Answer:
We know that for a line:
y = a*x + b
where a is the slope and b is the y-intercept.
Any line with a slope equal to -(1/a) will be perpendicular to the one above.
So here we start with the line:
3x + 4y + 5 = 0
let's rewrite this as:
4y = -3x - 5
y = -(3/4)*x - (5/4)
So a line perpendicular to this one, has a slope equal to:
- (-4/3) = (4/3)
So the perpendicular line will be something like:
y = (4/3)*x + c
We know that this line passes through the point (a, 3)
this means that, when x = a, y must be equal to 3.
Replacing these in the above line equation, we get:
3 = (4/3)*a + c
c = 3 - (4/3)*a
Then the equation for our line is:
y = (4/3)*x + 3 - (4/3)*a
We can rewrite this as:
y = (4/3)*(x -a) + 3
now we need to find the point where this line ( y = -(3/4)*x - (5/4)) and the original line intersect.
We can find this by solving:
(4/3)*(x -a) + 3 = y = -(3/4)*x - (5/4)
(4/3)*(x -a) + 3 = -(3/4)*x - (5/4)
(4/3)*x - (3/4)*x = -(4/3)*a - 3 - (5/4)
(16/12)*x - (9/12)*x = -(4/3)*a - 12/4 - 5/4
(7/12)*x = -(4/13)*a - 17/4
x = (-(4/13)*a - 17/4)*(12/7) = - (48/91)*a - 51/7
And the y-value is given by inputin this in any of the two lines, for example with the first one we get:
y = -(3/4)*(- (48/91)*a - 51/7) - (5/4)
= (36/91)*a + (153/28) - 5/4
Then the intersection point is:
( - (48/91)*a - 51/7, (36/91)*a + (153/28) - 5/4)
And we want that the distance between this point, and our original point (3, a) to be equal to 4.
Remember that the distance between two points (a, b) and (c, d) is:
distance = √( (a - c)^2 + (b - d)^2)
So here, the distance between (a, 3) and ( - (48/91)*a - 51/7, (36/91)*a + (153/28) - 5/4) is 4
4 = √( (a + (48/91)*a + 51/7)^2 + (3 - (36/91)*a + (153/28) - 5/4 )^2)
If we square both sides, we get:
4^2 = 16 = (a + (48/91)*a + 51/7)^2 + (3 - (36/91)*a - (153/28) + 5/4 )^2)
Now we need to solve this for a.
16 = (a*(1 + 48/91) + 51/7)^2 + ( -(36/91)*a + 3 - 5/4 + (153/28) )^2
16 = ( a*(139/91) + 51/7)^2 + ( -(36/91)*a - (43/28) )^2
16 = a^2*(139/91)^2 + 2*a*(139/91)*51/7 + (51/7)^2 + a^2*(36/91)^2 + 2*(36/91)*a*(43/28) + (43/28)^2
16 = a^2*( (139/91)^2 + (36/91)^2) + a*( 2*(139/91)*51/7 + 2*(36/91)*(43/28)) + (51/7)^2 + (43/28)^2
At this point we can see that this is really messy, so let's start solving these fractions.
16 = (2.49)*a^2 + a*(23.47) + 55.44
0 = (2.49)*a^2 + a*(23.47) + 55.44 - 16
0 = (2.49)*a^2 + a*(23.47) + 39.44
Now we can use the Bhaskara's formula for quadratic equations, the two solutions will be:
[tex]a = \frac{-23.47 \pm \sqrt{23.47^2 - 4*2.49*39.4} }{2*2.49} \\\\a = \frac{-23.47 \pm 12.57 }{4.98}[/tex]
Then the two possible values of a are:
a = (-23.47 + 12.57)/4.98 = -2.19
a = (-23.47 - 12.57)/4.98 = -7.23
Consider the expressions 7y + 5 − 3 and 7y + 2. Which statement is true?
Answer:
A.
Step-by-step explanation:
Start with
7y + 5 - 3
Combine like terms:
7y + 2
By combining like terms in 7y + 5 - 3, we end up with 7y + 2 which is the second expression.
