Answer:
A is correct
Step-by-step explanation:
What we need to do here is to multiply all the roots together
The roots are;
3, √5 and -√5
Let’s have them in form of a sum
if x = 3, then the root is x-3
If x = √5, then the root is x-√5
If x = -√5, then the root is x+ √5
Now we need to multiply all these together to arrive at the original polynomial
Let’s start by using the roots
(x-√5)(x+ √5)
we can use the difference of 2 squares here and we arrive at (x^2 -5)
So finally, the polynomial would be;
(x^2-5)(x-3)
= x(x^2-5) -3(x^2-5)
= x^3-5x-3x^2+15
By rearranging, we have;
x^3-3x^2-5x+15
Please help! I got 14 but it says it's incorrect! Find the maximum number of real zeros of the polynomial. f(x)=2x^(6)-3x^(3)+1-2x^(5)
Answer:
6
Step-by-step explanation:
The Fundamental theorem of Algebra states that a polynomial of degree n has n roots. These can be real, complex or both.
f(x) = 2[tex]x^{6}[/tex] - 3x³ + 1 - 2[tex]x^{5}[/tex] ← is a polynomial of degree 6
Thus the maximum number of real roots is 6
A circle has an area of n cm2. What is it’s radius. A. 1cm b. 2cm c. 1/2 cm d. Can’t be determined
Answer:
The answer is option D.
Step-by-step explanation:
Area of a circle is πr²
where r is the radius
from the question the area is n cm² which is a variable and not a number therefore cannot be used to determine the radius of the circle.
Hope this helps you
Answer:
thank you
Step-by-step explanation:
30 POINTS!! Given triangle ABC shown below, which graph shows the transformation (x-2, y+4)?
Answer:
Its C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Take point A at ( 4,-1)
We are shifting down 2 and to the right 4
(4-2, -1+4) becomes ( 2,3)
Choice C has A' at ( 2,3)
What is the measure of B? A = 35 degrees C = Right angle inside triangle
Answer:
55
Step-by-step explanation:
35+90=125
180-125=55
The interior angles of a triangle should always add up to 180 degrees
Answer:
B=55 degrees
Step-by-step explanation:
if the shape is a triangle then the sum of the angles of the triangle is 180
angles :A+B+C=180
35+B+90=180
B=180-125
B=55 degrees
Help is appreicated! (10 points!)
Answer:
5
Step-by-step explanation:
5
Hurry I need it now !
(04.01 MC)
Which characteristics will prove that ΔDEF is a right, scalene triangle?
Answer:
A right scalene triangle would have a 90 degree angle and 3 non congruent sides
Step-by-step explanation:
The area of a rectangle is 42 ft squared, and the length of the rectangle is 5 ft more than twice the width. Find the dimensions of the rectangle. length and width.
Answer:
Length = 12 ftWidth = [tex] \frac{7}{2} ft[/tex]
Step-by-step explanation:
Given,
Area of rectangle = [tex]42 \: {ft}^{2} [/tex]
Width = X
Length = 2x + 5
Now,
[tex]x(2x + 5) = 42[/tex]
[tex]2 {x}^{2} + 5x = 42[/tex]
[tex]2 {x}^{2} + 5x - 42 = 0[/tex]
[tex]2 {x}^{2} + 12x - 7x - 42 = 0[/tex]
[tex]2x(x + 6) - 7(x + 6) = 0[/tex]
[tex](2x - 7)(x + 6) = 0[/tex]
Either
[tex]2x - 7 = 0[/tex]
[tex]2x = 0 + 7[/tex]
[tex]2x = 7[/tex]
[tex]x = \frac{7}{2} [/tex]
Or,
[tex]x + 6 = 0[/tex]
[tex]x = 0 - 6[/tex]
[tex]x = - 6[/tex]
Negative value can't be taken.
So, width = [tex] \frac{7}{2} ft[/tex]
Again,
Finding the value of length,
Length = [tex]2x + 5[/tex]
[tex]2 \times \frac{7}{2} + 5[/tex]
[tex]7 + 5[/tex]
[tex]12[/tex]
Length = 12 ft
Answer:
length = 12 ft, width = 3.5 ft
Step-by-step explanation:
w = width
l = length = 2w + 5
A = wl = w(2w + 5) = 42
2w² + 5w - 42 = 0
(w + 6)(2w - 7) = 0
w + 6 = 0, w = -6 (dimension cannot be negative)
2w - 7 = 0, w = 3.5
l = 2(3.5) + 5 = 12
Dale is in a ski rental shop trying to decide which equipment to rent for the day. The shop offers 4 kinds of skis and 3 kinds of poles. A helmet is always a good idea, and the shop has 8 different helmets available. How many different sets of ski equipment can Dale rent? sets
Answer:
96
Step-by-step explanation:
Simply multiply all the numbers together.
