Answer:
Step-by-step explanation:
You know the intercepts occur at x = 0, so set each part of the factored form equal to zero and solve for x.
The first part, plain X = 0, so X = 0 is a root, an x-intercept
The second part (X-2)^2 = 0, so X = 2 is another root. Since the function is being squared, this root will happen twice. The function crosses this root twice.
The third part (x+4) = 0, so x = -4 is another root.
Finally, (x+1) so x = -1 is another root.
So you have X = 0, X = 2, X = -4, X = -1 as your x-intercepts
Use the pythagorean theorem to prove that this point lies on the unit circle. Find csc(0) where 0=-120.
By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.
How to prove this point lies on the unit circle?In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:
Reference angle = 180 - θ
Reference angle = 180 - 120
Reference angle = 60°.
For the coordinates, we have:
sin(-120) = -sin(60) = -1/2.
cos(-120) = -cos(60) = -√3/2.
By applying Pythagorean theorem, we have:
z² = x² + y²
z = √((-1/2)² + (-√3/2)²)
z = √(1/4 + 3/4)
z = √1
z = 1.
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Find each difference and show work please !!
Answer:
X-19
Step-by-step explanation:
First you need to distribute the three into the numbers in the parenthesis,
(3 * x) + (3 * -5) - (2x + 4)
That then turns into,
3x - 15 - (2x + 4)
but we aren't done distributing yet, because the second set of parenthesis has a negative sign in front of it we also have to distribute that. (this is because the negative sign is really just -1)
3x - 15 + (-1 * 2x) + (-1 * 4)
that turns into,
3x - 15 - 2x -4
from here all we have to do is add like terms,
(3x - 2x) + (-15 + -4)
and that leaves us with: 1x -19 or x-19
Hope that helped :))
the force, F newtons (N) between two particles is inversely proportional to the square of the distance, d m, between them. When the particles are 2m apart,
the force between them is 10 N. Find
1- the force between the particles when they are 5m apart,
2- the distance between the particles when the force between them is 25 N.
The force is 1.6N and the distance between them is 1.3 meters
The force between themAn inverse variation from force to the square of distance is represented s:
k = Fd^2
Where k represents the variation constant
When F = 10, d = 2.
So, we have:
k = 10 * 2^2
k = 40
Substitute k = 40 in k = Fd^2
Fd^2 = 40
When d = 5, we have:
F * 5^2 = 40
This gives
25F = 40
Divide by 25
F = 1.6
Hence, the force is 1.6N
The distance between themIn (a), we have:
Fd^2 = 40
When F = 25, we have:
25 * d^2 = 40
This gives
25d^2 = 40
Divide by 25
d^2 = 1.6
Take the square root of both sides
d = 1.3
Hence, the distance between them is 1.3 meters
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8. Find (f+g)(x) if f(x) = 4x² - 5x and g(x) = 3x² + 6x - 4.
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: (f + g)(x)[/tex]
[tex]\qquad \sf \dashrightarrow \: f(x) + g(x)[/tex]
[tex]\qquad \sf \dashrightarrow \: (4 {x}^{2} - 5x) + (3 {x}^{2} + 6x - 4)[/tex]
[tex]\qquad \sf \dashrightarrow \: 7 {x}^{2} + x - 4[/tex]
In which number is the value of the underlined digit ten times the value of the bold digit
Step-by-step explanation:
I don't see any numbers, so I just give you an example :
11
every position in a number is worth 10 times the value of the position to its very right.
so, in e.g. 11
the left 1 is worth 10 times the value of the right 1.
Here are the scores of 14 students on a geography test. 58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87 Notice that the scores are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
The five-number summary are as follows:
Minimum = 58Lower quartile(Q₁) = 67Median = 79Upper quartile(Q₃) = 82Maximum = 87Interquartile range = 15How to solve for five-number summary?The five-number summary is a set descriptive statistics which consist of the minimum, maximum, median, upper quartile, and lower quartile of a data distribution.