Therefore, the expressions are equivalent because they evaluate to equal values for every value of y.
Answer: A.
find the side of a cube whose surface area is 150² m
Answer:
6 m
Step-by-step explanation:
[tex]surface \: \: area = 4 {s}^{2} [/tex]
s is side
[tex]150 = 4 {s}^{2} \\ {s}^{2} = 37.5 \\ s = 6.1 \: m[/tex]
A store is having a sale on chocolate chips and walnuts. For 8 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $34. For 2 pounds of chocolate chips and 5 pounds of walnuts, the total cost is $17. Find the cost for each pound of chocolate chips and each pound of walnuts.
Answer:
chocolate chips are $2.00 per pound.
nd walnuts must be $3.50 per pound.
Step-by-step explanation:
Let x be the price of walnuts and y the price of chocolate chips.
2x + 5y = 17 (i)
8x + 3y = 34 (ii)
Multiply (i) by 4 to get
8x + 20y = 68
Subtract (ii) to get
17y = 34
Dividing by 17, we see that chocolate chips are $2.00 per pound.
Substituting y=2 in (i) or (ii), walnuts must be $3.50 per pound.
175 2/3 + 456 2/3
add and simplify
help pls
Answer:
460 1/3
Step-by-step explanation:
175 2/3 + 456 2/3
First convert to improper fraction,
527/3 + 854/3
=> 1381/3
Then After adding convert back to mixed fraction,
=> 460 1/3
For the rhombus below, find the measures of ∠1, ∠2, ∠3, and ∠4.
Answer:
∠1 = 116 ° , ∠2 = 32° , ∠3 = 116 ° and ∠4 = 32°
Step-by-step explanation:
∠2 = 32° (The diagonals of a rhombus bisect pairs of opposite angles)
Opposite sides of a rhombus are parallel ,so
∠2 = ∠4 (Alternate interior angles )
∠4 = 32°
32° + ∠4 + ∠3 = 180° (angle sum property of a triangle)
64° + ∠3 = 180°
∠3 = 180 - 64
∠3 = 116°
∠3 =∠1 (in a rhombus opposite angles are equal )
∠1 = 116°
I operate a small convenience store. Typically, I get about 10 customers per hour. If the mean time before I get my 25th customer is 2.5 hours, what is the standard deviation associated with the time until I see my 25th customer
Answer:
The standard deviation associated with the time until I see my 25th customer is of 2.5 hours.
Step-by-step explanation:
In this problem, we have the mean time between x successes, which characterizes the exponential distribution.
As in this question context, the important thing to note is that for the exponential distribution, the mean and the standard deviation are the same.
Mean time before I get my 25th customer is 2.5 hours, what is the standard deviation associated with the time until I see my 25th customer?
They are the same in the exponential distribution, so 2.5 hours.
A right cylinder has a radius of 3 and a height of 12. What is its surface area?
O A. 9077 units2
B. 72 units2
O C. 10877 units
D. 457 units2
Answer:
Option A, [tex]90\pi[/tex] [tex]units^{2}[/tex], is correct.
Step-by-step explanation:
The formula for the surface area of a cylinder is as follows:
A= [tex]2\pi rh+2\pi r^{2}[/tex]
We know that the radius, r, is 3, and the height, h, is 12.
r=3
h=12
Pi will be rounded to 3.14.
Thus, applying the known values to the formula:
A=[tex]2(3.14)(3)(12)+2(3.14)(3)^{2}[/tex]
A=226.08+56.52
A=282.6 [tex]units^{2}[/tex]
In accord with the given options, we must determine which one has a product of around 282.6:
A. [tex]90\pi =282.7433388[/tex]
B.[tex]72\pi =226.1946711[/tex]
C.[tex]108\pi =339.2920066[/tex]
D.[tex]45\pi =141.3716694[/tex]
Therefore, option A, [tex]90\pi units^{2}[/tex], is correct.
Write a situation that can be represented by 2x + 6 > 20.
Hm, interesting inequality.
If you know that it slightly simplifies to [tex]2x\gt14[/tex] then you could go about representing something in real life,
Buying shoes is always done in pairs, if u buy two pairs of shoes you bought 4 shoes. You can only ever buy an even number of shoes which is represented by [tex]2x[/tex].
So you are asking yourself how many pairs you had to buy in order to have more than 14 shoes. The answer is of course, 7 pairs means exactly 14 shoes but since you need more the answer is 8 pairs. Represented by,
[tex]x\gt7=\{8,9,10,\dots,\aleph_0\}[/tex]
assuming [tex]x\in\mathbb{N}[/tex], which is appropriate since you cannot buy negative shoe or [tex]0.43819[/tex] of a shoe pair.
However, if you cannot change the inequality at all, you can use the above paragraph but simply add, you have 3 pairs (6 shoes) of shoes that are indispensable and you want to know the minimum number of shoe pairs you need to buy so that you always have more than 20 shoes.
Notes
[tex]\aleph_0[/tex] is the number of natural numbers [tex]\mathbb{N}[/tex] there are.
[tex]\{\dots\}[/tex] is explicit set notation, ie. which values concretely satisfy the inequality.
Hope this helps :)
Answer:
= 2x > 20-6
= 2x > 14
= x > 7... then the answer includes the numbers greater than seven
A study was conducted to determine whether magnets were effective in treating pain. The values represent measurements of pain using the visual analog scale. Assume that both samples are independent simple random samples from populations having normal distributions. Use a 0.05 significance level to test the claim that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.
Sham n= 20 x=0.41 s=1.37
Magnet n= 20 x =0.46 s= 0.94
Identify the test statistic. F=
Identify P-Value=
What is the conclution for the hypothesis test?
A. Fail to reject the null hypothesis. There is insufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets
B. Reject the null hypothesis. There is insufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets
C.Fail to reject the null hypothesis. There is sufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets
D.Reject the null hypothesis. There is sufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets
Answer:
F statistic = 2.124
Pvalue = 0.0546
A. Fail to reject the null hypothesis. There is insufficient evidence to to support the claim that those given a sham treatment have reductions that vary more than those treated with magnets
Step-by-step explanation:
H0 : pain reduction is the same
H1 : pain reduction is varies more with sham.
Sham n= 20 x=0.41 s=1.37
Magnet n= 20 x =0.46 s= 0.94
α - level = 0.05
Using the Ftest statistic
Ftest = larger sample variance / smaller sample variance
Ftest = s1² / s2² = 1.37² / 0.94² = 1.8769 / 0.8836 = 2.124
The degree of freedom :
Numerator = n - 1 = 20 - 1 = 19
Denominator = n - 1 = 20 - 1 = 19
Pvalue(2.124, 19, 19) = 0.0546
Since ;
Pvalue > α ; WE fail to reject the Null ; Result is not significant
HELP NEEDED PLEASE!!!!
Answer:
A
Step-by-step explanation:
The period is stretched by 30 and divided by pi, meaning that the wheel rotates does a full rotation every 60 seconds. But the most important part is vertical stretch of 47 and shift up of 52. At the peak it would be 99 since the peak is 47 with the stretch but add 52 from the shift and it would be 99.
Enter the ratio as a fraction in lowest terms
6 minutes to 30 minutes.
6 minutes / 30 minutes
Divide the top and bottom by 6.
1 minute / 5 minutes
Fraction in lowest terms: 1/5
Hope this helps!
Drag each tile to the correct box.
Match each expression with its greatest common factor.
Answer:
Step-by-step explanation:
a store sells pencils pens and markers that sells two times as many markers as pencils and three times as many pens as pencils is the store sells a total of 1950 pencils and pens and markers in a week how many of each were sold
Answer:
Pencils = 325 ; Pens = 975 ; Markers = 650
Step-by-step explanation:
Let :
Number of Pencils = x
Number of pens = y
Number of markers = z
2 times as many markers as pencils
z = 2x
3 times as many pens as pencils
y = 3x
x + y + z = 1950
Write z and y in terms of x in the equation :
x + 3x + 2x = 1950
6x = 1950
Divide both sides by 6
6x / 6 = 1950 / 6
x = 325
Number of pencils = 325
Pens = 3 * 325 = 975
Markers = 2 * 325 = 650
Pencils = 325 ; Pens = 975 ; Markers = 650
HELP!!
Consider the polynomial
Answer:
1. coefficient of 3rd term = 1
2. constant term= 0
The coefficient of the third term is 1 while the constant term is 0 for the given expression.
What is an expression?An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.
For example 3x +5y
As per the given polynomial,
(1/2)a⁴ + 3a³ + a
Here a is a variable.
(1)
The third term is a and its coefficient is 1 as (1)a.
(2)
All terms have variable "a" thus none of the terms is constant so the constant term is 0.
Hence "For the following statement, the constant term has a coefficient of 0 and the third term has a coefficient of 1".
To learn more about expression,
https://brainly.com/question/14083225
#SPJ2
What is the diameter of a hemisphere with a volume of
62617
cm
3
,
62617 cm
Answer:
Step-by-step explanation:
Hemisphere Volume = (2/3) * PI * radius^3
sphere radius^3 = Hemisphere Volume / ((2/3) PI)
sphere radius^3 = 62,617 / 2.0943951024
sphere radius^3 = 29,897.4152147556
sphere radius = 31.0368674154
sphere diameter = 62.1 cm (rounded to nearest tenth of a centimeters)
Answer:
62.1
Step-by-step explanation:
→ Set up an equation
[tex]\frac{2}{3}[/tex] × π × r³ = 62617
→ Divide both sides by π
[tex]\frac{2}{3}[/tex] × r³ = 19931.61014
→ Divide both sides by [tex]\frac{2}{3}[/tex]
r³ = 29897.41521
→ Cube root both sides
r = 31.03686742
→ Double the answer to find the diameter
31.03686742 × 2 = 62.1
solve for x please help (show work)
Answer:
x = -1
Step-by-step explanation:
1/3(6x-3)+2(x-1) = -7
Distribute
2x-1 +2x-2 = -7
Combine like terms
4x -3 = -7
Add 3 to each side
4x-3+3 = -7+3
4x = -4
Divide by 4
4x/4 = -4/4
x = -1
[tex] \frak{ \frac{1}{3}(6x - 3) + 2(x - 1) = - 7}[/tex]
[tex]\twoheadrightarrow \frak{2x - 1 + 2x - 2 = - 7}[/tex]
[tex]\twoheadrightarrow \frak{4x - 3 = - 7}[/tex]
[tex] \twoheadrightarrow \frak{4x = - 7 + 3}[/tex]
[tex]\twoheadrightarrow \frak{4x = - 4}[/tex]
[tex]\star \: \underline{ \boxed{ \frak \green{{x = - 1}}}}[/tex]
there are 3 blouse and 2 pieces cloths for sale in the market. how many possible sets are there?
Answer:
Each item could be included in a set or not included. That gives 2^5 = 32 ways to choose sets, including 1 set with no items, 5 sets of 1 item, 10 sets of 2 items, 10 sets of 3 items, 5 sets of 4 items, and 1 set of 5 items.
Find x
Please help ASAP!!!!
Answer:
The answer for x = 30
Step-by-step explanation:
because as you see we got a 60 and you see that lil squares in the corners that squares represent 90 degrees now subtract 60-90 is 30 or you can do it other way just get a paper and graph it
9514 1404 393
Answer:
x = (3/2)√2
Step-by-step explanation:
The ratio of side lengths of the isosceles right triangle is ...
1 : 1 : √2
That means the short side of that triangle will be 6/√2 = 3√2.
__
The lengths of the sides of a 30°-60°-90° triangle have the ratios ...
1 : √3 : 2
The long side is the short side of the isosceles right triangle, 3√2, and the short side of the 60° triangle is half that.
x = (3/2)√2
find the equation of Straight line which passes through the point A(-5,10) makes equal intercept on both axes.
