The root of the polynomial function f(x) = 3x⁵ - 2x² + 7x is 0
How to determine the roots of the equation?The polynomial function is given as:
f(x) = 3x⁵ - 2x² + 7x
Set the function to 0
3x⁵ - 2x² + 7x = 0
Factor out x
x(3x⁴ - 2x + 7) = 0
Divide both sides by (3x⁴ - 2x + 7)
x = 0
Hence, the root of the equation is 0
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Answer:
B
Step-by-step explanation:
cause math
simplify √(x^2-10x+25) if -5≤x<5
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's simplify ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {x}^{2} - 10x + 25 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {x}^{2} - 5x - 5x + 25 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {x}^{} (x- 5) - 5(x - 5) } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ (x- 5) (x - 5) } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ (x- 5) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: (x- 5) [/tex]
value x lies between :
[tex]\qquad \sf \dashrightarrow \: - 5 \leqslant x \leqslant 5[/tex]
if the value of x is taken -5
[tex]\qquad \sf \dashrightarrow \: - 5 - 5[/tex]
[tex]\qquad \sf \dashrightarrow \: - 10[/tex]
if value of x is taken as 5
[tex]\qquad \sf \dashrightarrow \:5 - 5[/tex]
[tex]\qquad \sf \dashrightarrow \:0[/tex]
So, the possible values of the required expression lies between ~
[tex]\qquad \sf \dashrightarrow \: - 10 \leqslant \sqrt{ {x}^{2} - 10x + 25 } < 0[/tex]
I hope you understood the whole procedure. let me know if you have any doubts in given steps ~
Consider the following trapezoid.
Find the value of X.
Answer:
106º
Step-by-step explanation:
Because both the base angles are 74º. The known angles so far are 148º.
The top angles also have to be equal as they are on parallel lines so:
360 - 148 = 212º
212 / 2 = 106º
Answer:
x = 106 degrees
Step-by-step explanation:
74 plus 74 = 148
360 is the interior angle sum of all trapezoids
360-148=212
212 is the sum of both x and y
x and y are the same measure.
212/2 = 106
if spur gear system has a driver gear with 100 teeth and rotates at a speed of 10 RPM and is meshed with a driven gear of 20 teeth, then the driven gear will rotate at a speed of:
A. 200 RPM
B. 100 RPM
C. 50 RPM
D. 20 RPM
E. none of the above
100 teeth / 20 teeth = 5
5 x 10 rpm = 50 rpm
answer: 50 rpm
The volume of this rectangular prism is 2,016 cubic millimeters. What is the value of y?
Answer:
y = 12 mm
Step-by-step explanation:
Volume of a rectangular prism: length × width × height
V = L×W×H
v = 2,016 mm³l = 14 mmw = 12 mmh = y mmSubstitute the values above and solve for y:
2,016 = 14 × 12 × y
2,016 = 168y
2,016/168 = 1395v/168
12 = y
Final answer: 12 mm
Hope this helps!
Why are inscribed angles half the size of the central angles
Answer:
An angle inscribed in a circle is half of the central angle 2 that subtends the same arc on the circle, according to the inscribed angle theorem. As a result, the angle does not change as the vertex of the circle is moved around.
Step-by-step explanation:
A random sample of college football players had an average height of 66.35 inches. Based on this sample, (65.6, 67.1) found to be a 90% confidence interval for the population mean height of college football players. Choose the correct answer to interpret this interval. i. We are 90% confident that the population mean height of college football players is between 65.6 and 67.1 inches. ii. There is a 90% chance that the population mean height of college football players is between 65.6 and 67.1 inches. iii. We are 90% confident that the population mean height of college football palyers is 66.35 inches. iv. A 90% of college football players have height between 65.6 and 67.1 inches.
Answer:
We are 90% confident that the population mean height of college football players is between 65.6 and 67.1 inches.
Step-by-step explanation:
90% Confidence interval means that out of 100 different samples, for example, 90 out of 100 confidence intervals with include the true mean value (average height).
Which two answer choices below would give you a value of 4 times smaller than (20 x 100)? A) (20 x 100) 4 B) 204 x 100 C) 20 - 25 D) 5 x 25
The option (C) 20 – 25, and option (D) 5×25 are 4 times smaller than (20 × 100) option (C) and (D) are correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, —, ×, and ÷.
We have:
= (20 x 100)
= 2000
4 times smaller will be:
=2000/4
= 500
A) (20×100) 4 = 4000
B) 204×100 = 20400
C) 20 – 25 = -5
D) 5×25 = 100
-5 < 500
100 < 500
Thus, the option (C) 20 – 25, and option (D) 5×25 are 4 times smaller than (20 × 100) option (C) and (D) are correct.
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A can of vegetables with no label has a 1/8 chance of being green beans, and a
1/5 chance of being corn. What is the probability the can is green beans or
corn?
Answer:
13/40.
Step-by-step explanation:
We add the probability in this case.
So it is 1/5 + 1/8
= 8/40 + 5/40
= 13/40.
When the function is given in vertex form y = a (x minus h) squared + k, how is the vertex found? a. (k, h) c. (h, k) b. (x, y) d. (y, x)
For the form [tex]y = a(x-h)^2 + k[/tex], the vertex has coordinates (h, k). The vertex is found by (x, y).
What is the vertex form of a quadratic equation?If a quadratic equation is written in the form
[tex]y=a(x-h)^2 + k[/tex]
then it is called to be in vertex form.
It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
First of all, we used this vertex formula thing since it is visible that there are quadratic functions.
Otherwise, you had to use calculus to get critical points, then a second derivative of functions to find the character of critical points as minima or maxima or saddle, etc to get the location of vertex point.
This point (h,k) is called the vertex of the parabola that the quadratic equation represents.
For the form
[tex]y = a(x-h)^2 + k[/tex], the vertex has coordinates (h, k)
Thus, for the obtained form, we get the coordinates of the vertex as:
[tex]h = -b/2a,, \\ k = c - a\times(b/2a)^2[/tex]
Thus, the coordinates of vertex of [tex]y = ax^2 + bx + c[/tex]is:
[tex](h,k) = (-b/2a, c - a \times (b/2a)^2 )[/tex]
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Type the correct answer in the box. if necessary, use / for the fraction bar. you toss five fair coins. the probability that all five coins land heads is .
If all five coins land heads, the expected will 1. The probability that all five coins land heads is 1/32
What is probability?This is the likelihood or chance that an event will occur. Mathematically;
Probability = expected/total
If you toss five fair coins, the total outcome will be:
T = 2^5
T = 32
If all five coins land heads, the expected will 1. The probability that all five coins land heads is 1/32
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Can somebody help me with this
Probability = option(s) that we want / total number of possibilities
Options that we want = cash or credit card = 50 + 4 = 54
Total number of possibilities = cash, debit card, credit card = 50 + 2 + 4 = 56
54 / 56 = 0.96
Answer: 0.96
Hope this helps!
4. Which of the following is a true statement?
A. -4(2x - 3) = -8x - 12
B.-7(4x - 8) = -28x + 56
=
C. 5(3x + 6) = 15x + 6
D. 10-2(x + 5) = -2x + 20
2
3 D
5
6
8
9
10
x²-4
Which shows all the critical points for the inequality ²-5x+6
<<0?
O x=-2 and x = 2
Ox= 2 and x = 3
Ox=-3, x = -2, and x = 2
O x= -2, x = 2, and x = 3
The critical points for the inequality x²-5x+6 is x= 2 and x = 3.
What is critical point?In calculus, a critical point of a function is a point where the derivative of the function is either zero or undefined.
These points are important in determining the maximum and minimum values of a function, and can also help identify points of inflection and other important features of a curve.
To find the critical points for the inequality x²-5x+6, we need to find the values of x that make the expression equal to zero (i.e., the roots of the quadratic equation).
We can factor the expression as (x-2)(x-3) and set each factor to zero to find the critical points:
x-2 = 0 or x-3 = 0
x = 2 or x = 3
So the critical points are x = 2 and x = 3.
Therefore, the answer is x= 2 and x = 3.
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How can you prove that csc^2(θ)tan^2(θ)-1=tan^2(θ)
Answer:
Make use of the fact that as long as [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex]:
[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex].
[tex]\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}[/tex].
[tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex].
Step-by-step explanation:
Assume that [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex].
Make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] and [tex]\csc(\theta) = (1) / (\sin(\theta))[/tex] to rewrite the given expression as a combination of [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex].
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \left(\frac{1}{\sin(\theta)}\right)^{2} \, \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} - 1 \\ =\; & \frac{\sin^{2}(\theta)}{\sin^{2}(\theta)\, \cos^{2}(\theta)} - 1\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1\end{aligned}[/tex].
Since [tex]\cos(\theta) \ne 0[/tex]:
[tex]\displaystyle 1 = \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)}[/tex].
Substitute this equality into the expression:
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1 \\ =\; & \frac{1}{\cos^{2}(\theta)} - \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].
By the Pythagorean identity, [tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex]. Rearrange this identity to obtain:
[tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex].
Substitute this equality into the expression:
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].
Again, make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] to obtain the desired result:
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\\ =\; & \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} \\ =\; & \tan^{2}(\theta)\end{aligned}[/tex].
answer with procedure
Answer:
2
Step-by-step explanation:
there needs to be qtr with 88 by 779900
SOmeone please help me with this math puzzle
Answer:
1) (I) 1/4, 2) (B) 11/20, 3) (G) 3/20, 4) (C) 4/5
Step-by-step explanation:
Probability is Desired Outcome/All Possible Outcomes. For the first problem, we want apples, which is 25. Altogether though, there are 100 options. So, we get 25/100 or 1/4. For the second, oranges and grapes together (because either would be a desired outcome) are 55. So, we have 55/100, or 11/20. For the third, apples and oranges, the max can be 15, because that's how many total oranges (the lesser of the two) and you can't have anything other than that. So, we get 15/100 or 3/20. Finally, we're looking for everything but bananas, which is 100-20, or 80. For that, we get 80/100 or 4/5.
Hope this helped!
Answer:
Question 1: The Students favorite fruit is an apple is 1/4
Question 2: 3/20
Question 3: 2/5
Question 4: 4/5
Step-by-step explanation:
* All of the fruits equal up to 100, so 25 percent of 100 is 1/4 or 0.25
* Do 100/55. It should give you 5.8181818181818181818181818181818 which would be at least 3/20 because it is closer to 1.
* 25+15=40. 2/5=0.4 which is 40% of 100.
what is the value of X, Z, and Y.
Answer:
x= -64°, y= -63°, z=-57°
Step-by-step explanation:
→Solution,
Here,
60°=(-y-3)°[The opposite sides of a parallelogram are equal]
⇒y= -60°-3°
⇒y= -63°
⇒60°+(-2x-8)°=180°[Sum of co-interior angles is 180°]
⇒52°-2x=180°
⇒52°-180°=2x
⇒x= -128°/2
⇒x= -64°
⇒60°+(-2z+6)°=180°[Sum of co-interior angles is 180°]
⇒66°-2z=180°
⇒66°-180°=2z
⇒z= -114°/2
⇒z= -57°
1.) Prove that PAT is an isosceles triangle.
2.) State The Coordinates of R so that quadrilateral PART is a parallelogram.
( The image of the Question Is Given )
First one to answer with the correct answer gets marked
The triangle PAT is an isosceles triangle because the side lengths PA and AT are congruent
How to prove that the triangle is an isosceles triangle?The points are given as:
P = (1,6)
A = (4,5)
T = (5,2)
Calculate the distance between both points as follows:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]
So, we have:
[tex]PA = \sqrt{(1 -4)^2 + (6-5)^2}[/tex]
[tex]PA = \sqrt{10}[/tex]
[tex]PT = \sqrt{(1 -5)^2 + (6-2)^2}[/tex]
[tex]PT = \sqrt{32}[/tex]
[tex]AT = \sqrt{(4 -5)^2 + (5-2)^2}[/tex]
[tex]AT = \sqrt{10}[/tex]
Because the side lengths PA and AT are congruent, i.e. √10, then the triangle is an isosceles triangle
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Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus
A coordinate plane. The x- and y-axes each scale by one. A graph of a line goes through the points zero, four and one, six.
The equation of a line that is passing through the points (0, 4) and (1, 6) will be y = 2x + 4.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
A coordinate plane. The x-axis and y-axis are each scaled by one.
A graph of a line goes through the points (0, 4) and (1, 6) will be
The equation of a line that is passing through the points (0, 4) and (1, 6) will be
y - 4 = [6 - 4 / 1 - 0] (x - 0)
y - 4 = 2x
y = 2x + 4
The graph is given below.
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Answer:y=x-5
Step-by-step explanation:
khan academy
Please help!!!!!!!! Thank you sooo much!
Answer:
see explanation
Step-by-step explanation:
(a)
∠ XBC = 55° because it corresponds to ∠ AXY
(b)
since XB = XC then Δ XBC is isosceles with base angles congruent, that is
∠ XBC = ∠ XCB = 55°
the sum of the 3 angles in Δ XBC = 180° , then
∠ BXC + 55° + 55° = 180°
∠ XBC + 110° =180° ( subtract 110° from both sides )
∠ XBC = 70°
Draw and label a point, a line, a line segment, a ray, and an angle in a triangle
Answer:
a point
a line
a line segment
a ray
and an angle in a triangle
Step-by-step explanation:
A triangle has sides with lengths of 20 yards, 48 yards, and 52 yards. Is it a right triangle?
yes
no
Yes
Step-by-step explanation:
Because the sides of this triangle follow the Pythagorean Theorem.
i.e.
