Answer:
f(x) = x² - 12x + 36 = (x - 6)²
The correct answer is A.
The quadratic function that has only one \(x\)-intercept is A. [tex]\( f(x) = x^2 - 12x + 36 \)[/tex]
A quadratic function has only one [tex]\(x\)[/tex]-intercept if it touches the [tex]\(x\)[/tex]-axis at exactly one point, which happens when the discriminant [tex](\(\Delta\))[/tex] of the quadratic equation is zero. The discriminant of a quadratic function [tex]\(ax^2 + bx + c = 0\)[/tex] is given by:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
Let's calculate the discriminant for each given function to determine which one has only one [tex]\(x\)[/tex]-intercept.
Option A: [tex]\( f(x) = x^2 - 12x + 36 \)[/tex]
[tex]\[ a = 1, \, b = -12, \, c = 36 \][/tex]
[tex]\[ \Delta = (-12)^2 - 4 \cdot 1 \cdot 36 \][/tex]
[tex]\[ \Delta = 144 - 144 \][/tex]
[tex]\[ \Delta = 0 \][/tex]
Option B: [tex]\( f(x) = x^2 - 13x + 36 \)[/tex]
[tex]\[ a = 1, \, b = -13, \, c = 36 \][/tex]
[tex]\[ \Delta = (-13)^2 - 4 \cdot 1 \cdot 36 \][/tex]
[tex]\[ \Delta = 169 - 144 \][/tex]
[tex]\[ \Delta = 25 \][/tex]
Option C: [tex]\( f(x) = x^2 + 13x + 36 \)[/tex]
[tex]\[ a = 1, \, b = 13, \, c = 36 \][/tex]
[tex]\[ \Delta = 13^2 - 4 \cdot 1 \cdot 36 \][/tex]
[tex]\[ \Delta = 169 - 144 \][/tex]
[tex]\[ \Delta = 25 \][/tex]
Option D: [tex]\( f(x) = x^2 + 20x + 36 \)[/tex]
[tex]\[ a = 1, \, b = 20, \, c = 36 \][/tex]
[tex]\[ \Delta = 20^2 - 4 \cdot 1 \cdot 36 \][/tex]
[tex]\[ \Delta = 400 - 144 \][/tex]
[tex]\[ \Delta = 256 \][/tex]
Only option A has a discriminant of 0, which means it has exactly one \(x\)-intercept.
How do we figure out the value of a variable?
Answer:
To figure out the value of a variable you plug it into an equation solve for it using the equation around it.
Answer:
Step-by-step explanation:
Solve for the unknown variable(number) by moving everything to the other side of the equation.
September 6 is a Read Book Day.Polina read 5 times as many pages as Marcus read.Together,the read 108 pages.How many pages did each person read?
Answer:
The number of pages that Polina read was 90 and the number of pages that Marcus read was 18
Step-by-step explanation:
Let
x -----> number of pages that Polina read
y ----> number of pages that Marcus read
we know that
x+y=108 ----> equation A
x=5y -----> equation B
substitute equation B in equation A and solve for y
[tex]5y+y=108\\6y=108\\y=18[/tex]
Find the value of x
[tex]x=5y -----> x=5(18)=90[/tex]
therefore
The number of pages that Polina read was 90 and the number of pages that Marcus read was 18
The angles of a rectangle are equal.
always
sometimes
never
Answer: A rectangles angles are always equal.
Step-by-step explanation:
Suppose you have a rectangle, four sides, two pairs of parallel lines. in order to be a rectangle, the quadrilateral has to have equal angles, similar to a square, if they didn't, they could be a trapezoid, which is not a rectangle, because it only has one pair of parallel lines.
Hope this helps!
Answer:
They are always equal
Step-by-step explanation:
Because they all have equal sides they can be measured to confirm that the sides are equal.
the formula K=9/5[F-32]+273.15 converts temperatures from Fahrenheit F to Kelvin K.
a. solve the formula for F
b.The freezing point of water is 273.15 Kelvin. What is the temperature in Fahrenheit?
c.The temperature of dry ice is -78C. Which is colder, dry ice or liquid nitrogen
To solve for F in the conversion formula, subtract 273.15, multiply by ([tex]\frac{5}{9}[/tex]), and add 32. The freezing point of water in Fahrenheit is 32 °F. Liquid nitrogen is colder than dry ice.