Answer:
y = -x + 5
Step-by-step explanation:
The point is in quadrant 2, so the line must pass through points that look like (a, 0) and (0, a) where a is a positive number. The slope of such a line is -1.
If (x, y) is a point on the line, then the slope between points (x, y) and (-5, 10) is 1, and you can write
[tex]\frac{y-10}{x-(-5)}=-1\\y-10 = -1(x+5)\\y-10=-x-5\\y=-x+5[/tex]
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01
4
3
2
1
F
.
1
om
-3 -3 -2 -1
1
2
الم
T
X
w
Tu
TI
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Find the gradient of the straight line joining the two points. (1,7) and (-1,-7)
Points: (-1,-7), (1,7)
Formula (y=mx+b):
y = 7x
Slope m: 7
Y-intercept b: 0
Parallel lines: 7x + any number
Must click thanks and mark brainliest
Convert 16,000 feet per second into kilometers per hour. step by step
If ABCD is a rectangle, and m_ADB = 55°, what is the value of x? A. 80 O B. 90 O C. 40 O D. 70 O E. 110
===========================================================
Explanation:
Label a new point E at the intersection of the diagonals. The goal is to find angle CEB. Notice how angle AED and angle CEB are vertical angles, so angle AED is also x.
Recall that any rectangle has each diagonal that is the same length, and each diagonal cuts each other in half (aka bisect). This must mean segments DE and AE are the same length, and furthermore, triangle AED is isosceles.
Triangle AED being isosceles then tells us that the base angles ADE and DAE are the same measure (both being 55 in this case).
---------------------
To briefly summarize so far, we have these interior angles of triangle ADE
A = 55D = 55E = xFor any triangle, the three angles always add to 180, so,
A+D+E = 180
55+55+x = 180
110+x = 180
x = 180-110
x = 70
Find the length of the other two sides isosceles right triangle
Answer:
x=5 and h=5*sqrt(2)
Step-by-step explanation:
It's an isosceles right triangle, x=5. Use Pythagoras and compute h
Write the point-slope form of the line passing through (2, -12) and perpendicular to y = 3x.
Answer:
y+12 = -1/3(x-2)
Step-by-step explanation:
y = 3x
The slope is 3
Lines perpendicular have a slope that is the negative reciprocal
-1/3 is the slope of a line that is perpendicular
Point slope form is
y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point on the line
y --12 = -1/3(x-2)
y+12 = -1/3(x-2)
plot the points (0, -2) (4, 1)
Cho f là hàm chẵn, g là hàm lẻ. Tính giá trị của (g∘f)(−4,7), biết g(5,9)=7,9 và f(4,7)=5,9.
Step-by-step explanation:
yah language mujhe samajh mein nahin a rahi hai kya karu aapki is bataiye
PLZZZ HELP
This is due in 15 mins
I need 5
But I already have 4
So one more
Answer:
The hottest month for the northern hemisphere is August.
The hottest month for the southern hemisphere is January and February (these top two might be the opposite)
It's globally warmer during the months of June July and August
During april and november, the southern hemisphere and northern hemisphere are the same, or very close.
During July and August the southern and northern hemispheres have the largest difference in temperature
Your boss asked you to prepare a company party for 20 employees with a budget of Rs. 50, 000.00. You have a choice of ordering a dinner at Rs. 3, 000.00 (Package 01) from “X-Hut Restaurant” per person or a dinner at Rs. 2,500.00 (Package 02) per person from the same place (Delivery charges also included in the price of the meal). i. How many numbers (From package 01 & 02) can you order for the party by using up the budget? ii. How many numbers (From package 01 & 02) can you order for the party if the budget increases to Rs. 55, 000.00?
Step-by-step explanation:
........... ................
Craig and Cindy working together can mow the lawn in four hours working alone Cindy takes twice as long as Craig how long does it take Craig to mow the lawn alone
Answer:
12 hours
Step-by-step explanation:
1 : (1/4 : (2 + 1)) = 12
