We will investigate how to best represent a parabolic graph using a function description.
All parabolas are denoted as either a " U " or inverted " U ". There are two principal parameters of a parabola. The vertex i.e the maximum or minimum point attained by the parabola. The line of symmetry or focus point: The line of symmetry can either be vertical or horizontal but it always passes through the focus point.
We are given a graph of a parabola that has two zeros which can be read off from the plot.
We will locate these zeros and write them down:
[tex]\begin{gathered} x\text{ = 3} \\ x\text{ = 5} \end{gathered}[/tex]All parabolas are expressed by a quadratic polynomial function. The quadratic polynomial can be expressed in factorized form as follows:
[tex](\text{ x - }\alpha\text{ )}\cdot(x\text{ - }\beta\text{ )}[/tex]Where,
[tex]\begin{gathered} \alpha\text{ = 3 ( First Zero )} \\ \beta\text{ = 5 , ( Second Zero )} \end{gathered}[/tex]We will express our located zeros in the factorized quadratic expressed above:
[tex](\text{ x - 3 )}\cdot(x\text{ - 5 )}[/tex]Then we will try to solve the parenthesis and expand the factorized form as follows:
[tex]\begin{gathered} -5\cdot(x\text{ - 3 ) + x}\cdot(x\text{ - 3 )} \\ -5x+15+x^2\text{ - 3x} \end{gathered}[/tex]Group the similar terms and simplify:
[tex]x^2\text{ - 8x + 15 }[/tex]Therefore the function that best describes the given plot is:
[tex]y=x^2\text{ -8x + 15 }\ldots\text{ Option A}[/tex]Point C is located at (4, -2). It is translated 3 units to the left and 4 units up. Graph the location of the translated point.
Answer:
Step-by-step explanation: Refer to the photo taken.
I NEED HELP ASP ;-;. On the day of the test, the teacher instructed the students to take out no less than 2 pencils from their backpacks.
Determine which inequality represents this scenario.
2 ≥ p
2 ≤ p
2 > p
2 < p
The inequality that represents the given situation perfectly is (B) 2 ≤ p.
What exactly is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.Make use of the following steps to solve an inequality: Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator. Step 2 Combine like terms on both sides of the inequality to simplify. Step 3 Obtain the unknown on one side and the integers on the other by adding or subtracting quantities.So, the inequality that perfectly represents the given situation:
The teacher asks, to take out no less than 2 pencils.So, inequality can be:
2 = p and 2 < pCombine: 2 ≤ p
Therefore, the inequality that represents the given situation perfectly is (B) 2≤p.
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Correct question:
On the day of the test, the teacher instructed the students to take out no less than 2 pencils from their backpacks.
Determine which inequality represents this scenario.
A 2 ≥ p
B 2 ≤ p
C 2 > p
D 2 < p
What type of angle is shown on the protractor below?
Given data:
The given angle .
The given angle AOB is an obtuse angle.
Thus, third option is correct.
Can you help me please? If there is a solution what’s the solution as well
Solution:
Given;
[tex]-7y^2+7y+1=0[/tex]Where;
[tex]a=-7,b=7,c=1[/tex]Thus;
[tex]\begin{gathered} b^2-4ac=7^2-4(-7)(1) \\ \\ b^2-4ac>0 \end{gathered}[/tex]Hence, the quadratic equation has two different real solutions.
Then;
[tex]\begin{gathered} y=\frac{-7\pm\sqrt{7^2-4(-7)(1)}}{2(-7)} \\ \\ y=1.13,y=-0.13 \end{gathered}[/tex]A dinner party is being organized with the option of 7 dinner choices to serve at the venue. Since catering is expensive thehost asks everyone attending to rank each dish. The top ranked dish will be served at the venue. What is the probability thatyour favorite dish is the chosen dish served at the venue?• Write your answer as an exact fraction which is reduced as much as possible.
Given:
Total number of dinner choices = 7
Let's find the probability that your favorite dish is the chosen dish at the venue.
Given that you are to choose just one dish.
Probability can be said to be a measure of the likeklihood of an event to occur.