Solving the Temperature Conversion Formula
To solve the formula K = [tex]\frac{9}{5}[/tex][F-32] + 273.15 for F (Fahrenheit), we will isolate F in the equation. Here is the step-by-step process:
Subtract 273.15 from both sides: K - 273.15 = [tex]\frac{9}{5}[/tex][F - 32]
Multiply both sides by [tex]\frac{5}{9}[/tex] to get: F - 32 = (K - 273.15) × [tex]\frac{5}{9}[/tex]
Add 32 to both sides to solve for F: F = (K - 273.15) × [tex]\frac{5}{9}[/tex] + 32
Converting Kelvin to Fahrenheit
The freezing point of water is 273.15 Kelvin. To find this temperature in Fahrenheit:
F = (273.15 - 273.15) × [tex]\frac{5}{9}[/tex] + 32 = 32 °F
Comparing Temperatures
Dry ice has a temperature of -78°C, which is equivalent to -108.4°F. Liquid nitrogen boils at 77 K, which is about -196°C or -320.8°F. Therefore, liquid nitrogen is colder than dry ice.
(20 Points!!) Which expressions are equivalent?
Answer:
i think it is the last one
Step-by-step explanation:
Check your answer if unsure
( X^3 - 1 ) = ?
Plz answer
Answer:
(x - 1)(x² + x + 1)
Step-by-step explanation:
x³ - 1 is a difference of cubes and factors in general as
a³ - b³ = (a - b)(a² + ab + b²)
here a = x and b = 1, thus
x³ - 1 = (x - 1)(x² + x + 1)
Solve each equation for x.
4(x+4)+2x=52
Answer:
x = 6
Step-by-step explanation:
Distribute the 4:
4x + 16 + 2x=52
Add similar variables (4x + 2x)
6x + 16 = 52
Move the 16 to the other side by subtracting 16 from both sides
6x = 36
Divide both sides by 6 to get rid of the 6 in front of the x
x = 6
Answer:
x=6
Step-by-step explanation:
4(x+4)+2x=52
distribute
4x+16+2x=52
combine like terms
6x+16=52
subtract 16 from both sides
6x=36
divide by 6
x=6
What is the answer for y
Answer:
all work is shown/pictured
Answer: y = -7+3x
Step-by-step explanation:
Steps to solve will be your BFF
Best Favor Forever
slope of (8,11) (5,5)
Slope = 2/1
The work is provided in the image attached.
If f x = x2 + 2x − 5 and g x = 2x + 4, what is (f · g)(x) ?
[tex]\((f \cdot g)(x) = 2x^3 + 8x^2 - 2x - 20 \)[/tex].
To find [tex]\((f \cdot g)(x)\)[/tex], you need to multiply the functions \(f(x)\) and \(g(x)\).
Given:
[tex]\[ f(x) = x^2 + 2x - 5 \]\[ g(x) = 2x + 4 \]To find \( (f \cdot g)(x) \), multiply \( f(x) \) and \( g(x) \):\[ (f \cdot g)(x) = f(x) \cdot g(x) \]\[ (f \cdot g)(x) = (x^2 + 2x - 5) \cdot (2x + 4) \][/tex]
Now, use the distributive property to expand the expression:
[tex]\[ (f \cdot g)(x) = 2x^3 + 4x^2 + 4x^2 + 8x - 10x - 20 \]\[ (f \cdot g)(x) = 2x^3 + 8x^2 - 2x - 20 \][/tex]
So, [tex]\((f \cdot g)(x) = 2x^3 + 8x^2 - 2x - 20 \)[/tex].
I need help with this question please help me...
- 21+3x = -3
Answer:
x=6
Step-by-step explanation:
-21+3x=-3
+21 +21
3x=18
/3 /3
x = 6
Answer:
Step-by-step explanation:
Step one add 21 to each sides of the equal sign the you get
3x = 18
Divide by 3 on each side of the equal sign then your answer is
6
X = 6
FIRST ONE TO HELP ME GETS A BRAINLY!!! PLZ HELP ME, THIS IS DUE TOMMORROW!!!
Chris and Sandy run a half mile race. Sandy ran the race at a steady pace of 1/6 mile per minute and Chris ran at a steady pace of 1/5 mile per minute. How many seconds after Chris finished the race did sandy cross the finish line?
Answer:
Sorry if this is wrong but I think they ran at the same pace
Step-by-step explanation:
So if it is 1/6 then you do 60 divided by 6 it is ten then 60 divided by 5 is 12 so 1/5 is 12 and 1/6 is ten add it it is 60 the subtract it by 12 five times it is zero sorry if wrong
What is the vertical change on a graph described as?
