a) Line parallel to the line 3x+5y=-10 is -6x-10y=9
b) Line parallel to the line 2y-4x=5 and which goes through the point
(3,7) is y= 2x-1.
c) Line perpendicular to the line 8x+6y=-1 and which goes through the
point (-2,1) is 4y= 3x+ 10
The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y.
a) Equation parallel to 3x+5y=-10 is
-6x-10y=9
So, it satisfies: [tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}[/tex]
b)given equation into the form of y=mx+c,
2y-4x=5
we can find the gradient of the line.
2y= 5+4x
y= [tex]\frac{5}{2}[/tex] + 2x
Hence, the gradient is 2.
As, Parallel lines have the same gradient
Thus the line would also have a gradient of 2.
Substitute m=2 into the equation:
y= 2x +c
To find the value of c, substitute a pair of coordinates.
When x=3, y=7,
7= 2(3) +c
7= 6 +c
c=6-7
c= -1
So, equation of line be: y= 2x-1.
c) Given: 8x+6y=-1
6y= -1-8x
y= [tex]\frac{-1}{6} -\frac{4}{3}x[/tex]
Hence, m= [tex]-\frac{4}{3}[/tex]
We know, if two lines are perpendicular have m and m' as slope then,
m*m'=-1
[tex]\frac{-4}{3} *m'=-1[/tex]
m'= [tex]\frac{3}{4}[/tex]
Now, y= [tex]\frac{3}{4}[/tex] x +c
Put x= -1 and y=1
then, 1= [tex]\frac{3}{4}[/tex] (-2) + c
c= [tex]\frac{5}{3}[/tex]
So, y= [tex]\frac{3}{4}[/tex] x + [tex]\frac{5}{2}[/tex]
4y= 3x+ 10
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3. Find the probability of rolling a prime number when a 14-sided die is rolled.
Answer:
3/7
Step-by-step explanation:
Probability = number of favorable outcomes/total number of possible outcomes
We know the total number of possible outcomes is 14 since there are 14 sides to the dice.
Let's find how many of those numbers are prime numbers.
2, 3, 5, 7, 11, and 13 are all the prime numbers between 1 and 14, so there are 6 favorable outcomes.
Now create the fraction then reduce.
6/14 reduce by 2/2
3/7
If the radius of a clock is 5 inches, what is the distance around the edge of the clock between the two and the five to the nearest hundredth of an inch
plssss help
thank you
Answer:
7.85 inches
Step-by-step explanation:
It mentions distance around the edge of the clock, which is basically another term used for arc length.
Arc Length Formula :
Arc Length = 2πr × θ/360°
Values given :
Radius (r) = 5 inches
Turning angle (θ) = 3/12 × 2π = 1/4 x 2π = π/2 = 90°
Solving :
Arc Length = 2 x 3.14 x 5 x 90/360
Arc Length = 15.7 x 0.5
Arc Length = 7.85 inches
Find the surface of the cone in terms of pi.
144pi cm2
108pi cm2
90pi cm2
180pi cm2
please
Check the picture below.
if the diameter of its base is 12, then its radius must be half that, or 6.
[tex]\textit{surface area of a cone}\\\\ SA=\pi r\stackrel{\stackrel{slant~height}{sh}}{\sqrt{r^2+h^2}} + \pi r^2~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ sh=18 \end{cases}\implies SA=\pi (6)(\stackrel{sh}{18})+\pi (6)^2 \\\\\\ SA=108\pi +36\pi \implies SA=144\pi[/tex]
find the arc length of a central angel of 36 degrees in a circle whose radius is 2 inches
[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=2\\ \theta =36 \end{cases}\implies s=\cfrac{(36)\pi (2)}{180}\implies s=\cfrac{2\pi }{5}\implies s\approx 1.26~in[/tex]
I need help with this its like a fraction
[tex]\frac{10^8}{10^6} = 10^{8-6} = 10^2 = 100[/tex]
The rule used is
[tex]\frac{a^b}{a^c} = a^{b-c}[/tex]
Subtract the exponents when dividing exponentials like this of the same base.
Pls help :/
Find the expected value of the winnings from a game that has the following payout probability distribution.
I will give brainlies t
The expected value of the winnings from a game that has the following payout probability distribution is 2.3
What is expected value?In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values.
To calculate the expected value ,
we have to multiply each of the given probability by the individual payout value and then add the following answers
So, expected value
=0(0.45) + 2(0.3) + 4(0.1) + 8(0.1) + 10(0.05)
=0+0.6+0.4+0.8+0.5
= $2.3
Hence, the expected value is 2.3
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ACTUAL ANSWER:
3.1
Step-by-step explanation:
0.45(0) + 0.3(4) + 0.1(6) + 0.1(8) + 0.05(10)
= 3.1
Also I checked on on Acellus and it was correct.
Let's find 3/4+1/10
First write the addition with a common denominator.
Then add. 3/4+1/10=?/?+?/?=?/?
Answer:
[tex]\frac{34}{40}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}+\frac{1}{10}[/tex]=[tex]\frac{30}{40}+\frac{4}{40}[/tex]=[tex]\frac{34}{40}[/tex]A box has a width of 5 centimeters and a height of 6 centimeters. If the volume is 150 cubic centimeters, what is the length of the box?
A) 5 centimeters
B) 4 centimeters
C) 7 centimeters
D) 3 centimeters
Answer: A. 5
Step-by-step explanation:
Answer:
A) 5 cm.
Step-by-step explanation:
Volume = length * width * height
150 = length * 5 * 6
Length = 150 / (5*6)
= 150/30
= 5.
I need help solving this
Answer:
50° and 40°
Step-by-step explanation:
complementary angles sum to 90°
80% = [tex]\frac{80}{100}[/tex] = 0.8
let the 2 angles be x and 0.8x , then
x + 0.8x = 90
1.8x = 90 ( divide both sides by 1.8 )
x = 50
0.8x = 0.8 × 50 = 40
the 2 angles are 50° and 40°
There are 3 items in an order. They cost $14.65, $8.49, and $10.99. The sales tax for this order is 7.5%.
What is the total cost of the order?
$34.13
$35.84
$36.52
$36.69
Answer:
(d) $36.69
Step-by-step explanation:
The total cost of the order is the sum of the costs of the items and the tax on that subtotal.
__
The price after tax can be found using the multiplier (1 +tax rate) applied to the subtotal.
total cost = ($14.65 +8.49 +10.99)×(1 +0.075) = $34.13×1.075
total cost = $36.69
Answer: $36.69
Step-by-step explanation: K12 Test 8.02 Grade 7 Semester B Test - Part 1
Can someone help me with this
You want to draw a red then a blue marble. do you have a better chance of drawing a red then blue marble with or without replacing the first marble? explain your answer
Answer: Without replacing
Step-by-step explanation:
If you don't replace the first red marble, it decreases the number of red marbles in the mix, making the proportion of blue marbles relatively larger. For example, if there were 5 red and 5 blue marbles, there would be a 50% chance of drawing a blue marble. If the red drawn is not replaced, there is a 5/9 chance of drawing a blue marble, or a 55% chance of drawing one.
13+-2x=-17 help abs explain steps if u can please
A ring-shaped region is shown below.
Its inner diameter is 16 ft. The width of the ring is 2 ft.
it
16 ft
Find the area of the shaded region.
Use 3.14 for . Do not round your answer.
X5?
Answer:
Area = 213.52 sq.ft
Step-by-step explanation:
[tex]A_{s} =\pi (18)^{2} -\pi (16)^{2} =324\pi -256\pi =68\pi[/tex]
[tex]\pi =3.14[/tex]
[tex]A_{s} =68(3.14)=213.52sq.ft[/tex]
Hope this helps
Answer:
113.04 ft²
Step-by-step explanation:
The area of the ring can be found by multiplying its center-line length by its width.
__
The diameter of the circle that is the center-line of the ring is ...
16 ft + 2 ft = 18 ft . . . . center-line diameter
The length of the center-line is then ...
C = πd
C = 3.14(18 ft) = 56.52 ft
And the area of the ring is ...
A = LW = (56.52 ft)(2 ft) = 113.04 ft²
The shaded area is 113.04 square feet.
FIND B ONLY
WILL GET BRAINLIEST
Answer:
the answer is RATIONAL
Step-by-step explanation:
why u ask
becasue the number is less than 1
please mark brainiest
Question 3(Multiple Choice Worth 1 points)
(08.05 LC)
The graphs of f(x) and g(x) are shown below:
Answer:
The correct equation is D
in how many ways can 4 people be seated in a row of 12 chairs
Answer:
11,880.
Step-by-step explanation:
This is given by the number of permutations of 4 from 12
= 12P4
= 12!/(12-4)!
= 12!/8!
= (12*11*10*9*8*7*6*5*4*4*2*1) / (8*7*6*5*4*4*2*1)
= 12^11*10*9
= 11,880.
I really need help with my math someone please help
Answer:
∠ A = 56°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
2x + 3x + 40 = 180
5x + 40 = 180 ( subtract 40 from both sides )
5x = 140 ( divide both sides by 5 )
x = 28
then
∠ A = 2x = 2 × 28 = 56°
i don't know exactly what to do
Answer:
Step-by-step explanation: Just relax effortlessly. Communion Kant be for All unless we are primed for purpose...
Which expression is irrational?
A 18
B 18
C 64
D 364
Answer:
all of those answers are rational numbers
Step-by-step explanation:
You work for a cereal company that is looking to design some new boxes for their cereal. The cereal is sold in the size of 512 cubic units
You will be designing three rectangular prisms with unique dimensions. Find the surface area of each of your prisms, showing your work.
Dimensions and Surface Area
1)
2)
3)
If the dimension of the rectangular prism will be (4, 8, 16), (2, 8, 32), and (2, 4, 64). Then the surface area will be 448, 672, and 784 square units respectively.
What is a rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
You work for a cereal company that is looking to design some new boxes for their cereal.
The cereal is sold in the size of 512 cubic units.
You will be designing three rectangular prisms with unique dimensions.
The possible dimension of the rectangular prism will be
Volume = 512
Volume = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
Then we have
{(4, 8, 16), (2, 8, 32), (2, 4, 64)}
Then the surface area will be
If the dimension is (4, 8, 16). Then the surface area will be
Surface area = 2(4x8 + 8x16 + 16x4)
Surface area = 448 square units
If the dimension is (2, 8, 32). Then the surface area will be
Surface area = 2(2x8 + 8x32 + 32x2)
Surface area = 672 square units
If the dimension is (2, 4, 64). Then the surface area will be
Surface area = 2(2x4 + 4x64 + 64x2)
Surface area = 784 square units
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Given the expression: 3x¹0 - 48x²
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Which lists contain only rational numbers? Select all that apply.
104
54, 163,
63, 191, 142
F
81, 49
49,11,19
25
V4, V16, 36
36, V64, V100
64,19,781, 14, 121
48
28 , /31, 10, 12
1) Set up, but do not solve, a system of equations for the following application: A nurse mixes a 100% saline solution with a 20% saline solution to produce 160 milliliters of a 25% saline solution. How much of the 100% saline solution and how much of the 20% saline solution were used?
The systems of the equations for the word problem can be expressed as:
x + y = 500 --- (1)100x + 20y = 4000 --- (2)What is a system of equations?The system of equations is a set of simultaneous equations that comprises two or more equations expressed in algebraic terms.
From the given information, we are to determine two quantities
i.e.
For 100% saline solution (x) andFor 20% saline solution (y)So, 100% and 20% of saline solution produce 160 millimeters.
x + y = 160
Also, the combination of 100% and 20% of saline solution give an average of 25%.
The average now = sum of numbers/ the total numbers
25% = sum of numbers/160
sum of numbers = 25% (160)
Therefore, we can equate it to the mixture carried out by the nurse.
i.e.
25% (160) = 100%(x) + 20%(y)
100x + 20y = 4000
Therefore, the systems of the equations are:
x + y = 500 --- (1)
100x + 20y = 4000 --- (2)
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What is the sum of the interior angles of a polygon that has 6 sides
Answer:
720
Step-by-step explanation:
A polygon with 6 angles is called a hexagon
To find the sum of interior angles, we use the following formula:
(n-2)*180 (n is the number of angles)
4*180 = 720
al. Rajeshwari prepared 24 kg sweets to be distributed on Diwali. She packed the sweet in boxes. Each box contained kg. a.How many boxes of sweets were prepared? b. How much sweet was left unpacked with her? c.If she has 15 friends, will she be able to distribute the sweets to all her friends?
Answer:
9
Step-by-step explanation:
she have 24kg she gave 15kg so answer is 9
The cost of a kayak is $2,450 and the selling price is $3,560 find the nearest percent of markup on the selling price. round to the nearest tenth of a percent.
well, the markup or the bumped up amount is 3560 - 2450 = 1110.
if we take 2450 to be the 100%, what is 1110 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 2450 & 100\\ 1110& x \end{array} \implies \cfrac{2450}{1110}~~=~~\cfrac{100}{x}\implies \cfrac{245}{111}~~=~~\cfrac{100}{x} \\\\\\ 245x=11100\implies x=\cfrac{11100}{245}\implies x\approx 45.3[/tex]
arrange the following in order 9,09 909,09 0,099 0,909 0,0099 9,0099 9,909
Answer:
0.0099, 0.099,0.909, 9.0099, 9.09, 9.909, 909,09
Step-by-step explanation:
Here they are from least to greatest. Hope this helps. :)
Find the surface area of the figure?
Step-by-step explanation:
the surface area consists of 6 individual areas :
front and back (both are equal)
left and right (both are equal)
top and bottom
front and back are trapezoids.
the area of a trapezoid is
(base 1 + base 2)/2 × h
the bases are the 2 parallel sides.
in our case the area of one trapezoid is
(5 + 19)/2 × 12.1 = 145.2 ft²
front and back together then are 290.4 ft².
left and right are 8×14 rectangles:
8×14 = 112 ft²
together they are 224 ft².
the bottom is a 5×8 rectangle :
5×8 = 40 ft²
the top is a 19×8 rectangle :
19×8 = 152 ft²
so, the total surface area is
290.4 + 224 + 40 + 152 = 706.4 ft²
Factor the quadratic trinomial x²- 9x+18
(x + ) (x+ )
Answer:
(x - 6)(x - 3)
Step-by-step explanation:
x² - 9x + 18
consider the factors of the constant term (+ 18) which sum to give the coefficient if the x- term (- 9 )
the factors are - 6 and - 3 , since
- 6 × - 3 = + 18 and - 6 - 3 = - 9 , then
x² - 9x + 18 = (x - 6)(x - 3) ← in factored form
Answer:
(x - 3)(x - 6)
Step-by-step explanation:
x²- 9x+18
= x^2 - 6x - 3x + 18
= x(x - 6) - 3(x - 6)
= (x - 3)(x - 6).