The probability of an event is a number between 0 and 1.
To find the probability, apply the formula below:
[tex]\begin{gathered} P(\text{fav)}=\frac{\text{Number of favorite dish}}{\text{Total number of dishes}} \\ \\ P(\text{fav)}=\frac{1}{7} \end{gathered}[/tex]Therefore, the probability the that your favorite dish is the chosen dish at the venue is
[tex]\frac{1}{7}[/tex]ANSWER:
[tex]\frac{1}{7}[/tex]what does the g in 5 = g/8 ?
Given data:
The given expression is 5=g/8.
The given expression can be written as,
[tex]\begin{gathered} 5=\frac{g}{8} \\ g=40 \end{gathered}[/tex]Thus, the value of g is 40.
Grandma Meyer uses the recipe to make a soup.A.Draw a bar diagram to find how much vegetable stock and cream are needed.B. Find how many cups of soup will be made with all the ingredients. Explain your work.
Prior to plotting our chart, we need to convert these mixed fractions to decimals. Since denominators are 4, we can easily multiply both sides of the fraction by 25 to give the fraction in terms of 100 and thus, easily convert to decimal.
[tex]ChickenBroth\colon2\frac{3}{4}=\text{ 2 + (}\frac{3\times25}{4\times25}\text{)= 2 + }\frac{75}{100}=\text{ 2 + 0.75 = 2.75}[/tex][tex]Water\colon1\frac{1}{4}=\text{ 1 + (}\frac{2\times25}{4\times25}\text{)= 2 + }\frac{50}{100}=\text{ 2 + 0.5 = 1.5}[/tex][tex]Cream\colon1\frac{1}{4}=\text{ 1 + (}\frac{1\times25}{4\times25}\text{)= 1 + }\frac{25}{100}=\text{ 1 + 0.25 = 1.25}[/tex][tex]Vegetablestock\colon2\frac{3}{4}=\text{ 2 + (}\frac{3\times25}{4\times25}\text{)= 2 + }\frac{75}{100}=\text{ 2 + 0.75 = 2.75}[/tex]B.
The number of cups of soup will be a total of the ingredient,
[tex]\begin{gathered} \text{Total = 2.75 + 1.5 + 1.25 + 2.75 = 8.25} \\ To\text{ get back as mixed fractions,} \\ (8\text{ + }\frac{25}{100})\text{ + (8 +}\frac{1}{4}\text{) = 8}\frac{1}{4} \end{gathered}[/tex]Suppose you have a standard deck of 52 carts. What is the probability that if you select a card at random that it does not have a face value of 9? Round your answer to two decimals
A deck of cards has 13 face values: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. These face values are present for four different suits (Clubs, Diamonds, Hearts, and Spades) for a total of 52 cards.
An event's probability in an experiment with equally likely outcomes is defined by the following formula, where P (event) means the probability of the event occurring and is founding by dividing the number of outcomes in the event by the number of outcomes in the sample space:
[tex]P(event)=\frac{Number\text{ }of\text{ outcomes in the event}}{Number\text{ of outcomes in the sample space}}[/tex]The probability of not getting the event is given to be:
[tex]P^{\prime}(event)=1-\frac{Number\text{ }of\text{ outcomes in the event}}{Number\text{ of outcomes in the sample space}}[/tex]Since there are 4 cards with a face value of 9, the probability of getting a 9 is:
[tex]P(9)=\frac{4}{52}=\frac{1}{13}[/tex]Therefore, the probability of not getting a 9 is given to be:
[tex]\begin{gathered} P^{\prime}(9)=1-\frac{1}{13} \\ P^{\prime}(9)=\frac{12}{13} \end{gathered}[/tex]In two decimal places, the probability that the card picked does not have a face value of 9 is 0.92.
