The equation of the quadratic with a directrix of y= -5 and vertex of (-2, -3) is: y = 1/8 (x + 2)² - 3
How to write the equation of parabola with directrix of y = -5 and vertex of (-2,-3)Quadratic equation when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex
v (h, k) = (-2,-3)
h = -2
k = -3
P in this problem, is the distance between the vertex and the directrix
P = -3 - -5 = -3 + 5 = 2
p = 2
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - -2)² = 4 * 2 (y - -3)
(x + 2)² = 8 (y + 3)
rearranging the equation
8 (y + 3) = (x + 2)²
y + 3 = 1/8 (x + 2)²
y = 1/8 (x + 2)² - 3 (standard vertex form)
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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
A pair of Nike tennis shoes costs $29.10 more than a pair of Reeboks. If Josh buys one of each brand and spends a total of $154.10, what did each brand cost?
Answer:
Nike=RM106.15
Reeboks=RM47.95
PLS HELP !!!!! WILL GIVE BRAINLIEST!!
Answer:
ADB
Step-by-step explanation:
They are the same.
The weight of oranges growing in an orchard is normally distributed with a mean
weight of 5.5 oz. and a standard deviation of 1 oz. Using the empirical rule, determine
what interval would represent weights of the middle 68% of all oranges from this
orchard.
Which digit represents 100 times the value of the ones place
Depending upon the position of the digits represent the 100 times the place value of the ones place.
What is place value?
In mathematics, every digit can be defined as a place value in a number. Basically, it is completely depends on the position of the digits in a number. Most of the number has same digits, but their positions are different, which makes the number different.
According to the question, all the digits represents 100 times the place value of the ones place.
Those digits can be defined as [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]. But the position of the digit should be at the 100th place.
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Michael wants to buy a comic book and it costs $13.00. He has $6.85. How muchmore money does Michael need to buy the comic book?
To find how much more money Michael needs, you have to subtract his savings from the cost, as follows
$13.00 - $6.85 = $6.15
I need Geometry help
We have the points A(-2, 5) and B(12, 0).
And we must find the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 4 to 1.
To find the coordinates we must use the next equations
Where (x1, y1) and (x2, y2) are the given points and a:b is the given ratio.
- x-coordinate
[tex]\begin{gathered} -2+\frac{4}{4+1}(12-(-2)) \\ =-2+\frac{56}{5} \\ =\frac{46}{5} \end{gathered}[/tex]- y-coordinate
[tex]\begin{gathered} 5+\frac{4}{4+1}(0-5) \\ =5+\frac{-20}{5} \\ =1 \end{gathered}[/tex]Finally, the point P is
[tex]P(\frac{46}{5},1)[/tex]Solve each system of equations by GRAPHING. Clearly identify your solution.4x - y = 33x + y = 4
Answer:
( 1, 1 )
Step-by-step explanation:
Hope this helps :)
Question 5 of 10
What is the slope of the line that contains the points (-2, 7) and (2, 3)?
O A. -1
OB. -4
OC. 4
OD. 1
Answer: A. -1
Step-by-step explanation:
Δy / Δx
=3 - 7 / 2 --2
=-4 / 4
=-1
A 16-foot ladder leaning against the side of a house reaches 12 feet up the house. What angledoes the ladder make with the ground?
Given:
By the definition of sin
[tex]\begin{gathered} \sin \theta=\frac{opposite\text{ }}{\text{hypotenuse}} \\ \theta=\sin ^{-1}(\frac{opposite\text{ }}{\text{hypotenuse}}) \\ \theta=\sin ^{-1}(\frac{12}{16}) \\ \theta=48.59^{\circ} \end{gathered}[/tex]Answer:
[tex]\text{The ladder makes }48.59^{\circ}\text{ with the ground}[/tex]When are two events considered to be independent? A. when the occurrence of each event is not affected by the occurrence of the other event B. when the occurrence of the second event affects the occurrence of the first event C. when the occurrence of the first event affects the occurrence of the second event D. when the occurrence of each event affects the occurrence of the other
The two events are considered to be independent when the occurrence of each event is not affected by the occurrence of the other event
The event is defined as the outcome or the set of all the outcomes of the random experiment
Independent event is defined as the occurrence of the one event does not depends on the occurrence of another event
So we can say that, two events are independent events when the occurrence of the one event does not depends on the occurrence of the other event.
Hence, The two events are considered to be independent when the occurrence of each event is not affected by the occurrence of the other event
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A sample of people who recently hired an attorney yielded the following information about their attorneys.
Number of People
Would You Recommend Your Attorney to a Friend?
Yes
No
Not sure
Three people who provided information for the table were selected at random. Determine the probability that the first two would not recommend their attorney and the third is not sure if he or she would recommend their attorney.
Two angles are supplementary. The measure of one angle is x and the measure of the other angle is 4x, find the value of xa. 36b.18c.4d.5
we know that
If two angles are supplementary, then their sum is equal to 180 degrees
so
In this problem
x+4x=180
solve for x
5x=180
x=36
therefore
the answer is the option A
Part 2
I need help with my math
Given
Graph
Procedure
[tex]\begin{gathered} 3x+2y=-6 \\ 2y=-6-3x \\ y=\frac{-3x-6}{2} \\ y=-\frac{3}{2}x-3 \\ \end{gathered}[/tex][tex]\begin{gathered} 3y=2x+15 \\ y=\frac{2x+15}{3} \\ y=\frac{2}{3}x+\frac{15}{3} \\ y=\frac{2}{3}x+5 \\ \end{gathered}[/tex][tex]\begin{gathered} y-4x=8 \\ y=4x+8 \end{gathered}[/tex][tex]\begin{gathered} y-8=-\frac{1}{2}(x+4) \\ y-8=-\frac{1}{2}x-\frac{1}{2}4 \\ y=-\frac{1}{2}x-2+8 \\ y=-\frac{1}{2}x+6 \end{gathered}[/tex][tex]\begin{gathered} 3x-4y=8 \\ 4y=-8+3x \\ y=\frac{3x-8}{4} \\ y=\frac{3}{4}x-\frac{8}{4} \\ y=\frac{3}{4}x-2 \end{gathered}[/tex][tex]\begin{gathered} 6x-2y=10 \\ 2y=6x-10 \\ y=\frac{6x-10}{2} \\ y=\frac{6x}{2}-\frac{10}{2} \\ y=3x-5 \end{gathered}[/tex]identifica a que propiedad pertenece 9 a -3 potencia
We are asked to identify which properties of exponent to apply in order to reduce the expression:
[tex]9^{-3}[/tex]This is the property associated with negative exponents that include the fact that we are dealing with a division:
[tex]a^{-n}=\frac{1}{a^n}[/tex]This is the negative exponent property, so for our case we write;
[tex]9^{-3}=\frac{1}{9^3}=\frac{1}{729}[/tex]SO find the property I am higlighting in the image below:
if the sales tax rate is 6.25% in your city, find the final cost of the item diamond ring : $655.75discount rate: 40%
What is 40% of 655.75??
40% = 40/100 = 0.4
So,
655.75 * 0.4 = $262.30
On top of that, we have to pay a sales tax of 6.25%, which is
6.25% = 6.25/100 = 0.0625
So,
262.30 * 0.0625 = $16.39
We ADD this tax to get final amount:
Amount Paid = 262.30 + 16.39 = $278.69find the volume of the figure below. as you can see my teacher has already gaved the answer now she wants me to show how she got the answer.
The volume of any solid is the product of the base area and the height
[tex]V=b\mathrm{}A\times h[/tex]Let us find the area of the base of the given figure and multiply it by the height
The base is a right triangle of legs 9 mm and 26 mm, then its area is
[tex]\begin{gathered} b\mathrm{}A=\frac{1}{2}\times9\times26 \\ b\mathrm{}A=177mm^2 \end{gathered}[/tex]The height of the solid is 24 mm, then
[tex]\begin{gathered} V=177\times24 \\ V=2808mm^3 \end{gathered}[/tex]The volume of the figure is 2808 cubic mm
Answer C
Find the area of the rectangle that has a perimeter of 8x − 14 units and a length of x − 5 units.
Answer: Area = 4 square units
Perimeter of the rectangle = 8x - 14 units
Length of the rectangle = x - 5 units
Let the width of the rectangle = x units
Perimeter = 2( length + width)
8x - 14 = 2(x - 5 + x)
Solve the parenthesis for once
8x - 14 = 2(x + x - 5)
8x - 14 = 2(2x - 5)
8x - 14 = 4x - 10
Collect the like terms
8x - 4x = -10 + 14
4x = 4
Divide both sides by 4
4x/4 = 4/4
x = 1
Since, the length is x - 5 units
Length = 1 - 5
Length = - 4units
Length = 4 units
Width = 1 unit
Area = length x width
Area = 4 x 1
Area = 4 square units
What is the average rate of change of the function f(x)=5(2)xfrom x = 1 to x = 5? Enter your answer in the box.
Solution:
Given:
[tex]\begin{gathered} f(x)=5(2)^x \\ \text{from x = 1 to x = 5} \end{gathered}[/tex]The average rate of change of a function can be calculated by;
[tex]\begin{gathered} \text{Average rate of change=}\frac{f(b)-f(a)}{b-a} \\ \text{where a =1} \\ b=5 \end{gathered}[/tex]What is the H.c.f of 16 and 30
The HCF of 16 and 30 is 2.
What is HCF?The greatest number that totally divides two numbers is known as the Highest Common Factor (HCF). The Greatest Common Divisor (GCD) is another name for the Highest Common Factor (HCF) (GCD).The HCF of two numbers can be determined in a variety of methods. Using the prime factorization technique is one of the easiest techniques to determine the HCF of two or more numbers.SO, the given numbers are 16 and 30
The prime factorization of 16 and 30 are as follows:
16 = 2 × 2 × 2 × 230 = 2 × 3 × 5Multiply all the prime factors that both numbers share in order to determine the HCF:Thus, HCF is = 2.
With the help of prime factorization method we can conclude that the HCF of 16 and 30 is = 2.
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if Joey drives 222 3/4 miles 3 3/8 hours . if he drives at a constant rate how far will he drive in one hour ?
Start by making the mixed numbers into fractions using that:
[tex]A\frac{b}{c}=\frac{(A\cdot c)+b}{c}[/tex]According to this:
[tex]222\frac{3}{4}=\frac{(222\cdot4)+3}{4}=\frac{888+3}{4}=\frac{891}{4}[/tex][tex]3\frac{3}{8}=\frac{(8\cdot3)+3}{8}=\frac{24+3}{8}=\frac{27}{8}[/tex]To find the rate we divide the distance over the time
[tex]\frac{\frac{891}{4}}{\frac{27}{8}}=\frac{891\cdot8}{27\cdot4}=\frac{7128}{108}=\frac{66mi}{h}[/tex]The rate idicates that joey drives 66 miles in one hour.
Use interval notation to describe all the x-values within or including a distance of the given values. Use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters.Distance of 5 units from the number 7AnswerAnswer,AnswerAnswer
The sentence
"Distance of 5 units from the number 7"
The part "From the number 7" indicates that you have to start counting from 7 on. Then the left bound of the interval is number 7.
To determine the right bound of the interval you have to count 5 units starting from 7, so add 5 to 7
[tex]7+5=12[/tex]The right bound of the interval is 12.
So, the values of x within the distance described by the sentence are: (7,12)
Expand and simplufy (2x-3)(3x-5)
Answer:
6x² - 19x + 15
Step-by-step explanation:
(2x - 3)(3x - 5)
each term in the second factor is multiplied by each term in the first factor , that is
2x(3x - 5) - 3(3x - 5) ← distribute parenthesis
= 6x² - 10x - 9x + 15 ← collect like terms
= 6x² - 19x + 15
I need help on B and an explanation. Approximate bearinge angle
The bearing of a given point is the number of degrees in the angle measured in a clockwide direction from the north line.
Since we dont have a complete information about where point P is located with respect to point A and B, we can approximate the bearing point. Let's draw a picture of our problem:
As we can note, the approximate bearing angle is about 260 degres from point P.
Given csc A = 65 and that angle A is in Quadrant I, find the exact value of cot A insimplest radical form using a rational denominator.
The trigonometric expression for relation between csc A and cot A.
[tex]undefined[/tex]Two factory plants are making TV panels. Yesterday, Plant A produced 2000fewer panels than Plant B did. Four percent of the panels from Plant A and 2% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 880 defective panels?
Using a series of linear equations, the number of panels generated by Plant B is 16000.
Given,
Plant A produces 2000 fewer panels than Plant B.
Defective percentage of plant A = 4%
Defective percentage of plant B = 2%
To find: Number of useable panels of Plant A and Plant B if 880 are defective.
Let's take, panels produced by Plant B = b
and panels produced by Plant A , a = b - 2000 - - - - (1)
The total number of defective panels :
0.04a + 0.02b = 880 - - - - - (2)
From (1) :
0.04(b - 2000) + 0.02b = 880
0.04b - 80 + 0.02b = 880
0.06b = 880 + 80
0.06b = 960
b = 960 ÷ 0.06
b = 16,000
Therefore, plant B built 16,000 panels.
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20 points!!! A Local hamburger shop sold a combined total of 488 hamburgers and cheeseburgers on saturday. There were 62 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on saturday?
Answer:
182
Step-by-step explanation:
488 ÷ 2 = 244
244 + 62 = 306
488 - 306= 182
simplify (4z-13)+(9-9z)
Answer:
the answer is -5z-4
Step-by-step explanation:
you just combined the like terms
The bottom number. I need written in a way where there is no number above the square root symbol. (The number 4 that’s a live the square root symbol) I need it like simplified to where there is no number above the square root symbol
1) Let's rewrite that radical, in a way that we can eliminate the fourth root:
[tex]18\sqrt[4]{5}\Rightarrow(18\sqrt[4]{5})^8=18^8\cdot(\sqrt[4]{5})^8=18^8\text{ }\sqrt[]{25}[/tex]2) This way we can get rid of the fourth root by raising to the power (in this case 8) as the index of the root (4).
3) Hence, one possible way to rewrite it with no root is
[tex](18\sqrt[4]{5})^8=18^8\sqrt[]{25}[/tex]PLEASE HELP ASAP Rich needs $50,000 for a down payment on a home in 5 years. How much must he deposit into an account that pays 1.16% interest, compounded quarterly, in order to meet his goal?
Answer:
37,123.52
Step-by-step explanation:
I hope this helps! c:
Answer:
37 ,123.52
Step-by-step explanation:
27. In a neighborhood donut shop, one type of donut has 560 calories, two types of donuts have 400 calories, five types of donuts have 570 calories, six types of donuts have 450 calories, and seven types of donuts have 550 calories.Find the mean number of calories in these donuts. Round your answer to the nearest whole number, if necessary. caloriesFind the median number of calories in these donuts. calories
ANSWER:
Mean: 512 calories
Median: 550 calories
STEP-BY-STEP EXPLANATION:
The first thing is to determine the data necessary to calculate the mean and median, according to the statement, the data is as follows:
[tex]560,400,400,570,570,570,570,570,450,450,450,450,450,450,550,550,550,550,550,550,550[/tex]The mean is the average value of a set of numeric data, calculated as the sum of the set of values divided by the total number of values:
[tex]\begin{gathered} m=\frac{560+400+400+570+570+570+570+570+450+450+450+450+450+450+550+550+550+550+550+550+550}{21} \\ m=\frac{10760}{21}=512.38\cong512 \end{gathered}[/tex]The median is a central position statistic that splits the distribution in two, that is, it leaves the same number of values on one side as on the other. To calculate the median it is important that the data are ordered from highest to lowest, or conversely from lowest to highest, therefore, we organize:
[tex]400,400,450,450,450,450,450,450,550,550,550,550,550,550,550,560,570,570,570,570,570[/tex]The value in the middle after arranging is 550, therefore the median is 550 calories.