The other root is 1, and the correct answer is: c. 1
The quadratic equation [tex]x^2 - 3x + a = 0[/tex] has two roots, and given that one of the roots is 2, we can use the fact that the sum of the roots is equal to the coefficient of the linear term (-b/a).
In this case, the linear term is −3x, so the sum of the roots is 3. Since we know one root is 2, the other root must be such that when added to 2, the sum equals 3.
Therefore, the other root is 3 − 2 = 1.
This demonstrates the application of the sum of roots formula in solving for the other root when one root is known. Hence, the correct answer is 1, which is option (c).
Is 6 to the 3rd power equal to 2•2•2•3•3•3? Full explaination and reasoning.
Answer:
yes
Step-by-step explanation:
if you do 6^3 you get 216
6*6*6=216
6*6=36
36*6=216
2*2*2*3*3*3=216
2*2=4
4*2=8
8*3=24
24*3=72
72*3=216
What is the value of k?
k=
Answer:k=2
Step-by-step explanation:
For 12a-12d choose yes or no to show how to use the distributive property to break apart the dividend to find the quotient 132/6.
Answer:
Yes. (See explanation)
Step-by-step explanation:
The procedure is described as follows:
[tex]x = \frac{132}{6}[/tex]
[tex]x = \frac{126 + 6}{6}[/tex]
[tex]x = \frac{126}{6} + \frac{6}{6}[/tex]
[tex]x = \frac{6}{6}\cdot (21+1)[/tex]
[tex]x = 1 \cdot (21+1)[/tex]
[tex]x = 21 + 1[/tex]
[tex]x = 22[/tex]
Circle C has diameter AB. The coordinates of A are (5,1) and the coordinates of C are (6,10). Find the coordinates of B.
Answer:
(7, 19)
Step-by-step explanation:
We know that we are talking about circle C, which means that the center is point C. Since the diameter is AB, that means that AB goes through the center C and that center C is the midpoint of the segment AB.
Say the coordinates of B are (x, y). We can use the Midpoint Theorem to figure out B. The Midpoint Theorem states that for two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], the coordinates of the midpoint are: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex].
Here, our two points are A(5, 1) and B(x, y). Then, the midpoint is: [tex](\frac{5+x}{2} ,\frac{1+y}{2} )[/tex]. We already know the midpoint is C(6, 10), so we can just set 6 equal to [tex]\frac{5+x}{2}[/tex] and set 10 equal to [tex]\frac{1+y}{2}[/tex]:
6 = [tex]\frac{5+x}{2}[/tex] ⇒ 12 = 5 + x ⇒ x = 12 - 5 = 7
AND
10 = [tex]\frac{1+y}{2}[/tex] ⇒ 20 = 1 + y ⇒ y = 20 - 1 = 19
So, the coordinates of B is: (7, 19).
Hope this helps!
Answer:
(7 , 19)
Step-by-step explanation:
Centre is the midpoint of the diameter
C = Midpoint of AB
Let B: (x,y)
(6,10) = (x+5)/2, (y+1)/2
12 = x + 5
x = 7
20 = y + 1
y = 19
Yall are doing great thanks sm for the help
Answer:
That is an obtuse isosceles
Write 63 as a product of prime factors in ascending order. I don't need the answer but the explanation as to my friends one was not enough
Answer:
Step-by-step explanation:
63= 3 * 3 * 7
63 will come in 7th table. 7*9. here 7 is a prime and 9 is composite number. 3*3 = 9. So 63 = 3*3*7
Answer:
63 = 3 × 3 × 7
Step-by-step explanation:
Start dividing by the smallest prime divisor till you reach 1
Which is 3
63/3 = 21
21/3 = 7
7/7 = 1
So the prime factors are: 3,3,7
A Demolition ball weigths 2 tons . what is the weigtht in ounces?also what is a demolition ball?
Answer:
64,000 oz
Step-by-step explanation:
A demolition (wrecking) ball is a relatively large dense mass, often spherical, typically swung from a crane, used to demolish buildings or other structures.
We assume you want to convert from a US short ton (2000 pounds) to Avoirdupois ounces (16 ounces per pound).
Then your ball's weight is ...
(2 tons)(2000 lb/ton)(16 oz/lb) = 64,000 oz
Perform the operation and reduce the answer fully. 7 /20 - 3/8 =
Answer:
-1/40 or - 0.025
Step-by-step explanation:
7 /20 - 3/8 =
-1/40 or - 0.025
hope this helps!
Answer:
1/40 o - 0.025
7/20 - 3/8 =
-1/40 o - 0.025
¡espero que esto ayude!
Draw the image of the figure after a rotation of 180° around O.
Answer:
Around o is the center point
The center point 0 is usually on a graph and you should use x axis if it doesn't say what axis o is. X + y are both 0 usually.
When you have 0 as a central point you are actually moving the shape at equality around just like you would with a pertractor.
So We have a same shape shown and you can do this by rotating the shape 180 so it looks upside down to how its shown originally or previously.
You then maneuver it around to the opposite graph diagonally opposite is most likely to be 180 degree.
So if it starts in x axis right side it will be in y axis diagonally to the left
You just have to show vertices or edges meet symmetrically from the 0 point like a mirror but also facing opposite direction as it has been rotated.
Step-by-step explanation:
The description of rotation of image of 180 degree around O is discussed below.
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.
Around o is the center point.
If it doesn't specify what the axis o is, use the x axis as the graph's centre point (0). Typically, (x+ y) are both 0.
The form at equality is actually moved around when 0 serves as the Centre, much like you would with a pertractor.
You can achieve this by turning the identical shape 180 degrees such that it appears upside down relative to how it was originally or previously displayed.
Hence, if it starts on the right side of the x axis, it will be on the left side of the y axis.
Thus, show how vertices or edges come together symmetrically from the origin, mirror-like, but also facing the other way because of rotation.
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Plz help
Thank you very much!
Answer:
I believe the answer is 8.
Step-by-step explanation:
8.02 rounded to the nearest tenth is 8
Rewrite the equation by completing the square.
x^2-2x+1=0
Answer:
(x - 1)² = 0
Step-by-step explanation:
Given
x² - 2x + 1 = 0 ( subtract 1 from both sides )
x² - 2x = - 1
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 1)x + 1 = - 1 + 1
(x - 1)² = 0
Solve the equation 6.5 = -3+n
Answer:
9.5 = n
Step-by-step explanation:
6.5 = -3 + n
+3 +3 Add 3 to both sides
9.5 = n
If this answer is correct, please make me Brainliest!
Answer:
n = 9.5
Step-by-step explanation:
6.5 = -3 + n
+3 +3 (add 3 to both sides to cancel out the -3 and isolate the x variable)
__________
9.5 = n
Maggie leaves her home and travels 4 miles
east to the grocery store. She then travels 7 miles
to the north and stops to pick up pizza. How many
miles will she travel to return home, if she takes
the most direct route? (round to the nearest tenth)
To solve for the most direct route home, the Pythagorean theorem is applied to the distances Maggie traveled east and north. Calculating the values yields a most direct route home distance of approximately 8.1 miles.
Explanation:The student is asking about finding the most direct route home after traveling first to the east and then to the north. This scenario sets up a right-angled triangle where the legs represent the eastward and northward trips, and the hypotenuse represents the most direct route home. To find the length of this hypotenuse, which is the direct distance Maggie must travel to return home, we use the Pythagorean theorem:
a2 + b2 = c2
Where a = 4 miles (eastward distance), b = 7 miles (northward distance), and c is the direct distance home.
Calculating this gives us c = \2 + 72} = \.
Thus, c = approximately 8.1 miles (when rounded to the nearest tenth).
Maggie will travel approximately 8.1 miles to return home by the most direct route.
A picture is to be mounted on a board.
Show that the picture and the board are not mathematically similar.
A picture and the board it is mounted on are not mathematically similar because their corresponding sides do not have the same proportions, with the board generally having extra space around the picture that alters the length-to-width ratio. Additionally, artistic elements like tension and abstractness in images disrupt dimensional consistency that similarity requires.
Explanation:To show that a picture and the board it is mounted on are not mathematically similar, we must understand similarity in a mathematical context. For two figures to be similar, they must have the same shape but not necessarily the same size, meaning their corresponding angles are equal, and their corresponding sides are in proportion. When we mount a picture on a board, the picture itself has dimensions that are different from that of the board - the board is usually larger to provide a border or frame around the picture. Since the additional border provided by the board changes the overall dimensions, the two objects cannot be considered mathematically similar.
The concept of similarity also involves dimensional consistency. If the picture and the board were to be similar, the ratio of the length to width in the picture would have to be the same as that of the board. However, in most scenarios, a picture needs to be mounted with additional space around it, thus altering the ratio.
Additionally, from an artistic point of view, tension within a painting or an abstract representation might disrupt the dimensional consistency that mathematical similarity requires. Various factors such as perspective can create a visual illusion that skews perceived dimensions, making it impossible for the two to be similar. When a picture includes a pattern that has a specific repetition with variation, it does not satisfy the conditions of mathematical similarity when placed on a uniform board.
What is the length of the hypotenuse of the triangle?
