Answer:
1) graphical linear equation form (slope = -7, y-intercept = 2)
2) Standard linear form (slope = 2/3, y-intercept = -4/3)
Step-by-step explanation:
1) A graphical equation is always in the form of y = mx + c where y is the subject.
slope is the value before x which is -7
Y-intercept is where a line meets y axis so the value of x is 0. Y-intercept is 2.
y = -7x + 2
y= -7 (0) + 2 = 2
2) A standard form is where y is not the subject.
Step 1: Convert it into graphical equation form y = mx + c to identify the slope and y-intercept.
y + 2 = 2/3(x – 5)
y + 2 = 2/3x - 10/3
y = 2/3x - 10/3 -2
y= 2/3x - 4/3
slope is the value before x which is 2/3
Y-intercept is where a line meets y axis so the value of x is 0. Y-intercept is -4/3.
y= 2/3x - 4/3
y = 2/3 (0) - 4/3
y = -4/3
!!
The graph below shows a proportional relationship between x and y.
Answer:
4
Step-by-step explanation:
The problem statement tells you the constant of proportionality is y/x. The graph shows y=4 for x=1. Then y/x = 4/1 = 4.
The constant of proportionality is 4.
_____
Caveat
Before you copy this answer, be certain the graph in your problem statement is identical to this graph. If your marked point has different coordinates than (1, 4), your constant of proportionality may be different. It will still be computed as y/x, but you need to use the x and y values of the marked point on your graph (or those of any other point whose coordinates you can read).
What is the maximum number of times a line can cross the x-axis?
I needed help with the answer
Answer:
1 time
Step-by-step explanation:
A line is on straight thing that keeps going straight for ever so there for it can only cross the x axis once
What equation can be written from this sequence -50,-33,-16,1
Answer: [tex]a_n=-50+(n-1)17[/tex]
Step-by-step explanation:
The Arithmetic Sequence Formula is:
[tex]a_n=a_1+(n-1)d[/tex]
Where:
[tex]a_n[/tex] is the [tex]n^{th}[/tex] term of the sequence.
[tex]a_1[/tex] is the first term of the sequence.
[tex]n[/tex] is the term position.
[tex]d[/tex] is the common difference of any pair of consecutive numbers.
We can observe that the first term is:
[tex]a_1=-50[/tex]
Now, we need to find "d". This is:
[tex]d=-16-(-33)\\d=-16+33\\d=17[/tex]
Then, substituting, we get the following equation:
[tex]a_n=-50+(n-1)17[/tex]
How to find the degree of an angle without a protractor
Explanation:
The purpose of trigonometry and the trigonometric ratios sine, cosine, and tangent is to help you calculate angles based on the ratios of side lengths of triangles they are found in.
help, please and thank you
Answer:
see below
Step-by-step explanation:
The answer is a list of arcs. That means you can ignore the answer choices that are lists of angles or line segments.
The only requirement is that the end points of the arc lie on the circle. Points M, N, P, Q, R are all on the circle, and all are at the end of line segments that intercept them. Any combination of these letters will define an intercepted arc.
Can someone check this for me? Thanks!
Answer:
two or zero positive real roots, one or zero negative real roots
Step-by-step explanation:
f(x) = 9x³ − 2x² − x + 5
There are 2 sign changes, so the number of positive real zeros is 2 or an even number less than that. So there are two or zero positive real roots.
f(-x) = 9(-x)³ − 2(-x)² − (-x) + 5
f(-x) = -9x³ − 2x² + x + 5
There is 1 sign change, so the number of negative real zeros is 1 or an even number less than that. So there is exactly 1 negative real root.
Your answer is correct.
Reymonte went hiking last weekend. He started at an elevation of 49 feet below sea level, which can be thought of as an
elevation of -49 feet. At the end of the hike, his elevation was 281 feet higher than where he started. What was his
elevation relative to sea level, in feet, at the end of the hike?
