Answer:
y = 2x + 3
Step-by-step explanation:
Hi there!
We are given the points (-1, 1) and (3,9) which belong to a line
We want to write the equation of the line in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
First, let's find the slope of the line
The slope (m) can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
Let's label the values of the points before we start, to avoid confusion and mistakes
[tex]x_1 = -1\\y_1=1\\x_2=3\\y_2=9[/tex]
Now substitute into the formula (note: the formula has SUBTRACTION, and we have NEGATIVE numbers, so we'll end up subtracting a negative)
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{9-1}{3--1}[/tex]
Simplify
m=[tex]\frac{9-1}{3+1}[/tex]
m=[tex]\frac{8}{4}[/tex]
Divide
m = 2
The slope of the line is 2
We can substitute this as m in y=mx+b.
y = 2x + b
Now we need to find b
As the equation passes through the point (-1, 1) and (3, 9), we can use either point to help solve for b.
Taking (3, 9) for example:
substitute 3 as x and 9 as y.
9 = 2(3) + b
Multiply
9 = 6 + b
Subtract 6 from both sides
3 = b
Substitute 3 as b in the equation
y = 2x + 3
Hope this helps!
Topic: finding the equation of the line
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Which statements describe the graph of 2 and StartFraction 8 over 9 EndFraction greater-than-or-equal-to x on a number line? Select three options. There is an open circle on 2 and StartFraction 8 over 9 EndFraction. The graph contains the point 0 There is a closed circle on 2 and StartFraction 8 over 9 EndFraction. The arrow points to the left. The arrow points to the right.
Inequalities help us to compare two unequal expressions. The options that are correct about the given statement are B, C, and D.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The points that are correct about the given inequality 2(8/9)≥x are:
The graph contains the point 0There is a closed circle on 2 and StartFraction 8 over 9 EndFraction.The arrow points to the left.Hence, the options that are correct about the given statement are B, C, and D.
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What is the area of the triangle in the coordinate plane?
36 units²
38 units²
66 units²
72 units²
Answer:
36 units
Step-by-step explanation:
area of right angle triangle =1/2* b*h.
by counting the square,b=8 units and h=9 units
therefore,area 1/2* 8units * 9units
1/2*72units^2
36units^3
4. (x + 4)2 + (y – 5)2 = 25
Center:
Radius:
Answer:
Center = (-4, 5)
Radius = 5
Step-by-step explanation:
Equation of a Circle :
(x - h)² + (y - k)² = r²(h, k) = coordinates of the centerr = radiusFinding the center :
h = -(4) = -4k = 5Center = (-4, 5)Finding the radius :
r² = 25r = √25radius = 5
Between which x-values and y-values does the cluster lie
Answer:
See below ~
Step-by-step explanation:
x-values :
Lowest : 2Highest : 10Lies between 2 and 10y-values :
Lowest = 4Highest = 11Lies between 4 and 11Answer:B
Step-by-step explanation: The cluster is the 5 points in the bottom right corner or; between x-values 8 and 10 and y-values 4 and 6.
An aircraft is timetabled to travel from A to B. Due to bad weather it flies from A to C then from C to B, where AC and CB make angles of 27° and 66° respectively with AB. If |AC| = 220 km, calculate |AB|.
Answer:
|AB| = 240 km
Step-by-step explanation:
Finding ∠C :
⇒ 27° + 66° + ∠C = 180°
⇒ ∠C = 180° - 93°
⇒ ∠C = 87°
Applying the Law of Sines :
⇒ sin 66° / 220 = sin 87° / AB
⇒ 0.913545458 / 220 = 0.998629535 / AB
⇒ AB = 220/0.913545458 x 0.998629535
⇒ AB = 240.819981 x 0.998629535
⇒ AB = 240.489946
⇒ |AB| = 240 km (nearest whole kilometer)
Answer:
|AB| = 240 km (nearest km)
Step-by-step explanation:
Draw a sketch with the given information (attached).
Calculate the missing angle (shown in red on the attached diagram).
Given:
∠CAB = 27°∠CBA = 66°The interior angles of a triangle sum to 180°
⇒ ∠ACB + ∠CAB + ∠CBA = 180°
⇒ ∠ACB + 27° + 66° = 180°
⇒ ∠ACB = 180° - 27° - 66°
⇒ ∠ACB = 87°
Use Sine Rule for sides to calculate |AB|:
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
[tex]\implies \sf \dfrac{|AB|}{\sin ACB}=\dfrac{|AC|}{\sin CBA}[/tex]
[tex]\implies \sf \dfrac{|AB|}{\sin (87^{\circ})}=\dfrac{220}{\sin (66^{\circ})}[/tex]
[tex]\implies \sf |AB|=\dfrac{220\:\sin (87^{\circ})}{\sin (66^{\circ})}[/tex]
[tex]\implies \sf |AB|=240.4899459...[/tex]
[tex]\implies \sf |AB|=240\:km\:(nearest\:km)[/tex]
Pls tell how did she get
1.15m il will marke brainliat
Answer:
Step-by-step explanation:
1.15 represents a 15% increase so if you want a 15 % increase from last year, you would multiply 1.15 by m to get 1.15m
:)
The product of a 25 and a number, increase by 8 is 68. find the number.
Answer:
2.4
Step-by-step explanation:
set up an equation to find x, the number.
[tex]25x+8=68[/tex]
subtract 8 from both sides
[tex]25x=60[/tex]
divide both sides by 25 to get x (the variable) alone
[tex]x=\frac{60}{25}=\frac{12}{5}=2.4[/tex]
Joey is putting all of his trophies onto 7 shelves. If he places 7 trophies on each shelf but still has 4 trophies left over, how many
trophies does he have?
OA. 53
OB. 35
OC. 18
OD. 49
Answer:
53
Step-by-step explanation:
7 * 7 = 49 + 4 = 53
Answer:
A. 53
Step-by-step explanation:
Find number of trophies on shelves:
7 shelves x 7 trophies each = 49 trophies on shelves
Find total number of trophies:
49 trophies on shelves + 4 leftover = 53 trophies overall
So the answer is A. 53
A cylinder has a diameter of 5 centimeters and a height of 50 millimeters. Which of the following steps should be done
first in order to find the surface area of the cylinder?
O multiply the circumference of the circle by the height of the cylinder
o calculate the circumference of the circle
convert the diameter and the height to the same unit
o determine the radius and multiply by 2
NEXT QUESTION
ASK FOR HELP
TURN ITIN
Answer:
convert the diameter and the height to the same unit
Step-by-step explanation:
Answer: convert the diameter and the height to the same unit
Step-by-step explanation:
The surface area of a cylinder can be found with A = 2πrh + 2πr². To use this formula, all units of measurement must be the same.
This can be converting 5 centimeters to millimeters or converting 50 millimeters to 5 centimeters.
d. Your doctor tells you you are in the 30th percentile for blood pressure among US adults. What is your systolic BP? Round to 2 decimal places.
Using the normal distribution, it is found that your systolic blood pressure is of 110.45.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Researching the problem on the internet, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 122, \sigma = 22[/tex].
The 30th percentile is X when Z = -0.525, hence your BP is given as follows.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.525 = \frac{X - 122}{22}[/tex]
X - 122 = -0.525 x 22
X = 110.45.
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An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.
Answer:
Length = 15.14, width = 7.14 and height = 2.43 inches.
( correct to the nearest hundredth).
Step-by-step explanation:
Let the lengths of the squares cut out be x inches.
Then the width of the box will be 12 - 2x and the length will be
20 - 2x inches.
The height of the box is x inches.
Volume V = x(20-2x)(12-2x)
To find the value of x when V is a maximum we find the derivative and equate it to zero.
V = x( 240 - 64x + 4x^2)
V = 4x^3 - 64x^2 + 240x
dV/dx = 12x^2 - 128x + 240 = 0
4(3x^2 - 32x + 60) = 0
This won't factor so we use the formula:
x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6
= 8.24, 2.43.
So one of these gives a maximum Volume.
The second derivative
d^2V/dx^2 = 24x - 128
When x = 8.24, this = 69.6 (positive) so this gives a minimum.
x = 2.43 gives a negative value ( -49.7) so this is the maximum
So the dimensions are:-
length = 20 - 2(2.43) = 15.14
width = 12 - 2(2.43) = 7.14
height = 2.43.
7th grade end of year Escape! Please HELPPPPPP! i will give 100 points.
Count the marbles in the jar:
9 spotted ones
6 purple
10 green
25 total
a) 10/25 = 2/5
B) 19/25
C) 9/25 x 9/25 = 81/625
D) 2/5 x 6/25 = 12/125
E) 6/25 x 19/25 = 114/625
F) 6/25 x 5/24 = 1/20
G) 19/25 x 18/24 = 57/100
H) 6/25 x 14/24 = 7/50
Which set of numbers best describes the possible values of x in the equation below?
[x-1)=Lx]
all integer values of x
O all real number values of x
O only negative values of x
O only noninteger values of x
Answer:
Only noninteger values of x
Step-by-step explanation:
did this already
Only non integer values of x best describes the possible values of x in the equation [x-1]=[x]
What is Number system?A number system is defined as a system of writing to express numbers.
When x is an integer, the equation simplifies to [x-1] = [x], which means that the greatest integer less than or equal to (x-1) is equal to the greatest integer less than or equal to x.
This is only possible if x-1 and x are consecutive integers, so x must be an integer value of n + 1/2 for some integer n.
For non-integer values of x, we have x-1 < [x] < x, which means that [x] is equal to the greatest integer less than or equal to x-1.
So, the equation becomes x-1 < [x] < x, which simplifies to x-1 < x - {x} <= x, where {x} is the fractional part of x.
Therefore, we have x-1 < x - {x} and x - {x} <= x, which gives 1 < {x} and {x} <= 0, which is not possible.
Hence, the only values of x that satisfy the equation are non-integer values of x.
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Including Jose, there are eight people in his family.
If order matters, how many ways can he arrange his family members into a row of five seats if Jose must sit in the first seat?
35
840
1,680
2,620
Answer: b=840
Step-by-step explanation:
edge 2022
do good on your tests !!
There are 840 ways can he arrange his family members into a row of five seats if Jose must sit in the first seat
What is Combination?A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Since, the order matters, we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
ⁿPₓ = n! / (n - x)!
In this question:
The first seat is Jose's.
The remaining four are organized among the other 7 members. So
There is no difference. So, 7 people can be sit in different ways as;
ⁿPₓ = n! / (n - x)!
⁷P₄ = 7! / (7 - 4)!
= 7! / 3!
= 840
So, the correct answer is, 840
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Using the Data Set {125, 6, 133, 129, 125}, find the standard deviation:
Question 1-3
Find the average rate of change of the function, f (x) = log₂ (4x) on the interval of x = 2 to x = 8.
Answer:
1/3
Step-by-step explanation:
The average rate of change of a function f(x) on an interval [a, b] is given by the formula ...
rate of change = (f(b) -f(a))/(b -a)
__
For the given function and interval, this is ...
(log₂(4·8) -log₂(4·2))/(8 -2) = (5 -3)/(6) = 1/3
The average rate of change is 1/3.
_____
In the attached graph, the line between the points at the ends of the interval can be seen to have a rise of 1 for a run of 3. Its slope is 1/3.
the backyard is 20 inches long and 37 inches wide. What is the area of the backyard.
- - - - - - -- - - - - - - - - - - - - -- -
[tex]\diamond\large\textsf{\textbf{\underline{Given\:question:-}}}[/tex]
The backyard is 20 inches long and 37 inches wide. What is the area of the backyard?
[tex]\diamond\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
We are given the backyard's length (20 inches long) and the backyard's width (37 inches wide).
We are asked to find the area of the backyard, which can be found using the following formula:-
[tex]\boxed{\bold{A_{(rectangle)}=LW}}[/tex]
Where:-
A=Area of rectangleL=Length (20 inches)W=Width (37 inches)
Substitute the values:-
[tex]\boxed{\bold{A=20*37}}[/tex]
On simplification,
✳︎ [tex]\boxed{\bold{A=740\:in^2}}[/tex], which is our final answer.
Good luck with your studies.- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - -
Answer: 37·20=740
Step-by-step explanation:
Nadia is buying sweater for $17.69 and a pair of pants for $24.35. if Nadia pays with a $50 bill, how much change will she receive
NEED HELP ASAP 10 POINTS
Drag the values to order them from least to greatest with the least at the top 6pi-6, pi^3, and 99
Answer:
the square root of 99
6pi-6
pi^3
Step-by-step explanation:
The square root of 99 is approximately 9.9.
6pi-6 is approximately 12.8
pi^3 is approximately 12.8
Given that A = {1, 2, 3, 4, 5, 6] maps respectively to B = {3, 4, 5, 6, 7, 8). Find an injective function f(x) such that f: A → B. Hint: Can you depict any relationship between sets A and B?
Answer: f(x) = x + 2
Step-by-step explanation:
A = {1, 2, 3, 4, 5, 6]
B = {3, 4, 5, 6, 7, 8)
for each A, B is 2 more
f(1) = 1 + 2 = 3
f(2) = 2 + 2 = 4
f(3) = 3 + 2 = 5
and so on...
⇒ f(x) = x + 2
You pick a card at random.
6
7
8
9
What is P(less than 7)?
Write your answer as a fraction or
whole number.
Obisa has a radio which uses 18-volt batteries. Each battery has 1.5 volts. How many batteries does he need to use his radio?
Answer:
I believe he would need 12 batteries
A car originally priced at $8,900 is on sale at 15% off. If the sales tax rate is 8.25%, how many dollars is the sale price of the car
If there is 15% off and the sales tax rate is 8.25%. Then the price of the car will be $ 8,189.11.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
A car originally priced at $8,900 is on sale at 15% off. If the sales tax rate is 8.25%.
The cost after 15% off will be
→ 0.85 × $8,900
→ $ 7,565
Then the final cost after the sale tax of 8.25% will be
Cost = $ 7,565 × 1.0825
Cost = $ 8,189.11
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Pleas help ppppppp pls
Step-by-step explanation:
option A is correct answer
What is the surface area of this right rectangular prism?
Enter your answer as a mixed number in the simplest form.
ft²
Answer:
A≈32[tex]\frac{3}{10}[/tex]ft²
--
To find the surface area of a right rectangular prism you must use this formula A=2(wl+hl+hw)
Then plug in your variebles
A=2( 1.33*1.5+5+1.5+5+1.33)
This comes out to be A≈32 [tex]\frac{3}{10}[/tex]
Answer:
32 1/3 ft² for K12
Look at this equation.
6x - 4= -4(X-5)
What value of x makes the equation true?
Answer:
Step-by-step explanation:
Equation 6x - 4= -4(X-5) Remove the brackets
Solution
6x - 4 = -4x + 20 Add 4x to both sides
6x + 4x -4 = -4x+4x + 20 Combine
10x - 4 = 20 Add 4 to both sides
10x - 4 + 4 = 20 + 4 Combine
10x = 24 Divide by 10
10x/10 = 24/10
x = 2.4
Answer: x = 2.4
How to do this...(⊙o⊙)?
1. Are the side lengths congruent?
2. Are the opposite sides parallel?
3. Are the adjacent sides perpendicular?
4. The most specific name for this quadrilateral is:
Answer:
opposite sides are congruentopposite sides are paralleladjacent sides are not perpendicularthe figure is a parallelogramStep-by-step explanation:
An easy way to determine the nature of the quadrilateral is to look at the lengths and midpoints of the diagonals. Adding and subtracting the coordinates of one end point from the other can tell what you need to know.
The diagonals of a parallelogram are mutual bisectors. The diagonals of a rhombus are perpendicular. The diagonals of a rectangle are congruent.
__
diagonal ACThe difference of end points of diagonal AC is ...
C -A = (7, 2) -(-6, 1) = (13, 1)
The sum of the end points of diagonal AC is ...
C +A = (7, 2) +(-6, 1) = (1, 3)
diagonal BDThe difference of end points of diagonal BD is ...
B -D = (0, 7) -(1, -4) = (-1, 11)
The sum of end points of diagonal BD is ...
B +D = (0, 7) +(1, -4) = (1, 3)
comparison of diagonalsmidpoints
The two diagonals have the same end point sum, (1, 3), meaning their midpoints are coincident. The figure is a parallelogram.
lengths
The lengths of the diagonals will be the same if the sum of squares of the coordinates of the end-point differences are the same.
Σ(C -A)² = 13² +1² = 170
Σ(B -D)² = (-1)² +11² = 122 ≠ 170 . . . . . not a rectangle
perpendicularity
The diagonals will be perpendicular if the "dot product" of the end-point differences is zero.
x1·x2 +y1·y2 = 13(-1) +1(11) = -2 ≠ 0 . . . . not a rhombus
The most specific name for this quadrilateral is parallelogram.
_____
Opposite sides of a parallelogram are congruent and parallel.
Adjacent sides of a rectangle are perpendicular. This is not a rectangle, so adjacent sides are not perpendicular.
A parallelogram that is not a rectangle or rhombus is described most specifically as a parallelogram.
Help me out with this math problem for 50 points!!!
Answer:
see attached for a graph-1, -2.6, -497Step-by-step explanation:
The solution to a one-variable inequality can be graphed on a number line. The number line is shaded where the values satisfy the inequality. Boundaries of shaded regions are marked by points that are either a solid dot, or an open circle, depending on whether the point is included in the solution or not.
__
Here, the inequality tells us any value of x that is less than or equal to -1 will satisfy the inequality. Since -1 is part of the solution set, that boundary point will be marked with a solid dot. Values less than -1 are shown on a number line to the left of the point marked -1.
The graph will be a solid dot at x=-1, and shading to its left.
__
Possible solutions are any values less than or equal to -1. Some are ...
-1
-1.073
-429
1. Kyle put $300 of his birthday money in the bank. The bank offers an annual interest rate of 4%, compounded twice a
year. How much money will Kyle have after three years?
Answer:
300(1 + 0.04/2)3(2) = $337.85
Step-by-step explanation:
