Answers
Vertex = (4, 5)
focuse = (7, 5)
The vertex and focus lie on the same horizontal line; y = 5
So we will be applying the equation of horizontal parabola
[tex]\begin{gathered} \text{Equation of the parabola (horizontal):} \\ (y-k)^2=\text{ 4a(}x\text{ - h)} \end{gathered}[/tex]The focus lies on the right of the vertex, parabola opens upward as a result, a = positive
[tex]\begin{gathered} As\text{ the y coordinates are the same, }a\text{ = 7 - 4 } \\ a\text{ = 3} \\ \\ \text{Vertex: h = 4, k = 5} \end{gathered}[/tex]substituting the values:
[tex]\begin{gathered} (y-5)^2\text{ = 4(3)(x - 4)} \\ (y-5)^2\text{ = 12(x - 4)} \end{gathered}[/tex]Related Questions
mr peel started 7 meters away from the motion detector and 2 seconds later he was 3 meters away from the motion detector. find the average rate of changed or slope in meters per second
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He started at 7 meters away, so if after 2 seconds now he is 3 meters away, then he move:
[tex]7-3=4[/tex]So he move 4 meters in 2 seconds so to find the rate we divide the meters into the tiem so:
[tex]r=\frac{4}{2}=2[/tex]I need help pls pls pls
Answers
The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set2.7.15, 3, 12, 9, 15, 8, 3, 10 The range is 13(Simplify your answer.)The population mean is 8.4(Simplify your answer. Round to the nearest tenth as needed.)The population variance is(Simplify your answer. Round to the nearest tenth as needed.)The population standard deviation is (Simplify your answer. Round to the nearest tenth as needed)
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We have the following data set:
2,7,15,3,12,9,15,8,3,10
The range is the difference between the highest and lowest values in the set, to find the range, order the data set from least to greatest.
2,3,3,7,8,9,10,12,15,15
Then,
[tex]\begin{gathered} \text{Range}=15-2 \\ \text{Range}=13 \end{gathered}[/tex]Mean is represented by the following expression:
[tex]\text{Mean}=\frac{\text{Sum of all data points}}{Number\text{ of data po}ints}[/tex][tex]\text{Mean}=\frac{84}{10}=8.4[/tex]Population variance formula looks like this:
[tex]\begin{gathered} \sigma^2=\frac{\sum^{}_{}(x-\mu)^2}{N} \\ \text{where,} \\ \sigma^2=\text{population variance} \\ \sum ^{}_{}=addition\text{ of} \\ x=\text{each value} \\ \mu=population\text{ mean} \\ N=\text{ number of values in the population} \end{gathered}[/tex]Then, substituting:
[tex]\begin{gathered} \sigma^2=\frac{(2-14)^2+(3-14)^2+\cdots+(15-14)^2}{10} \\ \sigma^2=20.44 \end{gathered}[/tex]For the standard deviation:
[tex]\begin{gathered} s=\sqrt[]{\frac{\sum ^{}_{}(x-\mu)^2}{N}} \\ s=4.521 \end{gathered}[/tex]Find the x-intercepts and the vertex of the parabola y = (x − 4)(x + 2)Write as ordered pairsWrite the equation y =(x − 4)(x +2)in standard formuse the quadratic formula to identify the x-value of the vertex.Part IV: Substitute the x-value of the vertex from Part III into the original equation to find the y-value of the vertex. Then, write the coordinates of the vertex.
Answers
Solution
Step-by-step explanation:
we have:
Part 1) Find the x-intercepts of the parabola and write them as ordered pairs
The x-intercepts are the values of x when the value of y is equal to zero
so
For y=0
[tex](x-4)(x+2)[/tex]For x=4 and x=-2 the equation is equal to zero
therefore
The x-intercepts are the points (-2,0) and (4,0)
Part 2) Write the equation y=(x-4)(x+2) in standard form
The quadratic equation in standard form is equal to
[tex]y=ax^2+bx+c[/tex]applying distributive property
[tex]\begin{gathered} y=(x-4)(x+2) \\ y=x^2+2x-4x-8 \\ y=x^2-2x-8 \end{gathered}[/tex]where a = 1, b = -2, c = -8
Part 3) With the standard form of the equation from part ll, use the quadratic formula to identify the x-value of the vertex
we know that
the x-value of the vertex is -b/2a
we have
where a = 1, b = -2, c = -8
substitute
x = -b/2a = -2/2(1) = 1
therefore
The x-coordinate of the vertex is 1
Part 4) Substitute the x-value of the vertex from part lll into the original equation to find the y-value of the vertex.
we have
[tex]y=(x-4)(x+2)[/tex]For x=1
substitute and solve for y
[tex]\begin{gathered} y=(1-4)(1+2) \\ y=-3(3) \\ y=-9 \end{gathered}[/tex]therefore
The y-coordinate of the vertex is -9
The coordinate of the vertex is the point (1,-9)
What is the volume of this cone? Use I 3.14 and round your answer to the nearest hundredth. LI cubic inches
Answers
The volume of a cone is given by
[tex]V\text{ = }\frac{1}{3}\pi\text{ r}^2\text{ h }[/tex]Diameter = 34 in
radius = 34/2 = 17 in
Height = 17in
[tex]\begin{gathered} V\text{ = }\frac{1}{3}\text{ x 3.14 x 17 x 17 x17} \\ V\text{ =5142.27 inches} \end{gathered}[/tex]what is another way to write to 72-(-25)?A.72+ 25B.-72-25C.72-25D.-72-(-25)what is the value of -27-8?A.-35B.-19C.19D.35How much is 37 +13A.-50B.-29C.29D.51What is the solution to 40+(-11)?A.-51B.-29C.29D.50What is the value of -31 +30?A.-61B.-1C.1D.61Am sorry to bother you is there any way you can help me I didn't know if I was supposed to send this for people helps
Answers
So, basically, we need to simply the expression given to us.
The given expression is:
72 - (-25)
From the laws guiding signs, we know that:
- * - = +
Therefore, the expression becomes:
72 + 25
That is another way of writing the expression
help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
In the linear graph, the value of x such that f(x) = -3 is -2.
How to find coordinates in a linear graph?A linear graph is a straight line or straight graph which is drawn on a plane connecting the points on x and y coordinates.
Therefore, a linear graph is represented in the form of a straight line.
It shows the relationship between variables x and y.
x is the horizontal variables while y is the vertical variables.
Therefore, the graph of the given function is f(x).
Let's use the graph to find x such that f(x) = - 3
f(x) is the y coordinates of the linear graph.
Let's find x when f(x) = -3
Therefore,
x = - 2
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Emma younger brother and sister went on a carnival ride that has two separate circular track ana's brother rode in a blue car that traveled a total distance of 220 around the track and a sister Road in a green car that travels to total distance of 126 feet around the track and drew of the ride
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1. The distances of 220 feet and 126 feet are the circumferences of the two circles. We can see the circumference as a kind of 'perimeter' for a circle.
2. The radius of the circle of Ana's brother in the blue car is as follows:
a. We have that the circumference of a circle is given by the formula:
[tex]C=2\cdot\pi\cdot r[/tex]Then, we need to solve this equation for r. We have that pi = 3.14, and C = 220 feet. Then, we have:
[tex]220=2\cdot\pi\cdot r\Rightarrow r=\frac{220}{2\pi}\Rightarrow r=\frac{220}{2\cdot3.14}\Rightarrow r=35.0318[/tex]Rounding to the nearest tenth, we have that the radius is RB = 35.0 feet (or 35 feet).
3. We can apply the same procedure to find the radius of the circle made by Ana's sister in the green car (she traveled 126 feet).
[tex]126=2\cdot\pi\cdot r\Rightarrow r=\frac{126}{2\cdot3.14}\Rightarrow r=20.0637[/tex]Rounding to the nearest tenth, we have that the radius is RG = 20.1 feet.
4. The difference in the radii of the circles is the difference between the two ones already obtained. Then, we have:
[tex]d=rB-rG=35.0-20.1\Rightarrow d=14.9[/tex]Therefore, the difference is 14.9 feet.
(2x² + 7x - 15) + (x + 5)
Answers
We are given the below expression
[tex]\begin{gathered} (4x^2\text{ + x + 1) + (x - 2)} \\ \text{First, open the parentheses} \\ 4x^2\text{ + x + 1 + x - 2} \\ \text{Collect the like terms} \\ 4x^2\text{ + x + x + 1 - 2} \\ 4x^2\text{ + 2x - 1} \end{gathered}[/tex]From the quadratic function generated, we will be solving for x using the general formula
[tex]\begin{gathered} ax^2\text{ + bx + c = 0} \\ 4x^2\text{ + 2x - 1= 0} \\ \text{let a = 4, b= 2 and c = -1} \\ \text{The general quadratic formula is written as} \\ x\text{ = -b }\pm\text{ }\frac{\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ \text{Substitute the above values into the formula} \\ x\text{ = -(2) }\pm\text{ }\frac{\sqrt[]{2^2\text{ - 4 x 4(-1)}}}{2\text{ x 4}} \\ x\text{ = -2 }\pm\text{ }\frac{\sqrt[]{4\text{ -4(-4)}}}{2\text{ x 4}} \\ x\text{ = -2 }\pm\text{ }\frac{\sqrt[]{4\text{ + 16}}}{8} \\ x\text{ = -2 }\pm\text{ }\frac{\sqrt[]{20}}{8} \\ \sqrt[]{20}\text{ = }\sqrt[]{4}\text{ x }\sqrt[]{5} \\ \sqrt[]{20\text{ }}\text{ = 2}\sqrt[]{5} \\ \text{Hence,} \\ x\text{ = -2 + }\frac{2\sqrt[]{5}}{8}\text{ OR -2 - }\frac{2\sqrt[]{5}}{8} \\ x\text{ = 0.3090 or x = -0.8075} \end{gathered}[/tex]A farmer purchased 225 acres of land for $4,700/acre. He paid 25% down and obtained a loan for the balance at 6.75% APR over a 20-year period. How much is the annual payment? (Simplify your answer completely. Round your answer to the nearest cent.)
Answers
The annual payment is $73416.96
[tex]- Total \ cost \ of \ the \ land $=\$ 225 \times 4700$$$=\$ 1057500$$Down payment $=0.25 \times 1057500$$$=\$ 264375$$so, loan amount $=\$ 1057500-264375$$$=\$ 793125$$[/tex]
[tex]Present \ value,\ $P V=P M T\left[\frac{1-\left(1+\frac{r}{n}\right)^{-n t}}{\left(\frac{r}{n}\right)}\right]$$$P r=793125, r=0.0675 \text {, }$$$t=20$ years, $n=1$$$\therefore \quad P M T=\frac{P v}{\left[\frac{1-\left(1+\frac{r}{n}\right)^{-n t}}{\left(\frac{r}{n}\right)}\right]}$$$$=\frac{793125}{\left[\frac{1-\left(1+\frac{0.0675}{1}\right)^{-20}}{\left(\frac{0.0675}{1}\right)}\right]}$$$=73416.96$\\So, Annual payment $=\$ 73416.96$[/tex]
What is down payment ?A down payment is the first down payment when buying an expensive good/service, such as a car or house. It is usually paid in cash or equivalent at the time of the transaction. Then some kind of loan is needed to finance the rest of the payment. The biggest advantage of a down payment is that it reduces the amount of the loan you need. If you borrow less, you pay less interest.
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What is the radius of a circle whose circumference is 207.24 inches ?
Answers
The circumference of the circle C = 207.24 inches.
The formula for the circumference of circle is,
[tex]C=2\pi r[/tex]Assume the value of pi be 3.14.
Substitute 207.24 for C in the formula to determine the radius of circle.
[tex]\begin{gathered} 207.24=2\pi r \\ r\approx\frac{207.24}{2\cdot3.14} \\ =33 \end{gathered}[/tex]Thus radius of circle is 33 inches.
Additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate. What is the final price after the rebate if an envelope costs $0.35 and a 'forever' postage stamp costs $0.41?
Group of answer choices
$99.99
$10.76
$109.23
$100.75
Answers
If additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41,then the cost after all the rebates will be $100.75.
Given that additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41.
We are required to find the cost after all the rebates and envelopes provided.
The cost can be calculated as under:
Cost=109.99-10.00+0.35+0.41
=$100.75
Hence if additional memory for your computer sells for $109.99 with a $10.00 mail-in rebate, an envelope costs $0.35 and a 'forever' postage stamp costs $0.41,then the cost after all the rebates will be $100.75.
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For homework Rio is listing some examples of real numbers in a diagram natural 6 whole -1 integer 0 rational .5 Which number did Rio Place incorrectly?
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Whole numbers are similar to natural(non-negative, non-fractional). The only difference is that it includes the 0.
In this question, Rio placed -1 as an example of whole number. Since -1 is negative, it is not a whole number, so this the number which Rio placed incorrectly.
For a recent year, the mean fare to fly from Charlotte, North Carolina, to Chicago, Illinois, on a discount ticket was $267. A random sample of 13 round-trip discount fares on this route last month shows:
$321 $286 $290 $330 $310 $250 $270 $280 $299 $265 $291 $275 $281
1. What is the decision rule? (Round your answer to 3 decimal places.)
2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)
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1. The decision rule is:
t < 2.681: do not reject the null hypothesis.t > 2.681: reject the null hypothesis.2. The test statistic is: t = 3.42.
What are the hypothesis tested and the decision rule?At the null hypothesis, it is tested if there is not enough evidence that the mean ticket price has increased from $267, that is:
[tex]H_0: \mu \leq 267[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the mean ticket price has increased from $267, that is:
[tex]H_1: > 267[/tex]
For the decision rule, we need to consider that:
It is a right-tailed test, as we are testing if the mean is greater than a value.The t-distribution is used, as we have the standard deviation for the sample but not for the population.Due to the sample size of 13, there are 12 degrees of freedom.The critical value for the test is given by:
t* = 2.681.
Hence the rule is:
t < 2.681: do not reject the null hypothesis.t > 2.681: reject the null hypothesis.What is the test statistic?The test statistic is given by the following equation:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which the parameters are defined as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.Using a calculator from the given sample, and considering the values tested at the hypothesis, the values of the parameters are:
[tex]\overline{x} = 288.3, \mu = 267, s = 22.46, n = 13[/tex]
Hence the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{288.3 - 267}{\frac{22.46}{\sqrt{13}}}[/tex]
t = 3.42.
What is the missing information?The problems asks if the sample gives enough evidence to conclude if the mean ticket price has increased with a significance level of 0.01.
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Suppose the function f(x)=30(2)^x gives a beetle population after x weeks.How many beetles will there be after 56 days
Answers
Answer:
7,680 beetles
Explanation:
The function that gives the beetle population after x weeks is given below:
[tex]f\mleft(x\mright)=30\mleft(2\mright)^x[/tex]To determine the beetle population after 56 days, first convert 56 days to weeks.
[tex]56\text{ days=}\frac{57}{7}=8\text{ we}eks[/tex]Thus, the beetle population will be:
[tex]\begin{gathered} f(8)=30(2)^8 \\ =30\times256 \\ =7,680 \end{gathered}[/tex]There will be 7,680 beetles after 56 days.
Amaka gets N2 500 as pocket money. She spends N1 500
and saves the rest. What is the ratio of her savings to the
amount she spends?
Answers
Answer:
A the answer is a
Step-by-step explanation:
it's corn a beautiful thing for me it has the juice
1. A line goes through the point (2,1) and has a slope of 2A. Plot the point and use the slope to graph the line and find the y-interceptB. Write the equation of the line in slope intercept form
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The general equation of line with passing points (a, b) and slope m is :
y = m(x - a) + b
In the given question :
A line goes through the point (2,1)
Passing point (a, b) = (2, 1)
a slope of 2
Slope : m = 2
Substitute these value in the general equation of line :
y = m( x - a ) + b
y = 2 ( x - 2) + 1
y = 2x - 4 + 1
y = 2x - 3
y = 2x - 3
A)
To plot on the graph :
We have one coordinate ( 2, 1)
Find one more coordinate
Substitute x = 1 in the equation os line :
y = 2x - 3
y = 2(1) - 3
y = ( - 1 )
So, (x, y) = ( 1, -1)
Plot the coordinates ( 2, 1) & ( 1, - 1)
y- intercept is the point on the line where x = o
Substitute x = 0 in the given equation of line :
y = 2x - 3
y = 2( 0 ) - 3
y = ( -3 )
Y -intercept : y = ( -3) , (x, y) = ( 0, -3)
In the graph y -intercept is :
The purple point in the graph represent the y -intercept.
B)
The general form of the equation of line in the form of slope intercept form :
y = mx + b
The equation of line y = 2x - 3
On compare with the general equation of slope intercept form we have : m - 2, b = (-3)
So, equation of line in the slope intercept form is : y = 2x - 3
y = 2x - 3
Answer : A) ( x, y) = (0, -3)
B) y = 2x - 3
write the percent as a fraction or a mixed number in simplest form 4.8%
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Jonathan is deciding between two different movie streaming sites to subscribe to.Plan A costs $6 per month plus $2 per movie watched. Plan B costs $16 per monthplus $1 per movie watched. Let A represent the monthly cost of Plan A if Jonathanwatches x per month, and let B represent the monthly cost of Plan B if Jonathanwatches movies per month. Graph each function and determine the number ofmonthly movies watched, 2, that would make the two plans have an equal monthlycost.
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Gigi, this is the solution to the problem:
This is the information provided to us:
Plan A : $ 6 per month + $ 2 per movie wathced
Plan B : $ 16 per month + $ 1 per movie watched
Step 1: Let's calculate the number of movies that would make the two plans to have an equal monthly payment, as follows:
Let x to represent the number of movies watched by Jonathan
Plan A = Plan B
6 + 2x = 16 + 1x
Like terms:
2x - x = 16 - 6
x = 10
If Jonathan watches 10 movies per month the two plans will have an equal monthly cost
Step 2: Let's graph the functions that represent each plan, this way:
Expand the logarithm fully using the properties of logs. Express the final answer interms of log a, and log y.
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To solve this problem, we will use these rules
[tex]\begin{gathered} \log ab=\log a+\log b\rightarrow(1) \\ \log a^n=n\log a\rightarrow(2) \end{gathered}[/tex]The given expression is
[tex]\log x^5y[/tex]By using rule (1)
[tex]\log x^5y=\log x^5+\log y[/tex]Use the rule (2) with log x^5
[tex]\log x^5=5\log x[/tex]Then the last answer is
[tex]\log x^5y=5\log x+\log y[/tex]The answer is 5 log x + log y
in this equation , what is the value of b^2-4ac 2x^2+6x+5=0Note that the general form of a quadratic equation is ax^2+bx+c=0
Answers
Answer:
-4
Explanation
Given the standard form of a quadratic equation expressed as ax^2 + bx + c = 0
Comparing to the given equation 2x^2+6x+5=0
ax^2 = 2x^2
a = 2
bx = 6x
b = 6
c = 5
Get b^2 - 4ac
Substitute the values of a, b and c into b^2 - 4ac
b^2 - 4ac
= 6^2 - 4(2)(5)
= 36 - 40
= -4
Hence the value of b^2 - 4ac is -4
Evaluate.
(a − 2b)^3 when a = −2 and b = −1/2
Answers
Answer:
the answer is 1
Step-by-step explanation:
(a-2b)^3
(-2-2*-1/2)^3
(-2+1)^3
(-1)^3
=1
Marie is saving money to buy a prom dress that costs 225$. She already has 85$ and makes 20$ per day. Babysitting after school . Write & solve an inequality to determine how many days marie need to babysit in order to have enough money for the dress.
Answers
Given,
Total money needed = 225
Money already Marie has = 85
Marie per day Income = 20
Let it take x days for Marie to have enough money to buy the prom dress.
We can say:
Total Money = Money Marie already has + per day income
Using the given information, we can craft an inequality shown below:
[tex]85+20x\geq225[/tex]This means "85 already have plus 20 per day will need to be atleast 225".
Now, we can do algebra and solve for x. Steps are shown below:
[tex]\begin{gathered} 85+20x\geq225 \\ 20x\geq225-85 \\ 20x\geq140 \\ x\geq\frac{140}{20} \\ x\geq7 \end{gathered}[/tex]Thus, Marie needs 7 days more to have enough money to buy the prom dress.
what is the total area, in square inches, of the shaded sections of the trapezoid below?
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Answer: 81.9 in^2
7) What is the slope of the line below
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as this is a vertical line, the slope is undefined
and Subtract Fractions - Real World
3
Directions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
5
Mark and Lisa each had a water bottle which contained 4 liters of water.
Mark drank 3 liter of water. How much water does Mark have after drinking 3 liter of water?
After Lisa accidentally spilled her water, she had 5 liter of water left. How much water did Lisa spill?
Reset
Submit
liter(s)
liter(s)
Answers
Answer:mark has 1 liter, lisa has an impossible -1 liter
Step-by-step explanation:
Match the corresponding graph with the number. Note:a number can have multiple graphs.
Answers
(6) A function is increasing when the y-value increases as the x-value increases.
The domain is the set of allowable x-values
The following graphs increases over their entire domain:
B, E, I, J, N, G
(7) A function is said to be decreasing when the y-value decreases as the x-values increase.
The following graphs decreases over their entire domain:
A, F
there are 250 toothpicks in a regular-size box. A jumbo-size box is made by tripling the length, width, and height of the regular box. How many toothpicks will the jumbo box hold?
Answers
The number of toothpicks that the jumbo box hold is 6760.
How to calculate the value?From the information, there are 250 toothpicks in a regular-size box and jumbo-size box is made by tripling the length, width, and height of the regular box.
Therefore, the number of toothpicks will be illustrated by multiplying the value by the change. This will be:
= 250 × 3 × 3 × 3
= 6750
This was because the dimensions were tripled
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Help I don’t understand!!
Answers
Farm c is Marc's farm it have 60 % of purple flowers
To find percentage :
In Farm B it shows that 0.6 are purple flowers .
0.6 is 6 of 10 it is 60 %.
And other farms have 11/20 that is 55% in Farm A
For Farm C only 40 %.
Percentage :
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".Although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.The formula used to calculate percentage is: (value/total value)×100%.If you are required to convert a decimal number like 0.57 to a percentage, you simply multiply it by 100. That is, 0.57 x 100 = 57. Therefore, 0.57 as a percentage equals 57%.To find 10% of a number means dividing by 10 because 10 goes into 100 ten times. Therefore, to find 20% of a number, divide by 5 because 20 goes into 100 five times.To learn more about PERCENTAGE refer :
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Question 10 of 14 VIn the figure, CJ and CR are opposite rays. CP bisects NCW and CL bisects LJCN.RWIf MZICN = 8r – 2 and mZLCN = 3r + 15, find mZICL.
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From the diagram, we can see that CL bisects angle JCN. This means that CL divides the angle JCN into 2 equal halves. It means that
angle JCN = angle JCL + angle LCN
Given that angle JCN = 8r - 2 and angle LCN = 3r + 15, it means that
8r - 2 = angle JCL + 3r + 15
Since angle JCL = angle LCN, then
8r - 2 = 3r + 15 + 3r + 15
8r - 2 = 6r + 30
8r - 6r = 30 + 2
2r = 32
r = 32/2
r = 16
angle JCL = 3r + 15 = 3 * 16 + 15
angle JCL = 48 + 15
angle JCL = 63 degrees