Answer:
232 ft above sea level
Step-by-step explanation:
He started at -49 ft and then he was later 281 ft higher than that... so just do -49+281 or 281-49= 232
Reymonte started his hike 49 feet below sea level, or at an elevation of -49 feet. He then hiked up 281 feet. By adding these two numbers together, we find that Reymonte ended his hike at an elevation of 232 feet above sea level.
Explanation:The subject of this question is Mathematics, and it's specifically related to the topic of integers. In the context of this question, elevation is used to indicate height relative to sea level, with negative indicating below sea level and positive above. Reymonte started at an elevation of -49 feet, or 49 feet below sea level. He then hiked up 281 feet.
To find his final elevation relative to sea level, we add the increase in elevation to his initial elevation. So, we add 281 feet to -49 feet:
-49 feet + 281 feet = 232 feet
So at the end of the hike, Reymonte was at an elevation of 232 feet above sea level.
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On a map the scale in four inches to one mile. The distance on the map from Huntington to Northport is ten inches. How many miles apart are they?
Answer:
yall still in schoo
Step-by-step explanation:
Will someone please explain step by step how to do this question? Thank you!
Answer:
(1000, 179°)
Step-by-step explanation:
In rectangular coordinates, where east is the +x direction and north is the +y direction, the woman's final position is (1000 yards west, 20 yards north) or (-1000, 20).
This is translated to polar coordinates (r, θ) using ...
r = √(x² +y²)
θ = arctan(y/x) . . . . with attention to quadrant
The magnitude of the distance (r) is ...
r = √((-1000)² +20²) = √1000400 ≈ 1000.2 ≈ 1000
θ = arctan(20/-1000) in quadrant 2, so is 180° -1.15° = 178.85° ≈ 179°
In polar coordinates, the final position is (1000, 179°).
What is the longest side of a right triangle called?
Answer:
Step-by-step explanation:
hypotenuse
If n-3>8 and n+1<14, then which of the following could be a value for n?
A) 11
B) 12
C) 13
D) 14
Answer:
12
Step-by-step explanation:
12-3>8and 12+1<14
9>8 and 13<14
If the lengths of an object are measured in feet, then the area of the object will be measured in which of the following units of measurement?
feet
square feet
cubic feet
feet to the fourth power
Answer:
square feet
Step-by-step explanation:
Units multiply the same way any variable does:
(x ft)(y ft) = x·y ft·ft = x·y ft² . . . . . . the units of the product are square feet
Answer:
Square feet
Step-by-step explanation:
The area of the object will be measured in square feet.
Hope this helps!
PLZ HELP MARKIN BRAINIEST!!!
From the graph, when x = 1, y = 57,000.
Replace x with 1 in the equations and see if any of the Y 's equal 57,000 :
y = -2610.82(1) + 47860.82 = 45,250
y = 219(1)^2 - 6,506.78(1) + 59,385 = 219 - 6506.78 + 59385 = 53,097.22
y = 54041.5(0.9)^1 = 48,637.35
y = 10,504.6 (1.1)^1 = 11,555.06
The second equation is the closest. so try another x value to see if it is close to the Y value:
Let's try x = 14:
y = 219(14)^2 - 6506.78(14) + 59,385 = 42924 - 91094.92 + 59385 = 11,214.08
This is close to Y = 12,00 shown on the graph
SO the closest equitation is y = 219x^2 - 6506.78x + 59385
A wall of a building is 34 inches wide 16 inches is concrete and 4 inches is limestone what fraction of the wall is brick
Answer:
7/17
Step-by-step explanation:
16 inches of concrete plus 4 inches of limestone come to 20 inches of concrete and limestone combined. Subtracting 20 inches from 34 inches yields 14 inches. 14 inches of the total wall thickness (34 inches) is brick. This fraction is 14/34, or 7/17.
The fraction of the wall made up of brick is found by subtracting the concrete and limestone widths from the total width of the wall. The fraction is 14/34, which simplifies to 7/17.
Explanation:The question is asking us to find the fraction of the wall made up of brick. The total width of the wall is 34 inches. Substrating the concrete and limestone widths from the total width (34 inches - 16 inches for concrete - 4 inches for limestone) we get a result of 14 inches for the brick portion. To express this as a fraction of wall's total width, we place the number 14 (the width of the brick portion) over 34 (the total width of the wall). Therefore, the fraction of the wall that is brick is 14/34, which simplifies to 7/17 when reduced to lowest terms.