4 * 3 = 12
12 * 8 = 96
There are 96 possible combinations.
If this helped, please mark brainliest :D
Answer: 12 poles and 16 helmets
Step-by-step explanation:
3+4 =8
-4= -4
1.7
Which describes how square S could be transformed to square S prime in two steps? Assume that the center of dilation is the origin. A.) a dilation by a scale factor of Two-fifths and then a translation of 3 units up B.) a dilation by a scale factor of Two-fifths and then a reflection across the x-axis C.) a dilation by a scale factor of Five-halves and then a translation of 3 units up D.) a dilation by a scale factor of Five-halves and then a reflection across the x-axis
Answer:
The correct option is;
A.) A dilation by a scale factor of two-fifths and then a translation of 3 units up
Step-by-step explanation:
The given information are;
Square S undergoes transformation into square S'
From the figure, the dimension of S' = 2/5 dimension of S
Therefore, the scale factor of the dilation is two-fifths
The center of dilation = The origin
Therefore, given that the top right edge of S is at the center of dilation, the initial location of the dilated figure will be (0, 0), (2, 0), (2, -2), and (0, -2)
Given that the lowermost coordinates of S' are (0, 1) and (2, 1), and the lowermost coordinates of the initial dilation are (0, -2) and (2, -2), we have that the translation to S' from the initial dilation is T (0 - 0, 1 - (-2)) = T(0, 3) which is 3 units up.
Answer:
A
Step-by-step explanation:
What is the equation of the line that passes through the point (-6, 6) and has a
slope of
1/3?
Answer:
Using point-slope form we get:
y - 6 = 1/3(x + 6)
y - 6 = 1/3x + 2
y = 1/3x + 8
Determine the equation for the line of best fit to represent the data.
Answer:
Y= -1/5x + 1
Step-by-step explanation:
Just type it on a graphing calculator an click graph
Myra took a picture of the sky one afternoon when two jet airplanes appeared to draw a pair of parallel lines with their vapor trails. The vapor trails from two other jets flying from another direction crossed over the parallel trails. She printed her picture and labeled the angles and lines.
Parallel lines c and d are cut by transversals a and b. All angles are described clockwise, from uppercase left. The intersection of lines c and b form angles: 2, 4, 3, 1. The intersection of lines d and b form angles: 6, 8, 7, 5. The intersection of lines c and a form angles: 10, 12, 11, 9. The intersection of lines a and d form angles: 14, 16, 15, 13.
Assume lines c and d are parallel and Angle2 measures 98°. Which statements are true? Select three options.
Answer:
a, c. d
Step-by-step explanation:
Answer:
a c d
Step-by-step explanation:
What are the solutions of the equation (x+2)^2-2x(x+2)-15=0? Use u substitution to solve.
Answer:
3
Step-by-step explanation:
Answer: x = -5 and x = 3
Step-by-step explanation:
on edg
Which choice is equivalent to the expression below?
V-64
Explanation:
By definition, i = sqrt(-1)
Which means,
sqrt(-64) = sqrt(-1*64)
sqrt(-64) = sqrt(-1)*sqrt(64)
sqrt(-64) = i*sqrt(8^2)
sqrt(-64) = i*8
sqrt(-64) = 8i
On the second line, I used the rule sqrt(x*y) = sqrt(x)*sqrt(y). The fourth line used the rule sqrt(x^2) = x when x is nonnegative.
Answer:
Click 8i for Correct Answer
Step-by-step explanation:
Please HELP me with this question! I am really struggling with this...
A) 22°
Step-by-step explanation:∡DBG = (360° - BD - BG)/2
= (360° - 170° - 146°)/2
= 44°/2
= 22°
Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far (in miles) is it from Jeremy's home to school?
Answer:
Step-by-step explanation:
18/60-12/60= 4 miles
just my guess
Urgent help I need it right now!!!!
Answer:
[tex]\boxed{\sf 30 \ bean \ cans}[/tex]
Step-by-step explanation:
The ratio of bean cans to corn cans is 6 : 7
Given that Corn cans = 35
Let the bean can be x
So,
The proportion for it will be:
6 : 7 = x : 35
Product of Means = Product of Extremes
7 * x = 6 * 35
7x = 210
Dividing both sides by 7
x = 30
So, 30 bean cans have to be put on the table to hold the needed ratio
What is the smallest value of x that satisfies the equation 8x^2 - 38x + 35 = 0? Express your answer as a decimal.
