Considering that 12 is a root of the function, the value of coefficient Q is of 12.
What does it means that x is a root of a function f(x)?
It means that f(x) = 0.
In this problem, the function is given by:
f(x) = x² - 13x + q.
Since 12 is a root, we have that f(12) = 0, hence:
12² - 13 x 12 + q = 0
q - 12 = 0.
q = 12.
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I need help asap please
Step-by-step explanation:
you first multiply both sides by 4
hence,
40 > 5u > 30
then you just divide by 5 to get
8 > u > 6
Expand the brackets.
4(t – 5)
Step-by-step explanation:
[tex] = 4(t - 5)[/tex]
[tex] = 4t - 4 \times 5[/tex]
[tex] = 4t - 20[/tex]
Answer:
4t - 20
Step-by-step explanation:
[tex]4(t - 5)[/tex]
[tex]4t(5)[/tex]
[tex]= 20[/tex]
[tex]= 4t-20[/tex]
HI GUYS CAN SOMEONE PLEASE HELP??? ASAP??
TYSM!
what is the coordinate of the vertex for the following prabola: (x-10)^2 = 12(y+2)
Answer:
Hi,
Step-by-step explanation:
[tex](x-10)^2=12(y+2)\\y=\dfrac{(x-10)^2}{12}-2\\y'=0 == > 2(x-10)/12=0 == > x=10 == > y=-2\\\\Vertex\ is\ (10,-2)\\[/tex]
if a is factor of x what is the other factor
Answer:
x because say you have a prime number, 7, a will equal 1 and the other factor is 7 so it must be x
Answer:
[tex]\dfrac xa[/tex]
Step-by-step explanation:
[tex]\text{Let the other factor be k,}\\\\~~~~~~~a \times k =x\\\\\implies k = \dfrac x a\\\\\text{Hence, the other factor is}~ \dfrac xa[/tex]
a cone has a base with a diameter of 60 cm. the height of the cone is 24 cm. what is the approximate volume of the cone? use 3.14 or pi.
Answer:
22619.47
Step-by-step explanation:
V=π[tex]r^{2}[/tex][tex]\frac{h}{3}[/tex]
=π·30^2·24/3
≈22619.46711
The volume of a medal is 35 cm³
The medal is made from copper and tin.
The density of copper is 8.84 g/cm³
The density of tin is 7.38 g/cm³
Work out the mass of the medal.
volume of copper : volume of tin = 21:4
Answer:
301.224 g
Step-by-step explanation:
Let's divide in the ratio 21:4 the volume of the medal (35cm^3)
copper = (21/25)(35cm^3) = 29.4cm^3
tin = (35 - 29.4)cm^3 = 5.6cm^3
FOR THE COPPER
8.84 : 1 = X : 29.4
X = 259.896(g)
FOR THE TIN
7.38 : 1 = X : 5.6
X = 41.328(g)
(259.896 + 41.328)g = 301.224 g
What is the velocity (speed) of a car (in kilometres per hour) if it goes 40 kilometres in 35 minutes?
A: 70.27 km/hr
B: 67.52 km/hr
C: 68.57 km/hour
D: 69.88 km/hr
speed = distance / time
35 minutes / 60 minutes = 0.583 hours
speed = 49 km / 0.583 hours
Speed = 68.57 km/hr
answer: C. 68.57 km/hour
a
2
3
4
5
6
7
8
Which is the graph of f(x) = -(x+3)(x + 1)?
10
Answer:
graph C
Step-by-step explanation:
(x+3)(x+1) = 0
therefore x = -3 and x = -1
[tex]2h - (6h - 5)= -1[/tex]
Answer:
[tex]h=\frac{6}{4}[/tex]
Step-by-step explanation:
[tex]2h-(6h-5)=-1\\2h-6h+5=-1\\-4h+5=-1\\-4h=-6\\\boxed{h=\frac{6}{4}}[/tex]
distribute the negative sign to the parenthesiscombine like termssubtract [tex]5[/tex] from both sidesdivide both sides by [tex]-4[/tex]Find the perimeter of the parallelogram with these vertices. (-5,1) (-5,-4) (5,-2) (5,-7)
Answer:
10 + 2√109 ≈ 30.88
Step-by-step explanation:
what is the absolute value of 2x + 3 = 11
MATH!!! find the volume of the pyramid
The area of polygons formulas to V=2.56m^2
We have to determine,
The volume of the pyramid.
What is the volume of the pyramid?The volume of a pyramid is found using the formula,
V = (1/3) Bh
where 'B' is the base area and 'h' is the height of the pyramid.
hight =2.4m
base=1.4+1.8
base=3.2m
V = (1/3) (3.2)(2.4)
V=2.56m^2
As we know the base of a pyramid is any polygon,
we can apply the area of polygons formulas to find 'B.
V=2.56m^2.
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16-
15-
14-
13-
12-
11-
65
Distance (meters)
1698
master bedroom
living room
2nd bedroom.
X
0 1 2 3 4
5
6
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 2
Distance (meters)
What is the area of the kitchen floor in this floor plan?
6 5
y
4
3
2-
0
kitchen
entry-
bath
Answer:
[tex]\huge\bold\color{pink}{- Magdonal -}[/tex]
Gamitin mo utak mo bleh
[tex]\red{\rule{10pt}{999999pt}}\orange{\rule{10pt}{999999pt}}\green{\rule{10pt}{999999pt}}\blue{\rule{10pt}{999999pt}}\purple{\rule{10pt}{999999pt}}[/tex]
Each card in a standard deck of 52 playing cards is unique and belongs to 111 of 444 suits:
13 cards are clubs
13 cards are diamonds
13 cards are hearts
13 cards are spades
Suppose that Luisa randomly draws 4 cards without replacement.
What is the probability that Luisa gets 2 diamonds and 2 hearts (in any order)?
The probability that Luisa gets 2 diamonds and 2 hearts (in any order) is:
P = 0.022
How to get the probability?
The probability of getting a particular type of card, is given by the quotient between the number of cards of that type and the total number of cards.
Here, let's assume that the 4 draws are:
diamond-diamond-heart-heart.
In that order.
First, the probability of drawing a diamond card is equal to:
p₁ = 13/52
Because there are 13 diamond cards and 52 cards in total.
Bt after that draw, there will be 12 diamond cards and 51 cards in total, so the probability of getting the second diamond card is:
p₂ = 12/51.
Now, there are 13 heart cards and 50 cards in the deck, so the probability of getting the first heart card is:
p₃ = 13/50
And the probability of getting the second one is:
p₄ = 12/49.
The joint probability will be the product of the 4 individual probabilities, but we also need to take in account the possible permutations, these are:
(using D for diamond and H for heart).
D - D - H - H
D - H - D - H
D - H - H - D
H - D - D - H
H - D - H - D
H - H - D - D
So there are 6 permutations, this means that the probability is:
P = 6*p₁*p₂*p₃*p₄ = 6*(13/52)*(12/51)*(13/50)*(12/49) = 0.022
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2. Margie Spencer wants to have $100,000 in her savings account in 20 years. If her account pays 6.6% annual
interest compounded semiannually, how much must Margie deposit into her account now to meet her goal?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$100000\\ P=\textit{original amount deposited}\\ r=rate\to 6.6\%\to \frac{6.6}{100}\dotfill &0.066\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &20 \end{cases}[/tex]
[tex]100000=P\left(1+\frac{0.066}{2}\right)^{2\cdot 20}\implies 100000=P(1.033)^{40} \\\\\\ \cfrac{100000}{1.033^{40}}=P\implies 27288.97\approx P[/tex]
Find all angles, 0≤θ<360, that satisfy the equation below, to the nearest 10th of a degree.
4cos2θ+9=−14cosθ
Since cosine is negative in the second and 3rd quadrant, the required angles are 120 and 240 degrees
Trigonometry identityTrigonometry identities are expressed as a function of cosine, sine and tangent.
Given the trigonometry expression shown
4cos2θ+9=−14cosθ
Equate to zero
4cos2θ+9 + 14cosθ = 0
According to trig identity
cos2θ = 2cos²θ - 1
Substitute to have:
4(2cos²θ - 1)+9 + 14cosθ = 0
Expand
8cos²θ - 4 + 9 + 14cosθ = 0
8cos²θ+ 14cosθ + 5 = 0
let P = cosθ to have;
8P² + 14P + 5 = 0
Factorize the result
8P² + 10P + 4P + 5 = 0
2P(4P+5)+1(4P+5)=0
(2P+1) = 0 and 4P+5 = 0
2P = -1 and P = -5/4
P = -1/2 and -5/4
Recall that P = cosθ
If P = -1/2
cosθ = -1/2
θ = -60
Since cosine is negative in the second and 3rd quadrant, the required angles are 120 and 240 degrees
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HURRY PLEASE HELP!!!
The table represents a linear function. What is the slope of the function?
Answer:
-6
Step-by-step explanation:
you would use the slope formula y2-y1/x2-x1. the equation should be like 8-2/-2-(-1). Then simplify: 6/-1 or -6
solve pls brainliest
whitch of the following is closest to 8 62 61 65 66
Answer:
If the question is which is closest to 8, the answer is 61
Step-by-step explanation:
Which lists the steps in the correct order to find the median of this data set? 24, 16, 23, 30, 18, 29 O 1. Put the numbers in order. 2. Cross off high/low pairs. 3. Add the leftover numbers. 4. Divide the sum by 2. O1. Put the numbers in order. 2. Cross of high/low pairs. 1. Cross off high/low pairs. 2. Add the leftover numbers. 3.Divide the sum by 2. 1. Cross of high/low pairs.
Median is the central tendency of the data and always exists in the middle of the data set.
What is the median?The Median is the middlemost value of the numbers arranged in the ascending orders. Median is the central tendency of the data and always exists in the middle of the data set.
The process of finding the median if the number of data points is even is as follows:
Put the numbers or the data points in the order(increasing or decreasing i.e. ascending or descending order)Next cross of the high/ low pairsAdd the leftover numbersand divide the number( as obtained in the above step by 2)( if the number of data pints were even then we just need to arrange the numbers and cross the high/low pair and only one data point will be left which acts as the Median of the data set)
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Select the correct answer. in which career would you most likely apply concepts from geometry? a. food critic b. social worker c. radio dj d. computer game designer
Answer:
Computer game designer.
Step-by-step explanation:
If you want to design a game, you need to have some basic shapes and stuff in it. I'm not sure what else needs to be explained here lol
Beth says that the graph of g(x) = + 1 is a translation of 5 units to the left and 1 unit up of f(x) = . She continues to explain that the point (0, 0) on the square root function would be translated to the point (–5, 1) on the graph of g(x). Is Beth’s description of the transformation correct? Explain.
Beth's description of the transformation is incorrect
Complete questionBeth says that the graph of g(x)=x-5+1 is a translation of 5 units to the left and 1 unit up of f(x) = x. She continues to explain that the point (0,0) on the square root function would be translated to the point (-5,1) on the graph of g(x). Is Beth's description of the transformation correct? Explain
How to determine the true statement?The functions are given as:
g(x) = x - 5 + 1
f(x) = x
When the function f(x) is translated 5 units left, we have:
f(x + 5) = x + 5
When the above function is translated 1 unit up, we have:
f(x + 5) + 1 = x + 5 + 1
This means that the actual equation of g(x) should be
g(x) = x + 5 + 1
And not g(x) = x - 5 + 1
By comparison;
g(x) = x - 5 + 1 and g(x) = x + 5 + 1 are not the same
Hence, Beth's description of the transformation is incorrect
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Pls helpDetermine the area, in square units, of rectangle ABCD.
Enter the area of rectangle ABCD.
The area of the rectangle, as shown in the image given is calculated as: 48 square units.
What is the Area of a Rectangle?The area of a rectangle = length × width.
Find the length and width of the rectangle:
Length (BC) = 8 unitsWidth (AB) = 6 unitsArea of rectangle ABCD = 8 × 6 = 48 square units.
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m
1
8
What transformations were applied to ABCD to obtain A'B'C'D?
4
2
A. Rotate 90 degrees counterclockwise about the origin, then
translate 2 units up.
B. Rotate 180 degrees counterclockwise about the origin, then
translate 2 units down.
O C. Rotate 180 degrees counterclockwise about the origin, then
translate 2 units up.
D. Rotate 90 degrees counterclockwise about the origin, then
translate 2 units down.
← PREVIOUS
4
Answer:
A
Step-by-step explanation:
To answer this, look at one specific point for example, A. It is at the point (3,6). In order for this point to get to where it was moved to, you must rotate it counterclockwise () 90 degrees. Do this by changing the initial point from (x,y) to (-y,x). This is located at (-6,3). Then you can see that it was translated 2 units up from there.
I hope this helped.
Rotate 90 degrees counterclockwise then translate 2 units up.
Option B is correct.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
In the figure ABCD, is transformed to figure A'B'C'D'.
It is Transformed from Quadrant 1 to quadrant 2
So, the point (x,y) is (-y,x).
It is then moved up by 2 units.
Now, the figure is rotated counterclockwise and translated up by 2 units.
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Type the probability notation for choosing a red disk.
The probability notation for choosing a red disk is P(red disk)
How to determine the notation?From the question, we have the following highlights:
The scenario represents probabilityThe event is choosing a red flaskProbability notations are represented as:
P(Event)
Since the event is choosing a red flask, the probability would be
P(red disk)
Hence, the probability notation for choosing a red disk is P(red disk)
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How many different selections of 4 books can be made from a bookcase displaying 12 books?
Answer:
495
Step-by-step explanation:
12C4 = 12*11*10*9/(4*3*2*1) = 495
Answer:
495
Step-by-step explanation:
12C4 = 12*11*10*9/(4*3*2*1) = 495
The area of a sector of a circle is given by the equation uppercase A = StartFraction pi r squared uppercase S Over 360 EndFraction, where r is the radius of the circle and S is the angle measure of the sector. If Mia solved this equation for S, which of the following equations did she write?Which of the following equations is equivalent to S = pi r squared h?
A circle is a curve sketched out by a point moving in a plane. The equation that Mia will write is S = (360 × A)/(πR²).
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
Given the area of the sector of a circle is given by,
A = (πR²×S)/360°
Now, If Mia solved this equation for S, then the equation that she will write is,
S = (360 × A)/(πR²)
Hence, the equation that Mia will write is S = (360 × A)/(πR²).
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Answer: S = (360 × A)/(πR²).
Step-by-step explanation:
parallelogram ABCD has vertices A(0,0)B(3,6)C(11,2) find the possible coordinates of D
The parallelogram ABCD formed by vertices A(x, y) = (0, 0), B(x, y) = (3, 6) and C(x, y) = (11, 2) has a point D with the following coordinates: D(x, y) = (14, 8).
How to determine the missing vertex of a parallelogram
In this question we know only three vertices of the parallelogram. To determine the missing point we must understand the properties of parallelograms. Vectorially speaking, we can find the missing vertex by using the following property:
[tex]\overrightarrow{AB} = \overrightarrow {CD}[/tex]
[tex]\vec B - \vec A = \vec D - \vec C[/tex]
[tex]\vec D = \vec C + (\vec B - \vec A)[/tex]
D(x, y) = (11, 2) + [(3, 6) - (0, 0)]
D(x, y) = (11, 2) + (3, 6)
D(x, y) = (14, 8)
The parallelogram ABCD formed by vertices A(x, y) = (0, 0), B(x, y) = (3, 6) and C(x, y) = (11, 2) has a point D with the following coordinates: D(x, y) = (14, 8).
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The ocean was a magnet pulling me closer to it.
Group of answer choices
1:hyperbole
2:simile
3:metaphor
Answer:
Metaphor
Step-by-step explanation:
This is a comparison between the ocean and a magnet, but it did not use like or as, so it is a metaphor.
Answer: The correct answer is 3. metaphor.
Step-by-step explanation:
A hyperbole is an exagerration.
A simile is a comparison used with like or as.
A metaphor is a comparison used without like or as.
Therefore, "The ocean was a magnet pulling me closer to it." includes a metaphor.