Answer:
√(12² + 35²) = √(144 + 1,225) = √1,369
= 37 ft
The shape is a quadrilateral.
The shape has no right angles.
The shape has 4 sides of equal length.
A rhombus is a type of polygon distinct from squares and rectangles due to its lack of right angles.
This description fits a geometric shape known as a rhombus. A rhombus is a type of polygon that is a quadrilateral with all four sides of equal length. Unlike a square, a rhombus does not have to have right angles, which distinguishes it from rectangles and squares. The sum of the interior angles in a quadrilateral is always 360°, a property that applies to rhombuses as well.
Make x the subject of the formula
[tex]m = n + \frac{x}{p} \\ pm = pn + x \\ x = pm - pn \\ or \\ x = p(m - n)[/tex]
Answer:
[tex]x=p(m-n)[/tex]
Step-by-step explanation:
[tex]m=n+\frac{x}{p}[/tex]
Put n to the other side by subtraction.
[tex]m(-n)=n(-n)+\frac{x}{p}\\m-n=+\frac{x}{p}\\[/tex]
Use multiplication with 'p' to isolate x.
[tex](p)(m-n)=\frac{x}{p}(p)\\ p(m-n)=x[/tex]
x is now isolated.
[tex]x=p(m-n)[/tex]
How can you add decimals without a place-value chart to make sure you are adding
the same place values?
Answer:
You can make sure that you align the decimal dots together.
Step-by-step explanation:
34.5
24.650
You can see that the decimal dot is aligned.
f(x)=x squared + 2 find f(4x)
Look at the attached picture ⤴
Hope it will help u....:)
determine the number and type of zeros of the quadratic function based on the value of the discriminant? discriminant=0, discriminant=-36, discriminant=3, discriminant=2, discriminant=100, discriminant=-4
Answer with Step-by-step explanation:
We know that
Number of zeroes of a quadratic function are 2.
When discriminant D
D=0
Roots are equal and real
D>0
Roots are real and different
D<0
Roots are not exist.
a.D=0
Number of zeroes=2
Zeroes are equal and real.
b.D=-36
Zeroes of quadratic function does not exist.
c.D=3
Number of zeroes=2
zeroes are real and different
d.D=2
Number of zeroes=2
zeroes are real and different
e.D=100
Number of zeroes=2
zeroes are real and different
D=-4
Zeroes of quadratic function does not exist.
Which of the following are solutions to x-1 = 5x + 2 ? Check all that apply.
1
091
O A. x
B. x=
o c. x = 2
D. x -
SUBMIT
Answer:
Let's solve the equation \( x - 1 = 5x + 2 \) to find the solutions:
1. **Subtract \(5x\) from both sides**:
\[
x - 5x - 1 = 2
\]
2. **Combine like terms**:
\[
-4x - 1 = 2
\]
3. **Add 1 to both sides**:
\[
-4x = 3
\]
4. **Divide both sides by -4**:
\[
x = -\frac{3}{4}
\]
So, the solution to the equation is \( x = -\frac{3}{4} \).
Now, let's check which of the options are solutions:
A. \( x \): Yes, \( x = -\frac{3}{4} \) is a solution.
B. \( x = \): No, this is not a valid format for a solution.
C. \( x = 2 \): No, \( x = -\frac{3}{4} \neq 2 \).
D. \( x - \): No, this is not a valid format for a solution.
Therefore, the correct answer is **A. \( x \)**.
The correct options are [tex]\frac{-3}{4}[/tex].
To find the solutions to the equation [tex]\( x - 1 = 5x + 2 \)[/tex], we first need to solve for [tex]\( x \)[/tex]. Let's do that step by step:
Start with the given equation:
[tex]\[ x - 1 = 5x + 2 \][/tex]
Move all terms involving [tex]\( x \)[/tex] to one side of the equation and constants to the other side. To do this, subtract [tex]\( x \)[/tex] from both sides and subtract [tex]\( 2 \)[/tex] from both sides:
[tex]\[ x - 1 - x - 2 = 5x + 2 - x - 2 \][/tex]
[tex]\[ -1 - 2 = 4x \][/tex]
[tex]\[ -3 = 4x \][/tex]
Now, divide both sides by [tex]\( 4 \)[/tex] to isolate [tex]\( x \)[/tex]:
[tex]\[ \frac{-3}{4} = \frac{4x}{4} \][/tex]
[tex]\[ -\frac{3}{4} = x \][/tex]
Which graph grows the fastest?
A) black
B) blue
C) green
D) pink
Answer:
b
Step-by-step explanation:
Answer:
do u have a pic?
