Answer:
Correct option: First one -> real and distinct.
Step-by-step explanation:
To evaluate the roots of the equation 7x^2 + x - 1 = 0, lets find the discriminant Delta using the Bhaskara's formula:
[tex]\Delta = b^{2} - 4ac[/tex]
Where a, b and c are coefficients of the quadratic equation (in this case, a = 7, b = 1 and c = -1)
So we have that:
[tex]\Delta = 1^{2} - 4*7*(-1) = 29[/tex]
To evaluate the roots of the equation, we have the following cases:
[tex]\Delta > 0[/tex] : Two roots real and distinct
[tex]\Delta = 0[/tex] : Two roots real and equal
[tex]\Delta < 0[/tex] : Two roots not real
In our case, we have [tex]\Delta > 0[/tex], so the roots are real and distinct.
Correct option: First one
what does it mean by bisecting angles
Answer: A line that splits an angle into two equal angles.
Step-by-step explanation: ("Bisect" means to divide into two equal parts.)
Bisecting angles: A line that splits an angle into two equal angles.
Two parallel lines are crossed by a transversal. Parallel lines x and y are cut by transversal w. On line x where it intersects with line w, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 2, 4, 3, 1. On line y where it intersects with line w, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 6, 8, 7, 5. If mAngle6 = 123.5°, then mAngle1 is 56.5°. 67.5°. 123.5°. 136.5°.
Answer:
(A)[tex]56.5^\circ[/tex]
Step-by-step explanation:
From the diagram attached:
Angle 1 and Angle 6 are Co-Interior Angles.
The sum of co-interior angle is 180 degrees.
Therefore:
[tex]m\angle 1+ m\angle 6=180^\circ\\\\m\angle 6=123.5^\circ,$ therefore:\\m\angle 1+ 123.5^\circ=180^\circ\\m\angle 1=180^\circ-123.5^\circ\\m\angle 1=56.5^\circ[/tex]
The measure of angle 1 is therefore 56.5 degrees.
The correct option is A.
∠6 and ∠1 are same-side interior angles, m∠6 = 123.5°, therefore m∠1 will be: A. 56.5°
Recall:
Same-side interior angles are supplementary to each other. They add up to give 180°.The image showing the two parallel lines that is cut by a transversal creating angles is shown in the diagram attached below.
Given:
m∠6 = 123.5°
∠6 and ∠1 are same-side interior angles.
Therefore:m∠6 + m∠1 = 180°
Substitute123.5° + m∠1 = 180°
Subtract both sides by 123.5°m∠1 = 180° - 123.5°
m∠1 = 56.5° (Option A)
Learn more about same-side interior angles on:
https://brainly.com/question/16873218
Can somebody explain to me how to find vertex form from a graph?? I put an example graph if you need it :)))
Answer:
y = - 4(x + 3)² + 7
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
From the graph (h, k ) = (- 3, 7 ), thus
y = a(x + 3)² + 7
To find a we require a point on the graph other than the vertex
Using (- 2, 3) , substitute into the equation
3 = a(- 2 + 3)² + 7
3 = a + 7 ( subtract 7 from both sides )
a = - 4
Thus
y = - 4(x + 3)² + 7 ← in vertex form
if a rectangular painting is 3 feet long and 5/6 foot wide what is the area of the painting
Answer:
A = 2 1/2 ft^2
Step-by-step explanation:
The area of a rectangle is given by
A = l*w
A = 3 * 5/6
A = 5/2 ft^2
A = 2 1/2 ft^2
Answer:
A=2.5 ft^2
Step-by-step explanation:
A=3
A=3(5/6)
A=2.5 ft^2
use factoring to solve
3x^2-11x-6=0
Answer:
x = -0.62 and x = 4.29
These values are approximations !
Step-by-step explanation:
You can not use Factoring to solve this equation. Perhaps you did not use the exact notation as in the original question?
Anyway, to solve it, you can still use the ABC formula.
3x²-11x-6=0
a = 3
b =-11
c = -6
x = [11 + √{121 -4(3 *-6)} ]/ 2*3
x = [11 + √{121 -4(-24)} ]/ 6
x = [11 + √{121 + 96} ]/ 6
x = [11 + √{217} ]/ 6
x = 4.29 This is an approximation !
x = [11 - √{121 -4(3 *-6)} ]/ 2*3
x = [11 - √{121 -4(-24)} ]/ 6
x = [11 - √{121 + 96} ]/ 6
x = [11 - √{217} ]/ 6
x = -0.62 This is an approximation !
extra: see the graph.
Simplify the expression 4x3× 2x3
Answer:
8 x^6
Step-by-step explanation:
4x^3× 2x^3
Multiply the numbers
4*2 = 8
Then the variables
x^3 * x^3 = x^(3+3) = x^6
8 x^6
Answer:
[tex]8x^{6}[/tex] (I am assuming you meant [tex]4x^3*2x^3[/tex]
Step-by-step explanation:
First you multiply the coefficients 4 and 2 which equals 8
Then you multiply the x's and when you multiply variables that are raised to powers you add the powers
so [tex]x^3*x^3 = x^(3+3)[/tex]
Putting this together you get [tex]8x^{6}[/tex]
Given r,s,t are midpoints of AC,AB, and CB use the figure below to complete the following problem
Answer:
The first option, RT.
Step-by-step explanation:
A cylindrical container of five rubber balls has a height of 30 centimeters and a diameter of 6 centimeters. Each ball in the container has a radius of 3 centimeters. Find the amount of space in the container that is not occupied by rubber balls. Round your answer to the nearest whole number.
Answer:
There is 170 cm³ free space in the container.
Step-by-step explanation:
Cylindrical container: height = 18 cm ; diameter = 6 cm.
3 balls each have a radius of 3 cm.
Volume of a cylinder = π r² h
V = 3.14 * (3cm)² * 18 cm
V = 508.68 cm³
Volume of rubber ball = 4/3 π r³
V = 4/3 * 3.14 * (3cm)³
V = 113.04 cm³
113.04 cm³ * 3 balls = 339.12 cm³
508.68 cm³ - 339.12 cm³ = 169.56 cm³ or 170 cm³
Classify ∠COB in the image below as either Acute, Obtuse, Right, or Straight.
Answer:
obtuse
Step-by-step explanation:
The measure of ∠COB is 140° which is greater than 90° but less than 180° so it's an obtuse angle.
Angle COB is 140 degrees, which is Obtuse
Obtuse means between 90 degrees and 180 degrees, exclusive.
Solve for the value of x that would make line a parallel to line t?
Answer:
The value of [tex]x[/tex]:
[tex]x = 44[/tex]
Step-by-step explanation:
Find the value of [tex]x[/tex]:
[tex]2(x + 10) = 3(x-8)[/tex]
Use Distributive Property:
[tex]2(x + 10) = 3(x-8)[/tex]
[tex]2x +20 = 3x - 24[/tex]
-Subtract both sides by [tex]3x[/tex] and combine both [tex]2x[/tex] and [tex]-3x[/tex] together:
[tex]2x +20 - 3x = 3x - 3x - 24[/tex]
[tex]-x + 20 = -24[/tex]
-Subtract both sides by [tex]20[/tex]:
[tex]-x + 20 - 20 = - 24 - 20[/tex]
[tex]-x = -44[/tex]
Divide both sides by [tex]-1[/tex]:
[tex]\frac{-x}{-1} = \frac{-44}{-1}[/tex]
[tex]x = 44[/tex]
So, the final answer would be [tex]x = 44[/tex].
TRIG PROBLEM: Help me solve this, please. I will give Brainliest!
Please show all work. I have no idea where to start :(
Let's start with part a, finding the maximum and minimum.
Answer a: Max temp is -5 C on day 200. Min temp is -79 C on day 500.
Sine model.
We're looking for a model
T(n) = A sin( ωn - p ) + o
where T(n) is the estimated temperature on day n, A the amplitude of the variation, omega the radial frequency of variation, p a phase shift and o an offset, the average temperature.
Averaging min and max gives -42 C; that's the offset, what we get when the sine is zero. o = -42 C.
That's pretty close to the value on day 0 so we'll just use a sine function without any phase shift, p = 0.
Subtracting min from max gives a total span of 74 C degrees, so a sinusoidal amplitude that's half that, A = 37 C.
From max to min is a half period, or about a half period since we're only seeing every 100 days. That's 300 days, so a full cycle about every 600 days.
We want the argument to sine to go from 0 to 2pi as we complete a single period, 600 days, So when n=600 this term must be 2π, so it's of the form
ωn = 2 π n / 600.
Putting it all together we get our model:
Answer b: T(n) = 37 sin(2 π n / 600) - 42
We already estimated the period at 600 days. That's a full year.
Answer c: 600 days
We can see a full period is closer to 700 days (compare day 500 and day 1200, and also day 600 and day 1300) and the phase shift might need adjusting, but I think we pretty much did as they asked so I'll stop here.
How do you go from 98 to 720 using just one letter?
RIDDLE...
Answer:
Add an "x" between "ninety" and "eight". Ninety x Eight = 720.
90 x 8 = 720
After proving two triangles are congruent, then one can prove parts of a triangle are congruent using the reasoning CPCTC.
True
False
Answer:
The answer is True because CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent.
Solve the linear equation. 7x +10 = 18x − 1
Answer:
x =1
Step-by-step explanation:
7x + 10= 18x -1 ==> 7x - 18x = -1 -10 ==> -11x = -11 ==>x = 1
7x+10=18x-1
+1. +1
7x+11=18x
-7x. -7x
11=11x
Divide it all by 11
1=x
X=1
A 2-column table with 2 rows. The labels for the columns and rows are blank. First column entries are 5 x squared, 10 x. Second column entries are negative 2 x, negative 4. Which factors can be multiplied together to make the trinomial 5x2 + 8x – 4? Select two options. (x + 1) (2x + 1) (x + 2) (5x + 1) (5x – 2)
Answer:
(5x – 2) and (x + 2)Step-by-step explanation:
In order to know the two factors we are to multiply together to get the trinomial function 5x² + 8x – 4, we need to factorize the quadratic function given. On factorizing;
[tex]= 5x^{2} +8x-4\\= (5x^{2} +10x)-(2x-4)\\\\factoring\ out\ the\ common\ term\\= 5x(x+2)-2(x+2)\\= (5x-2)(x+2)\\[/tex]
The factors that can be multiplied together are (5x – 2) and (x + 2)
Answer:
The Answer On Edge Is C.) and E.), Have Fun Dreamers!
Step-by-step explanation:
Which values are equivalent to the fraction below? 6^7/6^5
Answer:
36
Step-by-step explanation:
Because the bases are the same we can just subtract the exponents to get us 6² or 36.
The velocity of an object in meters per second varies directly with time in seconds since the object was dropped, as represented by the table. The acceleration due to gravity is the constant of variation. What is the acceleration due to gravity of a falling object?
Answer: 10.2
Step-by-step explanation:
Salvador has saved 130 sand dollars and wants to give them away equally to n friends. How could you write this?
Answer:
[tex]\frac{130}{n}[/tex]
Step-by-step explanation:
Each friend would get [tex]\frac{130}{n}[/tex] sand dollars.
As they would get an equal proportion based on the population size.
Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the area of land mowed in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points? It takes Aaron about 1 hour to mow 2 acres. Aaron’s rate for mowing lawns is 0.5 acres per hour. The ratio of acres to time is 5 acres to 3 hours. The rate to mow a lawn is 0.6 hours per acre
Answer:
Slope of this line is given by:
Aaron’s rate for mowing lawns is 0.5 acres per hour
Step-by-step explanation:
It is given that time is tracked by Aaron related to x coordinate.
and the area of land mowed in acres is related to y coordinate.
Two of his points are given as:
(3, 1.5) and (5,2.5)
We know that the coordinates are represented in the form of (x,y)
i.e. first coordinate represents x coordinate and
second coordinate represents y coordinate.
So, it can be observed that:
[tex]x_1=3, y_1=1.5\\x_2=5, y_2=2.5[/tex]
Change in x coordinate = [tex]x_2-x_1=5-3 = 2[/tex]
i.e. total time taken is 2 hours.
Change in y coordinate = [tex]y_2-y_1=2.5-1.5 = 1[/tex]
i.e. total land mowed taken is 1 acre.
In other words, it takes 2 hours for Aaron to mow 1 acre of land.
So, "option 1) It takes Aaron about 1 hour to mow 2 acres." is incorrect.
Rate of mowing lawn is the land mowed by Aaron in 1 hour.
Land mowed in 2 hours = 1 acre
Land mowed in 1 hours = [tex]\frac{1}{2}[/tex] acre i.e. 0.5 acre
Also, slope of a line is given as:
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
Here [tex]y_2 - y_1 = 1[/tex]
[tex]x_2 - x_1 = 2[/tex]
As per formula:
[tex]m = \dfrac{1}{2} = 0.5[/tex]
So, option 2) Aaron’s rate for mowing lawns is 0.5 acres per hour.
Using the slope concept, it is found that the correct option is:
Aaron’s rate for mowing lawns is 0.5 acres per hour.
---------------------------
A linear function has the following format:
[tex]y = mx + b[/tex]
The slope is m, which is the rate of change, that is, by how much the output y changes when the input changes by 1.---------------------------
In this question, the input is the time in hours and the output is the area of land mowed, thus the slope represented the rate of area mowed per hour.Two points, (3, 1.5) and (5, 2.5). The slope is change in y divided by the change in x, thus:[tex]m = \frac{2.5 - 1.5}{5 - 3} = \frac{1}{2} = 0.5[/tex]
Thus, the correct option is:
Aaron’s rate for mowing lawns is 0.5 acres per hour.
A similar problem is given at https://brainly.com/question/17460142
To determine the mean number of electoral votes, add all of the votes in the table and divide by .
There are a total of 535 electoral votes. The mean is votes per state.
The median of the electoral votes is .
Answer:
The median is the 268th observation.
Step-by-step explanation:
The mean of a data set is the value representing the entire data set.
The formula to compute the mean is:
[tex]\text{Mean}=\frac{1}{n}\sum\limits^{n}_{i=1}{x_{i}}[/tex]
The median of a data set is the middle most value in the data set.
For odd number of observations the median is given by:
[tex]\text{Median}=[\frac{n+1}{2}]^{th}\ \text{observation}[/tex]
For even number of observations the median is given by:
[tex]\text{Median}=\frac{[\frac{n}{2}]^{th}\ \text{observation}\ +\ [\frac{n}{2}+1]^{th}\ \text{observation}}{2}[/tex]
In this case the mean number of votes per state is:
[tex]\text{Mean}=\frac{\text{Total number of electoral votes}}{\text{Total number of states}}[/tex]
There are n = 535 observations, This value is an odd number.
Then the median of the electoral votes is:
[tex]\text{Median}=[\frac{n+1}{2}]^{th}\ \text{observation}[/tex]
[tex]=[\frac{535+1}{2}]^{th}\ \text{observation}\\\\=268^{th}\ \text{observation}[/tex]
Thus, the median is the 268th observation.
Answer:
To determine the mean number of electoral votes, add all of the votes in the table and divide by
✔ 50
.
There are a total of 535 electoral votes. The mean is
✔ 10.7
votes per state.
The median of the electoral votes is
✔ 8
.
Step-by-step explanation:
What is the probability brittnie gets at least 35 hits in her next 100 at bats? (round to 3 decimal places.)?
Answer:
0.350
Step-by-step explanation:
Probability is defined as the chances that an event will occur or not occur. The entire idea of probability has to do with 'chance' events. Thus, the probability that an event will surely occur is 1, while the probability that an event will never occur is zero. Probabilities range between 0-1.
Probability of an event is obtained from
Probability= expected outcome/total number of outcomes
In this case,
Expected outcome= 35
Total number of outcomes = 100
Probability= 35/100= 0.350
which expression is equivalent to __
Answer
[tex]\sqrt[6]{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{2} = \sqrt[6]{8}[/tex]
[tex]\sqrt[3]{2} = \sqrt[6]{4}[/tex]
If f(x) = 5x + 40, what is f(x) when x = –5? pls help a. -9 b. -8 c. 7 d, 15
Answer:
D.
Step-by-step explanation:
f(5) = -25 + 40
f(5) = 15
Answer:
The answer is D) 15
Step-by-step explanation:
F(x)= 5x + 40 (substitute -5 for x)
= F(x)= 5(-5)+ 40
= F(x)= -25+40
F(x)= 15
Factor completely 3x2 − x − 4.
Answer:
(3x-4)(x + 1)
Step-by-step explanation:
first, split the middle term,
3x^2-x-4
= 3x^2 + 3x - 4x - 4
= 3x( x+ 1) - 4( x + 1)
= (3x-4)(x + 1)
plz mark as brainliest
Answer:
(3x − 4)(x + 1)
Step-by-step explanation
Which fraction is equivalent to StartFraction 2 Over 6 EndFraction? StartFraction 3 Over 7 EndFraction, because StartFraction 2 Over 6 EndFraction = StartFraction 2 + 1 Over 6 + 1 EndFraction = StartFraction 3 Over 7 EndFraction StartFraction 3 Over 9 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 9 EndFraction StartFraction 3 Over 12 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 12 EndFraction StartFraction 3 Over 8 EndFraction, because StartFraction 2 Over 6 EndFraction = one-half = StartFraction 2 + 1 Over 6 + 2 EndFraction = StartFraction 3 Over 8 EndFraction
Question:
Which fraction is equivalent to [tex]\frac{2}{6}[/tex]?