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[30 points] Please give an explanation! Buses to Manchester leave London Victoria bus station every 24 minutes.
Buses to Birmingham leave the same bus station every 20 minutes.
A bus to Manchester and a bus to Birmingham both leave the station at 09.00.
When will a bus to Manchester and a bus to Birmingham next leave the bus
station at the same time?
THANK YOU! :)
You need to find the least common multiple of 24 and 20.
[tex]24=2^3\cdot3\\20=2^2\cdot5\\\\\text{lcm}(20,24)=2^3\cdot 3\cdot 5=120[/tex]
120 min = 2 h
9:00 + 2:00=11:00
So, the answer is at 11:00
Final answer:
To find the next time both the Manchester and Birmingham buses leave London Victoria bus station at the same time, calculate the Least Common Multiple (LCM) of their departure intervals, which is 120 minutes. The buses will next leave together 2 hours after their 09:00 departure, at 11:00.
Explanation:
The question involves finding a common multiple of the times buses to Manchester and Birmingham leave the station. Since Manchester buses leave every 24 minutes and Birmingham buses leave every 20 minutes, we need to calculate the Least Common Multiple (LCM) of 24 and 20. To find the LCM of 24 and 20, we can list the multiples of each number until we find the smallest multiple they have in common.
Multiples of 24: 24, 48, 72, 96, 120, 144, ...Multiples of 20: 20, 40, 60, 80, 100, 120, ...The smallest common multiple is 120 minutes, which is 2 hours. Since both buses leave at 09:00, the next time both buses will leave at the same time will be 2 hours later, at 11:00.
At a party, there are 2 six-packs of regular cola, 1 six-pack of diet cola, 1 six-pack of cherry cola, and 1 six-pack of vanilla cola. If a can of cola is chosen at random, what is the probability it will be a cherry cola or a vanilla cola?
A. 1/5 B. 2/5 C. 1/4 D. 1/2 Please select the best answer from the choices provided
A B C D
Answer:
B.
Step-by-step explanation:
There are 5 total 6-packs of cola. 1 is cherry and the other is vanilla. 2 out of 5 are the flavors. This means you have a 2 in 5 chance of getting a cherry or vanilla cola.
Final answer:
The probability of randomly choosing a cherry cola or vanilla cola from all the cans available is 2/5, since there are 12 such cans out of a total of 30 cans.
Explanation:
To find the probability that a can of cola chosen at random will be either cherry cola or vanilla cola, we first need to count the total number of cans and then count the number of cherry and vanilla cola cans.
There are 2 six-packs of regular cola, which amounts to 12 cans. There is 1 six-pack each of diet cola, cherry cola, and vanilla cola, which adds up to 6 + 6 + 6 = 18 cans. In total, there are 12 + 18 = 30 cans of cola.
Out of these, there are 6 cans of cherry cola and 6 cans of vanilla cola, totalling 12 cans. Thus, the probability of choosing a cherry or vanilla cola is the number of cherry and vanilla cans divided by the total number of cans, which is 12/30.
When we simplify 12/30, we get 2/5. Therefore, the correct answer is B. 2/5.
Which of the following is the quotient of the rational expressions shown here?
For this case we must find the quotient of the following expression:
[tex]\frac {\frac {x} {x-1}} {\frac {1} {x + 1}}[/tex]
Applying double C we have the following expression:
[tex]\frac {x (x + 1)} {x-1} =[/tex]
Applying distributive property to the terms within the parentheses of the numerator we have:
[tex]\frac {x ^ 2 + x} {x-1}[/tex]
Thus, the quotient is given by option A
Answer:
Option A
Answer:
The answer is option A. (x^2 + x)/(x-1)
Step-by-step explanation:
To solve this problem, we must first understand how to divide fractions. When dividing fractions, the first fraction is unchanged and is multiplied by the reciprocal of the second fraction. If we apply this knowledge to this problem, we get:
x/x-1 * x+1/1
When we multiply fractions, we simply multiply both of the numerators together and both of the denominators together to create a single fraction.
In this case we get:
x(x+1)/x-1
When we simplify this single fraction by using the distributive property, we get the following:
(x^2 + x)/(x-1)
Therefore, your answer is option A.
Hope this helps!
PLS HELP SHOW ALL YOUR WORKING
A - rolling exactly one six
[tex]P(A)=\dfrac{1}{5}\cdot\dfrac{4}{5}+\dfrac{4}{5}\cdot\dfrac{1}{5}=\dfrac{4}{25}\cdot \dfrac{4}{25}=\dfrac{16}{625}[/tex]
What does d = in this equation? d — =21 7
which description matches the transformations y=cos x undergoes to produce y=-2cos3x?
A. horizontal compression by factor 3, vertical stretch by factor 2, then reflection across the x-axis.
B. horizontal shift left 2 units, then vertical shift up by 3 units.
C. reflection across the y-axis, vertical shift up by 2 units, horizontal shift right by 3 units.
D. horizontal stretch by factor 2, reflection across the x-axis, then vertical stretch by factor 3.
Answer:
horizontal compression by factor 3, vertical stretch by factor 2, then reflection across the x-axis ⇒ answer A
Step-by-step explanation:
* Lets revise some transformation
- A vertical stretching is the stretching of the graph away from
the x-axis
# If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched
by multiplying each of its y-coordinates by k.
# If k should be negative, the vertical stretch is followed by a reflection
across the x-axis.
- A horizontal compression is the squeezing of the graph toward
the y-axis.
# If k > 1, the graph of y = f(k•x) is the graph of f(x) horizontally
compressed by dividing each of its x-coordinates by k.
* Lets solve the problem
∵ y = cos x
∵ y = -2 cos 3x
- At first cos x multiplied by -2
∵ y multiplied by -2
∵ 2 > 1
∴ y = cos x is stretched vertically by factor 2
∵ The factor 2 is negative
∴ y = cos x reflected across the x-axis
∴ The function y = cos x stretched vertically with factor 2 and then
reflected across the x-axis ⇒ (1)
∵ cos x changed to cos 3x
∵ x multiplied by 3
∵ 3 > 1
∴ y = cos x compressed horizontally by factor 3
∴ The function y = cos x compressed horizontally by factor 3 ⇒ (2)
- From (1) and (2)
* The function y = cos x has horizontal compression by factor 3,
vertical stretch by factor 2, then reflection across the x-axis to
produce y = -2 cos 3x
Answer:
It is A
Step-by-step explanation:
AP3x
A baseball diamond has an angle of 90 degrees at home plate. The manager assigns each of 3 assistant coaches a section of the ball field to monitor during a game. The angle measures of the sections at home plate can be ( 7x - 49); ( 2/3x + 21), and ( 3/4x + 17). What are the angle measures of each of the three sections? Explain how you got your answer?
Answer:
the three angle measures are 35°, 29°, 26°
Step-by-step explanation:
The sum of the angle measures will be 90°, assuming the sections do not overlap. Then ...
( 7x - 49) + ( 2/3x + 21) + ( 3/4x + 17) = 90
(8 5/12)x -11 = 90 . . . . . simplify
x = 101/(8 5/12) = 12 . . . divide by the coefficient of x
Then the angles are ...
7x -49 = 7·12 -49 = 35
2/3x + 21 = 2/3·12 +21 = 29
3/4x +17 = 3/4·12 +17 = 26
The angle measures are 35°, 29°, 26°.
_____
Check
35 +29 +26 = 90 . . . . the sum of the covered section angles is 90°
_____
We assume you can manage addition of fractions and division by a mixed number or improper fraction. If not, convert all of the coefficients of x to multiples of 1/12. Instead of dividing by the coefficient of x, multiply by the inverse of the coefficient of x.
To find the angle measures of each of the three sections at home plate, the equation (7x - 49) + (2/3x + 21) + (3/4x + 17) = 90 is solved to find that x equals 12. Substituting 12 for x, the angle measures are calculated to be 35 degrees, 29 degrees, and 26 degrees.
Explanation:Since the angle at home plate is 90 degrees, the sum of the angles for the sections must also be 90 degrees. This allows us to set up the following equation:
(7x - 49) + (2/3x + 21) + (3/4x + 17) = 90
To solve this equation, we combine like terms. First, find a common denominator for the x terms, which is 12. So, we convert all terms into twelfths:
(84/12)x - (49)(8/12)x + (21)(9/12)x + (17)Combining these we get:
(101/12)x - 11 = 90
Add 11 to both sides to isolate the variable term:
(101/12)x = 101
Now, divide both sides by (101/12):
x = 12
Now we will substitute this value for x into the original expressions to get the angle measures:
(7x - 49) = (7*12 - 49) = 35 degrees(2/3x + 21) = (2/3*12 + 21) = 29 degrees(3/4x + 17) = (3/4*12 + 17) = 26 degreesTherefore, the angle measures for the sections are 35 degrees, 29 degrees, and 26 degrees.
What is the probability that you will select someone from the survey that does not watch ABC?
13/45
16/45
4/9
9/20
Answer:
4/9
Step-by-step explanation:
1 Point
What is the remainder for the synthetic division problem below?
Answer:
A. 3
Step-by-step explanation:
see attached for the tableau
___
As you know, the number on the bottom row is multiplied by the divisor to get the next middle-row number to the right. Top and middle rows are added to get the bottom row.
Simplify: 5x+50/x+5 • 1/x+10
[tex]\bf \cfrac{5x+50}{x+5}\cdot \cfrac{1}{x+10}\implies \cfrac{5~~\begin{matrix} (x+10) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{x+5}\cdot \cfrac{1}{~~\begin{matrix} x+10 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \cfrac{5}{x+5}[/tex]
Answer:
The correct answer option is C. [tex] \frac { 5 } { x + 5 } [/tex].
Step-by-step explanation:
We are given the following expression and we are to simplify it:
[tex] \frac { 5 x + 5 0 } { x + 5 } . \frac { 1 } { x + 1 0 } [/tex]
We would take the common terms out and then cancel any like terms present in the expression to get the simplest form.
[tex] \frac { 5 ( x + 1 0 ) } { x + 5 } . \frac { 1 } { x + 1 0 } [/tex]
[tex] \frac { 5 } { x + 5 } [/tex]
Therefore, the correct answer option is C. [tex] \frac { 5 } { x + 5 } [/tex].
Find the number of real number solutions for the equation. x2 + 5x + 7 = 0 0 cannot be determined 1 2
[tex]\Delta=5^2-4\cdot1\cdot7=25-28=-3[/tex]
[tex]\Delta<0[/tex] so 0 solutions.
Answer:
No Real roots to this Quadratic Equation
Step-by-step explanation:
Our Quadratic equation is given as
[tex]x^2+5x+7=0[/tex]
In order to find that do we have the real roots of a quadratic equation , the Discriminant must be greater or equal to 0. The Discriminant is denoted by D and given by the formula
[tex]D= b^2-4ac[/tex]
Where b is the coefficient of the middle term containing x, a is the coefficient of the term containing [tex]x^{2}[/tex] and the c is the constant term.
Hence we have
a = 1 , b = 5 and c = 7
Calculate D
[tex]D=b^2-4ac\\D=5^2-4*1*7\\D=25-28\\D=-3[/tex]
Hence we see that the Discriminant (D) is less than 0, our answer is no real roots to this quadratic equation.
Please help!!??? Will give brainliest!
Explanation:
Divide the frequency numbers by their total to get the relative frequency. Plot that on your graph.
