Answer:
(1) B
(2) D
Step-by-step explanation:
(1)
Let the quadratic function be:
[tex]y = ax^{2} + bx + c[/tex]
For the point, (0,-1),
[tex]y = ax^{2} + bx + c[/tex]
[tex]-1=(a\times0)+(b\times0}+c\\-1=c\\c=-1[/tex]
Then the equation is:
[tex]y = ax^{2} + bx -1[/tex]
For the point (-1, -8) ,
[tex]y = ax^{2} + bx -1[/tex]
[tex]-8=(a\times (-1)^{2})+(b\times -1)-1\\-8=a-b-1\\a-b=-7...(i)[/tex]
For the point (1, 2) ,
[tex]y = ax^{2} + bx -1[/tex]
[tex]2=(a\times (1)^{2})+(b\times 1)-1\\2=a+b-1\\a+b=3...(ii)[/tex]
Add the two equations and solve for a as follows:
[tex]a-b=-7\\a+b=3\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\2a = -4\\a = -2[/tex]
Substitute a = -2 in (i) and solve for b as follows:
[tex]a-b=-7\\-2-b=-7\\b=5[/tex]
Thus, the quadratic function is:
[tex]f(x)=-2x^{2}+5x-1[/tex]
The correct option is (b).
(2)
The ordered pairs are:
(5, 7), (7, 11), (9, 14), (11, 18)
Represent them in an XY table as follows:
X : 5 | 7 | 9 | 11
Y : 7 | 11 | 14 | 18
Compute the difference between the Y values as follows:
Diff = 11 - 7 = 4
Diff = 14 - 11 = 3
Diff = 18 - 14 = 4
Now compute the difference between the Diff values:
d = 3 - 4 = -1
d = 4 - 3 = 1
Since the differences between the differences of the y-values is not consistent, the ordered pairs do not represent a quadratic equation.
The correct option is D.
when Rons truck was full, it weighed 7.5 tons. The weight he carried at that time was 3.25 tons. How many tons does Ron's truck weigh when it is empty?
7.5-3.25=4.25 tons.
The truck weights 4.25 tons.
Check with other answers, although I'm pretty sure its correct.
Heart if helpful :D
Suppose a pack of candy bars has 4 bars. Each bar weighs 5.78 ounces. How much does the pack weigh?
Answer:
23.12 ounces
Step-by-step explanation:
On a time limit answer asap pls
Answer:
160°
Step-by-step explanation:
Take notice that m∠1 and m∠2 are supplementary angles, meaning their angle measures will add up to 180°.
Since we know m∠2, we can find m∠1 easily.
180-20=160°
Hope this helped!
The table shows ordered pairs of the function. What is the value of y when? A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 1, 1, 4, 8, 10. The second column is labeled y with entries 14, 10, 6, 0, question mark, negative 12. –20 –8 8 48
I need this quick;-;
Answer:
-8
Step-by-step explanation:
i checked it out on ... and it was negative eight
Answer:
B: -8
Step-by-step explanation:
edg2021
Just plug 8 into the equation.
How many lbs. of mixed nuts that contain
37% peanuts must Ashley add to 17 lbs. of
peanuts to make a mixture with 88%
peanuts?
-Answer:
4 lbs of 37% mixed nuts
Step-by-step explanation:
[tex]\frac{\left(17+.37x\right)}{17+x}\:=\:.88[/tex]
x = 4
This rectangle has side lengths r and s.
For each expression, say whether it gives the perimeter of the rectangle, the area of the
rectangle, or neither.
1. rts
2. r.s
3. 2r + 2s
4.72 +82
Answer:
1.) Neither
2.) Area
3.) Perimeter
4.) Neither
Step-by-step explanation:
Given that the lengths of the rectangle are r and s
The perimeter of the rectangle will be:
Perimeter = 2r + 2s
Perimeter = 2(r+s)
While the area will be:
Area = r × s
Area = rs
For each expression, say whether it gives the perimeter of the rectangle, the area of the
rectangle, or neither.
1. rts = neither
2. r.s = Area of rectangle
3. 2r + 2s = Perimeter of rectangle
4.72 +82 = neither.
Select the correct answer. This set of ordered pairs defines a function. {(-49,7), (-56,8), (-63,9), (-70,10)} Which table represents the inverse of the function defined by the ordered pairs? A.
In the future, you should post all possible answer choices to have a complete post. However, there's enough information to get the answer.
The original set has points in the form (x,y)
The first point is (x,y) = (-49,7) making x = -49 and y = 7. When we find the inverse, we simply swap the x and y values. The inverse undoes the original function and vice versa. So if (-49, 7) is in the original function, then (7, -49) is in the inverse. The rest of the points follow the same pattern.