Answer:
1.25
Step-by-step explanation:
8x² -38x + 35 = 0
8x² - 10x - 28x + 35 = 0
2x(4x - 5)-7(4x - 5) = 0
(4x−5)(2x−7) = 0
4x - 5 = 0 or 2x - 7 = 0
x = 5/4 or x = 7/2
x = 1.25 or 3.5
Smallest value being = 1.25
Please answer it now in two minutes
Answer:
7.3 mi
Step-by-step explanation:
*Make sure your calculator is in degree mode*
Do this with the SOHCAHTOA method using angle V. Since we are trying to find the side that is the opposite of angle V (WY) and since the hypotenuse is already given, you would use SOH (sinΘ=[tex]\frac{opposite}{hypotenuse}[/tex])
sin(27)=[tex]\frac{x}{16}[/tex]
Multiply by 16 on both sides to cancel out the fraction:
16sin(27)=x
7.3=x
what is a continent To eliminate the terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? First equation: 9x + 3y = -18 Second equation: 8x + 7y = 10
Answer:
To eliminate solve for y, we need to eliminate x and we will do that by multiplying the first equation by 8 and multiply the second equation by 9.
y=6
Step-by-step explanation:
In the equations:
9x + 3y = -18 -----------------------------------------------------------------(1)
8x + 7y = 10 --------------------------------------------------------------------(2)
To solve for y, we will have to eliminate x
To eliminate x, we will follow the steps below;
multiply equation (1) through by 8 and multiply equation (2) through by 9
The resulting equations are
72x + 24y = -144 ----------------------------------------------------------(3)
72x + 63y = 90 -----------------------------------------------------------(4)
Then we will go ahead and subtract equation (4) from equation (3)
39y =234
divide both-side of the equation by 39
39y /39=234/39
y=6
if you apply the changes below to the quadratic parent function f(x)=x^2.which of these in the equation of the new function? shift 1 unit right ,vertically stretch by a factor of 3,reflects over x-axis
Answer:
Transformed [tex]\,\,f(x)= -3\,(x-1)^2[/tex]
Step-by-step explanation:
The process of shifting the graph of the function 1 unite to the right can be obtained by subtracting 1 to the x-coordinate in the expression of the function:
[tex]f(x)=x^2\\new\,f(x) =(x-1)^2[/tex]
The process of stretching vertically the function, would be accomplished by multiplying now the full function by "3":
[tex]new \,\,f(x)= 3\,(x-1)^2[/tex]
the reflection over the x-axis is obtained by multiplying the full function by the constant "-1":
[tex]new \,\,f(x)= -3\,(x-1)^2[/tex]
An oblique prism has trapezoidal bases and a vertical height of 10 units. An oblique trapezoidal prism is shown. The trapezoid has base lengths of x and 2 x, and a height of x. The distance between the 2 trapezoid bases is 20. The vertical height of the prism is 10. Which expression represents the volume of the prism? 10x3 cubic units 15x2 cubic units 20x3 cubic units 30x2 cubic units
Answer:
30x² cubic units
Step-by-step explanation:
The volume of an Oblique prism = Base Area × Height
This oblique prism has trapezoidal bases.
Area of a Trapezoid = 1/2 × h × ( b1+b2)
where h = height
b1 and b2 = bases of the Trapezoid.
From the question,
h = 20
b1 = x
b2 = 2x
Area of the Trapezoid =
1/2 × x ×( x + 2x)
1/2 × x × (3x)
3x²/2 square units.
Remember, the volume of an Oblique prism = Base Area × Height
Height of the prism = The distance between the 2 trapezoid bases = 20 units.
Base Area = 3x²/2 square units × 20 units
= 30x² cubic units
Answer:
d
Step-by-step explanation:
I need help with this
Answer:
86.55 ft
Step-by-step explanation:
First find the perimeter for 3 sides of the rectangle that are solid
24+15+24 = 63
The we find the circumference for 1/2 of the circle
C = pi d
The diameter is 15 and pi = 3.14
But we only want 1/2
1/2 C = 1/2 pi d
= 1/2 ( 3.14) * 15
=23.55
Add the lengths together
23.55+63 =86.55 ft
Find the probability of rolling a three first and then a ten when a pair of dice is rolled twice
Answer:
1/216
Step-by-step explanation:
When a pair of dice is rolled, there are 36 possible different outcomes.
Of those 36 different outcomes, a sum of 3 is obtained in 2 different ways: 1, 2 and 2, 1.
Of those 36 different outcomes, a sum of 10 is possible in 3 different ways: 6, 4; 5, 5; 4, 6.
p(3 followed by 10) = p(3) * p(10) = 2/36 * 3/36 = 1/18 * 1/12 = 1/216
Complete the sequences below :
• please explain the formula in simple words.
a) 18035, 18070 , 18105, ........... , .............. .
b) 3800, 4100, 4400, ............, ............ .
c) 17200, 18300, 19400, .............. , ............ .
