Answer:
The answer is x + 4y = 7
Equation of a line is y = mx + c
Where m is the slope
c is the y intercept
Slope of the line between the points
(-1, 2) and (3, 1) is
Slope = 1-2/ 3+1 = - 1/4
Equation of the line using point
(-1, 2) is
y - 2 = -1/4(x + 1)
4y - 8 = - x - 1
x + 4y = 7
Hope this helps you
Which ordered pairs are solutions to the inequality –2x+y>-4?
Select each correct answer.
(3, -1)
0 (-1, 1)
(0, -5)
(1, - 2)
0 (0,1)
Answer:
answer is (0,1)
Step-by-step explanation:
check
by substituting x=0 and y=1 in the equation above
- 2(0)+1> -4
1> -4
Thereby (0,1) is the required solution to the inequality
Identify the surface area of the composite figure in terms of π.
Answer:
78π m²
Step-by-step explanation:
The lateral area of the cylinder is ...
LA = 2πrh
LA = 2π(3 m)(8 m) = 48π m²
The lateral area of one cone is ...
LA = πrh . . . . where h is the slant height
LA = π(3 m)(5 m) = 15π m²
Then the total surface area of the figure is the area of the two cones plus that of the cylinder:
S = 2(cone area) + cylinder area
S = 2(15π m²) +(48π m²)
S = 78π m²
From the equation, find the axis of symmetry of the parabola.
y = 4x+ 32x+ 61
a. x= 3
x=-4
C.
b. X= 4
d. X=-3
Which of the following are reasons used in the proof that the angle-bisector construction can be used to bisect any angle?
Check all that apply
A. Any Line segment can be extended indefinitely
B. All of the radii of a circle are congruent
C .CPCTC
D. SSS triangle congruence postulate
Answer: B C D
Step-by-step explanation:
just answered it for AP3X
Reasons used in the proof that the angle-bisector construction can be used to bisect any angle are as follows:
B. All of the radii of a circle are congruent
C .CPCTC
D. SSS triangle congruence postulate
What is angle bisector ?" Angle bisector is defined as the ray which divides the angle into two equal parts."
According to the question,
A. Any Line segment can be extended indefinitely is not required to bisect any angle .
Therefore , it is not a correct option.
B. All of the radii of a circle are congruent : To bisect an angle draw an arc with same radii is used in constructing an angle bisector .
Therefore , Option B is a correct option.
C. CPCTC : Corresponding parts of a congruent triangle are congruent is required to proof angle bisector. As it proofs two triangles are congruent.
Therefore, Option C is the correct option.
D. SSS triangle congruence postulate : It is required an important step to prove that two triangles are congruent which imply proof of angle - bisector construction.
Therefore, Option D is the correct option.
Hence, Option B, Option C , Option D are the correct answer.
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PLEASE HURRY Solve for X assume that lines that which appear tangent are tangent
Answer:
x = 8
Step-by-step explanation:
In a circle if two chord intersects as shown in figure
and length of a chord at point of intersection is a and b
and length of another chord at point of intersection is c and b
a*b = c*d
using this relation here, we have
8*(x+7) = 10 * (4 +x)
=> 8x + 56 = 40 + 10x
subtracting 40 and 8x from both sides
=>8x + 56 - 8x -40= 40 + 10x -8x -40
=> 16 = 2x
=> x = 16/2 = 8
Thus, x = 8
Trying to find the missing segment to the triangle in the attached image.
Answer:
25
Step-by-step explanation:
The Side Splitter Theorem says that if a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally. Therefore:
6/15 = 10/?
6*? = 10*15
? = 10*15/6
? = 25
Find the y-intercept of the line. Y=16/13x - 19/6
Answer:
y intercept is -19/6
Step-by-step explanation:
The slope intercept form of a line is given by
y = mx+b where m is the slope and b is the y intercept
y = 16/13x - 19/6
The slope is 16/13 and the y intercept is -19/6
Answer:
[tex]\boxed{-\frac{19}{6} }[/tex]
Step-by-step explanation:
Use slope-intercept formula.
[tex]y=mx+b[/tex]
[tex]m[/tex] is the slope of the line.
[tex]b[/tex] is the y-intercept of the line.
The equation of the line is already in slope-intercept form.
[tex]y=\frac{16}{3} x+-\frac{19}{6}[/tex]
[tex]b= -\frac{19}{6}[/tex]
How many solutions a system of linear equations have if: Questions. 1.the equations have different slopes? 2.the equations have the same slope and different y-intercepts. 3.the equations have the same slope and same y-intercepts. Answers. A.no solutions. B.infinetly as many solutions C.two solutions. D.one solution
Answer:
see below
Step-by-step explanation:
1.the equations have different slopes? They will intersect at one point so one solution
2.the equations have the same slope and different y-intercepts. They are parallel lines with a different y intercept so they will never intersect - no solutions
3.the equations have the same slope and same y-intercepts. they are the same line so they have infinite solutions
Answer:
1. One solution
2. no solution
3. infinite number of solutions.
Step-by-step explanation:
How many solutions a system of linear equations have if: Questions.
(assuming a system of two equations)
1.the equations have different slopes?
One unique solution, which is at the intersection point.
2.the equations have the same slope and different y-intercepts.
The equations/lines are then parallel but NOT coincident. They will never meet, therefore NO solution.
3.the equations have the same slope and same y-intercepts.
The two lines/equations are in effect coincident. Therefore there is an infinite number of solutions.
Answers. A.no solutions. B.infinetly as many solutions C.two solutions. D.one solution
8
Express it in slope-intercept form.
6
Enter the correct answer.
OOO
DONE
Clear all
2
6 8
Answer:
I'm confused what's the question ?
PLEASE HELP Order these numbers from least to greatest. 2 1/10, 61/10, 3.122, 3.19
Answer: 2 1/10, 3.122, 3.19, 61/10
Step-by-step explanation:
Let's first turn each number into decimal form: (1/10=.1, 2/10=.2,etc.)
2.1, 6.1, 3.122, 3.19. Obviously, the smallest number is 2.1, because it has a 2 in the ones place. Next, we see a tie in the ones place between 3.122 and 3.19. Then we look at the tenths place and see another tie. Then, at the hundredths place, we see that 3.19 is greater that 3.122. Thus, the order of the numbers is 2.1,3.122,3.19,6.1.
Hope it helps <3
Can someone please help with this maths
Hey there! :)
Answer:
C. (0, 5)
Step-by-step explanation:
Where the equation crosses the y axis is known as the y-intercept.
In the equation y = mx + b, the b value represents the y-intercept where x = 0. Therefore:
Rearrange the equation pictured:
y = 5 - 3x --> y = -3x + 5
The b value in this equation is 5, so
The y-intercept of this equation is (0, 5).
Answer:
(0,5)Option C is the correct option.
Here,
y=5-3xWhen X=0
y= 5-3*0
= 5-0
=5
x=0
y=5
Hope this helps...
Good luck on your assignment..
A department store stocks pants and shorts in the colors black and blue. The relative frequency of their orders for blue pants is half the relative frequency of their orders for black shorts. Which two-way frequency table could represent the data from the store's orders?
Answer:
Table 2
Step-by-step explanation:
The question is to identify the table where the relative frequency of orders for blue pants is half the relative frequency of their orders for black shorts.
We are interested in the number of blue pants and black shorts.
If we name them as p and b respectively, then we are looking for a table where s/p=2
Let's verify relevant data in all tables:
Table 1:
p= 82, s= 41 ⇒ s/p= 41/82 ≠ 2, no, not this oneTable 2:
p= 57, s= 114 ⇒ s/p= 114/57 = 2, yes, it is the oneTable 3:
p= 78, s= 110 ⇒ s/p= 110/78 ≠ 2, no, not this oneTable 4:
p= 44, s= 150 ⇒ s/p= 150/44 ≠ 2, no, not this oneSo only one of tables- the second one from top represents the required data.
Answer:
The second table
Step-by-step explanation:
I did the test.
A math class consists of 25 students, 14 female and 11 male. Three students are selected at random to participate in a probability experiment. Compute the probability that a. a male is selected, then two females. b. a female is selected, then two males. c. two females are selected, then one male. d. three males are selected. e. three females are selected.
Answer:
(a) The probability that a male is selected, then two females is 0.4352.
(b) The probability that a female is selected, then two males is 0.3348.
(c) The probability that two females are selected, then one male is 0.4352.
(d) The probability that three males are selected is 0.0717.
(e) The probability that three females are selected is 0.1583.
Step-by-step explanation:
We are given that a math class consists of 25 students, 14 female and 11 male. Three students are selected at random to participate in a probability experiment.
(a) The probability that a male is selected, then two females is given by;
Number of ways of selecting a male from a total of 11 male = [tex]^{11}C_1[/tex]
Number of ways of selecting two female from a total of 14 female = [tex]^{14}C_2[/tex]
Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]
So, the required probability = [tex]\frac{^{11}C_1 \times ^{14}C_2}{^{25}C_3}[/tex]
= [tex]\frac{\frac{11!}{1! \times 10!} \times \frac{14!}{2! \times 12!} }{\frac{25!}{3! \times 22!} }[/tex] {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{1001}{2300}[/tex] = 0.4352
(b) The probability that a female is selected, then two males is given by;
Number of ways of selecting a female from a total of 14 female = [tex]^{14}C_1[/tex]
Number of ways of selecting two males from a total of 11 male = [tex]^{11}C_2[/tex]
Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]
So, the required probability = [tex]\frac{^{14}C_1 \times ^{11}C_2}{^{25}C_3}[/tex]
= [tex]\frac{\frac{14!}{1! \times 13!} \times \frac{11!}{2! \times 9!} }{\frac{25!}{3! \times 22!} }[/tex] {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{770}{2300}[/tex] = 0.3348
(c) The probability that two females is selected, then one male is given by;
Number of ways of selecting two females from a total of 14 female = [tex]^{14}C_2[/tex]
Number of ways of selecting one male from a total of 11 male = [tex]^{11}C_1[/tex]
Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]
So, the required probability = [tex]\frac{^{14}C_2 \times ^{11}C_1}{^{25}C_3}[/tex]
= [tex]\frac{\frac{14!}{2! \times 12!} \times \frac{11!}{1! \times 10!} }{\frac{25!}{3! \times 22!} }[/tex] {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{1001}{2300}[/tex] = 0.4352
(d) The probability that three males are selected is given by;
Number of ways of selecting three males from a total of 11 male = [tex]^{11}C_3[/tex]
Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]
So, the required probability = [tex]\frac{^{11}C_3}{^{25}C_3}[/tex]
= [tex]\frac{ \frac{11!}{3! \times 8!} }{\frac{25!}{3! \times 22!} }[/tex] {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{165}{2300}[/tex] = 0.0717
(e) The probability that three females are selected is given by;
Number of ways of selecting three females from a total of 14 female = [tex]^{14}C_3[/tex]
Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]
So, the required probability = [tex]\frac{^{14}C_3}{^{25}C_3}[/tex]
= [tex]\frac{ \frac{14!}{3! \times 11!} }{\frac{25!}{3! \times 22!} }[/tex] {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{364}{2300}[/tex] = 0.1583
(a) The probability that a male is selected, then two females is 0.4352.
(b) The probability that a female is selected, then two males is 0.3348.
(c) The probability that two females are selected, then one male is 0.4352.
(d) The probability that three males are selected is 0.0717.
(e) The probability that three females are selected is 0.1583.
Determine both the x and y intercepts. Please help! Will mark brainliest!
Answer:
y-intercept: (0, 2.5)
x-intercept: (1.67, 0)
Step-by-step explanation:
Right now, you have 3x + 2y = 5. You want to change it into slope-intercept form to make the problem easier to solve.
2y = -3x + 5
y = -3/2x + 5/2
From here, you can see that the y-intercept is (0, 5/2). You can also say that the y-intercept is (0, 2.5).
To get the x-intercept, substitute 0 for y.
0 = -3/2x + 5/2
3/2x = 5/2
3x = 5
x = 5/3
So, the x-intercept is (5/3, 0). You can also say that the x-intercept is (1.67, 0).
Hope this helps!
Answer:
Step-by-step explanation:
To find the x-intercept, let y = 0. Then 3x = 5 and x = 5/3, or x = 1.667, and the x-intercept is (1.667, 0).
To find the y-intercept, let x = 0. Then 2y = 5 and y = 5/2 or 2.5. Then the y-intercept is (0, 2.5).
How do you do this [tex]||x-3|-2| ≤1[/tex]
If you're good at trigonometry please help me with question nine a and b and show full working out tyyyyyyyy ;)
Problem 9, part a)
Compass bearings always have north as the starting point. This is where 0 degrees is situated, and 360 degrees as well. As the bearing angle increases, you'll turn to the right toward the eastward direction. Effectively you're sweeping out a clockwise rotation. The bearing 322 degrees is in a northwest position as the diagram shows (place the ship at the bottom right corner of the triangle). The bottom right acute angle of the triangle is 322 - 270 = 52 degrees. This is the reference angle we'll use for finding the distance d.
With respect to the reference angle of 52 degrees, the side 18.5 is the opposite side and d is the adjacent side. Use the tangent ratio to get...
tan(angle) = opposite/adjacent
tan(52) = 18.5/d
d*tan(52) = 18.5
d = 18.5/tan(52)
d = 14.4537840903742
The approximate value of d is 14.4537840903742 km
This rounds to 14.5 when rounding to one decimal place.
Answer: 14.5 km=======================================================
Problem 9, part b)
Recall that
distance = rate*time
where "rate" is another term for "speed" or "velocity"
We can solve this for the time to get
time = distance/rate
------
We found the distance back in part a) above. We are given the rate of 48 km/h
So,
time = distance/rate
time = 14.4537840903742/48
time = 0.3011205018828
This is the time it takes in hours. Multiply by 60 to convert to minutes
0.3011205018828 hours = 60*0.3011205018828 = 18.067230112968 minutes
This rounds to the whole number 18
Answer: 18 minutesI need help asap for this question
Answer:
B. 12 and 16Step-by-step explanation:
Well since AB/DE = 3/4 and AB/DE = BC/EF, then BC/EF must also be 3/4.
We now only need to find a fraction that simplifies to 3/4.
8/12 = 2/3 [tex]\neq[/tex] 3/4
12/16 = 3/4 ✅
4/6 = 2/3 [tex]\neq[/tex] 3/4
6/9 = 2/3 [tex]\neq[/tex] 3/4
This means that the correct answer is B. 12 and 16.
I'm always happy to help :)Answer:
B. 12 and 16
Step-by-step explanation:
A container of club soda has a volume of 3200 cubic meter. How many liters of soda does the container hold
Answer:
3200000
Step-by-step explanation:
multiply the volume value by 1000
Given the figure below, find the values of x and z.
Answer:
X= 6°z= 112°Solution,
Finding the value of X,
[tex]11x + 2 = 68[/tex]
( being vertically opposite angles)
[tex]11x = 68 - 2 \\ 11x = 66 \\ x = \frac{66}{11} \\ x = 6[/tex]
Value of X is 6
Now, finding the value of z
[tex]z + 68 = 180[/tex]
(sum of angle in linear pair)
[tex]z = 180 - 68 \\ z = 112[/tex]
Value of z is 112.
Hope this helps....
Good luck on your assignment...
A weather station on the top of a mountain reports that the temperature is currently 0℃ and has been falling at a constant rate of 3.5℃ per hour. What will the temperature at the top of the mountain be in 5 hours?
Answer:
-17.5℃
Step-by-step explanation:
Current temperature = 0 ℃
Rate of falling per hour = -3.5 ℃
Temperature in 5 hours = -3.5 * 5 = -17.5 ℃
Factorise fully 72-2y^2
Answer: 2(y + 6)(-y + 6)
Step-by-step explanation: Factor 72 - 2y^2
-2y^2 + 72
= 2(y + 6)(-y + 6)
Answer:
[tex]-2\left(y+6\right)\left(y-6\right)[/tex]
Step-by-step explanation:
[tex]72-2y^2[/tex]
[tex]-2y^2+72[/tex]
Factor out GCF.
[tex]2(-y^2+36)[/tex]
Apply difference of two squares formula.
[tex]-2\left(y+6\right)\left(y-6\right)[/tex]
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each expression to the scenario it represents.
The correct expression with the correct statement has matched below.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is equivalent to the quantity of that value between 1 and 100, and it is highly helpful for forecasting. For instance, if you say 678, we must also know the whole number, but if you say 80%, it is obvious.
The price of a game that’s been discounted by 18% of its list price
It will be (x - 0.18x) = 0.82x
The price of a toy that sells for 18% more than the amount needed to build the toy
It will be (x + 0.18x) = 1.18x
The volume of water remaining in a tank after 3/10 of its original volume is drained out.
It will be [ x - (3/10)x ] = 7/10x
The total amount of flour in a bakery after receiving new stock equal to 3/10 of the current stock.
It will be [ x + (3/10)x ] = 13/10x
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Which of the points are solutions to the inequality?
Check all that apply.
O (-2,-5)
0 (0.-4)
(1.1)
(3.5)
D (5.5
Answer:
A, C and D
Step-by-step explanation:
The missing inequality is:
y > 2x -4
To verify if a point is a solution, replace x into the equation, compute y, and see their relationship.
Option A: (-2,-5)
2(-2) -4 = -8
y = -5 > -8
then, the point is solution
Option B: (0,-4)
2(0) -4 = -4
y = -4 = -4
then, the point is not solution
Option C: (1,1)
2(1) -4 = -2
y = 1 > -2
then, the point is solution
Option D: (3,5)
2(3) -4 = 2
y = 5 > 2
then, the point is solution
Option E: (5,5)
2(5) -4 = 6
y = 5 < 6
then, the point is not solution
A triangles angle measures are in the ratio 3: 4: 7. Find the measures of the angles
Step-by-step explanation:
total ratio = 3+4+7 = 14
3/14×180= 38.57°
4/14×180= 51.43°
7/14×180 = 90°
Answer:
total ratio = 3+4+7 = 14
3/14×180= 38.57°
4/14×180= 51.43°
7/14×180 = 90°
Step-by-step explanation:
A rectangular wall has length 3 less than 4 times the width . I wish to put a silver line along the corners of the wall. The lining costs 25 cents per foot and I spent a total of $18.50 for the lining on the corners of the wall. If painting costs 20 cents per square foot , how much dose it cost to paint the wall? PLEASE ANSWER correctly. I WILL GIVE BRAINLIEST ANSWER TO U IF U DO
Answer:
Step-by-step explanation:
Let width = w units
Length = 4w - 3
Cost for lining corners of wall = $ 18.50
Perimeter of the wall = 18.50/0.25 = 74 ft
2*(length +width ) = 74
2*(4w - 3 + w) =74
2*(5w - 3) =74
10w - 6 = 74 {Add 6 to both sides}
10w - 6 + 6 = 74 + 6
10w = 80
Divide both sides by 10
10w/10 = 80/10
w = 8 ft
Length = 4w - 3 = 4*8 - 3 = 32 - 3
Length = 29 ft
Area of the wall = length * width
= 29 * 8
= 232 square ft
Cost of painting the wall per square feet = 20 cents = 0.20
Cost of painting 232 square feet = 232 * 0.20
= $ 46.40
In how many ways can we put five identical fruits into three bowls? Note that the bowls may be empty.
Answer:
20
Step-by-step explanation:
PLSSSS HELP! Find all real zeros and complex of each solution x^3-5x^2+7x-35=0. SHOW WORK!!!
Hey there! :)
Answer:
x = 5, x = -i√7, x = i√7
Step-by-step explanation:
We can factor the equation x³ - 5x² + 7x - 35 = 0 by grouping:
x²(x - 5) + 7(x -5) = 0
We get:
(x² + 7)(x - 5) = 0
or
(x + i√7)(x - i√7)(x - 5) = 0
Use the Zero Product Property to solve for the solutions:
x - 5 = 0
x = 5.
-----------
x² + 7 = 0
x² = -7 (We will have imaginary solutions in this instance)
x = ±i√7
Therefore, the zeros of this equation are:
x = 5, x = -i√7, x = i√7
Three tins, A, B and C, each contain buttons.
Tin A contains x buttons.
Tin B contains 4 times the number of buttons that tin A contains.
Tin C contains 7 fewer buttons than tin A.
The total number of buttons in the three tins is 137
Work out the number of buttons in tin C.
The number of buttons in C is 17 buttons
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the three tins be A , B and C respectively
The number of buttons in tin A = x
The number of buttons in tin B = 4 times the number of buttons in tin A
= 4x
The number of buttons in tin C = 7 fewer buttons than tin A
= x - 7
The total number of buttons in tin A , tin B and tin C together = 137 buttons
So , the total number of buttons =
number of buttons in tin A + number of buttons in tin B + number of buttons in tin C
So , the equation will be
Total number of buttons = x + 4x + ( x - 7 )
x + 4x + ( x - 7 ) = 137
6x - 7 = 137
Adding 7 on both sides , we get
6x = 144
Divide by 6 on both sides , we get
x = 24 buttons
So , the number of buttons in tin A is 24 buttons
So , number of buttons in tin B = 4 x 24
= 96 buttons
Therefore , the number of buttons in tin C = 17 buttons
Hence , the number of buttons in tin C is 17 buttons
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What is the ratio of 76,000 and 100,000
Answer:
19 : 25
Step-by-step explanation:
You are making a welding fixture and must cut down a length of copper tubbing from 15 1/8 inches to 8 3/4 inches. If the leftover piece is long enough, you will use it in another fixture . How long will the leftover piece be ? 23 and 7/8 1 and 51/70 7 and 1/8 6 3/8
Answer: [tex]6\dfrac{3}{8}\text{ inches}[/tex]
Step-by-step explanation:
Given: Original length = [tex]15\dfrac{1}{8}[/tex] inches
[tex]=\dfrac{8\times15+1}{8}=\dfrac{121}{8}[/tex] inches ( In improper fraction )
Length of piece cut from original = [tex]8\dfrac{3}{4}[/tex] inches
[tex]=\dfrac{4\times8+3}{4}[/tex][tex]= \dfrac{35}{4}[/tex] inches ( In improper fraction )
Length of piece leftover piece = (Original length ) - (Length of piece cut )
[tex]=\dfrac{121}{8}-\dfrac{35}{4}\\\\=\dfrac{121-2\times35}{8}\\\\=\dfrac{121-70}{8}\\\\=\dfrac{51}{8}\\\\=6\dfrac{3}{8}\text{ inches}[/tex]
Hence, the leftover piece will be [tex]6\dfrac{3}{8}\text{ inches}[/tex] long.