Answer:
i believe it is rise
Step-by-step explanation:
3649 * 7 use the distributive property to solve
Answer:
Step-by-step explanation:
7(3,649)
=7(3,000+600+40+9)
=(7*3,000)+(7*600)+(7*40)+(7*9)
=21,000+4,200+280+63
=25,480+63
=25,543
I need help on This question please read it and give Me The answer
Answer:
1/4
Step-by-step explanation:
Zoe decided to measure the hand length of each of her classmates. First she marked a line across each student's wrist and lined up a ruler from this mark to the top of the middle finger to measure the length. Then she recorded the measurements in the table below.
Answer:
the ruler is marked in centimeters, but Zoe recorded data in ruler
Step-by-step explanation:
I just checked and I got it right
Answer: A. The ruler is marked in centimeters, but Zoe recorded data in inches.
Step-by-step explanation: I got a 100% on this quiz
Lucia ordered 3 pizzas for delivery, and the total cost is $27.89. The pizza arrived quickly, so Lucia wants to tip the delivery person 20%. How much is the tip?
What was the total cost for the pizza including the tip?
Answer:
Total cost =$33.47 Tip=$5.58
Step-by-step explanation:
$27.89÷5=5.578 5.578 rounded up to 2 digits=$5.58
$27.89+$5.58=$33.47
total cost is $33.47 tip=$5.58
Lucia should tip $5.58 for a 20% tip on her $27.89 pizza order. The total cost including the tip is $33.47.
To compute the tip Lucia should give for her pizza delivery, we need to calculate 20% of the total cost of the pizzas, which is $27.89. We first convert the percentage into decimal form by dividing 20 by 100, which gives us 0.20. Then we multiply this decimal by the total cost of the pizzas:
Tip = 0.20 imes $27.89 = $5.578
Since we usually round money to the nearest cent, the tip would be approximately $5.58. Now, to find the total cost including the tip, we add the tip to the original total:
Total Cost = Original Cost + Tip
Total Cost = $27.89 + $5.58 = $33.47
Therefore, the total amount Lucia would pay for the pizzas, including a 20% tip, is $33.47.
Harry needs 21 square meters of fabric for every 6 wizard cloaks he makes. How many cloaks could he make with 7 square meters of fabric
Answer: 2
Step-by-step explanation:
First, set up a proportion based on the amount of square meters over the number of cloaks he can make:
21/6 = 7/x
Cross multiply to get your next proportion and result with this:
21x = 42
Divide both sides by 21 (always divide the side with the variable):
21x/21 = 42/21
Cancel out the 21 (it's being divided by 21 so that makes it equivalent to 1 so you wind up with just x)
x = 2
Answer: 2
Step-by-step explanation:
Given : Harry needs 21 square meters of fabric for every 6 wizard cloaks he makes.
Using Unitary method , The number of cloaks can be made in 1 square meter fabric will be :-
[tex]6\div21=\dfrac{6}{21}=\dfrac{2}{7}[/tex]
Now , the number of cloaks made in 7 square meters of fabric will be :-
[tex]\dfrac{2}{7}\times7=2[/tex]
Hence, the number of cloaks made in 7 square meters of fabric =2
the koala is 72 meters tall.the zebra is three times as tall as the koala.the elephant is four times as tall as the zebra.how tall is the elephant
Answer:
The elephant is 864 meters tall
Step-by-step explanation:
this is because the zebra is 3 times as tall as the koala. so we do 72 times 3
we get 216. So the elephant is 4 times as tall as the zebra. so 216 times 4 is 864
its so late at night lol
If you have any questions feel free to ask in the comments.
Geometry unit 1 lesson 1
Final answer:
Geometry unit 1 lesson 1 typically covers basic understandings, vocabulary, and objectives related to geometry, such as points, lines, angles, and shapes.
Explanation:
In geometry, unit 1 lesson 1 typically covers basic understandings, vocabulary, and objectives related to geometry. Students learn about concepts such as points, lines, angles, and shapes. They also explore properties and relationships between geometric figures.
For example, students might learn that a point represents a specific location in space, a line is a straight path with no endpoints, and an angle is formed by two rays with a common endpoint.
By studying geometry, students develop spatial reasoning skills and learn to apply geometric principles in problem-solving situations.
What is the length of the line
Answer:
any idea about the length of the box
It appears to show a line segment with endpoints (1,4) and (7,0).
Without any additional information about the context of the graph, it is impossible to determine a definitive solution. However, I can offer some general observations about the line segment.
The slope of the line is calculated as m is;[tex][ \text{Slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}} ]Let’s calculate the slope using the given values\\ \\\text{Slope} = \frac{{7 - 1}}{{0 - 4}} = \frac{{6}}{{-4}} = -\frac{{3}}{{2}}[/tex]
The y-intercept of the line is 4, which means the line passes through the point (0,4).The equation of the line can be written in slope-intercept form as.[tex]The coefficient of (x) (the number in front of (x)) is (-\frac{3}{2}). This represents the slope of the line.[/tex]What is the value of y?
A.cannot be determined
B.60°
C.65°
D.120°
5•3/4 need help ASAP
Answer:
3 3/4
Step-by-step explanation:
5×[tex]\frac{3}{4}[/tex]
5 3
/ × /
1 4
= 15/4
=3 3/4
Chloe bought 12 chicken wings for $15. What was the cost of the wings in dollars per wing? Express your answer in simplest form.
The cost of the wings in dollars per wing would be $1.25.
To find this, all you need to do is divide the $15 by your amount of chicken wings, which is 12. 15/12 = 1.25.
Answer:
1.25
Step-by-step explanation:
each wings costs 1 $ and 25 cents
ATTACHMENT please help
Answer:
8.55 × [tex]10^{7}[/tex]
Step-by-step explanation:
Given
7.9 × [tex]10^{7}[/tex] + 6.5 × [tex]10^{6}[/tex] ( factor out [tex]10^{6}[/tex] )
= [tex]10^{6}[/tex]( 7.9 × [tex]10^{1}[/tex] + 6.5)
= [tex]10^{6}[/tex](79 + 6.5)
= [tex]10^{6}[/tex] × 85.5
= [tex]10^{6}[/tex] × 8.55 × [tex]10^{1}[/tex]
= 8.55 × [tex]10^{7}[/tex]
Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Select three options. The graph of f(x) = x2 is shifted down 50 units. The graph of f(x) = x2 is shifted up 50 units. The graph of f(x) = x2 is shifted left 10 units. The graph of f(x) = x2 is shifted right 10 units. The graph of f(x) = x2 is reflected over the x-axis.
Answer:
The graph of f(x) is shifted up 50 units
The graph of f(x) is shifted right 10 units
The graph of f(x) is reflected over the x-axis
Step-by-step explanation:
we have
[tex]f(x)=x^{2}[/tex]
This is a vertical parabola open upward
The vertex is a minimum
The vertex is the origin (0,0)
[tex]g(x)=-5x^{2}+100x-450[/tex]
This is a vertical parabola open downward
The vertex is a maximum
The first thing to note is that fx) is a parabola that opens up and g(x) opens down, so a reflection across the x-axis must have been applied.
Find the vertex of g(x)
Convert to vertex form
[tex]g(x)=-5x^{2}+100x-450[/tex]
Complete the square
[tex]g(x)=-5(x^{2}-20x)-450[/tex]
[tex]g(x)=-5(x^{2}-20x+100)-450+500[/tex]
[tex]g(x)=-5(x^{2}-20x+100)+50[/tex]
[tex]g(x)=-5(x-10)^{2}+50[/tex]
The vertex is the point (10,50)
so
To translate the vertex of (0,0) to (10,50)
The rule of the translation is
(x,y) ------> (x+10,y+50)
That means ----> The translation is 10 units at right and 50 units up
therefore
The transformations are
The graph of f(x) is shifted up 50 units
The graph of f(x) is shifted right 10 units
The graph of f(x) is reflected over the x-axis
I have 3 hundreds, 13 tens and 10 ones. What number am I?
Answer:
440
Step-by-step explanation:
3 hundreds = 300
13 tens= 13 times 10=130
10 ones=10
300+ 130+ 10=
440
The number 440 as per the statement 3 hundreds (300), 13 tens (130), and 10 ones = 10. Putting them together gives you 440.
Let's analyze the statement to find the number
3 hundreds, 13 tens, and 10 ones.
3 hundreds: This means you have three sets of one hundred. Each hundred is represented as 100. So, 3 hundreds would be
3 × 100 = 300.
13 tens: You have thirteen sets of ten. Each ten is represented as 10.
So, 13 tens would be 13 × 10 = 130.
10 ones: You have ten individual ones.
Now, let's add up all these components:
300 (for the hundreds) + 130 (for the tens) + 10 (for the ones) = 440
Therefore, the number describing in the statement is 440.
learn more about statement here
brainly.com/question/17029275
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The Haynes family is building an addition to their house that includes a new
bedroom and a new bathroom. Both rooms will have the same length. Mr.
Haynes created a model on a piece of paper as shown below:
22 Feet
______________
NEW BATHROOM
12 Feet
NEW BEDROOM W _____________
Part A:Write an expression for the total area of both rooms by using the Distributive Property.
Part B:If the width of the bedroom is 18 feet, what is the total square footage of the two room
Answer:
Part A
[tex]A_{t}=22(12+w)[/tex]
Applying Distributive property: [tex]A_{t}=264+22w[/tex]
Part B
[tex]A_{t}=660\ ft^2[/tex]
Step-by-step explanation:
Attached is the model that belongs to this exercise (The model was missing)
The formula for calculate the area of a rectangle is:
[tex]A=lw[/tex]
Where "l" is the lenght and "w" is the width.
Part A
Notice that the dimensions of the new bathroom are:
[tex]l=22\ ft\\w=12\ ft[/tex]
We do not know the width of the new bathroom, but we know that both rooms will have the same length. Knowing this, we can write an expression for the total area of both rooms by using the Distributive Property:
[tex]A_{t}=22(12+w)[/tex]
Applying Distributive property:
[tex]A_{t}=264+22w[/tex]
Part B
If the width of the bedroom is 18 feet, you need to substitute this value into the expression [tex]A_{t}=264+22w[/tex] in order to find the total square footage of the two rooms:
[tex]A_{t}=264+22w\\\\A_{t}=660\ ft^2[/tex]
Final answer:
The expression for the total area of both rooms, using the distributive property, is L × (12 ft + W). Given the width of the bedroom as 18 feet, the total square footage of the addition is 660 square feet.
Explanation:
Calculating the Area of Rooms
Part A: To write an expression for the total area of both rooms using the distributive property, let's denote the width of the new bedroom as W and the common length of both rooms as L. Both rooms have the same length, 22 feet, so L = 22 feet. The total area can be represented as the sum of the areas of both the new bathroom and the new bedroom.
Area of New Bathroom = L × 12 ft (since the width of the bathroom is given as 12 ft)
Area of New Bedroom = L × W (width of the bedroom is W)
Total Area = Area of New Bathroom + Area of New Bedroom
Using distributive property: Total Area = L × (12 ft + W)
Part B: Given the width of the bedroom is 18 feet, we can calculate the total square footage:
Total Area = 22 ft × (12 ft + 18 ft)
Total Area = 22 ft × 30 ft
Total Area = 660 square feet
Therefore, the total square footage of the two rooms is 660 square feet.
write 3.01 (1 repeating) as a mixed fraction?
Answer:
3 1/100
Step-by-step explanation:
7.
Call me maybe? The graph displays the cu
tive relative frequency of the lengths of phone
made from the math department office at Gabalo
High last month.
Cumulative relative
frequency (%)
0
5
10
35
40
45
15 20 25 30
Call length (min)
(a) About what percent of calls lasted 30 minutes or
more?
(b) Estimate the interquartile range (IQR) of the
distribution.
Answer:
a) 35%
b) 19 minutes
Step-by-step explanation:
The graph for this question is attached in the image below.
Part a) Percent of calls that lasted 30 minutes or more
As seen in the graph, the x-axis represent the duration of the call in minutes and y-axis represent the cumulative frequency of the calls.
From the graph we can see that the cumulative frequency against the point 30 minutes is about 65%. This means, 65% of the calls lasted for less than 30 minutes.
Since, out of 100%, 65% of the calls lasted for less than 30 minutes, the percentage of call that lasted for 30% or more would be:
100% - 65% = 35%
This means, 35% of calls lasted 30 minutes or more.
Part b) The interquartile range (IQR) of the distribution.
Interquartile range is defined as the difference of the 3rd Quartile and the 1st Quartile.
3rd Quartile is the point, below which 75% of the data values are present.
1st Quartile is the point, below which 25% of the data values are present.
So, from the cumulative frequency graph we have to look for the values on time axis against the cumulative frequency of 25% and 75%.
The amount of time against 25% cumulative frequency is approximately 13 minutes.
So, 1st Quartile = 13 minutes
The amount of time against 75% cumulative frequency is approximately 32 minutes.
So, 3rd Quartile = 32 minutes
Therefore,
IQR = 3rd Quartile - 1st Quartile
IQR = 32 - 13
IQR = 19 minutes
The interquartile range (IQR) of the distribution is 19 minutes.
Answer:
A,B,E,AND F
Step-by-step explanation:
HOPE THIS HELPS