Step-by-step explanation:
please help !!! :(
1 and 2 form a linear pair, if the measure of 1 is 113 find the measure of 2
Answer:
67
Step-by-step explanation:
A linear pair is two angles which form a straight angle when combined (or 180 degrees). Thus do 180 - 113 to get 67 degrees for Angle 2
The measure of angle 2 is 67°.
It is required to find the measure of angle 2.
What is angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.
Given :
<1=113°
We know that
A linear pair adds to 180 degrees.
<1 + <2 =180°
113°+ <2 = 180°
<2 = 180°-113°
<2 =67°
Hence, the measure of angle 2 is 67°.
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During a workout, a football player pushes a blocking dummy a distance of 30 m. While pushing the dummy the same
distance a second time, what would the player need to change to be certain that power output increases?
The player would need to use a greater force and take more time.
The player would need to use a greater force and take less time.
The player would need to use a smaller force and take more time.
The player would need to use a smaller force and take less time.
55 POINTS
Answer:the speead i think
Step-by-step explanation:
To increase power he must Increase force and decrease time.
The answeris : The player would need to use a greater force and take less time.
What is the slope ? Please help
Answer:
-2/3
Step-by-step explanation:
Okay, this is a fairly simple question.
First, you want to pick two pairs of coordinates (X,Y).
In this case, I chose (-3, 5) and (3, 1)
Now, you want to use the formula to find slope : y2-y1/x2-x1
1-5/3-(-3)
-4 divided by 6
=-2/3
Answer:
y = -2/3x + 3 pic below to show proof i hope this helps! :)
Step-by-step explanation:
looking at the photo this slope is negative
we can see 2 given points (0,3) and (3,1)
y = +/- ?/?x +/- ?
from the point (0,3) we move down 2
y = -2/? x + ?
from the point that was moved down 2, we move over 3 to get to (3,1) y = -2/3x + ?
the line crosses the 3 on the y-axis
y = -2/3x + 3
Solve similar triangles
Solve for x
x=
Answer:
X=4 ;)
Step-by-step explanation:
4+8=12
12:12=1:1
4:4=1:1
Answer=4
Hope this helped!!!
a square pizza box has a width of 24 in. What is the area of the largest circular pizza that could fit in the box?
Answer: 72 in
Step-by-step explanation:
If the area is 96 inches the it would be 72
Evaluate -4n^2+ 11 when n= 3
Since you know the value of n, you can substitute/plug it into the equation:
-4n² + 11 Plug in 3 into "n" since n = 3
-4(3)² + 11 Find 3² --> 3 x 3 = 9
-4(9) + 11 Multiply -4 and 9
-36 + 11
-25
Final answer:
To evaluate the expression -4n^2 + 11 for n = 3, substitute 3 for n and simplify to get -25.
Explanation:
To evaluate the expression -4n^2 + 11 when n = 3, you substitute the value of 3 for n into the expression and simplify.
First step: Substitute n with 3.
-4(3)^2 + 11
Second step: Calculate the square of 3.
-4(9) + 11
Third step: Multiply -4 by 9.
-36 + 11
Fourth step: Add 11 to -36.
The result is -25.
The value of the expression -4n^2 + 11 when n = 3 is -25.
pls help I really need it
Answer:
400cm squared
Step-by-step explanation:
8 x 5 = 40
(since there are 2 flaps it is 80)
10 x 8 = 80
(there are 4 of these)
80 x 4 = 320
80 + 320 = 400 cm squared
Answer:
its 102
Step-by-step explanation:
hope this helps
find the surface area of the composite 3D figure below. leave in terms of pi, numerical value only
Given:
The diameter of the cylinder = 34 m
So, the radius (r) = 17 m
The height (h) of the cylinder = 12 m
The slant height (l) of the cone = 20 m
To find the surface area of the given figure.
Surface area of the given fig = surface area of cylinder + surface area of the cone
Formula:
The surface area of the cylinder is [tex]2 \pi r(r+h)[/tex]
The surface area of the cone is [tex]\pi rs[/tex]
Now,
The surface area of the cylinder is given by
[tex]SA=2 \pi 17(17+12)[/tex]
[tex]=2 \pi 17(29)[/tex]
[tex]=2 \pi (493)[/tex]
[tex]SA=986 \pi[/tex]
The surface area of the cylinder is 986π m²
The surface area of the cone is given by
[tex]SA=\pi rs[/tex]
[tex]SA=\pi (17)(20)[/tex]
[tex]=340 \pi[/tex]
Thus, the surface area of the cone is 340π m²
The surface area of the composite figure is given by
Surface area = Surface area of cylinder + Surface area of cone
Substituting the values, we get;
[tex]SA=986\pi +340 \pi=1326 \pi \ m^2[/tex]
Thus, the surface area of the composite figure is 1326π m²