[tex]52^{2} = {20}^{2} + {48}^{2} [/tex]
[tex]\boxed{\textbf{Therefore it IS a right triangle}} [/tex]
Math ahh need done ASAP
Answer:
a) 3Step-by-step explanation:
Use the nth tern equation of the AP
[tex]a_n=a_1+(n-1)d[/tex]We have
[tex]a_1=-2[/tex] and [tex]a_{10}=25[/tex]Find the value of d
25 = - 2 + (10 - 1)d25 + 2 = 9d27 = 9dd = 27/9d = 3Correct choice is a)
Now
a_n=a+(n-1)d25=-2+9d9d=27d=3(05.01 LC)
NEED HELP ASAP ILL MARK BRAINLIEST IF CORRECT
What is the slope of the line segment?
1/4
-1/4
4
−4
Answer:
We can tell by looking at the graph that it is a positive slope, so we can eliminate answers b and d.
It is rise over run. from a point, it goes up 4, and over 1.
4/1
which would be 4. The answer is C! Hope this helps!
Step-by-step explanation:
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's consider two points on the line and calculate its Slope ~
(4 , 1)(8 , 2)Slope (m) of a line is :
[tex]\qquad \sf \dashrightarrow \: m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex]\qquad \sf \dashrightarrow \:m = \dfrac{2 - 1}{8 - 4} [/tex]
[tex]\qquad \sf \dashrightarrow \:m = \dfrac{1}{4} [/tex]
Lance rides his bike at an average speed of 32 mph.
If he has 3072 miles to ride, how many hours will it take him?
How many days is that?
Answer:
96 days. Divide 3072 by 32 and you get 96.
A cupboard is 1.2 m wide.
Will a stick 1m 5cm long fit across the cupboard?
Give reasons for your answer.
Answer:
cupboard is 1.2 m wide.
Will a stick 1m 5cm long fit across the cupboard?
Give reasons for your answer
E
Describe the transformation that maps figure RSTU onto figure RSTU
611
6
4
S
U
S2
R
E
R
6-4-2 O
2
4
6
Drag the labels to explain your answer. Labels may be used once more than once, or not at all
Figure RSTU is the image of figure RSTU after a translation
units left and
units down, and a reflection across
the
#1
.: 2
14
+ X-axis
- y-axis
Answer:
8 then 2 and reflection on y axes
Find the distance between the pair of points. Give an exact answer and an approximation.
(3,4) and (5,11)
Answer: [tex]\displaystyle d=\sqrt{53}[/tex]
Step-by-step explanation:
We will use the distance formula to solve. See attached and view the work below.
[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]
[tex]\displaystyle d=\sqrt{(5-3)^2 +(11-4)^2}[/tex]
[tex]\displaystyle d=\sqrt{(2)^2 +(7)^2}[/tex]
[tex]\displaystyle d=\sqrt{4+49}[/tex]
[tex]\displaystyle d=\sqrt{53}[/tex]
Since 53 is prime, this is the simplest form. Since it asks for an exact answer, we are done.
Select the table that represents a linear function.
Answer: C.
Step-by-step explanation: In a linear function, both numbers rise or fall in a steady way. This means the answer would be c, where the x rises in increments of one, and y increases by multiplying by three each time.
Consider parallelogram ABCD below.
Use the information given in the figure to find m of angle B, x, and m of angle BCA.
Answer:
Step-by-step explanation:
1) Opposite angles in a parallelogram are congruent, so angle B measures 82 degrees.
2) Opposite sides of a parallelogram are congruent, so 12=6x. Hence, x=2.
3) Opposite sides of a parallelogram are congruent, so by the alternate interior angles theorem, the answer is 62 degrees.
Answer:
see explanation
Step-by-step explanation:
the opposite angles of a parallelogram are congruent , then
∠ B = ∠ D = 82°
the opposite sides of a parallelogram are parallel and congruent , then
AD = BC , that is
6x = 12 ( divide both sides by 6 )
x = 2
∠ BCA and ∠ DAC are alternate angles and are congruent , then
∠ BCA = ∠ DAC = 62°
