{70-70}{7}=0[/tex]step 3: Determine the probability that he did better in the history test.
Thus, from the normal distribution table,
[tex]Pr(history)=0.9088[/tex]step 4: Determine the probability that he did better in the biology test.
From the normal distribution table,
[tex]Pr(biology)=0.5[/tex]Since the probability that he did better in history is higher than the probability he did better in the biology test, this implies that he did better in the history test, relative to the rest of the class.
The correct option is B.
If a person travels at a speed of 33 m/s and travels 132 meters, how long does the trip take?
Answers
Answer: 4 seconds.
Step-by-step explanation: Simply divide 132 meters by 33 m/s. This gives you four. (as in the trip took four seconds.)
It is a uniform rectilinear movement which is one in which an object moves in a straight line, in one only direction, with a constant speed.
When we spoke of constant speed we mean that the movement retains the same speed, that is; that the object does not move faster, or slower and always at the same speed.
If a person travels at a speed of 33 m/s and travels 132 meters, how long does the trip take?We obtain the data according to the exercise.
Data:
V = 33 m/s
D = 132 m
t = ?
We have that the uniform motion formula is:
[tex]\large\displaystyle\text{$\begin{gathered}\sf V=\dfrac{d}{t}, \to where \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf V=Speed \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf D=distance \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf T=Time \end{gathered}$}[/tex]We solve for time, since that is what we are asked to calculate. And substitute data in the formula.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{t=\dfrac{d}{V} } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{t=\frac{132 \not{m}}{33 \ \frac{\not{m}}{s} } } \end{gathered}$}}[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{t=4 \ s} \end{gathered}$}}}[/tex]
I brought on the trip, a time of 4 seconds.