What is the measure of the 5x+25
As you can see:
RM+MT = RT
Where:
RM = 5x + 9
MT = 8x - 6
RT = 198
Replacing the data:
5x + 9 + 8x - 6 = 198
Add like terms:
(5x + 8x) + (9 - 6) = 198
13x + 3 = 198
Solve for x:
Subtract 3 from both sides:
13x + 3 - 3 = 198 - 3
13x = 195
Divide both sides by 13:
13x/13 = 195/13
x = 15
Given PQRS is a parallelogram, find the value of x and the value of y* Р 0 (4y + 7) 13x + 15 19x - 9 (10y - 37) S R 4 5 6 7 10 14 15 None of these y= horollalaram find the msc. (do not enter units) * 3 points
If PQRS is a parallelogram, we know that:
- PS and QR have the same length.
-
Then, we can calculate x as:
[tex]\begin{gathered} PS=QR \\ 13x+15=19x-9 \\ 13x-19x=-9-15 \\ -6x=-24 \\ x=\frac{-24}{-6} \\ x=4 \end{gathered}[/tex]And we can calculate y as:
[tex]\begin{gathered} m\angle Q+m\angle R=180\degree \\ (4y+7)+(10y-37)=180 \\ 14y-30=180 \\ 14y=180+30 \\ 14y=210 \\ y=\frac{210}{14} \\ y=15 \end{gathered}[/tex]Answer: x=4 and y=15
Are the triangle below congruent? If so, write a congruence statement and say why
6)Find the solution set of the quadratic equation over the set of complex numbers.5x2 + 12x + 8 = 0A)x = −34 − i4 or −34 + i4B)x = −65 − 2i5 or −65 + 2i5C)x = −25i(11 − 2i) or −25i(11 + 2i)D)x = −16i(11 − 2i) or −16i(11 + 2i)
The given quadratic equation is expressed as
5x^2 + 12x + 8 = 0
The standard form of a quadratic equation is expressed as
ax^2 + bx + c = 0
By comparing both equations, we have
a = 5, b = 12, c = 8
We would solve for x by applying the general formula for solving quadratic equations which is expressed as
[tex]\begin{gathered} x\text{ = }\frac{-\text{ b }\pm\sqrt[]{b^2-4ac}}{2a} \\ By\text{ substituting the values, we have} \\ x\text{ = }\frac{-\text{ 12}\pm\sqrt[]{12^2-4(5\times8)}}{2\times5}\text{ } \\ x\text{ = }\frac{-\text{ 12 }\pm\sqrt[]{144\text{ - 160}}}{10}\text{ = }\frac{-\text{ 12}\pm\sqrt[]{-\text{ 16}}}{10} \\ x\text{ = }\frac{-\text{ 12}\pm4i}{10} \\ x\text{ = }\frac{-\text{ 12 + 4i}}{10}\text{ or x = }\frac{-\text{ 12 - 4i}}{10} \\ x\text{ = }\frac{-\text{ 12}}{10}\text{ + }\frac{4i}{10}\text{ or x = }\frac{-\text{ 12}}{10}\text{ - }\frac{4i}{10} \\ x\text{ = }\frac{-\text{ 6}}{5}+\text{ }\frac{2i}{5}\text{ or x = }\frac{-6}{5}-\text{ }\frac{2i}{5} \end{gathered}[/tex]What is the approximate area of the shaded region? 6 5 3 a 2 1 X 0 1 2 3 4 5 6 O A. 3 units? B. 6 units c. 10 units D. 13 units
Area aof shaded region is
Difference of areas between square, and circle
Area of square is = (5-1)^2 = 16
Area of circle is = π•[(5-1)/2]^2 = π•2^2 = π•4
Shaded Area = 16 - (π•4) = 16 - 12.564 = 3.436
THEN option A , is the value most aproximate to 3.436
Mrs. Thompson hosts an annual art contest for kids, and she keeps a record ofthe number of entries each year.Art contest entriesYear Number of entries201128201227332013201420152735According to the table, what was the rate of change between 2013 and 2014?entries per yearSubmit
We were given a table that describes teh relationship between the year of an art contest entry, and the number of entries for that year. From these datapoints we need to calculate the rate of change between the years of 2013 and 2014.
The rate of change describes how the function is increasing or decreasing for a particular point. For our case, since the two datapoints are only one year apart, we can subtract the number of entries, and that should give us the desired result. This is done below:
[tex]\begin{gathered} \text{rate}=27-33 \\ \text{rate}=-5 \end{gathered}[/tex]The function rate of change between 2013 and 2014 was -5 entries per year.
Please help!! I keep getting crazy fractions for the one for equation of a line and for the other one I have no idea how to solve. I'll be eternally grateful!
We will find the equation of the line passes through the points:
[tex](\frac{5}{8},\frac{31}{16})and(-\frac{-5}{7},\frac{13}{14})[/tex]The general neral
Square Root Function and inverse
Answer:
[tex]f^-^1(x)=\frac{x+1}{8}[/tex]
Step-by-step explanation:
f(x) = 8x - 1
==> replace "f(x)" with y
y = 8x - 1
==> inter exchange x and y
x = 8y - 1
==> solve for y now, first step would be to add 1 to both sides
x + 1 = 8y
==> divide both sides by 8
(x+1)/8 = y
==> replace y with f^-1(x)
f^-1(x)=(x+1)/8y
Choose the graph that illustrates both g (x) andg (x+4)
Explanation:
If we have a function f(x) = g(x + c), we can say that f(x) is g(x) shifted c units to the left.
So, the graph of g(x + 4) will be the same graph of g(x) shifted 4 units to the left
Answer:
The only graph that has two functions and one if equal to the other shifted 4 units to the left is the following:
Piper works at a camera store. He is paid an hourly rate plus 16% commission on everything he sells. One week, he was paid $515 for working 20 hours and selling $1,500 worth of camera equipment. What is his hourly rate?
His hourly rate is $13.75
Here, we want to get Piper's hourly pay at work
Let the hourly rate be h
Thus, for working 20 hours, the amount for this will be; 20 * h = 20h
Now, out of the $1500 sales, he is entitled to 16%
That means;
[tex]\frac{16}{100}\times\text{ 1500 = 240}[/tex]Thus, we have it that;
[tex]\begin{gathered} 20h\text{ + 240 = 515} \\ 20h\text{ = 515-240} \\ 20h\text{ = 275} \\ h\text{ = }\frac{275}{20} \\ h\text{ = \$13.75} \end{gathered}[/tex]If 10 is increased to 15, the increase is what percent of the original number? (This is known as the percent change.)Answer = Write your resulting percent in decimal form with three decimal places of accuracy. Example: Write 2% as 0.02. Write 5.66% as 0.057.
we have the following:
[tex]\begin{gathered} \frac{10}{100}=\frac{15}{x} \\ x=\frac{100\cdot15}{10} \\ x=150 \end{gathered}[/tex]15 represents 150%, therefore:
[tex]150-100=50[/tex]The percentage with respect to the original is 50%.
[tex]\frac{50}{100}=0.5[/tex]form decimal = 0.5
14) What is the slope of the line below *
How to solve precalc logarithmic question - 50 points
The predicted value for the logarithm ㏒ ₐ 3⁴ is equal to 4 · g.
What is the predicted value associated to a logarithm in accordance with logarithm properties?
In this problem we have the definitions of three logarithms and we are asked to find the predicted value related to at least one of the logarithms described in the statement, this can be done by means of logarithm properties. Herein we proceed to use the following logarithm property related to logarithms of a power:
㏒ ₐ b = n · ㏒ ₐ bⁿ
First, define the logarithm described in the statement of the problem:
㏒ ₐ 3⁴
Second, use the logarithm property for a power in the given expression:
4 · ㏒ ₐ 3
Third, substitute the logarithm ㏒ ₐ 3 defined in the statement of the problem:
4 · g
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What is the perimeter of the figure below?34 mm40 mm88 mm96 mmI probably doing
The perimeter is the sum of the length of the sides that form a boundary of the figure.
That is
[tex]\text{ The Perimeter =}8+2+4+6+12+8[/tex]Therefore
[tex]\text{ The Perimeter =}40\text{ mm}[/tex]The perimeter is 40 mm
Solve the system using the addition method 5x-2y=32x-y=0What is the y-valueA. 3B. 6C. -3D. none of the above
First, we multiply the first equation by "2":
[tex]\begin{gathered} 2\times\lbrack5x-2y=3\rbrack \\ 10x-4y=6 \end{gathered}[/tex]Then, we multiply the second equation by "-5":
[tex]\begin{gathered} -5\times\lbrack2x-y=0\rbrack \\ -10x+5y=0 \end{gathered}[/tex]The two new equations are:
[tex]\begin{gathered} 10x-4y=6 \\ -10x+5y=0 \end{gathered}[/tex]We add both equations and solve for y. The steps are shown below:
[tex]\begin{gathered} 10x-4y=6 \\ -10x+5y=0 \\ ----------- \\ y=6 \end{gathered}[/tex]The correct answer is y = 6.
AnswerBThe quadrilateral is a kite.Find the values of x and y.х621°y
Remember that in a kite, the greater diagonal bisect the small diagonal
so
that means
x=6
Find the value of y
Remember that
the greater diagonal divide the kite into two congrient triangles
therefore
y=21 degrees
answer is
x=6
y=21 degrees
Distributive Property equation8x4=(_x_)+(_x_)
Answer:
8 x 4 = (8 x 2) + (8 x 2)
Explanation:
The distributive property says that:
a x (b + c) = (a x b) + (a x c)
Then, we can write 4 as (2 + 2), so:
8 x 4 = 8 x ( 2 + 2)
Now, we can apply the distributive property:
8 x 4 = (8 x 2) + (8 x 2)
Therefore, the answer is:
8 x 4 = (8 x 2) + (8 x 2)
Solve:y = 3xx = -2y + 70
Equation1: y = 3x
Equation 2: x = -2y + 70
To solve this system, we will use the value of x of the second equation into the fist equation:
y = 3x = 3(-2y + 70) = -6y + 210
y = -6y + 210
y + 6y = 210
7y = 210
y = 210/7 = 30
y = 30
Now, we will tusethe value of y into the second equation to find the value of x:
x = -2y + 70 = -2(30)+80 = -60 + 70 = 10
x = 10
Answer:
x = 10
y = 30
In ABCD, the measure of ZD=90°, CB = 37, BD = 12, and DC = 35. What is the valueof the sine of ZB to the nearest hundredth?
First we need to draw the triangle:
now that we have the triangle we have to remember that the sine function is defined as:
[tex]\sin \theta=\frac{\text{opp}}{\text{hyp}}[/tex]Then, in this case we have:
[tex]\begin{gathered} \sin B=\frac{35}{37} \\ \sin B=0.95 \end{gathered}[/tex]Therefore the sine of B is 0.95 to nearest hundreth
on a graph if it has (-5,5) and (5,5) is it proportional or non- proportional
A proportional graph is when y increases/decreases, if x increases. The graph shows that as x increases, the value of y stays the same, therefore it is not proportional.
I don’t understand how I’m supposed to do this problem I know it’s three times X but I got to figure out what X is this
We need to solve the following equation:
[tex]3x+9=-36[/tex]Solving an equation is the same as finding the value of x.
In order to do so, we need to apply a sequence of the same operations on both sides of the equation, until we isolate the variable x on the left side of the equation, and find its value.
First, let's isolate 3x on the left side. We need to subtract 9 from both sides:
[tex]\begin{gathered} 3x+9-9=-36-9 \\ \\ 3x+0=-45 \\ \\ 3x=-45 \end{gathered}[/tex]Now, to end with x on the left side, we need to divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=-\frac{45}{3} \\ \\ \frac{3}{3}x=-15 \\ \\ 1x=-15 \\ \\ x=-15 \end{gathered}[/tex]Answer: B) x = -15
I need help finding my equation for the question. I’m very confused
1)
The ratio of cookies to hours spent cooking = C : H
= 300 : 4
= 75 : 1
2)
How many hours does it take to bake 225 cookies
[tex]\begin{gathered} =\text{ }\frac{225}{75}\text{ } \\ =\text{ 3 hours} \end{gathered}[/tex]