Which of the following is the quadratic parent function?
A. F(x) = x + 1
B. F(x) = Ixl
C. F(x)=x²
D. F(x) = 2x
Answer:
C
Step-by-step explanation:
A quadratic has to have an exponent of 2 somewhere. The only one of these functions that does is C
The quadratic parent function is f ( x ) = x²
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
f ( x ) = x²
The graph of the function f(x) = x² is a parabola that opens upward, symmetric with respect to the y-axis, and its vertex is at the origin (0, 0)
Now , the value of y is the square of x
Hence , the parent function is f ( x ) = x² and graph is plotted
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una cuerda al vibrar tiene una frecuencia fundamental de 200 Hz. Si su longitud se reduce en una cuarta parte, ¿cual será la nueva frecuencia fundamental? ¿se ha alterado la rapidez de la onda al acortar la cuerda? Suponga que la tensión es constante
I thank the answer is B
Step-by-step explanation:
10
The two-way table below shows the number of students in a school who like mathematics and/or physics: Like Mathematics Do Not Like Mathematics Total Like Physics 15 20 35 Do Not Like Physics 5 25 30 Total 20 45 65 How many more students like physics than mathematics? 10 15 20 25
The number of students like physics more than mathematics is 15 , Option B is the correct answer.
What is a Number ?A mathematical way of expressing quantity of a substance is called a Number.
Number of students in a school who like mathematics = 20
Number of students in a school who like physics = 35
number of students in a school who like only physics is 20
number of students who like only Mathematics is 5
the number of students like physics more than mathematics is 20-5 = 15
Therefore Option B is the correct answer.
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Which expressions are equivalent to the one below? Check all that apply.log(10^7)
The value of expression is 7.
What is expression?An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
Given:
[tex]log 10^{7}[/tex]
Now, using property of log
[tex]log b^{a} =[/tex] a log b
So,
[tex]log 10^{7}[/tex]= 7 log 10
As log 10 = 1
[tex]log 10^{7}[/tex]= 7 (1)
[tex]log 10^{7}[/tex]= 7
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Help!! Please and thank you!
It is clear that T lies on the perpendicular bisector of NP. See the explanation below.
Given that M (X,Y) is the midpoint of NP
X thus = (5+1)/2
= 3
Y = (7+1)/2
= 4
Hence, we have M (3,4)
Consequent on the above:
Slope TM (m') = (4-2) / (3-6) = - 2/3
Slope of NP (m) = (7-1) / (5-1) = 6/4 = 3/2
M' = -1/m
Hence
TM ⊥ NP; and NP ⊥ TM
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If the sales tax on a $825 television set is 7%, how much will you pay in total?
Answer:
$882.75
Step-by-step explanation:
825 x 7% = 57.75 <- thats the price of the tax
57.75 + 825 = 882.75
debbie is a cook in a restaurant that is open 6 days a week. she is responsible for recording and monitoring the amount of money she spends on food. in the summer she uses an average of 9 loaves and bread per day.
The quantity of bread that Debbie uses each week on the average is = 54 loaves of bread
Calculation of weekly quantity of breadThe number of days the restaurant opens per week = 6 days.
The number of bread she uses everyday is = 9 loaves.
Therefore, the quantity of bread that Debbie uses each week on the average is = 6×9 = 54 loaves of bread.
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Please help me with this question 1/11
The value of a₄₃ is 3.
What is Matrices?Matrices is a plural form of a matrix, which is a rectangular array or a table where numbers or elements are arranged in rows and columns.
Here, aₓₙ is the element of matrix in which x represents the number of row and n represents the number of column of element.
So, a₄₃ means element from 4th row and 3rd column.
4th row = [2 9 3 7]
3rd column = [tex]\left[\begin{array}{ccc}8\\6\\1\\3\end{array}\right][/tex]
the common value between them is 3.
Thus, the value of a₄₃ is 3.
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use the graph below to answer this question: find the average rate of change for the given function from x=1 to x=2.
Answer: D. 2
Step-by-step explanation:
The question is asking for the rate of change from x=1 to x=2. Remember that the rate of change is also the slope, which can be seen as [tex]\frac{rise}{run} or \frac{y}{x}[/tex]. The rise would be going up/down the graph and the run would go left/right of the graph. Let's look at where x=1 and x=2 on the graph.
First, look at where the line falls between x=1 and x=2. Then, on where x=1, go up, then right on the graph, until you find the point where x=2. In this case, the rise over run is [tex]\frac{2}{1}[/tex]. This can be simplified to 2.
Therefore, the answer is 2.
I hope this helps!! Pls mark brainliest :))
Given the following exponential function,
identify whether the change represents
growth or decay, and determine the
percentage rate of increase or decrease.
y = 4300(0.042)
X
The change is decay and the percentage rate of decrease will be 95%.
An exponential function is a function where a number is raised to the variable i.e. base is raised to the exponent times.
Here given the exponential function is y= 4300(0.042)ˣ
Now we have to identify if the change in exponential function represents growth or decay, and have to determine the percentage rate of increase or decrease.
Here in the exponential function, the base is less than 1 so the change is decay.
The equation represents exponential decay because the decay factor is lesser than 1.
The general form of the exponential equation is:
y(x)= a(1-r)ˣ such that r is the decay.
equating with the equation
y= 4300(0.042)ˣ
a= 4300
and 1-r=0.042
⇒r= 1-0.042
⇒r= 0.958
the perecentage of decay will be r*100= 0.958*100= 95%
Therefore the change is decay and the percentage rate of decrease will be 95%.
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Denver has a current temperature of -5°, while Barcelona has a current temperature of 54°. What is the difference in temperature between Denver and Barcelona?
Answer:
59°
Step-by-step explanation:
Difference=54-(-5)
=54+5=59
A recent order for 15,000 items of building supplies was composed of bolts and nails. Nails cost 5 cents each. The entire order arrived at an expense of 1500 dollars. If there were 2500 bolts, what is the cost of each bolt?
The cost of each bolt according to the task content is; 35c.
What is the cost each bolt?Since, there were 2500 bolts, it follows that there were 12500 nails.
The total cost of nail is therefore; 12500 × 5c. = 62500c = 625$.
Hence, the total cost of bolts is; 1500$ -625$ = $875 = 87,500c.
Consequently, the cost of each bolt is; 87,500c/2500 = 35c.
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The pieces of a puzzle are placed half by Giulio, one fifth by Marco and Fabrizio in equal parts, while Michele arranges on the 90 pieces of the frame. how many pieces does Marco place?
The number of pieces that Marco places is given as follows:
30 pieces.
How to obtain the number of pieces that Marco places?The number of pieces that Marco places is obtained applying the proportions in the context of the problem.
The fractions of each person are given as follows:
Giulio: 1/2.Marco and Fabricio: 1/5.Hence the fraction composed by these three people is given as follows:
1/2 + 1/5 = (5 + 2)/10 = 7/10 = 0.7.
Hence Michele's fraction is given as follows:
1 - 0.7 = 0.3.
As Michele arranges 90 pieces, the total number of pieces is given as follows:
0.3x = 90
x = 90/0.3
x = 300.
Marco arranged one tenth, hence the number is:
0.1 x 300 = 30.
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Triangle EFG is isosceles.Find the measure of angles
As angles opposite congruent sides in a triangle are congruent, and also since the interior angles of a triangle add to 180 degrees, if we let angle EFG have a measure of x, then angle GEF also measures x, and thus:
82+x+x=180
2x=98
x=49
Thus, angle EFG is 49 degrees.
So, by the exterior angle theorem, angle DEG measures 82+49=131 degrees
kacee spent half of the money in her bank account, then deposited $15 more. if she now has $29, how much did she have begin with.
Answer:
Step-by-step explanation:
Solution
Before she put anything back into her account, she had 29 - 15 = 14 dollars.
She started with 2 * 14 = 28 dollars.
Answer: 28 dollars.
which expression is equivalent to. 5 32x^5 y ^10 z^15
HURRY NOW
Answer:
the answer is B
Step-by-step explanation:
5th root of 32 = 2
5 / 5 = cancels
10 / 5 = 2
15 / 5 = 3
2xy²z³
Answer:
2xy^2z^3
Step-by-step explanation:
WILL GIVE BRAINLIEST
Stephen is training for the upcoming sports season by running each morning. Below are the distances he ran this week. How far has Stephen run?
Distances (in km)
Monday 1.3
Tuesday 1.75
Wednesday 2.25
Thursday 2.5
Friday 3.0
A. 10.8 km
B. 9.5 km
C. 6.9 km
D. 11.6 km
Answer: A. 10.8 km
Step-by-step explanation:
add up all the days:
1.3 + 1.75 + 2.25 + 2.5 + 3 = 10.8 km
Select the correct answer. A line each runs from point B through points A and C. First arc, centered at B, cuts line B A at J and line B C at K. A line runs rightward from point D. Second arc, centered at D, cuts the line at L and third arc, centered at L, cuts the line at M. What needs to be corrected in the following construction for copying ∠ABC with point D as the vertex?
In order to make point D as the vertex in the construction as triangle ABC, the third arc should cross the second arc.
What is an arc?In Geometry, an arc can be defined as a trajectory that is generally formed when the distance from a given point has a fixed numerical value.
In order to make point D as the vertex in the construction as triangle ABC, you must ensure that the third arc crosses the second arc as illustrated in image attached below.
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Answer: The third arc should cross the second arc.
Step-by-step explanation: The guy above me clearly stated it, just wanted to clear up that he is correct :)
It is given that x² - y² = 30 and x - y = 5. Find the value of (x + y)².
Answer:
36
Step-by-step explanation:
when solving for two variables, we need to find one variable in terms of the other.
so, we can turn:
x - y = 5
into
x - y = 5
+ y + y
x = y + 5
Then, we can substitute "x" in the given equation with "y + 5"
x² - y² = 30
(y+5)² - y² = 30
(y + 5)(y + 5)
F: y² O: +5y I: +5y L: 25 {foil}
y² + 10y + 25 - y² = 30 {cancel y² - y²}
10y + 25 = 30
-25 -25
10y = 5
÷10 ÷10
y = 0.5
x = y + 5
x = 0.5 + 5
x = 5.5
check:
(5.5)² - (0.5)²
30.25 - 0.25 = 30
30 = 30
(TRUE)
now, we must find the value of:
(5.5 + 0.5)²
= (6)²
= 36
So, the value of (x + y)² is found to be 36
hope this helps!!
Answer:
(x + y)² = 36
Step-by-step explanation:
x² - y² ← is a difference of squares and factors as
(x - y)(x + y) , then
5(x + y) = x² - y² = 30 ( divide both sides by 5 )
(x + y) = 6 , then
(x + y)² = 6² = 36
BRANILIST PLS HELP
The triangles below are similar.
Triangle S R P. Angle S is 54 degrees, R is 41 degrees, P is 85 degrees. Triangle X Y Z. Angle X is 54 degrees, Z is 41 degrees, and Y is 85 degrees.
Which similarity statements describe the relationship between the two triangles? Check all that apply.
Triangle P R S is similar to triangle X Y Z
Triangle R S P is similar to triangle Z X Y
Triangle S R P is similar to triangle X Z Y
Triangle P S R is similar to Triangle Z Y X
Triangle R P S is similar to triangle Z Y X
Answer:
RSP, ZXY
SRP, XZY
RPS, ZYX
Step-by-step explanation:
Obviously, the numbers match each other.
ex. R = 41, Z = 41
Those two have the ability to pair in the same order
What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12
Answer:
x≥20
Step-by-step explanation:
-3(6-2x)≥4x+12
or, -18+6x≥4x+12
or, -18-12≥4x-6x
or, -40≥-2x
or, -40/2≥-x
or, -20≥-x
or, 20≥x
= x≥20
Frankie wants to build a path from one corner of his yard to the opposite corner. his yard measures 20 ft. x 32 ft. what will be the length of his path to the nearest tenth of a foot?
21.5 ft
25.0 ft
32.6 ft
37.7 ftfrankie wants to build a path from one corner of his yard to the opposite corner. his yard measures 20 ft. x 32 ft. what will be the length of his path to the nearest tenth of a foot?
21.5 ft
25.0 ft
32.6 ft
37.7 ft.
The length of his path to the nearest tenth of a foot is 37.7 ft option fourth is correct.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
We have:
Frankie wants to build a path from one corner of his yard to the opposite corner. his yard measures 20 ft. x 32 ft.
From the Pythagoras theorem:
Perpendicular(P) = 32 ft
Base(B) = 20 ft
H = √(32²+20²)
H = √1424
H = 37.7 ft
Thus, the length of his path to the nearest tenth of a foot is 37.7 ft option fourth is correct.
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Answer:
D) 37.7
Proof:
Please help me! I need help. Please help me, I need help, please help me!
Answer:
17x
Step-by-step explanation:
3x+4+4x+4+3x-4+3x-4+4x
Collect liketerms
13 t-shirts cost total of $156. What is the unit cost per t-shirt?
Step-by-step explanation:
please mark me as brainlest
If we can preach that it has 2 pairs of parallel sides, one pair of consecutive sides perpendicular and perpendicular diagonals.(check image)
Answer:
Prob Online
Step-by-step explanation:
Can't really think of one
Which of the following terms best describes a vertical line that the graph of a
function approaches but never intersects?
A Horizontal asymptote
B Proportion
C Vertical asymptote
D Inverse variation
My supersonic jet burns 4 gallons of jet fuel in 3 seconds. How many gallons of jet fuel do I need to fly for an hour?
7% tax on a $3 soda with an $8 burger
Step-by-step explanation:
please mark me as brainlest
In a school, the number of girls is 70 more than boys. the total number of students is 1280. find the number of girls and boys
Answer:
Step-by-step explanation:
Conditions
Let the girls = g
Let the boys = b
Equations
g + b = 1280
g = b + 70
Solution
Put the value for the girls (second equation) into the first equation.
b + 70 + b = 1280 Subtract 70 from both sides
b + 70 - 70 + b = 1280 -70 Combine
2b = 1210 Divide both sides by 2
2b/2 = 1210/2
b = 605 Substitute this value into the top equation
g + 605 = 1280 Subtract 605 from both sides
g + 605 - 605 = 1280 - 605
g = 675
Answer
# boys = 605
# girls = 675
Picture shown PLEASE HELP
Answer:
m= –4
So, you only need to of the points to find the slope, why not choosing the first two:
[tex]m = \frac{y2 - y1}{x2 - x1} = = = > \\ m = \frac{12 - 8}{ - 3 - ( - 2)} = = = > \\ m = \frac{4}{ - 1} = - 4[/tex]
so basically, this is the slope your looking for