Therefore,
Given:
58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87
Therefore,
Minimum = 58
Lower quartile(Q₁) = 67
Median = 79 + 79 / 2 = 79
Upper quartile(Q₃) = 82
Maximum = 87
Interquartile range = Q₃ - Q₁ = 82 - 67 = 15
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Find the sum.
14 + 42 + 70 + ... + (28n − 14)
Answer:
14n^2.
Step-by-step explanation:
This is Arithmetic with first term a = 14 and common difference d = 28.
Sum of n terms = n/2[2a + (n-1)d]
= n/2(28 +( n -1)28]
= n/2(28 + 28n - 28)
= 14n^2
Answer:
14n²
Step-by-step explanation:
14 = 14 *1
42 = 14 *3
70 = 14 *5
28n -14 = 14*2n - 14 = 14*(2n -1)
14 + 42 + 70 + ........+(28n -14) = 14*1 + 14*3 + 14*5 + ....... + 14*(2n - 1)
= 14 * (1 + 3 + 5 + ......+ (2n-1) )
= 14 * n²
= 14n²
1 + 3 + 5 + .... +(2n -1) -> sum of first 'n' odd numbers.
Formula for finding sum of first 'n' odd numbers = n²
PLEASE HELP
place the figure in a coordinate plane and find the indicated length a square with side length n; Find the length of the diagonal
Thanks
For the square with side length n, the diagonal measures:
[tex]d = \sqrt{2} *n[/tex]
How to get the length of the diagonal?The sidelength of the square is n, and we want to get the length of the diagonal d.
Notice that the diagonal is the hypotenuse of a right triangle whose catheti measure n.
Then we can use the Pythagorean theorem, which says that the square of the hypotenuse is equal to the sum of the squares of the cathetus;
[tex]d^2 = n^2 + n^2\\\\d^2 = 2n^2\\\\d = \sqrt{2n^2} \\\\d = \sqrt{2}*n[/tex]
That is the length of the diagonal.
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Mrs. Pollo was making pizza. She used 3/8 of a cup of olives to make 1 pizza. At this rate, what amount of olives would she use on 1/2 of a pizza?
The area of the trapezoid shown is one 20 cm². Find the sum of the links of the two parallel sides.
The sum of the links of the two parallel sides is 5cm
Area of a trapezoidThe formula for calculating the area of a trapezoid is expressed as:
A = 0.5(a+b)h
where
h is the height of the trapezoid
a+b is the sum of the sides
Substitute
20 = 0.5(a+b)8
40 = 8(a+b)
a+b = 40/8
a+b = 5cm
Hence the sum of the links of the two parallel sides is 5cm
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Which best explains why the rotation represents an
isometric transformation?
the angle at point d remained a right angle.
the rectangle did not change shape or size..
point c remained the center of the rectangle.
point c did not remain the center of the rectangle.
The best explanation for why the rotation is isometric is "The rectangle did not change shape or size". Hence the second option is the right choice.
There are four main categories of transformations:
Translation (figure slides in any direction)Reflection (figure flips over a line)Rotation (figure turns about a fixed point)Dilation (the figure is enlarged or reduced)A stiff transformation known as an isometry maintains perimeter and area while also preserving length and angle measurements. In other words, there is congruence between the preimage and the image. Translations, reflections, and rotations are therefore isometric, but dilations are not since the image and preimage are comparable, rather than congruent figures.
The transformation in the question will be isometric when the preimage of the rectangle before 360° rotation, will be congruent to the image after the rotation.
The congruency is best described by the option "The rectangle did not change shape or size", as that is the basis of congruency.
Thus, the best explanation for why the rotation is isometric is "The rectangle did not change shape or size". Hence the second option is the right choice.
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The provided question is incomplete. For the complete question, refer to the attachment.
What part of this question is an hour
Peter sells ice cream for a living. On Monday, his revenue was 150 dollars. On Tuesday, his revenue was 100 dollars. Finally, on Wednesday, his revenue was 50 dollars. How much is Peter's revenue so far?
Answer:
300 dollars
Step-by-step explanation:
Note that:
{Peter's revenue on Monday: 150 dollars
Peter's revenue on Tuesday: 100 dollars
Peter's revenue on Wednesday: 50 dollars}
---------------------------------------------------------------
In this problem, we need to find how much is Peter's revenue so far (total).
We need to use addition to determine how much Peter's revenue is in total.
So, add 150, 100, and 50.
We get 150 + 100 + 50 = 300
Finally, Peter's revenue in total is 300 dollars.
Answer:
$300
Step-by-step explanation:
add 150+100+50
=300
Someone help pls, its urgent! ASAP!!! (Geometry)
“Complete the proofs”
Question 11
1) [tex]\overline{BA} \cong \overline{FA}[/tex], [tex]\angle 1 \cong \angle 2[/tex] (given)
2) [tex]\angle A \cong \angle A[/tex] (reflexive property)
3) [tex]\triangle AEB \cong \triangle ACF[/tex] (ASA)
4) [tex]\overline{AC} \cong \overline{AE}[/tex] (CPCTC)
Question 12
1) Isosceles [tex]\triangle ACD[/tex] with [tex]\overline{AC} \cong \overline{AD}[/tex], [tex]\overline{BC} \cong \overline{ED}[/tex] (given)
2) [tex]\angle ACD \cong \angle ADC[/tex] (angles opposite congruent sides in a triangle are congruent)
3) [tex]\angle ACB[/tex] and [tex]\angle ACD[/tex] are supplementary. [tex]\angle ADC[/tex] and [tex]\angle ADE[/tex] are supplementary (angles that form a linear pair are supplementary)
4) [tex]\angle ACB \cong \angle ADE[/tex] (supplements of congruent angles are congruent)
5) [tex]\triangle ABC \cong \triangle AED[/tex] (SAS)
6) [tex]\overline{AB} \cong \overline{AE}[/tex] (CPCTC)
7) [tex]\triangle ABE[/tex] is an isosceles triangle (a triangle with two congruent sides is isosceles)
Note: I changed the names of the segments in Question 11 because of the word filter.
PLS HELPPP!!!! Look at pic
The correct option regarding whether the equation x² = y² is a function is:
No, since if you solve the equation for x, then [tex]x = \pm y[/tex]
What is needed for a relation to represent a function?In a function, each value of x can be associated with only one value of y.
In this problem, the equation is:
[tex]x^2 = y^2[/tex]
Then:
[tex]x = \pm \sqrt{y^2}[/tex]
[tex]x = \pm \sqrt{y}[/tex]
x is associated with two values, [tex]-\sqrt{y}[/tex] and [tex]\sqrt{y}[/tex], hence it is not a function.
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how many bit strings of length 9 have exactly two 1'S or two 0'S( this is one question, so you should have one answer)
Answer:
72.
Step-by-step explanation:
Number of strings with exactly 2 1's
= 9C2
= 9*8/2*1
= 36.
Same for 2 0s
= 36.
When the decision maker must consider several possible outcomes for each alternative, each with a given probability of occurrence, this is decision making under a. uncertainty. b. risk. c. duress. d. certainty.
This is considered as decision making under risk.
Decision Making Under Risk
A circumstance in which the implications of the chosen course of action and the likelihood that it will occur are understood is referred to as decision-making under risk . For instance, the lottery selection tasks are frequently employed to examine the nature of decision-making in risky situations.
We make the assumption that there are two or more choices and that each alternative's characteristics are explicitly specified. For each attribute, the CV (coefficient of variation) is configured in case of such decision under risks. And, since in the given question, decision maker is supposed to consider several possible outcomes for each alternative, each with a given probability of occurrence. Thus the decision made will be decision under risk.
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Please list how long it takes for each person to pack a shelf alone
Jay and Kay can pack the shelves in one aisle of the supermarket in 30 minutes.
Kay and Elle take 35 minutes to do the same job.
When Jay and Elle work together, the job takes 42 minutes.
How long would each person take working individually?
It takes Jay, Elle and Kay to work individually for 70 minutes, 105 minutes and 52.5 minutes respectively
What is Rate and Ratio ?A ratio can sometimes be regarded as fraction. While rate has something to do with time.
Given that Jay and Kay can pack the shelves in one aisle of the supermarket in 30 minutes. Kay and Elle take 35 minutes to do the same job. When Jay and Elle work together, the job takes 42 minutes.
Let
J = Jay K = KayE = ElleThe interpretation of the question go thus;
1/J + 1/K = 1/30 ........ (1)
1/K + 1/E = 1/35 .........(2)
1/J + 1/E = 1/42 .........(3)
Make 1/J and 1/E the subject of formula in equation 1 and 2 respectively and substitute them in equation 3
1/J = 1/30 - 1/K ........ (4)
1/E = 1/35 - 1/K .........(5)
1/30 - 1/K + 1/35 - 1/K = 1/42
Collect the like terms
- 1/K - 1/K = 1/42 - 1/30 - 1/35
-2/K = (35 - 49 - 42)/1470
-2/K = -56/1470
1/K = 28/1470
Reciprocate both sides
K = 1470/28
K = 52.5 minutes.
Substitute K in both equation 4 and 5
1/J = 1/30 - 28/1470
1/J = (49 - 28)/1470
1/J = 21/1470
Reciprocate both sides
J = 1470/21
J = 70 minutes
1/E = 1/35 - 28/1470
1/E = (42 - 28)/1470
1/E = 14/1470
Reciprocate both sides
E = 1470/14
E = 105 minutes
Therefore, it takes Jay, Elle and Kay to work individually for 70 minutes, 105 minutes and 52.5 minutes respectively
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HELP‼️‼️‼️‼️‼️‼️
1. If 8x + 4y = 44, what is the value of 6x + 3y?
Answer:
33.
Step-by-step explanation:
8x + 4y = 44
4(2x + y) = 44
2x + y = 44/4 = 11.
6x + 3y
= 3(2x + y)
= 3 * 11
= 33.
first sequence: 3 8 13 18 23 second sequence: -2 4 10 16 . find the TWO numbers that are in both number sequences.
[tex]a(n) = 3 + 5n[/tex]
[tex]b(n) = - 2 + 6n[/tex]
[tex]a(n) = b(n) \\ 3 + 5n = - 2 + 6n \\ 5 = n \\ n = 5 \: (6th \: term)[/tex]
[tex]a(5) \: or \: b(5) = 3 + 5(5) = 28[/tex]
8 x -1/4 x -7 cara ngerjain nya bagaimana?
using a calculator, or otherwise,determine the value of(12.3)² - (0.246÷3) and write the answer
(i)exactly
(ii)correct to two significant figures
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Assuming the equation is:}[/tex]
[tex]\mathsf{(12.3)^2 - (0.246 \div 3)}[/tex]
[tex]\huge\textbf{If so, let's start simplifying it:}[/tex]
[tex]\mathsf{(12.3)^2 - (0.246 \div 3)}[/tex]
[tex]\mathsf{= (12.3\times 12.3) - (0.246 \div 3)}[/tex]
[tex]\mathsf{= (151.29) - (0.246 \div 3)}[/tex]
[tex]\mathsf{= 151.29 - 0.246 \div3}[/tex]
[tex]\mathsf{= 151.29 - 0.082}[/tex]
[tex]\mathsf{= 151.208}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\large\boxed{\mathsf{Exactly \rightarrow} \frak{\ 151.208\ } \& \textsf{ Corrected to two significant figures}\rightarrow \frak{150 \ or \ 151}}\large\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]NEED HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
A
Step-by-step explanation:
The function has vertical asymptotes at x=7 and x=-3, so the denominator needs to have factors (x-7) and (x+3).
This eliminates all the options except for A.
Find the arc length if the measure of the central angle is 80° and the radius
is 8 inches.
Answer:
[tex]\frac{32\pi }{9}[/tex] or [tex]11.17[/tex]
Step-by-step explanation:
The formula for arc length is [tex]2\pi r( \frac{x}{360} )[/tex] where "r" stands for radius and "x" stands for your angle[tex]2\pi 8(\frac{80}{360} )[/tex]
[tex]=16\pi (\frac{80}{360} )[/tex]
[tex]=16\pi (\frac{2}{9})[/tex]
[tex]=\frac{32\pi }{9}[/tex]
Select the output of this algorithm
START
SET n = 4
SET d = 1
SET sum = 0
WHILE d < = n
IF n/d is integer THEN
sum = sum + d
ELSE
sum = sum + 0
END IF
d = d+1
END WHILE
OUTPUT sum
END
Answer:
bvjh
Step-by-step explanation:
bn
An example of a qualitative variable is Multiple Choice number of children in a family. weight of a person. color of ink in a pen. miles between oil changes.
Due to its subject-specific classification, ink color in pens is a qualitative variable.
What is a Qualitative variable?The factors that cannot be measured with a numerical value are known as qualitative variables. In order to define anything, these quantities are not quantified or tallied; instead, data is categorized.There is no numerical way to express it.Quantitative variableThe other choices are erroneous because the variables that are numerically specified in the other choices—an individual's weight, the number of children, and the number of miles—are these.Therefore, all of those are quantitative variables.Consequently, option (C) is the appropriate choice.
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HELP HELP HELP HELP
HELP HELP HELP HELP
Answer:
Vertex - (2, -1)
Axis of Symmetry - x = 2
X intercept - (3,0) (1, 0)
Y intercept (0, 3)
Domain - (negative infinity, positive infinity)
Range - [-1, infinity)
Step-by-step explanation:
I graphed with desmos and found it.
PLS HELP ME PLEASE
To measure the distance across a lake, a surveyor has taken the measurements shown in the diagram below. Determine the distance across the lake.
Using the law of cosines, it is found that the distance across the lake is of 978.5 feet.
What is the law of cosines?The law of cosines states that we can find the angle C of a triangle as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
in which:
c is the length of the side opposite to angle C.a and b are the lengths of the other sides.In this problem, the parameters are:
a = 800, b = 900, C = 70º.
Hence the distance across the lake is c, found as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
c² = 800² + 900² - 2(800)(900)cos(70º)
c² = 957491
[tex]c = \sqrt{957491}[/tex]
c = 978.5.
The distance across the lake is of 978.5 feet.
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How would I do these questions?
A parabola has x- ints of -1 and 2 and passes through (4,10). Find its equation.
A parabola has x-ints of -2 and 3 and y int of -3. Find its equation.
A parabola has x-ints of 1/2 and 2 and passes through the point (1,3). Find its equation.
Any help will be greatly appreciated. I don't know the format of writing it out, so try to explain it easily so I can understand it. Thank you!
Answer:
Step-by-step explanation:
hello :
1)
the equation is : f(x)= a(x+1)(x-2) because : x- ints of -1 and 2 means :
f(-1)=0 and f(2)=0
calculate : a given f(4)=10
so : a(4+1)(4-2)=10
10a =10 so : a = 1
the equation is : f(x)= (x+1)(x-2)
2) and 3) same method but * y int of -3* meanes : f(0)= - 3
THE FIRST ONE TO ANSWER GETS BRAINLIEST OR FIVE STARS!! The earnings of part-time employees at a local computer repair store can be modeled by the equation y = 22x + 125, where x represents the number of hours worked and y represents the total earnings. Jasmine works at a competing store where she earns the same hourly rate. After working for 15 hours, she earned $555. Write an equation to represent Jasmine’s total earnings.
(picture just if I made a typo)
Answer:
In total she got $555 so we have to divide that to see how much she got per hour.
Step-by-step explanation:
y/x=?
$555/15= $37
Now how much money multiplied by how many hours
$37 X 15 = $555
I hope this helps, if you need any more information just comment!
Have an Amazing Day!!!