P(0 heads) = 4/80 = 0.05
P(1 head) = 8/80 = 0.10
P(2 heads) = 36/80 = 0.45
P(3 heads) = 20/80 = 0.25
P(4 heads) = 12/80 = 0.15
Ryan is trying a low-carbohydrate diet. He would like to keep the amount of carbs consumed in grams between the levels shown in the following compound inequality:
110 < 2x + 10 and 2x + 10 < 310
Solve for x in this inequality, and explain what the answer represents.
x > 50 and x < 150; Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.
x < 50 and x > 150; Ryan needs to consume less than 50 grams of carbohydrates or more than 150 grams of carbohydrates.
x > 60 and x < 160; Ryan needs to consume more than 60 grams of carbohydrates, but less than 160 grams of carbohydrates.
x < 60 and x > 160; Ryan needs to consume less than 60 grams of carbohydrates or more than 160 grams of carbohydrates.
Answer:
Option A (x > 50 and x < 150; Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates).
Step-by-step explanation:
There are two inequalities. One is 110 < 2x + 10 and 2x + 10 < 310. x is the amount of carbs consumed in grams, the first inequality is the lower limit, and the second inequality is the upper limit. The question requires to solve the two inequalities.
1)
110 < 2x + 10.
100 < 2x.
50 < x (or x > 50).
2)
2x + 10 < 310.
2x < 300.
x < 150.
Now combining the two inequality gives:
50 < x < 150.
So Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates. Therefore, Option A is the correct answer!!!
Answer:
a
Step-by-step explanation:
ASAP!!! Use the pythagorean theorem to prove that the point (√2/2, √2/2) lies on the unit circle. I need setup, explination, answer
Answer:
In brief, apply the pythagorean theorem to show that the distance between the point [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] and the origin is [tex]1[/tex].
Step-by-step explanation:
The pythagorean theorem can give the distance between two points on a plane if their coordinates are known.
A point is on a circle if its distance from the center of the circle is the same as the radius of the circle.
On a cartesian plane, the unit circle is a circle
centered at the origin [tex](0,0)[/tex]with radius [tex]1[/tex].Therefore, to show that the point [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] is on the unit circle, show that the distance between [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] and [tex](0,0)[/tex] equals to [tex]1[/tex].
What's the distance between [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] and [tex](0,0)[/tex]?
[tex]\displaystyle \sqrt{\left(\frac{\sqrt{2}}{2}-0}\right)^{2} + \left(\frac{\sqrt{2}}{2}-0\right)^{2}} = \sqrt{\frac{1}{2} + \frac{1}{2}}= \sqrt{1}= 1[/tex].
By the pythagorean theorem, the distance between [tex](\sqrt{2}/2,\sqrt{2}/2) [/tex] and the center of the unit circle, [tex](0,0)[/tex], is the same as the radius of the unit circle, [tex]1[/tex]. As a result, the point [tex](\sqrt{2}/2,\sqrt{2}/2)[/tex] is on the unit circle.
which of these figures must be a rectangle?
Answer:
A rectangle is a parallelogram with at least one right angle is the best choice ⇒ answer A
Step-by-step explanation:
* Lets revise the properties of the rectangle
# Each two opposite sides are parallel
# Each two opposite sides are equal in length
# Its two diagonals bisect each other and equal each other
# Its four angles are right angles
- The parallelogram can be a rectangle if:
# Two adjacent sides are perpendicular to each other means one
angle of its four angles is a right angle
- OR
# Its two diagonals are equal in length
* Lets solve the problem
- We will study the answers to chose the best one
# Answer A
- A rectangle is a parallelogram with at least one right angle
∵ Each tow opposite angles are equal in the rectangle
∵ One of the is right angle means its measure is 90°
∴ The measure of the opposite angle is also 90°
∵ The sum of the measures of the four angles is 360°
∴ The sum of the measures of the other two angles is;
360 - (90 + 90) = 180°
∵ They are equal to each other (opposite angles)
∴ The measure of each one = 180 ÷ 2 = 90°
∴ The measure of the four angles are 90°
∴ The four angles of the rectangle are right angles
* A rectangle is a parallelogram with at least one right angle is the
best choice
Answer:it is A
Step-by-step explanation:
PLEASE HELP ME FAST!!!!!!!
Answer:
I think it is (5, -2)
I hope it helps.
Step-by-step explanation: