Answers
4)
Given:
The vertex form is given as,
[tex]y=-\frac{1}{3}(x+6)^2-1[/tex]The objective is to convert the vertex form to standard form.
The standard form can be obtained as,
[tex]\begin{gathered} y=-\frac{1}{3}(x+6)^2-1 \\ =-\frac{1}{3}(x^2+6^2+2(x)(6))-1 \\ =-\frac{1}{3}(x^2+36+12x)-1 \\ =-\frac{x^2}{3}-\frac{36}{3}+\frac{12x}{3}-1 \\ =-\frac{x^2}{3}-12+4x-1 \\ =-\frac{x^2}{3}+4x-13 \end{gathered}[/tex]Here,
[tex]\begin{gathered} a=-\frac{1}{3} \\ b=4 \\ c=-13 \end{gathered}[/tex]Hence, the required standard form of the equation is obtained.
Related Questions
Determine the smallest integer value of x in the solution of the following inequality.3x + 4> -18
Answers
We have the following inequality:
3x + 4 > -18
Subtracting 4 from both sides we got:
3x > -22
Dividing both sides by 3 we got:
x > -22/3
Since -22/3 is between -7 and -8 and x must be equal or greater than -22/3, the smallest integer value in the solution of the inequality is -7 (note that -8 isn't part of the solution)
Based on sample data, newborn males have weights with a mean of 3242.4 g and a standard deviation of 844.4 g. Newborn females have weights with a mean of 3095.9 g and a standard deviation of 508.6 g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700 g or a female who weighs 1700 g?
Answers
The formula for calculating z score is expressed as
z = (x - μ)/s
where
x is the sample mean
μ is the mean
s is the sample standard deviation
Considering the newborn males,
x = 1700
μ = 3242.4
s = 844.4
Thus,
z = (1700 - 3242.4)/844.4
z = - 1.83
Considering the newborn females,
x = 1700
μ = 3095.9
s = 508.6
Thus,
z = (1700 - 3095.9)/508.6
z = - 2.74
The most extreme value is the z score that is furthest from zero. It is z = - 2.74. Thus, the female who weighs 1700 g is more extreme relatively
Since the z score for the male is z = - 1.83 and the z score for the female is z = - 2.74, the female has the weight that is more extreme.
Find the reference angle for a rotation of 129º.
Answers
In order to find a reference angle, we need to find the smallest possible angle formed between the x-axis and the terminal line of the given angle, going either clockwise or counterclockwise.
Since the given angle is 129°, and 90<129<180, it will look something like this:
As we can see, the reference angle will be
[tex]180-129=51[/tex]so it will be 51°.
find the volume of a right rectangular prism with the following measurements by multiplying The edge lengths. length 3/4 width 1/2 heigth 2/3
Answers
Explanation
The volume of a rectangular prism is given by:
[tex]\text{Volume}=\text{ length}\cdot width\cdot height[/tex]then,Let
length= 3/4
width=1/2
heigth=2/3
Now, replace,
[tex]\begin{gathered} \text{Volume}=\text{ length}\cdot width\cdot height \\ \text{Volume}=(\frac{3}{4}\cdot\frac{1}{2}\cdot\frac{2}{3}) \\ \text{Volume}=\frac{3\cdot1\cdot2}{4\cdot2\cdot3}=\frac{1}{4} \\ \text{Volume}=\frac{1}{4}\text{cubic units} \end{gathered}[/tex]I hope this helps you
It is equally probable that the pointer on the spinner Shown will land on any one of the eight regions number one through eight if the pointer lands on the borderline spin again. find the probability that the pointer will stop on an even number or number greater than three
Answers
SOLUTION
The even numbers here are 2, 4, 6 and 8. That is 4 numbers.
The numbers greater than 3 are 4, 5, 6, 7, and 8, that is 5 numbers.
And we have a total of 8 numbers.
Let P(A) be the probability of the pointer landing on an even number
Let P(B) be the probability of the pointer landing on a number greater than 3
Let P(A or B) be the probability that the pointer stops on an even number or number greater than three
From the probability formula,
[tex]P(\text{A or B) = P(A) + P(B) - P(A}\cap B)[/tex][tex]\text{ P(A}\cap B)\text{ means probability of A and B}[/tex]Hence
[tex]\begin{gathered} P(A)=\frac{4}{8} \\ P(B)=\frac{5}{8} \end{gathered}[/tex][tex]\begin{gathered} \text{ For P(A}\cap B)\text{ we can s}ee\text{ that betwe}en\text{ } \\ \text{the even numbers 2, 4, 6, 8 and } \\ n\text{umbers greater than 3, which are 4, 5, 6, 7, 8} \\ \text{what is common is 4, }6,\text{ 8} \\ So,\text{ } \\ \text{P(A}\cap B)=\frac{3}{8} \end{gathered}[/tex]Therefore, P(A or B) becomes
[tex]\begin{gathered} \frac{4}{8}+\frac{5}{8}-\frac{3}{8} \\ \frac{4+5-3}{8} \\ \frac{6}{8} \\ =\frac{3}{4} \end{gathered}[/tex]How many possible triangles can be created if measure of angle B equals pi over 6 comma a = 20, and b = 10?
Answers
First, we have to find the height using the following equation:
[tex]h\text{ = }b\sin (B)[/tex][tex]h\text{ = 10}\times\sin (\frac{\pi}{6})=5[/tex]We have found the height. If h < b < a, we can have only one triangle. That is the case. So the answer will be 1 triangle.
3. B 8 cm 9 cm D F 5 cm x cm A CITO 4 CM Α' ο cm D' F O 75 cm o Scale Factor: Scale Factos
Answers
Scale factor on a map
Suppose a spherical snowball is melting and the volume is decreasing at a constant rate, changing from 12 in^3/min to 10in^3/min in 30min. How fast is the radius changing when the volume is 8in^3/min? (Answer in terms of pi)
Answers
The radius changing when the volume is 8in^3/min by: -512π /30 in³ /min.
How to find the radius?First step is to find the radius changing over time at a constant rate
dr/dt = 10-12 /30
= -2/30 in/min
Now let find the how fast is the radius changing using this formula
dV/dt = 4πr²(dr/dt)
Where,
r =8
Hence,
dV/dt = 4π (8in)² × -2/30 in/min
dV/dt = 4π (64in) × -2/30 in/min
dV/dt = -512π /30 in³ /min
Therefore the change in radius is -512π /30 in³ /min.
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If there are four independent events E1, E2, E3, and E4, then the probability P(E1 and E2 and E3 and E4) equals ____________________.
Answers
Answer:
The probability of having all four events is;
[tex]P(E_1)\times P(E_2)\times P(E_3)\times P(E_4)[/tex]Explanation:
Given that there are four independent events E1,E2,E3 and E4.
[tex]E_1,E_2,E_3,E_4[/tex]The probability of having all the four events;
[tex]P(E_1-and-E_2-and-E_3-and-E_4)[/tex]would be the product of the probability of each of the events;
[tex]P(E_1-and-E_2-and-E_3-and-E_4)=P(E_1)\times P(E_2)\times P(E_3)\times P(E_4)[/tex]Therefore, the probability of having all the four events is;
[tex]P(E_1)\times P(E_2)\times P(E_3)\times P(E_4)[/tex]How do I simplify -88/4
Answers
The numbers of products a store sold on 4 consecutive days were x,x+5,x+3 and x+12. if the daily average of the products sold was 13. What is the value of x?
Answers
Answer:
x = 8
Step-by-step explanation:
average is calculated as
average = [tex]\frac{sum}{count}[/tex]
given daily average is 13 , then
[tex]\frac{x+x+5+x+3+x+12}{4}[/tex] = 13 ( multiply both sides by 4 to clear the fraction )
4x + 20 = 52 ( subtract 20 from both sides )
4x = 32 ( divide both sides by 4 )
x = 8
what value of x makes this equation true?[tex]12x - 15 = 6 - 3x[/tex]
Answers
The value of x that makes the equation true is;
[tex]x\text{ = }\frac{7}{5}[/tex]Here, we want to get the value of x that makes the equation true
All have to do here is to solve the equation for x
We have this as follows;
[tex]\begin{gathered} 12x-15\text{ = 6-3x} \\ 12x\text{ + 3x = 6 + 15} \\ 15x\text{ = 21} \\ x\text{ = }\frac{21}{15} \\ \\ \text{ x = }\frac{7}{5} \end{gathered}[/tex]kiran ran 1/5 the length of the road which is 9 miles how many miles did he run?
Answers
Answer:0.02
Step-by-step explanation:
ProbabilityHello need help Thank you. A phone number in Cameroon consists of 9 digits. From the theoretical capacity of the Cameroonian telephone network, say whether the 4 current operators (CAMTEL MTN, NEXTTEL and ORANGE) can meet a demand for 150 million subscriptions. 1) How many different ways can you arrange four people in four numbered chairs? 2)How many ways can you distribute 10 balloons to 3 children, 4 for the first and 3 for each of the other two?
Answers
Answer:
1) 24
2)66
Explanation:
1) How many different ways can you arrange four people in four numbered chairs?
Answer: we have 4 people ands 4 chairs, so we use the factorial of 4 to find the number of ways that we can arrenge the people:
[tex]4!\text{ = 4}\cdot3\cdot2\cdot1=24[/tex]we can arrange 4 people in 4 chairs in 24 different ways
2)How many ways can you distribute 10 balloons to 3 children?
To distribute "n" objects to "r" people (in this case n=10, and r = 3) we use the following combinarions formula:
[tex]C(n+r-1,r-1)[/tex]substituting our values we get:
[tex]C(10+3-1,3-1)[/tex][tex]C(12,2)[/tex]and since C(a,b) is defined as:
[tex]C(a,b)=\frac{a!}{b!(a-b)!}[/tex]For C(12,2) we get the following:
[tex]C(12,2)=\frac{12!}{2!(12-2)!}[/tex]which simplifies to:
[tex]C(12,2)=\frac{12!}{2!(10)!}=66[/tex]We can distribute 10 balloons to 3 people in 66 ways
The graph shows a relationship between two quantities.ДУ200018001600140012001000800600400200ХOd-8 -6 4-2 0 2 4Which equation best represents the relationship between the variables?
Answers
First let't find the slope
Pick any two point and locate its coordinate
(0, 1500) and (2, 1800)
x₁ = 0 y₁=1500 x₂=2 y₂=1800
substitute the values into the formula below to find the slope
[tex]\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]=\frac{1800-1500}{2-0}[/tex][tex]=\frac{300}{2}=150[/tex]The y-intercept(b) of the graph is b=1500
Substitute the values of the slope and intercept into y=mx +b
This gives the equation of the graph.
That is:
[tex]y=150x\text{ + 1500}[/tex]7 m The side lengths of the base of a triangular prism are 7 meters, 5 meters, and 8 meters. The height of the prism is 12.5 meters. 12.5 m 6 m What is the lateral surface area of the prism in square meters? 5 m
Answers
Given a triangular prism with side lengths of the base as a, b, and c, and height h, then the lateral surface area, A is given by
[tex]A=(a+b+c)h[/tex]In our case,
[tex]a=5m,b=6m,c=7m,\text{ and }h=12.5m[/tex]Hence,
[tex]A=(5+6+7)12.5=18\times12.5=225m^2[/tex]Therefore, the lateral surface area in square meters is 225
After 3 hours, they are ____ miles apart. (Round to the nearest mile as needed.)
Answers
Since Mike drove at 65 mph for 3 hours, we have that he traveled:
[tex]3\cdot65=195\text{ miles}[/tex]for Sandra, we have the following:
[tex]3\cdot70=210\text{ miles}[/tex]notice that both trajectories with the distance apart segment form a right triangle, then, using the pythagoren theorem, we get:
[tex]x=\sqrt[]{(210)^2+(195)^2}=\sqrt[]{44100+38025}=\sqrt[]{82125}\approx287\text{ miles}[/tex]therefore, Sandra and Mike are approximately 287 miles apart after 3 hours
sin(??? ) O A. O V3 ОВ. 2 Oc. O D.
Answers
The correct option is D
[tex]-\frac{1}{2}[/tex]Explanation:[tex]\sin(\frac{7\pi}{6})=-\frac{1}{2}[/tex]question number 2! I already have the answer of the number one
Answers
If we have f(x) = sin(x), then:
[tex]f(2x)=\sin2x[/tex]f(2x) = sin(2x) is a vertical shrink if we compare it with f(x) = sin(x). Then, the graph of each function is:
Every rational number is also an integer.TrueorFalse
Answers
Every rational number is also an integer.
we have that
The rational numbers include all the integers
so
the answer is truewhat does 1,580÷25=I know the answer, I need to show how I got it.
Answers
In the image below ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯∥⎯⎯⎯⎯⎯⎯⎯⎯⎯LM¯∥OP¯. Given the lines are parallel, ∠≅∠∠LMN≅∠PON because and that ∠≅∠∠LNM≅∠ONP by the , you can conclude the triangles are similar by the AA Similarity Theorem. If NP = 20, MN = x+ 6, NO = 15, and LN = 2x - 3 then x = .
Answers
Given:
Required:
We need to answer the questions
Explanation:
Angle LMN and angle PON are the congruent because both are alternate angles
Now angle LNM and angle ONP are also congruent because those two triamgles are similar and both are internal angles
Now to find the value of x
[tex]\begin{gathered} \frac{NP}{MN}=\frac{NO}{LN} \\ \\ \frac{20}{x+6}=\frac{15}{2x-3} \\ \\ 40x-60=15x+90 \\ 25x=150 \\ x=6 \end{gathered}[/tex]Final answer:
x=6
A chemist is using 328 milliliters of a solution of acid and water. If 13.7% of the solution is acid how many milliliters of acid are there? Round to nearest tenth
Answers
Hello
Let's find 13.7% of 328
[tex]\begin{gathered} \frac{13.7}{100}=\frac{x}{328} \\ x=\frac{13.7\times328}{100} \\ x=44.94 \end{gathered}[/tex]From the calculation above, 44.94mL of acid is present in the solution
5/12×6/34 pls help me
Answers
The given numerical expression can be simplified as a fraction as 5/68 .
The given expression is 5/12 × 6/34
This is a multiplication of fractions.
therefore here we will multiply the numerators and divide it by the product of the denominators.
5/12 × 6/34
or , (5×6) ÷ (12×34)
or, 30 ÷ 408
or, 5 / 68
therefore the required expression is 5 / 68
Expressions are statements in mathematics that include variables, numbers, or both, as well as at least two terms connected by an operator. Addition, subtraction, multiplication, and division are examples of mathematical operations.
Expressions can be classified into two categories in mathematics: algebraic expressions, which also contain variables, and numerical expressions, which only contain numbers. It seems like a fixed amount of money.
A variable is a symbol without a known value. One constant, one variable, or a collection of variables and constants multiplied or divided can make up a term. The coefficient in an equation is a number that is further multiplied by a variable.
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Put the following equation of a line into slope-intercept form, simplifying all
fractions.
12y-2x = 108
Answers
Answer: y= x/6+9
Step-by-step explanation:
If there are three black, four white, two blue, and four gray socks in a drawer, what would be the probability of picking a blue sock? Round your answer to the nearest tenth.15.4%25%22%15.38%
Answers
The formula for determining probability is expressed as
Probability = number of favorable outcomes/number of total outcomes
number of favorable outcomes = number of blue socks = 2
number of total outcomes = number of all socks = 3 + 4 + 2 + 4 = 13
Thus, the probability of picking a blue sock is
2/13 = 0.1538
Converting to percentage, we would multiply by 100. We have
0.1538 x 100
= 15.38%
Solve: x^3= -65 This is for homework
Answers
Step 1
Solve the equation by graphing
You can rewrite the equation as
[tex]x^3+65=0[/tex]step 2
Using a graphin calculator as Desmos
x=-4.021
The solution is x=-4.021
-
z divided by 13=28 i need the answers this is hard for me
Answers
Answer:
364
Step-by-step explanation:
z/13 = 28
z = 13 x 28
z = 364
Which of the following is a simplified version of 11 + 4(x + 3) = 10? A 4x + 4 = 10 B В 4x + 23 = 10 15x + 3 = 10 15x + 45 = 10
Answers
11 + 4(x + 3) = 10
Apply distributive property:
11+ 4(x)+4(3) = 10
11+ 4x+12 = 10
Combine like terms:
4x+11+12 = 10
4x +23 = 10
How do you figure out what the order pairs are in this equation? 2x-2=y
Answers
Equations express relationships between variables and constants. The solutions to two-variable equations consist of two values, known as ordered pairs, and written as (a, b) where "a" and "b" are real-number constants. An equation can have an infinite number of ordered pairs that make the original equation true.
Here, the given equation is,
[tex]2x-2=y[/tex]Rewriting this equation in terms of x, we have,
[tex]\begin{gathered} 2x-2=y \\ 2x=y+2 \\ x=\frac{y+2}{2} \end{gathered}[/tex]So, now creating a table, with the values, we get the ordered pair. For example, let us take x as 1, then ,
[tex]\begin{gathered} 1=\frac{y+2}{2} \\ 2=y+2 \\ y=0 \end{gathered}[/tex]So, (1,0) is an ordered pair in this equation.
If x =0,
[tex]y=0-2=-2[/tex]So the pair is, (0,-2).