We end up with this answer
{ (7, -49), (8, -56), (9, -63), (10, -70) }
i need help anybody ?
Answer and Step-by-step explanation:
Simply use the Pythagorean Theorem to solve.
The Pythagorean Theorem is used to solve for a side in right triangles.
[tex]A^{2} +B^{2}= C^{2}[/tex]
Plug the sides values into the equation.
[tex]A^{2} + 13^2 = 20^2\\\\A^2 + 169 = 400\\\\A^2 = 231\\\\A = 15.1987[/tex]<- This is the answer.
#teamtrees #PAW (Plant And Water)
Both please please………
Answer:
Step-by-step explanation:
First one - Because it says 2 years ago, you can do 60000-4% for one year and then take the answer and - another 4% for the second year to get her income from 2 years ago. (I commented on this)
Second one - 1/3 - Take 1/6*200%=1/6*2=2/6, 2/6=1/3. So 1/3 or 2/6 of the students have a engineering major
helppppppp please I beg
Answer:2/6, 7/21, 15/45
Step-by-step explanation:
So we know that 6,21,45 are all multiples of 3
To find the numerator we have to divide each multiple by 3
so for the first one it would be 6/3 which is 2. So 2 is the numerator and the answer for the first one is 2/6
now we have to do the same method for the next fraction so we do 21/3=7
so the numerator is 7 and the fraction is 7/21
now for the last one we have to do the same method again
45/3=15 so the numerator is 15 and the answer is 15/45
You can use this method for any question like this
so the final answers are 1/3=2/6=7/21=15/45
Hope this helps
72.3 + (-39.1)
☝
Rewrite the expression by breaking up each of the place values. In this case, the place values are tens, ones, and tenths.
Answer:
72.3 - 39.1 = 4tens - 7ones + 2tenth
Step-by-step explanation:
Give the expression 72.3 + (-39.1)
opening the parenthesis:
= 72.3 + (-39.1)
= 72.3 - 39.1
Breaking the decimal values into place values
72.3 = 7tens + 2units + 3tenth
72.3 = 7(10)+2(1)+3(1/10)
72.3 =70+2+0.3
Similarly for 39.1
39.1 = 3tens + 9units + 1tenth
39.1 = 3(10)+9(1)+1(1/10)
39.1 =30+9+0.1
72.3 - 39.1 = 70+2+0.3 - (30+9+0.1)
72.3 - 39.1 = 70+2+0.3 - 30-9-0.1
72.3 - 39.1 = 70-30+2-9+0.3-0.1
72.3 - 39.1 = 40 - 7 +0.2
72.3 - 39.1 = 4tens - 7ones + 2tenth
Answer:
72.3 - 39.1 = 70 + 2 + 0.3 + (-30) +(-9) + (0.1)
Step-by-step explanation:
got it from edmentum
*This Question Has 3 Questions in it
Question 1 Use a calculator to find [tex]\sqrt{61.6}[/tex] to the nearest hundredth.
Question 2 Which of the following statements is true?
Refer to Question 2 . PNG
Question 3 simplify [tex]\sqrt{0.81}[/tex]
Answer:
Ques 1: 7.85
Ques 2: both [tex]\sqrt{0.25}[/tex] and [tex]-\sqrt{16}[/tex] are rational.
Ques 3: 0.9
Step-by-step explanation:
Ques 1:
Solving the [tex]\sqrt{61.6}[/tex], we get 7.8485.
Rounding off to nearest hundredth, we see that next digit is 8, so we increase the previous digit by 1.
So, the answer to nearest hundredth is 7.85.
Ques 2:
[tex]\sqrt{0.25}[/tex] and [tex]-\sqrt{16}[/tex]to be checked whether they are rational or irrational.
We know that [tex]\sqrt{16}[/tex] is equal to 4.
[tex]-\sqrt{16}[/tex] = -4 which is a rational value.
Let us solve [tex]\sqrt{0.25}[/tex] now.
[tex]\sqrt{0.25} = \sqrt{\dfrac{25}{100}}\\\Rightarrow \dfrac{5}{10}[/tex]
Which is a rational value.
So, both are rational.
Ques 3:
Simplify [tex]\sqrt{0.81}[/tex]
0.81 can be written as [tex]\frac{81}{100}[/tex] in rational form.
Now, taking the square root, we need to take the square root for both Numerator and Denominator and then we can divide to get the desired square root.
[tex]\sqrt{0.81} = \sqrt{\dfrac{81}{100}}\\\Rightarrow \dfrac{9}{10} = \bold{0.9}[/tex]
So, the answers are:
Ques 1: 7.85
Ques 2: both [tex]\sqrt{0.25}[/tex] and [tex]-\sqrt{16}[/tex] are rational.
Ques 3: 0.9
solve for the value of C
Answer:
Step-by-step explanation:
8. Which expression is greatest? Justify your answer.
a. 4 X -5
b. -5 + 4
c. -4- (-5)
Answer:
c
Step-by-step explanation:
i think this is the greatest because if you solve all of the expressions you will find out that this is the greatest.
a.4×-5=-20
b.-5+4=-1
c.-4-(-5)=1
therefore 1 is the greatest so the expression c is the greatest.
I hope this helps
i  genuinely dont know help
Answer:
-13 1/2 < -6/8
Step-by-step explanation:
*Any negative in either the numerator or denominator will make the entire fraction negative.
1/2 = .5
-13 1/2 = -13.5
-6/8 = -3/4
-3/4 = -0.75
-6/8 = -0.75
-13 1/2 = -13.5
Which means:
-13 1/2 < -6/8
Hope this helped.
Answer:
[tex] < [/tex]
Step-by-step explanation:
[tex] \frac{6}{8} [/tex]
Is close to 0 (to positive) you can use a time line to determine which is a correct answer
Which relation is also a function?
{ (1,0), (2,2), (1,3) }
{ (1, 2), (1, 4), (2, 6) }
{ (2, 1), (2, 2), (2, 3) }
{ (0, 0), (4, 0), (6, 0) }
Answer:
{ (0, 0), (4, 0), (6, 0) }
Step-by-step explanation:
In order to be a function, ordered pairs must have values of x, or the domain, that are different and do not repeat.
Which value of x satisfies the equation
Answer:
x=6
Step-by-step explanation:
(0.6)(x-1.5)=2.7
(x-1.5)=4.5
x=6
What is the area of the trapezoid shown below?
Answer:
180 units
Step-by-step explanation:
In order to solve this, we need to find the length of the missing side of the triangle using the Pythagorean theorem.
a²+b²=c²
a= 7
b=x
c= 25
7²+x²=25²
49+x²=625
Subtract 49 from both sides
x²=576
x=24
The length of the missing side of the triangle is 24, which is also the base of the triangle. We need to find the area of the triangle so we use the formula for the area of a triangle, A=1/2bh.
A= 1/2 (24 x 7)
A=84
Now, we need to find the area of the rectangle.
Formula for area of rectangle: A= bh
A= bh
A= 4 x 24
A= 96
Next, we add the areas of both shapes to get the area of the entire figure.
96+84=180
Area of figure= 180
Answer:
area = 180
Step-by-step explanation:
will make it simple and short
area of a trapezoid = (a + b) h/2
h = sqrt(25² - 7²) = 24
Area = (4 + 11) * 24/2
area = 180
#3 1/3x = 15 Find value of X
Answer:
x = 45
Step-by-step explanation:
1/3x = 15 (Given)
3(1/3x) = 15(3) (Multiply 3 on both sides)
x = 45 (Simplify)
Answer:
45
Step-by-step explanation:
1/3x = 15
Multiplying 3 on both sides,
3(1/3x) = 15(3)
x = 15 x 3
x = 45
The sum of the ages of Noi's and Noy's is 26 years. The different between four times Noi's age and two times Noy's age is 28 years. Find the age of Noi and Noy.
WRITE AS AN EQUATION
Answer:
The age of Noi is 13.333 Years and the age of Noy is 12.67 years
Step-by-step explanation:
The given information are;
The sum of the ages of Noi and Noy = 26 years
Four times Noi's age - Two times Noy's age = 28
Let the age of Noi = X and let the age of Noy = Y
We have;
X + Y = 26 years.................(1)
4X - 2Y = 28 years.............(2)
Divide equation (2) by 2 to get;
(4X - 2Y)/2 = (28 years)/2 which gives;
2X - Y = 14 years.................(3)
Add equation (3) to equation (1), to get;
X + Y + 2X - Y = 26 years + 14 years
3X = 40 years
X = 40/3 = 13.333 Years
From equation (1), X + Y = 26 years, therefore;
Y = 26 - X = 26 - 13.33 = 12.67 years
Therefore, the age of Noi = 13.333 Years and the age of Noy = 12.67 years.
(4*10^4)+(6*10^2) Standard form
Answer:
40600
Step-by-step explanation:
(4 * 10^4) + (6 * 10^2) =
= 4 * 10000 + 6 * 100
= 40000 + 600
= 40600
Answer:
4.06 x 10^4
Step-by-step explanation:
I need help comrades, I will give you 5 stars and A big thank you comrades
Answer:
dicontinuity at (-4.-2)zero at (-2.0)
Step-by-step explanation:
answer c
this shoud be correct
Look at this cube
If the side lengths are halved, then which of the following statements about its surface area will be true?
Answer:
all of them
Step-by-step explanation:
Algunos granos de maíz al ser calentados revientan y pierden agua de manera explosiva.
En promedio se puede considerar que tienen una masa de 125 mg y cuando explotan (palomitas
de maíz) su masa es de 106 mg. ¿Cuántos granos de maíz pira se requerirán para obtener una
libra de palomitas de maíz?
Answer:
Step-by-step explanation:
4280 granos de maíz pira se requerirán para obtener una libra de palomitas de maíz.
CálculoDado que algunos granos de maíz al ser calentados revientan y pierden agua de manera explosiva, y en promedio se puede considerar que tienen una masa de 125 mg y cuando explotan (palomitas de maíz) su masa es de 106 mg, para determinar cuántos granos de maíz pira se requerirán para obtener una libra de palomitas de maíz se debe realizar el siguiente cálculo:
453592 mg = 1 lb453592 / 106 = X4279.16 = XPor lo tanto, 4280 granos de maíz pira se requerirán para obtener una libra de palomitas de maíz.
Aprende más sobre cálculo en https://brainly.com/question/2193984
Plz help me out with this ;)
The U.S. swim team won 13 gold medals in a recent competition against two other countries.Of the total 60 medals awarded, there were 20 each of bronze, silver, and gold. Spain won 5gold medals. France won one-third of all the medals and had an equal number of silver andbronze medals. How many silver and bronze medals did France win?
The number of silver and bronze medals that France won are 9 silver and bronze medals.
Since there are 60 medals awarded, and there were 20 each of bronze, silver, and gold. This means that there are 20 gold, 20 bronze and 20 silver.
Since U.S. swim team won 13 gold medals and Spain won 5gold medals, then the gold won by France will be:
= 20 - (13 + 5)
= 20 - 18
= 2 gold medals
France won 2 gold medals.
Since France won one-third of all the medals, the number of medals won by France will be:
= 1/3 × 60
= 20 medals
Since France won 2 golds medals, then the number of silver and bronze will be:
= 20 - 2
= 18 silver and bronze medals.
Since France won equal number of silver and bronze medals. This will be:
= 18/2
= 9 silver and bronze medals.
Read related link on:
https://brainly.com/question/19972449
Factorize
4a^2-24a^2b^2+9b^2
PLZ HELP!!!!!!!!!!!!!! WILL MARK BBRAINLIST
Answer:
B. The second choice.
Step-by-step explanation:
A function cannot have two points with the same x-coordinate.
If you graph two different points that have the same x-coordinate, they will both lie on the same vertical line. Therefore, if in a relation, more than one point lie on the same vertical line, then the relation is not a function.
Please solve the problem
Treat the matrices on the right side of each equation like you would a constant.
Let 2X + Y = A and 3X - 4Y = B.
Then you can eliminate Y by taking the sum
4A + B = 4 (2X + Y) + (3X - 4Y) = 11X
==> X = (4A + B)/11
Similarly, you can eliminate X by using
-3A + 2B = -3 (2X + Y) + 2 (3X - 4Y) = -11Y
==> Y = (3A - 2B)/11
It follows that
[tex]X=\dfrac4{11}\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\dfrac1{11}\begin{bmatrix}7&-10\\-7&11\end{bmatrix} \\\\ X=\dfrac1{11}\left(4\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\left(\begin{bmatrix}48&-12\\40&88\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\begin{bmatrix}55&-22\\33&99\end{bmatrix} \\\\ X=\begin{bmatrix}5&-2\\3&9\end{bmatrix}[/tex]
Similarly, you would find
[tex]Y=\begin{bmatrix}2&1\\4&4\end{bmatrix}[/tex]
You can solve the second system in the same fashion. You would end up with
[tex]P=\begin{bmatrix}2&-3\\0&1\end{bmatrix} \text{ and } Q=\begin{bmatrix}1&2\\3&-1\end{bmatrix}[/tex]
Step-by-step explanation:
hence it has been done . check the file .
hope this helped you
any problem then comment it .
7(8+a)=189 please help and give me step by step
Answer: a = 19
Step-by-step explanation:
Given
7 (8 + a) = 189
Divide 7 on both sides
7 (8 + a) / 7 = 189 / 7
8 + a = 27
Subtract 8 on both sides
8 + a - 8 = 27 - 8
a = 19
Hope this helps!! :)
Please let me know if you have any questions