Answer:
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = ((- 2, 3) and (x₂, y₂ ) = (4, 1)
m = [tex]\frac{1-3}{4+2}[/tex] = [tex]\frac{-2}{6}[/tex] = - [tex]\frac{1}{3}[/tex] , thus
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 2, 3), then
3 = [tex]\frac{2}{3}[/tex] + c ⇒ c = 3 - [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex]
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{7}{3}[/tex] ← equation of line
How does the value of the 8 in 20,831 compare to the value of the 8 in 20,381?
Answer:
The eight in the first number is ten times larger than the eight in the second number.
Find the approximate side length of a square game board with an area of 131 in2.
Answer:
11.4
Step-by-step explanation:
You find the square root
Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculator.
log4(2x2 - 20x + 12y)
Answer:
[tex]f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})[/tex]
Step-by-step explanation:
Let be [tex]f(x,y) = \log_{4}(2\cdot x^{2}-20\cdot x +12\cdot y)[/tex], this expression is simplified by algebraic and trascendental means. As first step, the second order polynomial is simplified. Its roots are determined by the Quadratic Formula, that is to say:
[tex]r_{1,2} = \frac{20\pm \sqrt{(-20)^{2}-4\cdot (2)\cdot (12\cdot y)}}{2\cdot (2)}[/tex]
[tex]r_{1,2} = 5\pm \sqrt{25-6\cdot y}[/tex]
The polynomial in factorized form is:
[tex](x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})[/tex]
The function can be rewritten and simplified as follows:
[tex]f(x,y) = \log_{4} [(x-5-\sqrt{25-6\cdot y})\cdot (x-5+\sqrt{25-6\cdot y})][/tex]
[tex]f(x,y) = \log_{4} (x-5-\sqrt{25-6\cdot y})+\log_{4} (x-5+\sqrt{25-6\cdot y})[/tex]
A pack of paper costs $3.75, including tax. Mr. Cooper wants to purchase packs of paper for his class and has a $20 budget. Write an inequality to solve for the number of packs of paper Mr. Cooper can purchase.
Answer:
($3.75)n ≤ $20
Step-by-step explanation:
Represent this number by n. Then the total purchase price can be represented by ($3.75)n ≤ $20, which is appropriate because Cooper can't spend more than $20.
The desired inequality is ($3.75)n ≤ $20. If a solution is desired, divide both sides by $3/75):
$20
n ≤ ______ = 5 1/3.
$3.75
Cooper can purchase up to 5 whole packs of paper and have a bit of money left over.
What are the possible values of x and y for two distinct points, (5, –2) and (x, y), to represent a function? The value of x can be .
Answer:
x ≠ 5
Step-by-step explanation:
For the two points to represent a function, the value of x cannot be repeated. The only restriction on the values of x and y is that x is not 5. (x can be anything but 5.)
Answer:
The value of x can be
✔ any real number except 5
.
The value of y can be
✔ any real number
Step-by-step explanation:
i got it correct on edguinty
A bulb after certain testing had a life of 25 months. The standard deviation based on this sample of size one is
Answer:
25 monthsStep-by-step explanation:
Using the formula for calculating the standard error of the mean to get the standard deviation. The standard error of the mean is expressed as;
SE = S/√n where;
S is the standard deviation
n is the sample size
Given SE = 25 months and n = 1, on substituting this parameters into the formula, we will have;
25 = S/√1
25 = S/1
cross multiply
S = 25*1
S = 25 months
Hence the standard deviation based on the sample is 25 months
What is the value of x & y?
Answer:
x=23, y=14
Step-by-step explanation:
The triangles are indeed simular
Please help........................
Answer:
a. (0,0), (2,0), (4,0)
b. (0,0)
Step-by-step explanation:
To find the x-intercept points, you set the equation equal to 0.
0=x³-6x²+8x [factor out an x]
0=x(x²-6x+8) [factor (x²-6x+8)]
0=x(x-2)(x-4) [set each factor equal to 0]
x=0
x-2=0 [add both sides by 2]
x=2
x-4=0 [add both sides by 4]
x=4
Now, we know our x-intercept points: (0,0), (2,0), (4,0).
To find the y-intercept points, we know that it is located on the y-axis, meaning x=0. We plug in 0 for x, and we will know our y-intercept point.
y=(0)³-6(0)²+8(0) [multiply]
y=0
The y-intercept point is (0,0).
Find the coordinates of the midpoint of a segment with the endpoints M(6, −41) and N(−18, −27). Then find the distance between the points.
Answer:
Midpoint is (-6,-34)
Step-by-step explanation:
(6+(-18))/2. (-41+(-27))/2
-12/2. (-68)/2
-6. , - 34
Distance =(6--18)^2 +(-14--27)^2
23^2. +13^2
529 +169
= 698
So u will find the square root of 698
The ans u get is the distance
Write an equation of the line that passes through the points (1,-4) and (2,-1).
An equation of the line is y=
]
PLEASE HELP!!
Answer:
y = 3x -7
Step-by-step explanation:
The 2-point form of the equation of a line is useful for this.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (-1 -(-4))/(2 -1)(x -1) -4
y = 3(x -1) -4
y = 3x -7
Use back substitution to solve this problem
Answer:
z = -5
y = 1
x = 4
Step-by-step explanation:
2z = -10 ➡ z = -5
4y -(-5) = 9 ➡ 4y = 4 and y = 1
2x + 3 + (-5) = 6 ➡ 2x = 8 and x = 4
What is the domain of the function? f(x)=[tex]\frac{x-3}{2x^{2}+x-21 }[/tex] (−∞,3)∪(3,∞) (−∞,−3)∪(−3,72)∪(72,∞) (−∞,−72)∪(−72,∞) (−∞,−72)∪(−72,3)∪(3,∞)
Answer:
(−∞,−7/2)∪(−7/2,3)∪(3,∞)
Step-by-step explanation:
(x-3)
----------------
2x^2 +x -21
First factor the denominator
(x-3)
----------------
( 2x +7) (x-3)
The domain is restricted when the denominator goes to zero
2x+7 =0 x-3 =0
2x = -7 x-3=0
x = -7/2 x =3
This two points are not in the domain
(−∞,−7/2)∪(−7/2,3)∪(3,∞)
In 5 blank, 278, the difference between the value of the digits in the blank and the blank. What is the blank digit in
Answer: The digit in the thousand place is '9'.
Step-by-step explanation: The given number is 5_278.
The difference between the values of the digits in the thousandth place and the tenth place is 8930.
The digits in the tenth place is already given, which is 7
Let's assume the digits in the thousandth place is x,
There are five members on a student council. Two of these members will serve on a spring formal committee. How many possible spring formal committees are there
Answer:
10
Step-by-step explanation:
Given that:
There are a total of 5 members on a student council.
2 of these members will serve in Spring Formal Committee.
To find:
How many possible spring formal committees can be there ?
Solution:
If the observe this problem closely, we are actually asked nothing but the number of ways to select 2 members out of 5.
This is a simple selection problem in which we have to find the number of ways to select [tex]r[/tex] objects out of [tex]n[/tex].
The number of ways = [tex]_nC_r =\frac {n!}{r!(n-r)!}[/tex]
Here,
[tex]n = 5\\r=2[/tex]
Hence, the required number of ways are:
[tex]_5C_2 =\frac {5!}{2!(5-2)!}\\\Rightarrow \dfrac {5!}{2!3!} = \dfrac {5\times 4\times 3!}{2!3!}\\\Rightarrow \dfrac {5\times 4}{2} = \dfrac{20}{2}\\\Rightarrow \bold{10}[/tex]
So, the number of possible spring formal committees are 10.
If a student is selected at random, what is the
probability that the student is a graduate
(rounded to the nearest percent)? [? ]%
Answer: 24%
Step-by-step explanation:
There are a total of 2610 graduates and if that is the divided by the total which is 10730 you will get 0.2432 which is about 24%
Answer:
24%
Step-by-step explanation:
I checked it on the test to make sure, I have acellus too.
What is the area of a table with a diameter of 28 inches? How did you figure it out? pls help i need the answer asap
Answer:
The answer is 615 inches
Step-by-step explanation:
The formula for solving the area of a circle is :
A= 1/4 π d^2
So since we only know the diameter the formula would be:
A= 1/4 of 3.14 x 28^2
The first thing you need to do is square 28 which is 784Them times 784 by 3.14 which is 2461.76After all that, your equation should look like this: A = 1/4 of 2461.76So then you would times 2461.76 by 1/4 which is 615.75216 or 615.75Hope this helped :)
6. b. In the figure, suppose CD = 11.5 cm, DE = 5.3 cm, and the
perimeter of the figure is 73.8 cm.
What is GE?
Answer:
GE = 11 cm.
Step-by-step explanation:
The figure provided is attached below.
The information given is:
CD = 11.5
DE = 5.3
BC = 8
AH = 11
Perimeter = 73.8
BC = FG = EF
HA = GH
AB = GE
The perimeter of any figure is the sum of all its sides.
The perimeter of the figure provided is:
Perimeter = AB + BC + CD + DE + EF + FG + GH + HA
Perimeter = AB + BC + CD + DE + BC + BC + HA + HA
[tex]73.8=AB+8+11.5+5.3+8+8+11+11[/tex]
[tex]73.8=AB+62.8[/tex]
[tex]AB=11[/tex]
The value of side AB is 11 cm.
Then the value of GE is also 11 cm.
What is the solution set to the inequality 1 + 7x + 5x< 13?
Answer:
[tex]x<1[/tex]
Step-by-step explanation:
So we have the inequality:
[tex]1+7x+5x<13[/tex]
First, combine like terms:
[tex]1+12x<13[/tex]
Subtract 1 from both sides:
[tex]12x<12[/tex]
Divide both sides by 12:
[tex]x<1[/tex]
And that's our answer :)
Answer:
Step-by-step explanation:
12x + 1 < 13
12x < 12
x < 1
4x=x+18 solve for x
Answer:
X = 6
Step-by-step explanation:
Subtract 1 x from both sides so the equation will be 3x = 18. Then divide 3x by 3 and 18 by 3 to get 6
Answer: [tex]x=6[/tex]
Subtract x from both sides
[tex]4x-x=x+18-x\\3x=18[/tex]
Divide both sides by 3
[tex]3x=3=18/3\\x=6[/tex]
F(x)=x^2+7x-30
Find the intercepts, domain and range
Answer:
domain (-inf, +inf)
range [-30, +inf)
y-int = -30
x-int = -10, 3
Step-by-step explanation:
The answer to 48:(4+4)
Answer:
6:1
Step-by-step explanation:
48:( 4+4 )
= 48:8
= 6:1
Which is equivalent to3/4
Answer:
75%
Step-by-step explanation:
Answer:
6/8
Step-by-step explanation:
An easy way to do this is to draw a giant rectangle. when you do you simply want to stay a line going straight across in the middle. draw 3/4 ontop and 6/8 on the bottom. or another fraction that's close to it. then shade in 3/4 and the same with 6/8. if the shading is the same length, that's how you know it's equivalent
Evaluate if m = 16 and p = 2. 1/2m + 3p A) 10 B) 14 C) 18 D) 48
Answer:
B) 14
Step-by-step explanation:
We can plug in the values of m and p into the equation:
1/2 m + 3p = 1/2 (16) + 3 (2) = 8 + 6 = 14.
Two lines intersect in a plane in form for angles what are the angles formed fathers intersect is a 53° angle what are the measures of the other three angles explain your answer
Answer:
53°, 127°, 127°
Step-by-step explanation:
Two intersecting lines form two pairs of angles:
Pair of vertical angles. They are opposite to each other and are equalPair of adjacent angles which are supplementary angles and their sum is 180°So if one of the angles is measured 53°, then the other angles are:
53°- vertical angle with the first one180° - 53° = 127°180° - 53° = 127°3
Which function family does f(x)=-1/2x + 7 belong to?
Answer:
Linear
Step-by-step explanation:
Answer:
the answer is Linear
Step-by-step explanation:
Find the midpoint of the segment with the following endpoints.
(6,4) and (9,1)
Answer:
[tex]=\left(\frac{15}{2},\:\frac{5}{2}\right)[/tex]
Step-by-step explanation:
[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(6,\:4\right),\:\left(x_2,\:y_2\right)=\left(9,\:1\right)\\\\=\left(\frac{9+6}{2},\:\frac{1+4}{2}\right)\\\\=(\frac{15}{2} , \frac{5}{2} )\\\\[/tex]
Express 0.2 degrees without decimals
Write 100 as a product of prime factors
Prime factorization of 100 is 2 * 2 * 5 * 5
100 as a product of prime factors will be 2 ×2×5×5 .
Given,
Number = 100
Now,
To write 100 as prime factor product ,
Take LCM of 100
LCM 100 = 2 ×2×5×5
Thus the factors obtained in the LCM is prime factors only .
So we can write 100 as the product of prime factors:
100 = 2 ×2×5×5
Know more about prime factors,
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I WILL MARK BRAINIEST PLEASE HELP ME ON THIS QUESTION
Lulu Ruby and Emma went shopping went a total of £261. Each of them had different amount of money. Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money. Each of them spent the same amount of money.how much did money did they begin with?
Answer:
Lulu's money = £81
Ruby's money= £108
Emma's money= £72
Step-by-step explanation:
Let
Lulu's money = x
Ruby's money= y
Emma's money= z
x+y+z= 261
Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.
2/3x = 1/2y= 3/4z
2/3x= 1/2y
4/3x= y
2/3x= 3/4z
8/9x= z
x+y+z= 261
x+4/3x+8/9x= 261
9x+12x+8x= 2349
29x= 2349
X= 81
4/3x= y
4/3(81) =y
108= y
8/9x= z
8/9(81)= z
72= z
Answer:
Step-by-step explanation:
Each of them had different amount of money. Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.
1 answer
·
Top answer:
Answer:Lulu= £81Ruby=£108Emma=£ 72
1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m². 2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm. 3. Find the area of the equilateral triangle whose each side is 8 cm. 4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m².
a = 51 m, b = 37 m, c = 20 m
semiperimeter: p = (51+37+20):2 = 54 m
Area of triangle:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}\\\\A=\sqrt{54(54-51)(54-37)(54-20)}\\\\A=\sqrt{54\cdot3\cdot17\cdot34}\\\\A=\sqrt{9\cdot2\cdot3\cdot3\cdot17\cdot17\cdot2}\\\\A=3\cdot2\cdot3\cdot17\\\\A=306\,m^2[/tex]
Rate: ₹ 3 per m².
Cost: ₹ 3•306 = ₹ 918
2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm.
a = 5 cm
a+2b = 11 cm ⇒ 2b = 6 cm ⇒ b = 3 cm
p = 11:2 = 5.5
[tex]A=\sqrt{5.5(5.5-3)^2(5.5-5)}\\\\ A=\sqrt{5.5\cdot(2.5)^2\cdot0.5}\\\\ A=\sqrt{11\cdot0.5\cdot(2.5)^2\cdot0.5}\\\\A=0.5\cdot2.5\cdot\sqrt{11}\\\\A=1.25\sqrt{11}\,cm^2\approx4.146\,cm^2[/tex]
3. Find the area of the equilateral triangle whose each side is 8 cm.
a = b = c = 8 cm
p = (8•3):2 = 12 cm
[tex]A=\sqrt{12(12-8)^3}\\\\ A=\sqrt{12\cdot4^3}\\\\ A=\sqrt{3\cdot4\cdot4\cdot4^2}\\\\A=4\cdot4\cdot\sqrt{3}\\\\A=16\sqrt3\ cm^2\approx27.713\ cm^2[/tex]
4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
a = 2x
b = 3x
2x + 2•3x = 32 cm ⇒ 8x = 32 cm ⇒ x = 4 cm ⇒ a = 8 cm, b = 12 cm
p = 32:2 = 16 cm
[tex]A=\sqrt{16(16-8)(16-12)^2}\\\\ A=\sqrt{16\cdot8\cdot4^2}\\\\ A=\sqrt{2\cdot8\cdot8\cdot4^2}\\\\ A=8\cdot4\cdot\sqrt2\\\\ A=32\sqrt2\ cm^2\approx45.2548\ cm^2[/tex]