Answers
y = a(x -h)² +k . . . . . . . . for some stretch factor "a" and vertex (h, k)
1. Vertex = (h, k) = (0, 0). Stretch factor can be found from the given point (x, y).
8 = a(-2 -0)² +0
8 = 4a . . . . . . . . simplify
2 = a . . . . . . . . . divide by the coefficient of "a"
Your equation is y = 2x².
Note the above method for solving these problems. It repeats.
2. As above, substitute what's given and solve for what's not.
3 = a(1 -2)² +0
3 = a
Your equation is y = 3(x -2)²
3. Repeat
-4 = a(-5 +3)² +0
-4 = 4a
-1 = a
Your equation is y = -(x +3)²
4. Are you seeing the pattern yet?
0 = a(-1 -0)² +1
0 = a +1
-1 = a
Your equation is y = -x² +1
5 & 6. You know that if you want a zero (x-intercept) to be located at x=a, then a factor of the quadratic will be (x -a). Multiply the factors together to get your quadratic function.
5. y = (x -0)*(x -2) = x² -2x
6. y = (x +5)*(x -5) = x² -25 . . . . . . . . . . you should recognize this "special form", the factoring of the difference of squares
Related Questions
If a family has three children draw a tree diagram representing the possible outcomes for the genders of the children and then list the sample space
Answers
Order the group of quadratic functions from widest to narrowest graph. y = 6x2, y = −4.5x2, y = −x2
Answers
[tex] y=ax^{2}+bx+c [/tex]
Where [tex]a [/tex] is the leading coefficient.
If the leading coeficient is closer to zero, the parabola is widest,if it has a larger positive or negative value, the parabola is narrowest.
Therefore, by knowing the information above, you have that the answer is:
[tex]y=- x^{2} \\ y=-4.5 x^{2} \\ y=6 x^{2} [/tex]
y = 6x2, y = −4.5x2, y = −x2
This should be correct answer:) He got it mixed up in his answer below when graphing.:)
Help please on properties of exponents? will give a medal!
A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle.
a. 3 to the 2 over 3 power inches squared
b. 3 to the 8 over 3 power inches squared
c. 9 inches squared
d.9 to the 2 over 3 power inches squared
2.)Explain how the Quotient of Powers was used to simplify this expression.
2 to the fifth power, over 8 = 2 to the 2nd power
a.By finding the quotient of the bases to be one fourth and cancelling common factors
b. By finding the quotient of the bases to be one fourth and simplifying the expression
c. By simplifying 8 to 23 to make both powers base two and subtracting the exponents
d. By simplifying 8 to 23 to make both powers base two and adding the exponents
3.)the cube root of 2 to the seventh power
a. 2 to the 3 over 7 power
b. 2 to the 7 over 3 power
c. 2^21
d. 2^4,
Answers
1) c. 9 inches squared
2) c. By simplifying 8 to 23 to make both powers base two and subtracting the exponents
3) b. 2 to the 7 over 3 power
Explanation.
Question 1
The area of a rectangle is given by
area=l×w
=〖81〗^(1/3)×3^(2/3)
3^(4/3)×3^(2/3)=3^(4/3+2/3)
=3^(6/3)=3^2=9 inches squared
Question 2
Finding the 2^5/8=2^2
The steps for finding this is first to write 8 as 23. Then divide.
2^5/8=2^5/2^3
When dividing exponents with the same base you subtract the powers.
=2^(5-3)=2^2
Question 3
The question wants us to solve, ∛(3^7 ).the cube root of a number can be written as a power of a third.
So,
∛(3^7 )=3^(7×1/3 )
=3^(7/3)
Ques 1)
Option: C is the correct answer.
c. 9 inches square.
Ques 2)
Option: c
c. By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents.
Ques 3)
Option: b
b. 2 to the 7 over 3 power
Step-by-step explanation:Ques 1)
A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches.
i.e. let 'l' and 'b' denote the length and width of the rectangle.
i.e.[tex]l=\sqrt[3]{81}\\\\l=(3^4)^{\dfrac{1}{3}}\\\\l=3^{\dfrac{4}{3}[/tex]
since,
[tex](a^m)^n=a^{mn}[/tex]
and
[tex]w=3^{\dfrac{2}{3}}[/tex]
Hence, the area of rectangle is given by:
[tex]Area=l\times w\\\\\\Area=3^{\dfrac{1}{3}}\times3^{\dfrac{4}{3}}\\\\\\Area=3^({\dfrac{1}{3}+\dfrac{4}{3}})\\\\\\Area=3^{\dfrac{6}{3}}\\\\\\Area=3^2\\\\\\Area=9\ square\ inches[/tex]
As we know that:
[tex]a^m\times a^n=a^{m+n}[/tex]
Hence, Area=9 square inches.
Ques 2)
2 to the fifth power, over 8 = 2 to the 2nd power
i.e. we need to prove that:
[tex]\dfrac{2^5}{8}=2^2[/tex]
As we know that:
[tex]\dfrac{2^5}{8}=\dfrac{2^5}{2^3}=2^{5-3}=2^2[/tex]
( since
[tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex] )
Hence, the correct answer is: Option: c
Ques 3)
The cube root of 2 to the seventh power.
i.e.
[tex]\sqrt[3]{2^7}\\\\=(2^7)^{\dfrac{1}{3}}\\\\=2^{\dfrac{7}{3}}[/tex]
Since,
[tex]\sqrt[n]{x}=x^{\dfrac{1}{n}}[/tex]
and
[tex](a^m)^n=a^{mn}[/tex]
Hence, the correct answer is: option: b
why is 5 a rational number?
Answers
5 is a rational number because it can be expressed as the quotient of two integers: 5÷ 1
Hope this helps!! ;))
Have a grat day!! <3
If AB is a tangent then point b must be the point of tangency true or false
Answers
Moa finished 60% of her homework in 45 minutes how many minutes does it take her to do the whole thing
Answers
The whole homework is 100%.
The total amount of time it will take Moa to finish the homework will be given by:
100/60×45
=75 min
=1 hour 15 min
Will give brainliest answer!!
Answers
5:8
Explanation:
First, we will compute the ratio between the two volumes as follows:
1000 / 4096 = 125 / 512
which is equivalent to 125 : 512
Then, we will get the cubic root of the ratio. This is because volume of cube is computed by cubing its side length.
Therefore, similarity ratio iR³ will be:
125 : 512
(5)³ : (8)³
5 : 8
Hope this helps :)
**NEED HELP!!!
Bo’s gross annual income is $45,408. He is paid semimonthly and has 6% deducted from his paychecks for his 403(b). His employer matches his deduction, up to 3%.
How much is deposited into Bo’s 403(b) each payday?
Answers
Answer:
170.28
Step-by-step explanation:
I just took the test and am reviewing the correct answers.
HELP:
Whic reformer was not a journalist who investigated corruption in business or government?
(Points : 3)
Ray Stannard Baker
Upton Sinclair
Lincoln Steffens
William Booth
i wend with D
Answers
Use the equation and type the ordered-pairs.
y = 3^x
(-1,__), (0,__), (1,__), (2,__), (3,__), (4,__)
Answers
Answer: [tex](-1,\frac{1}{3}),\ (0,1),\ (1,3),\ (2,9),\ (3,27),\ (4,81)[/tex]
Step-by-step explanation:
The given exponential function :
[tex]y=3^x[/tex]
At x = -1, we get
[tex]y=3^{-1}=\dfrac{1}{3}[/tex]
At x = 0, we get
[tex]y=3^{0}=1[/tex]
At x = 1, we get
[tex]y=3^{1}=3[/tex]
At x = 2, we get
[tex]y=3^{2}=9[/tex]
At x = 3, we get
[tex]y=3^{3}=27[/tex]
At x = 4, we get
[tex]y=3^{4}=81[/tex]
Hence, the completed ordered pairs are : [tex](-1,\frac{1}{3}),\ (0,1),\ (1,3),\ (2,9),\ (3,27),\ (4,81)[/tex]
Look Ray 0.45 hour to rake the leaves and 3/4 hour to mow the lawn how many minutes did it take him to do both tasks
Answers
0.75*60=45
27+45=72
The answer is 72 minutes
Find m∠A given ΔABC where a=4, b=6, c=3.
Answers
The law of cosines is the following equation:
[tex]a^2=b^2+c^2-2(b)(c) \cos(A)[/tex]
We know the values of a, b, and c. We want to find the measure of angle A.
[tex]a=4[/tex]
[tex]b=6[/tex]
[tex]c=3[/tex]
Now, plug in these values into the equation.
[tex]4^2=6^2+3^2-2(3)(6) \cos(A)[/tex]
[tex]16=45-36 \cos(A)[/tex]
Add both sides by [tex]36 \cos(A)[/tex] and subtract both sides by 16
[tex]36 \cos(A)=29[/tex]
Divide both sides by 36
[tex]\cos(A)= \dfrac{29}{36}[/tex]
Take the inverse cosine, or arc cosine, of both sides.
Using a calculator, you'll get the following result.
[tex]A \approx 36.3^O[/tex]
The measure of angle A should be 36.3 degrees. Hope this helps! :)
Find two numbers that multiply to make the first number and add to make the second number. (I understand how to do it, I’m just having some issues. It’s not registering.)
Answers
x-----------> the first number
y-----------> the second number
we know that
x*y=x-----------> y=x/x----------> y=1
and x+y=y------> x=y-y---------> x=0
the answer is
the first number is 0
the second number is 1
The student's question pertains to solving a system of equations to find two numbers that multiply to a given product and add to a given sum. The solution involves testing pairs of factors of the product until the pair that also sums to the required number is found, for example, finding that 3 and 8 multiply to 24 and add to 11.
The student is looking to solve a classic problem in algebra: finding two numbers that, when multiplied together, result in a given number (the product), and when added together, sum to another given number (the sum). This is often related to factoring a quadratic equation or finding the roots of a polynomial. The solution involves setting up a system of equations based on the given conditions and solving for the two unknown numbers. This process typically requires identifying the correct pair of numbers that satisfy both the multiplication and addition conditions. Let's take an example:
Suppose we need to find two numbers that multiply to make 24 and add to make 11. We can denote these numbers as x and y, leading to the following equations:
x . y = 24 (multiplication condition)x + y = 11 (addition condition)By systematically testing pairs of factors of 24 (e.g., 1 and 24, 2 and 12, 3 and 8, 4 and 6), we find that 3 and 8 satisfy both conditions, because 3 . 8 = 24 and 3 + 8 = 11. Therefore, the two numbers are 3 and 8.
Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º. Scarlett's height is 1.65 meters, so the height of the dam is meters. NextReset
Answers
h = x + 1.65 m,
where:
x = 90 m · tan 26°
x = 90 · 0.4877
x = 43.90
h = 43.90 m + 1.65 m = 45.55 m
Answer:
The height of the dam is 45.5 m.
Answer:
The height of dam =45.5 m.
Step-by-step explanation:
We are given that Scarlett stands 90 m away from the dam and records the angle of elevation to the top of the dam to be [tex]26^{\circ}p[/tex]
Scarelett's height is 1.65 meters.
We have to find the height of the dam.
Let h be the height of dam
AC=AB+BC
BC=x
h=1.65+x
CD=EB=90 m
In triangle ABE
[tex]\theta=26^{\circ}[/tex]
[tex]tan\theta=\frac{perpendicular\;side}{Base}[/tex]
[tex]tan26^{\circ}=\frac{AB}{90}[/tex]
[tex]0.4877=\frac{x}{90}[/tex]
[tex]x=0.4877\times 90[/tex]
[tex]x=43.893 m[/tex]
Therefore, the height of dam=1.65+43.893=45.543 m
Answer: The height of dam =45.5 m
Andrew has a coupon for $2.80 puppy treats. One bag of treats usually costs $9.94 and contains 42 of the treats. If Andrew uses his coupon what will be the price per puppy treats
Answers
1. The regular price for a bag of treats $9.94
2. There are 42 treats in a box
3. The coupon worths $2.80
In order to find out how much it would be per puppy treats
You will have to do the following steps:
Step1 find out how much it would be after the discount:
Regular price 9.94 － The worth of the coupon 2.80 = $7.14
Now know how much it would be after the discount we'll have to find out how much it would be per puppy treat.
Step2 dividing the # of treats and the price after discount
The discount price 7.14 / The amount of treats per bag 42 = $0.17 per treat
So it would be $0.17 for each treat.
Hope this helps!
Andrew's price per puppy treat, after using a $2.80 coupon on a $9.94 bag that contains 42 treats, will be $0.17.
Andrew has a coupon that will reduce the price of puppy treats. Without the coupon, one bag of treats costs $9.94 and contains 42 treats. To find the price per treat after using the $2.80 coupon, we first subtract the coupon value from the original price of the bag. This gives us the discounted price of the bag:
Discounted Price = Original Price - Coupon Value = $9.94 - $2.80 = $7.14
Next, we find the price per treat by dividing the discounted price of the bag by the number of treats in the bag:
Price per Treat = Discounted Price ÷ Number of Treats = $7.14 ÷ 42 = $0.17 (rounded to two decimal places)
After using the coupon, the price per puppy treat will be $0.17.
A population has size 25 at time t = 0, with t measured in years. (a) if the population decreases by 4 people per year, find a function for the population size, p, at time t. enter your answer as an equation with p on the left side, and an expression involving t on the right
Answers
p = population
t: time in years
The equation that best fits this problem is a linear equation of the form:
p = -4t + 25
Note that for t = 0 the value of p is 25, which represents the initial population.
Answer:
a function for the population size, p, at time t is:
p = -4t + 25
The sum of two numbers is 58 . the smaller number is 10 less than the larger number. what are the numbers?
Answers
X-Y=18 ADD
----------------
2X=76
X=76/2
X=38 ANS. FOR THE LARGER NUMBER.
38+Y=58
Y=58-38
Y=20 ANS. FOR THE SMALLER NUMBER.
PROOF:
38-20=18
18=18
In the previous problem, Ken predicted a drop in temperature. Explain why a drop in temperature would lead to adding a negative integer.
Answers
Answer:
Because a drop in temperature means decrease in temperature therefore, we take an integer with negative sign and added to previous temperature.
Step-by-step explanation:
Drop in temperature means decrease in the temperature .When the temperature decreases then we take decrease value of temperature in negative integer. Because decrease means the temperature fall down .Hence , the decrease in temperature measure with negative sign .
For example, if we take temperature T= 70°C.
If the temperature decreases by 5°c then the temperature
Decrease in temperature=-5°C
Hence, the temperature T= 70+(-5)=65°C.
Therefore , from example we can say that when temperature decreases by some value in integer . Then ,we get final temperature obtained by adding drop in temperature ( negative integer ) in previous value of the temperature.
1. Add or subtract.
a. (x^2 - 4 x + 5) + (7x^2 + 2x + 3)
b. (7x^2 + 4x - 6) - (2x^2 - 3x + 1)
Answers
1a.
Answer is 8x² - 2x + 8
(x² - 4x + 5) + (7x² + 2x + 3)
The parentheses can go away since this is all addition (associative property of addition)
x² - 4 x + 5 + 7x² + 2x + 3
Combine like terms.
(x^2 + 7x²) + (-4x + 2x) + (5 + 3) = 8x² - 2x + 8
======
1b.
Answer is 5x^2 + 7x - 7
(7x² + 4x - 6) - (2x² - 3x + 1)
Distribute the negative into the right parentheses.
(7x² + 4x - 6) - (2x² - 3x + 1)
= 7x² + 4x - 6 - 2x² + 3x - 1
= (7x² - 2x²) + (4x + 3x) + (-6 - 1)
= 5x^2 + 7x - 7
Which net matches the figure?
Answers
help please
integral of sqrt (x^2+6x) dx
Answers
Because this is not an integration with specific bounds, you must include a constant at the end. In general, to integrate, add 1 to the exponent of x and then whatever number is the exponent of x, divided the number in front of x by that.
1) when to use the median to describe the measure of center of a data set, 2) what measures of spread can we find when using box-plots, 3) what measure of spread is most appropriate to describe symmetrical data sets, 4) how does an outlier affect the mean of data set and give an example,
Answers
2) Using a box plot, you can find the range and interquartile range. The range is the distance from the smallest number to the largest. The interquartile range is the distance from the first quartile to the third quartile. All these values are found on a box plot.
3)The best measure of spread to describe symmetrical data sets is the mean absolute deviation. This tells us how far on average the numbers are spread out from the mean.
4) See the answer given in #1 for the explanation. An example would be a student who scores 8, 9, 10, 9, 10, 2 on 6 quizzes. The mean would be an average of 8, which is not a good number to represent the score this student normally gets. The median of 9 is a better number to show how this student normally performs.
Answer:
what the dude above me put he wrong
Step-by-step explanation:
MATH HELP PLEASE WILL GIVE BRAINLIEST!!!
This figure shows circle A with inscribed ∠RSQ .
m∠RSQ=24°
What is the measure of RSQ?
Answers
For a better understanding of the solution and the explanation given here please go through the diagram in the file attached.
By definition, measure of an arc is the angle subtended by the arc at the centre of the circle. Thus, the measure of the arc [tex] \overarc {RSQ} [/tex] is the measure of the [tex] \angle RAQ [/tex] (in red) which the arc [tex] \overarc {RSQ} [/tex] subtends at the center.
Now, in order to find the measure of the [tex] \angle RAQ [/tex] (in red) we will have to use the information given in the question. We have been told that [tex] m\angle RSQ=24^{\circ} [/tex]. Now, we know that the double angle theorem says that, the angle subtended at the centre of a circle is double the size of the angle subtended at the circumference from the same two points. Therefore, applying this theorem we get:
[tex] \angle RAQ =2\times 24^{\circ}=48^{\circ} [/tex]
Thus if [tex] \angle RAQ [/tex] (in red)=[tex] 48^{\circ} [/tex], then [tex] \angle RAQ [/tex] (in green) will be equal to measure of the arc [tex] \overarc {RSQ} [/tex]. Now, [tex] \angle RAQ [/tex] (in green) will obviously be:
[tex] \angle RAQ [/tex] (in green)=[tex] 360^{\circ}-\angle RAQ [/tex] (in red)
[tex] \angle RAQ [/tex] (in green)=[tex] 360^{\circ}-48^{\circ} [/tex]
[tex] \angle RAQ [/tex] (in green)=[tex] 312^{\circ} [/tex]
Thus, the measure of arc [tex] \overarc {RSQ} [/tex]=[tex] 312^{\circ} [/tex]
Tyler is 9 years old his sister Olivia is 6 years less than twice his age writ a numerical expression for Olivia’s age
Answers
The following will show you
T = tyler
O = olivia
O = 2t - 6
when you include numbers, it is represented by:
O = (2 * 9) - 6
Now, let's solve this to find out just how old Olivia is.
2 * 9 = 18
18 - 6 = 12
Olivia is 12
This means that olivia is 3 years older than tyler
I hope I helped!
~ Fire
John rolls a number cube twice. What is the probability that the sum of the 2 rolls is less than 7, given that the first roll is a 1?
one over six
one over three
one over two
five over six
Answers
There are 6 ways we can roll two dice and have the first number be a 1:
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
Out of these, 5 possibilities give us a sum less than 7:
1, 1
1, 2
1, 3
1, 4
1, 5
Thus we have 5/6.
Answer: The correct option is (d) five over six.
Step-by-step explanation: Given that John rolls a number cube twice. We are to find the probability that the sum of the 2 rolls is less than 8 given that he first roll is a 1.
The sample space of an event of rolling a cube is
S = {1, 2, 3, 4, 5, 6}.
That is, n(S) = 6.
Now, let 'A' be the event that the sum of the two rolls is less than 7, then
A = {1, 2, 3, 4, 5}.
That is, n(A) = 5.
So, the probability of happening of event A is given by
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{5}{6}.[/tex]
Thus, the required probability is five over six.
Option (d) is correct.
What are the zeros of the quadratic function f(x) = 8x2 – 16x – 15? x = –1 – and x = –1 + x = –1 – and x = –1 + x = 1 – and x = 1 + x = 1 – and x = 1 +
Answers
To find the zeros of the quadratic function [tex]\( f(x) = 8x^2 - 16x - 15 \)[/tex], you need to solve for [tex]\( x \) when \( f(x) = 0 \)[/tex].
So, you set \( f(x) \) equal to zero:
[tex]\[ 8x^2 - 16x - 15 = 0 \][/tex]
To solve this quadratic equation, you can use the quadratic formula:
[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \]where \( a = 8 \), \( b = -16 \), and \( c = -15 \).[/tex]
Plugging these values into the quadratic formula:
[tex]\[ x = \frac{{-(-16) \pm \sqrt{{(-16)^2 - 4(8)(-15)}}}}{{2(8)}} \]\[ x = \frac{{16 \pm \sqrt{{256 + 480}}}}{{16}} \]\[ x = \frac{{16 \pm \sqrt{{736}}}}{{16}} \][/tex]
Now, you simplify the expression under the square root:
[tex]\[ \sqrt{736} = \sqrt{16 \times 46} = 4\sqrt{46} \][/tex]
So, the expression becomes:
[tex]\[ x = \frac{{16 \pm 4\sqrt{46}}}{{16}} \][/tex]
Now, you can simplify further:
[tex]\[ x = \frac{{4(4 \pm \sqrt{46})}}{{4 \times 4}} \]\[ x = \frac{{4 \pm \sqrt{46}}}{{4}} \][/tex]
This gives you two solutions:
[tex]\[ x = \frac{{4 + \sqrt{46}}}{{4}} \]\[ x = \frac{{4 - \sqrt{46}}}{{4}} \][/tex]
These are the zeros of the quadratic function [tex]\( f(x) = 8x^2 - 16x - 15 \).[/tex]
Complete question :
What are the zeros of the quadratic function f(x) = 8x2 - 16x - 15?
plz help me on this question
Answers
So the answer is:
g(x) = f(x) - 2
(B)
A cube has a volume of 27 squared feet. What is the length of each side?
Answers
The formula for volume of a cube is [tex]V= a^{3} [/tex]; you are given the volume, so plug it into the formula for [tex]V[/tex].
[tex]V= a^{3} [/tex]
[tex]27= a^{3} [/tex]
Take the cube root of each side:
[tex]27= a^{3} [/tex]
[tex] \sqrt[3]{27} = a^{3} [/tex]
[tex]3=a[/tex]
Answer:
The length of each side is 3 cubic feet.
a=v^1/5=27^1/5=3
to checking your answer
v=a^3
3^3
27
the answer for your question is 3
x/10=2/4?
or x over 10
equals to 2 over 4
Answers
_______________________________________________
Note the following:
_______________________________________________
2/4 = 1/2 ;
1/2 = (1*5) / (2*5) = 5/10 ;
2/4 = 1/2 = 5 / 10 .
or: 2/4 = 1/2 = 0.5 = 5/ 10 .
The answer: " x = 5 " .
___________________
Or: x/ 10 = 2/4 ;
Cross-multiply:
4x = (2)(10) ;
4x = 20 ;
Divide each side by "4" ;
4x / 4 = 20/4 ;
" x = 5 " ;
_____________________
Or: x/10 = 2/4 ;
Note: "2/4 = 1/2" ; so rewrite as:
x/10 = 1/2 ; and cross-multiply:
2x = (10)(1) ;
2x = 10 ;
Divide each side of the equation by "2" ;
2x / 2 = 10 / 2 ;
" x = 5 " .
______________________________________
What is the simplified form of (3 / x^3) / (1 / x^2) ?