Answer:
a) T(0) = 18035, D = 35, so formula is T(n) = 18035 + 35n
b) T(0) = 3800, D = 300, so formula is T(n) = 3800 + 300n
c) T(0) = 17200, D = 1100, so formula is T(n) = 17200 + 1100n
Step-by-step explanation:
They are all arithmetic progressions (AP) with a common difference, i.e. all differences of one term from the subsequent term are identical.
The general formula is
T(n) = T(0)+n*D
where
n = the term number
T(n) = nth term (considering the first term to be the zeroth term.
D = common difference
a) T(0) = 18035, D = 35, so formula is T(n) = 18035 + 35n
b) T(0) = 3800, D = 300, so formula is T(n) = 3800 + 300n
c) T(0) = 17200, D = 1100, so formula is T(n) = 17200 + 1100n
Solve the equation. 2x + 4 = 3x – 2
Answer:
X=6
Step-by-step explanation:
2x+4=3x-2
-4 -4
2x=3x-6
-3x -3x
-1x=-6
--- ---
-1 -1
X=6
Answer:
6
Step-by-step explanation:
2x+4=3x-2
2x-3x=-2-4
-x=-6
(divide both sides by -1)
X=6
simultaneous equations 5x+y=28 x+y=2
Answer:
[tex]( \frac{13}{2} \:, - \frac{9}{2} )[/tex]Step-by-step explanation:
[tex]5x + y = 28[/tex]
[tex]x + y = 8[/tex]
Solve the equation for y by moving 'x' to R.H.S and changing its sign
[tex]5x + y = 28[/tex]
[tex]y = 2 - x[/tex]
Substitute the given value of y into the equation 5x + y = 28
[tex]5x + 2 - x = 28[/tex]
Solve the equation for x
Collect like terms
[tex]4x + 2 = 28[/tex]
Move constant to R.H.S and change its sign
[tex]4x = 28 - 2[/tex]
Subtract the numbers
[tex]4x = 26[/tex]
Divide both sides of the equation by 4
[tex] \frac{4x}{4} = \frac{26}{4} [/tex]
Calculate
[tex]x = \frac{26}{4} [/tex]
Reduce the numbers with 2
[tex]x = \frac{13}{2} [/tex]
Now, substitute the given value of x into the equation y = 2 - x
[tex]y = 2 - \frac{13}{2} [/tex]
Solve the equation for y
[tex]y = - \frac{9}{2} [/tex]
The possible solution of the system is the ordered pair ( x , y )
[tex](x \: y) = ( \frac{13}{2} , \: - \frac{9}{2} )[/tex]-------------------------------------------------------------
Let's check if the given ordered pair is the solution of the system of equation:
plug the value of x and y in both equation
[tex]5 \times \frac{13}{2} - \frac{9}{2} = 28[/tex]
[tex] \frac{13}{2} - \frac{9}{2} = 2[/tex]
Simplify the equalities
[tex]28 = 28[/tex]
[tex]2 = 2[/tex]
Since , all of the equalities are true, the ordered pair is the solution of the system.
[tex](x \:, y \: ) = ( \frac{13}{2} \: , - \frac{9}{2}) [/tex]
Hope this helps....
Best regards!!
Answer:
[tex]\boxed{x=6.5} \\ \boxed{y=-4.5}[/tex]
Step-by-step explanation:
5x + y = 28
x + y = 2
Subtract both equations. (eliminating y variable)
4x + 0 = 26
4x = 26
Divide both sides by 4.
x = [tex]\frac{26}{4}[/tex]
x = 6.5
Plug x as 6.5 in the second equation and solve for y.
6.5 + y = 2
Subtract 6.5 on both sides.
6.5 - 6.5 + y = 2 - 6.5
y = -4.5
Which expression is equivalent to -80
Answer:
what expressions?
Step-by-step explanation:
If log3=0.4771 and log2=0.3010,Find the value of log12
Answer:
log 12 = 1.0761
Step-by-step explanation:
log 12
=log(3*2*2)
= log 3 +log 2+ log 2
=0.4771+0.3010+0.3010
=1.0761
Answer:
Log 12 = 1.0791
Step-by-step explanation:
=> log (12)
Prime Factorizing 12
=> log (2×2×3)
Using log rule : [tex]log (a*b) = log a+logb[/tex]
=> Log 2 + log 2 + log 3
Given that log 2 = 0.3010 , log 3 = 0.4771
=> 0.3010 + 0.3010 + 0.4771
=> 1.0791
Which of these is a solution to the equation graphed below?
Answer:
see explanation
Step-by-step explanation:
Any point that lies on the line is a solution to the equation.
Thus
(0, 1 ), (2, 0 ), (- 2, 2), (4, - 1 ) are all solutions
Answer:
[tex]\boxed{(6, -2)}[/tex]
Step-by-step explanation:
Any of the points that lies on the line is the solution to the equation of the line.
(-2, 2), (0, 1), (2, 0), (4, -1), (6, -2) are all solutions.
