Answer:
[tex](x-5)^2=4(y+2)[/tex]
Please note that alternative forms of this equation (vertex and standard) are in the explanation.
Step-by-step explanation:
Standard form of a parabola with a vertical axis of symmetry:
[tex]\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}[/tex]
Vertex = (h, k)Focus = (h, k+p)Given:
Vertex = (5, -2)Focus = (5, -1)Therefore:
h = 5k = -2k + p = -1Calculate p:
[tex]\implies -2+p=-1[/tex]
[tex]\implies p=-1+2[/tex]
[tex]\implies p=1[/tex]
Substitute the values of h, k and p into the formula to create an equation of the parabola with the given parameters:
[tex]\implies (x-5)^2=4(1)(y-(-2))[/tex]
[tex]\implies (x-5)^2=4(y+2)[/tex]
In vertex form:
[tex]\implies y=\dfrac{1}{4}(x-5)^2-2[/tex]
In ax² + bx + c form:
[tex]\implies y=\dfrac{1}{4}x^2-\dfrac{5}{2}x+\dfrac{17}{4}[/tex]
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
1. Ali collects comic books. He buys 2
comic books a week. This year after 5
weeks he has 17 comic books in his
collection. Write an equation relating
the number of comic books c to the
number of weeks w.
xw + 5w - 17 = 0 is the required equation.
How to find the required related equation?Given,
Ali buys 2 comic books a week.
After 5 weeks he has 17 comic books this year.
Solution:
Let w be weeks and c be comic books.
Since Ali buys 2 comic books a week.
1w = 2c
For 5 weeks, he would have,
5w = 10c, if he bought 2books per week.
But he had 17 books,
i.e, he would have collected some books last year.
Let x be the no of unknown weeks last year.
(x + 5)w = 17c
(x+5)w-17c= 0
xw + 5w - 17 = 0 is the required equation.
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Find the derivative of the function with solutions.y = In( e^(3 - x^2 ) + 9 ))
Answer:
[tex]\frac{dy}{dx}=-\frac{2xe^{3-x^2}}{e^{3-x^2}+9}[/tex]Explanation:
We were given the function:
[tex]y=\ln\left(e^{3-x^2}+9\right)[/tex]We are to find the derivative of this function, we have it shown below:
[tex]\begin{gathered} y=\operatorname{\ln}(e^{3-x^{2}}+9) \\ If:y=ln(u) \\ Then:y^{\prime}=\frac{u^{\prime}}{u} \\ y^{\prime}=\frac{dy}{dy} \\ u=e^{3-x^2}+9 \\ u^{\prime}=-2xe^{3-x^2} \\ y^{\prime}=\frac{u^{\prime}}{u} \\ \Rightarrow y^{\prime}=\frac{-2xe^{3-x^2}}{e^{3-x^2}+9} \\ But:y^{\prime}=\frac{dy}{dx} \\ \frac{dy}{dx}=-\frac{2xe^{3-x^2}}{e^{3-x^2}+9} \\ \\ \therefore\frac{dy}{dx}=-\frac{2xe^{3-x^2}}{e^{3-x^2}+9} \end{gathered}[/tex]PLEASE HELP BRO WILL GIVE BRAINLI
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n.
Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠n + m∠p
Step 4: So, m∠m + m∠n = m∠p
In which step did the student first make a mistake and how can it be corrected? (4 points)
Step 2; it should be m∠o − m∠p = 90 degrees (complementary angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
Step 3; it should be m∠m + m∠n + m∠o = m∠o + m∠p
Answer:
Step 3; it should be angle m + angle n + angle o = angle o + angle p
Step-by-step explanation:
yes, the sum of the inner angles of the triangle, m, n, o must be 180°.
yes, the sum of supplementary angles (which the pair of inner and outer angles always is) p and o must be 180°.
so, step 3 wants to show that the sum of the 3 inner angles is the same as the sum of the inner/outer angle pair. m + n + o = o + p = 180.
but instead of o the student suddenly wrote n in the right side of the equation. and that is wrong. n + p can't be 180°, as both are inner angles, and that would make the third inner angle 0°, which is not really possible.
so, once n is replaced by o on the right side of the equating in step 3, all is correct again.
and step 4 is correct anyway (it fixed the mistake in step 3 of the original proof by another mistake, coming to the right conclusion just by coincidence), now that step 3 is corrected.
Kamryn’s doctor recommended that she drink 64 fluid ounces of water every day. There are about 30 milliliters in 1 fluid ounce. Which measurement represents the number of milliliters in 64 fluid ounces?
help my teacher wants the answer in 15 minutes please help!!!
The 64 fluid ounces of water, as suggested by Kamryn's doctor to drink everyday, will be equal to 1920 millilitres.
Writing the equation as per the relation between millilitres and fluid ounces -
1 fluid ounce = 30 millilitres
Now, we will perform multiplication to find the number of milliliters in 64 fluid ounces. Writing the expression representing relation between millilitres and fluid ounces
Number of milliliters = 30×64
Performing multiplication between the numbers 30 and 64
Number of milliliters = 1920
Therefore, on drinking 64 fluid ounces by Kamryn on her doctor's recommendation will drink 1920 millilitres of water everyday.
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3y+2x=-1 solve for x
Answer:
Answer down below!
Step-by-step explanation:
Your answer would be -3/2y + (-1/2)
If you need the steps, refer to the image below!
Helpppppppssssss hehe
Answer:
Step-by-step explanation:
a. From 4 to 7 is 3 units. 7-10 is another 3 units and so on. The constant 3 units is the common difference.
The formula for a arithmetic sequence is
[tex]a_{n}=a_{1}+d(n-1)[/tex]
Where d is the common difference and a_1 is the first term.
[tex]a_{1}=4[/tex] and [tex]d=3[/tex]. Thus the equation of the nth term is
[tex]a_{n}=4+3(n-1)[/tex]
2. Write in standard form: one hundred dollars and fourteen cents
1
Please help me im getting stressed with solution
The personal assets and liabilities of a plumber are listed below.
What is the total value of the plumber's liabilities?
$149,367
$167,925
$241,231
$273,881
The total value of the plumber's liabilities = $441,806
How to calculate the total of something?One of the four fundamental operations of mathematics is addition, which is typically denoted by the plus sign (+). The other three are subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.
It is one of the fundamental mathematical operations we employ on a daily basis. We employ number addition in a variety of contexts. When we work with time or money, such as when adding up invoices and receipts, adding numbers is one of the most frequently used operations in daily life.
The total value of the plumber's liabilities :
is to simply add all the values and we will get
$441,806
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Answer:
Option B.) $167,925
Step-by-step explanation:
Liability is money you owe to another person or institution, including a credit card balance, mortgage and so on.
So the plumber's liabilities
= 149,367 + 6,283 + 12,275
= $167,925
The question is clearly in the pic
A) The slope represents the probability of winning for each rank.
B) The y-intercept means the probability of winning for an unranked school.
C) The probability of winning for a school ranked number 4 is; 78%
How to Interpret Linear Equation Graphs?The formula representing the general form of an equation in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
A) From the given graph, we see that the y-axis represents the probability of winning for each rank while the x-axis represents the ranks of the schools. Thus;
Slope unit = Probability of winning/Rank
B) The y-intercept is the point at which the graph crosses the y-axis. In this case, it means no ranked school and that is the probability of winning for an unranked school.
C) The linear equation is given by the formula;
y = -6.4x + 103.8
Thus, for a rank of 4, we have;
y = -6.4(4) + 103.8
y = 78.2 ≈ 78%
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u/3 = -51 solve for u simplify your answer as much as possible
Answer:
u = -153
Step-by-step explanation:
u/3 = -51
multiply both sides by 3:
3(u/3) = 3(-51)
u = -153
Find an equivalent statement for the following absolute value equation |x - 5] = 1x +6
ANSWER:
STEP-BY-STEP EXPLANATION:
PLS HELP ME
The following table shows the distance from the bus stop as a function of time:
Time (in minutes) Distance (in meters)
(x) f(x)
0 45
3 40
6 35
9 30
12 25
Find and interpret the meaning of the x-intercept in this scenario. (4 points)
(45, 0); the distance away from the bus stop
(27, 0); the time it takes to reach the bus stop
(45, 0); the time it takes to reach the bus stop
(27, 0); the distance away from the bus stop
The x-intercept is (27,0). The time it takes to reach the bus stop
We first find the equation between time and distance as a linear function by finding the slope and y-intercept from the table values.
If we write the Time as x-values and Distance as y-values, we get the points,
(0,45), (3,40), (6,35), (9,30), (12,25)
We can find the slope from these points considering two points (0,45) and (3,40)
Slope = 45-40/0-3 = -5/3
The y-intercept of the function is the value of f(x) at x = 0.
Here, from the table, when x = 0, y = 45.
So y-intercept = 45
Then the equation of distance in terms of time is,
y = -(5/3)x+45
The x-intercept is the x-value when y = 0.
So when y = 0,
0 = -(5/3)x+45
⇒ (5/3)x=45
⇒ x = 45x 3/5
⇒ x = 27
Therefore, x-intercept = (27,0).
It is the time (in minutes) when distance = 0 meters.
So x-intercept is the time it takes to reach the bus stop.
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Answer:
B) (27,0); the time it takes to reach the bus stop
Topic: Nonlinear Systems of EquationsCreate a system of equations that includes one linear equation and one quadratic equation.Show all work in solving your system of equations algebraically.
Answer:
• Equations
[tex]y=x+2[/tex][tex]y=x^2[/tex]• Solutions (2, 4) and (–1, 1)
Explanation
System of equations
• Linear equation
[tex]y=x+2[/tex]• Quadratic equation
[tex]y=x^2[/tex]We have to set both equations to 0 and equalize them:
• 1. Setting them to 0:
[tex]0=x+2[/tex][tex]0=x^2[/tex]• 2. Equalizing them:
[tex]x+2=x^2[/tex]To solve the system using the General Quadratic Formula, we have to set the equation in the form ax² + bx+ c = 0:
[tex]x^2-x-2=0[/tex]Thus, in this case a = 1, b = -1 and c = -2. Using the formula:
[tex]x_{1,2}=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-2)}}{2(1)}[/tex][tex]x_{1,2}=\frac{1\pm\sqrt{1+8}}{2}[/tex][tex]x_{1,2}=\frac{1\pm\sqrt{9}}{2}[/tex]Finding both solutions:
[tex]x_1=\frac{1+3}{2}=\frac{4}{2}=2[/tex][tex]x_2=\frac{1-3}{2}=\frac{-2}{2}=-1[/tex]Finally, replacing these values in the linear equation to find y:
[tex]y_1=2+2=4[/tex][tex]y_2=-1+2=1[/tex]Therefore, the solutions are (2, 4) and (–1, 1).
The price of an item yesterday was $140. Today, the price rose to $357. Find the percentage increase.
Answer: 70% is percentage increase
Step-by-step explanation:
230-140/140 x 100 =90/140 x100 =0.7 x 100=70
If F(n) = -n Then F(-6)= ?
Answer: 6
Step-by-step explanation:
-n plug -6 in so -(-6)=6
Answer:
boo ba loob
Step-by-step explanation:
sweating in saucy bbq sauce
The population of City A is 8.59 x 10^4. The population of City B is 3.2 x 10^3 Select all of the values that show the difference in population of City A and City B
The difference of population in these two cities are 85900- 3200
= 82,700
How do you calculate difference?
Subtract the largest number from the lowest number to determine the difference between two integers. The difference between the two numbers is the product of this sum. As a result, there are 55 between the numbers 45 and 100.
Given: Population of city A= 8.59 x 10^4
and population of city B = 3.2 x 10^3
This can also be written as :
Population of city A= 85,900
and population of city B = 3200
Thus the difference of population in these two cities are 85900- 3200
= 82,700
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y = 3x + 5
y = 4x² + x
The system of equations has two solutions, these are:
(-0.89, 2.33) and (1.4, 9.2)
How to solve the system of equations?Here we have the following system of equations:
y = 3x + 5
y = 4x² + x
We can see that y is already isolated in both equations, so we can write the equation:
3x + 5 = y = 4x² + x
3x + 5 = 4x² + x
now we can solve this for x, this is just a quadratic equation:
3x + 5 - 4x² - x = 0
-4x² + 2x + 5 = 0
Using the quadratic formula, we can see that the two solutions are:
[tex]x = \frac{-2 \pm \sqrt{2^2 - 4*(-4)*5} }{2*-4} \\\\x = \frac{-2 \pm 9.17}{-8}[/tex]
So the solutions are:
x = (-2 +9.17)/-8 = -0.89
x = (-2 - 9.17)/-8 = 1.4
Evaluating the linear equation in these values, we get:
y = 3*(-0.89) +5 = 2.33
y = 3*(1.4) + 5 = 9.2
So the solutions of the system are:
(-0.89, 2.33) and (1.4, 9.2)
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suppose arya stark draws a sample of 10 observations with a mean of 50 and a population standard deviation of 4. she would like to establish a 95% confidence interval. which formula would you tell her to use?
The formula Arya stark will use to find the 95% confidence interval is normal approximation of the distribution.
What is termed as the confidence interval?A confidence interval shows the likelihood that a parameter would then fall between two values near the mean.The amount of uncertainty as well as certainty inside a sampling method is measured by confidence intervals.They are also used to test hypotheses and perform regression analysis.For the given question, the data is-
Mean μ = 50Standard deviation σ = 4Confidence interval 95%Sample size n = 10.Sample mean = xThe formula for finding the 95% confidence interval is normal approximation of the distribution.
z = (x - μ)/s
Where, s = σ/√n
The corresponding value of z for 96% is taken from the z score table.
Thus, formula Arya stark will use to find the 95% confidence interval is normal approximation of the distribution.
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an office ceiling is 9 feet high file boxes are each 3/4 feet tall. what is the greatest number of these file boxes that can be stacked in the office? Show how you know.
Answer:
12
Step-by-step explanation:
Equation:
[tex]9 /\frac{3}{4}[/tex] [tex]=x[/tex]
[tex]12=x[/tex]
Check!
[tex]12(\frac{3}{4} )=9[/tex]
Therefore, the greatest number of file boxes that can be stacked is 12.
Which number line shows the points −125 and –2.8?
A. Alternative Text
B. Alternative Text
C. Alternative Text
D. Alternative Text
The number line having -2.4 and -2.8 is attached below
What is number line?Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series. The endpoints of this line go on forever. Some will have a defined beginning and end. We refer to these as closed number lines. Number lines may alternatively be left empty or blank. A number ladder is a vertical number line.
Given number: −12/5 and –2.8
As, we can write -12/5 in decimal form= -2.4
Now, we have to put the number on the number line
As, -2.4 lies between -2 and -3 on the left side of zero.
and, -2.4 lies between -2.5 and -3.0 on the left side of zero.
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help me its so hard !!!
For the rectangle given, considering its diagonal properties, the value of x=4, while the angle VUR=36°
Angles and properties of plane shapesTo answer this question, let us recall the following:
The diagonals of a rectangle bisects each other into four eqaul length.The base angles of an Isosceles triangle are equal.Complementary angles add up to give a total of 90°.Hence;
the lengths RV and SV are
so, 3x+8=6x-4
6x-3x=8+4 [collecting like terms]
3x=12
when we divide both sides of the equation by 3, we have the value of x=4.
the angles VRS and VRU are complementary
so, 54°+VRU = 90°
VRU = 90°-54°
VRU = 36°
The triangle RUV is an Isosceles
so, angles VRU and VUR are equal, therefore angle VUR = 36°.
We can reduce from our workings that the value of x = 4 and the angle VUR is 36°.
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4. Which statement is NOT true about the diagram below?
O AD = DC
O m<CDB =92
O m<ADB =88
O DB is a perpendicular of AC
Answer:
DB is a perpendicular of AC
The single inequality y > |x + 2| is equivalent to which of the following systems?
Answers:
1.y > x + 2
y > –x + 2
2.y > x + 2
y > –x – 2
3.y > x + 2
y < –x + 2
4.y > x + 2
y < –x – 2
The single inequality y > |x + 2| is equivalent to:
4. y > x + 2
y < –x – 2
What is an inequality?It should be noted that an inequality is simply used to show the relationship between the expressions that aren't equal.
The non-negative value of a real number x, regardless of its sign, is its absolute value or modulus | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5. One way to think about a number's absolute value is as its distance from zero on the real number line.
It should be noted that based on the information, the inequality is:
y > |x + 2|. This is the positive part of the modulus.
This is the same as y < –x – 2 when the signs are changed. This is the negative part of the modulus.
In conclusion, the correct option is 4.
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What is the
Range??
Help me out plsss
Answer:
1 ≤ y ≤ 4
Step-by-step explanation:
Range is all possible y values
a point is written as (x, y)
The line starts at point (0, 1) and ends at (3, 4)
so the range of the y values is 1 to 4
I DONT KNOW PLS HELPP
Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0 and σ=15.0. A random sample of 61 people is taken.What is the probability that the mean IQ score of people in the sample is less than 98? Round your answer to 4 decimal places, if necessary.
To find the probability that the mean IQ score of people in the sample is less than 98, first we need to convert the value into z-score by using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Then, when x=98:
[tex]\begin{gathered} z=\frac{98-100.0}{15.0} \\ z=\frac{-2.0}{15.0} \\ z=-0.1333 \end{gathered}[/tex]By checking in a standard normal table z=-0.1333 has a p-value=0.4471.
Then the probability is 0.4471 that also can be expressed as 44.71%
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (-8, -5); y= -3x + 5
Step-by-step explanation:
a parallel line must have the same slope (otherwise it cannot be parallel).
a slope-intercept form looks like
y = ax + b
"a" (the factor of x) is always the slope, "b" is the y-intercept (the y-value when x = 0).
so, we know from y = -3x + 5 that the slope of the new line is also -3.
to get b we use the coordinates of the given point :
-5 = -3×-8 + b = 24 + b
-29 = b
that means the line equation is
y = -3x - 29
Aldo has 61 miles remaining after 48 minutes of driving. How many miles will
be remaining after 60 minutes of driving?
Answer:
76.25
Step-by-step explanation:
61:48 = x:60
48x=3660
3660/48 = 76.25
So the answer is 76.25 miles are left.