- [tex]\frac{3}{7}[/tex] because [tex]\frac{2}{6}= \frac{2 + 1}{6 + 1}[/tex]
- [tex]\frac{3}{9}[/tex] because [tex]\frac{2}{6}= \frac{1}{3}[/tex] and [tex]\frac{1}{3} = \frac{3}{9}[/tex]
- [tex]\frac{3}{12}[/tex] because [tex]\frac{2}{6}= \frac{1}{3}[/tex] and [tex]\frac{1}{3} = \frac{3}{9}[/tex]
- [tex]\frac{3}{8}[/tex] because [tex]\frac{2}{6}= \frac{1}{2} = \frac{2+1}{6+2} = \frac{3}{8}[/tex]
Answer:
- [tex]\frac{3}{9}[/tex] because [tex]\frac{2}{6}= \frac{1}{3}[/tex] and [tex]\frac{1}{3} = \frac{3}{9}[/tex]
Step-by-step explanation:
Two fractions are said to be equal if and only if they give the same value when simplified.
The equivalent of [tex]\frac{2}{6}[/tex] is as explained in the selected option;
First, divide numerator and denominator by 2
[tex]\frac{2/2}{6/2}[/tex]
Then simplify
2/2 = 1 and 6/2 = 3; So;
[tex]\frac{2/2}{6/2} = \frac{1}{3}[/tex]
Multiply numerator and denominator by 3
[tex]\frac{1*3}{3*3} = \frac{3}{9}[/tex]
Hence, [tex]\frac{2}{6}[/tex] is equivalent to [tex]\frac{3}{9}[/tex]
Answer:
B
Step-by-step explanation:
StartFraction 3 Over 9 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 9 EndFraction
to determine the percentage of students interested in volunteering for a holiday food drive, franklin high school conducts a phone survey of all currently enrolled seniors. this is an example of _____.
A.) Collecting data
B.) Describing data
C.) Making an inference
Answer: A Collecting data
Step-by-step explanation:
just did the quiz
Please help ASAP! Which ordered pair is a solution of this
equation?
-5x - 9y = -8
Click on the correct answer
A.
(2,-1)
B.
(-1,2)
C.
(-22)
D.
(2,-2)
========================================================
Explanation:
For each possible answer choice, you'll plug in the given coordinates to see which results in a true equation or not.
If we try choice A, then we plug in x = 2 and y = -1 to get
-5x-9y = -8
-5(2)-9(-1) = -8
-10+9 = -8
-1 = -8 which is false
So (x,y) = (2,-1) is not a solution. We can cross choice A off the list.
You'll find a similar situation happens with choices B and D. They don't work either.
-------
Choice C works because...
-5x-9y = -8
-5(-2)-9(2) = -8 .... replaced x with -2, replaced y with 2
10-18 = -8
-8 = -8
We get a true equation. So (-2,2) has been confirmed to be a solution.
help me
Factor: 5x2 – 15x – 20.
(a) 5(x-4)(x+1),
(b) -2(x-4)(x+5),
(c) -5(x+4)(x-1),
(d) 5(x+4)(x+1).
Answer:
C
Step-by-step explanation:
5×2=10
10-15x-20
-10-15x
5(-2-3x), or -5(x+4)(x-1) solve it and find your answer
Simplify 5x+3x+2y+4y halp
Answer:
8x+6y
Step-by-step explanation:
5x+3x+2y+4y
5x+3x= 8x
2y+4y= 6y
The simplified the expression is 2(4x+ 3y).
What is expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
5x+3x+2y+4y
Now, moving the like terms aside
As, 5x + 3x are one pair
and, 2y+ 4y is second like term pair
So, 5x+3x+2y+4y
= (5x+ 3x) + (2y+ 4y)
= x(5 +3)+ y (2+4)
= x(8)+ y(6)
= 8x+ 6y
= 2(4x+ 3y)
Hence, the simplified the expression is 2(4x+ 3y).
Learn more about Expression here:
https://brainly.com/question/14083225
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Triangle ABC was translated according to the rule T4.5, –6.2(x, y) to form A’B’C’ as shown. What are the coordinates of point C of the pre-image
Answer:
(-5.5, 3.2)
Step-by-step explanation:
According to the question, the data provided in the question is as follows
(x,y) = (x + 4.5 , y -6.2)
Now
(x + 4.5 , y -6.2) = (-1,-3)
Therefore
x + 4.5 = -1
So, the x equals to
= -1 - 4.5
= -5.5
Now
y - 6.2 = -3
So, the y is
= - 3 + 6.2
= 3.2
hence, the coordinates of point C of x and y is (-5.5, 3.2)
Therefore the third option is correct
Answer:
C
Step-by-step explanation:
