Answer:
[tex]\frac{15}{ \sqrt{31} - 4}} = \sqrt{31} + 4[/tex]
Step-by-step explanation:
[tex]\frac{15}{\sqrt{31} - 4}\\\\=\frac{15}{\sqrt{31} - 4} \times \frac{\sqrt{31} + 4}{\sqrt{31}+ 4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ rationalizing \ the \ denominator \ ]\\\\=\frac{15( \sqrt{31} + 4 )}{(\sqrt{31})^2 - (4)^2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (a-b)(a+b) = a^2 - b^2 \ ]\\\\=\frac{15 ( \sqrt{31} + 4)}{31 - 16}\\\\=\frac{15 (\sqrt{31} + 4)}{15}\\\\= \sqrt{31} + 4[/tex]
Solve for x.
Help me please
Answer:
x = 24
Step-by-step explanation:
mathematically, in a cyclic quadrilateral, two opposite angles are supplementary
what this mean is that they add up to be 180
From what we have in the question, the two angles are supplementary and that means they add up to equal 180 degrees
thus, we have it that;
(4x + 9) + (3x + 3) = 180
4x + 3x + 9 + 3 = 180
7x + 12 = 180
7x = 180-12
7x = 168
x = 168/7
x = 24
A cable 45 m long runs from the top of a utility pole to a point on the ground 40 m from the base of the pole. How tall is the utility pole, to the nearest tenth?
20.6 m
85 m
5 m
60.2 m
Answer:
20.6 m
Step-by-step explanation:
Hi there!
Assuming that the utility pole makes a 90-degree angle with the ground, this scenario creates a right triangle.
The 45 m-long cable is the hypotenuse and the 40 m between the base of the pole and the cable is one of the legs.
We must solve for the height of the utility pole, which is essentially the other leg of the right triangle.
We can use the Pythagorean theorem: [tex]a^2+b^2=c^2[/tex] where a and b are the legs and c is the hypotenuse
Plug in the known information (leg=40, hyp=45)
[tex]40^2+b^2=45^2\\1600+b^2=2025\\b^2=2025-1600\\b^2=425\\b=20.6[/tex]
Therefore, when rounded to the nearest tenth, the height of the utility pole is 20.6 m.
I hope this helps!
I need help with all of em please
Answer:5/4
Step-by-step explanation: i think this is the answer
Answer:
The area is 30 units squared, the perimeter is 17 units, and the answer to the question below is 9
Step-by-step explanation:
A cube with an edge length s has a volume of 8 cubic units. What is the length of s?
Answer:
Perimeter on one face =4× side =8
Hence the side of the cube is 2 units.
So the volume of the cube is (side)^3=(2)^3=8 cubic units
Step-by-step explanation:
Make r the subject of the formula t = r/r - 3
Pls help asap
Answer:
statement not complete
Jacob and sumalee each improved their yards by planting daylilies and geraniums. They bought their supplies from the same store. Jacob spent $107 on 11 daylilies and 4 geraniums. Sumalee spent $60 on 4 daylilies and 12 geraniums. Find the cost of one daylilies and the cost of one geranium.
Answer:
Daylily: $9
Geranium: $2
Step-by-step explanation:
1 daylily costs x.
1 geranium costs y.
11x + 4y = 107
4x + 12y = 60
Multiply the first equation by 3 and subtract the second equation from it.
29x = 261
x = 9
4x + 12y = 60
4(9) + 12y = 60
12y = 24
y = 2
Answer:
Daylily: $9
Geranium: $2
Answer:
1) Set up a system of equations. Assign each plant a variable. I used X for Daylillies and Y for Geraniums. In this case:
11x + 4y = 107
4x + 12y = 60
2) Get one variable by itsef. You can choose to either get the X or the Y by itself. For the sake of ease, I'll go with achieving X.
3) Using the equation 4x + 12y = 60, isolate the 4x.
4x = -12y + 60
4) Divide both sides by 4.
x = -3y + 15
5) X is isolated. Now plug in that isolated X into another remaining equation in order to isolate Y. Don't forget to combine like terms.
11(-3y + 15) + 4y = 107
-33y + 165 + 4y = 107
-29y + 165 = 107
-29y = -58
y = 2
6) You have your Y, which means that each Geranium costs $2 each. Now, you need to find X. Plug in Y into any of the first two equations that we started with.
4x + 12(2) = 60
4x + 24 = 60
4x = 36
x = 9
7) You now have both X and Y. Daylillies cost $9 each, and Geraniums cost $2 each.
8) You can double-check your answers by plugging in your final X and Y values into any of the first equations you wrote. If it comes out equal, it works.
plss, help me!!!
Each of four friends orders a sweatshirt from a catalog. There are 16 colors of sweatshirts, 7 of which are all cotton and 9 wich are blend. Each one orders a different color ( no repeats) at random. What is the probability that the friends order only cotton sweatshirts?
===========================================================
Explanation:
Let's label the friends as A,B,C,D.
Person A has a probability of 7/16 when it comes to ordering a certain color of cotton sweatshirt.
Then 6/15 is the probability for person B. Note how the 7 and 16 drop by 1 for each. This is because no repeats are allowed. If person A goes for a blue sweatshirt, then person B cannot select blue as well.
Person C's probability is 5/14 and person D has a probability of 4/13
-------------------------
So we have these fractions: 7/16, 6/15, 5/14, 4/13
Once again, we have the numerators and denominators counting down by 1 each time.
Multiplying those fractions gets us...
(7/16)*(6/15)*(5/14)*(4/13)
(7*6*5*4)/(16*15*14*13)
840/43680
(1*840)/(52*840)
1/52
So if you did 52 trials of this, then you should expect about 1 of those trials is where each friend orders a different color cotton sweatshirt.
1/52 = 0.0192 = 1.92% approximately
So this happens about 1.92% of the time.
What will you use if you are looking for the space bounded by a rectangle A. 2(I + w) B. S² C. B × h ________ 2 D. I × w
Answer:
A. 2(I + w)
Step-by-step explanation:
The space bounded by a rectangle is its perimeter. So, I would use 2(l + w) where l = length of rectangle and w = width of rectangle.
As an example, suppose we have a rectangle of length, l = 40 meters and width, w = 20 meters and seek to find its perimeter that is, the space bounded by the rectangle, we substitute the values of l and w into the equation for the perimeter.
So, P = 2(l + w)
substituting the values of l and w into the equation, we have
P = 2(l + w)
P = 2(40 m + 20 m)
P = 2(60 m)
P = 120 m
So the space bounded by the rectangle is 120 m.
So, to find the space bounded by a rectangle, we use 2(l + w).
So, the answer is A.
Which graphs are the graphs of even functions?
HELP ASAP
Answer:
Step-by-step explanation:
Even functions have symmetry about the y-axis, so the graphs of even functions are the bottom 2.
. Out of 140 students, 50 passed in English and 20 passed in both Nepali and English. The number of students who passed in Nepali is twice the number of students who passed in English. Using a Venn-diagram, find the number of students who passed in Nepali only and who didn't pass in both subjects.
Answer:
80 ;
10
Step-by-step explanation:
Given :
Total number of students = μ = 140
Let :
Number of students who passed in English = E
Number of students who passed in Nepali = N
n(NnE) = 20
n(E) only = n(E) - n(NnE) = 50 - 20 = 30
Students who passed English only = 30
Number of students who passed in Nepali is twice the number who passed in English
n(N) = 2 * n(E) = 2 * 50 = 100
Number of students who passed in Nepali only
n(N) only = n(N) - n(NnE) = 100 - 20 = 80
Students who passed Nepali only = 80
The number who didn't pass both subjects :
μ - (English only + Nepali only + English and Nepali)
140 - (30 + 80 + 20)
140 - 130
= 10
How do you work out the volume of a cube
Answer:
V=a cubed
Step-by-step explanation:
Plz help me solve this ASAP and show the work thank you
Answer:
14
Step-by-step explanation:
The diagram is right angle triangle so we can use SOHCAHTOA
So in the diagram we have 62 degree opposite to x and the hypotenuse
Step 1
Sin62=x/16
Step 2
X=16sin62 by cross multiplication
Step 3
X=14.13
X=14
PLEASEEE HELPPPPPPP
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 9(1.04)d
What is the average rate of change of the function f(d) from d = 3 to d = 9, and what does it represent?
Answer:
0.4476
Step-by-step explanation:
Can someone please be generous and help me
Answer:
The point slope form is [tex]y-y_{1} =m(x-x_{1} )[/tex]
The slope(m) can be calculated using [tex]\frac{y-y_{1} }{x-x_{1}}[/tex]:
[tex](x, y)=(4,-3)\\(x_{1} ,y_{1} )=(5,0)\\\\\frac{0-(-3)}{5-4} =\frac{0+3}{1} =\frac{3}{1} =3[/tex]
Using Point One, the point-slope form is determined as:
[tex]y-(-3)=3(x-4)\\y+3=3(x-4)[/tex]
The y-intercept(b) can be calculated as:
[tex](5,0)\\y=3x+b\\0=3(5)+b\\0=15+b\\b=-15\\(0,-15)[/tex]
Which of the following equations correctly represents the law of cosines?
A. 2 = 22 + b2 - 2ab.cos(B)
B. 2 = 22 + c2 - 2ac.cos(C)
C. a2 = b2 + c2 - 2bc.cos(A)
D. b2 = 22 +62 - 2bc.cos(B)
Answer:
D. b2 = 22 + 62-2bc.cos(B)
Help please
What value of x will ensure that the shelves are parallel?
for the to be parallel both the angle must be equal
so 7x - 20 = 3x + 20 - > 4x = 40⁰
x = 10⁰
Order the steps and justifications in solving the system of linear equations. Equation 1: 4x+3y=8 Equation 2: −2x−3y=−4
Answer:
See explanation
Step-by-step explanation:
The two linear equations can be solved simultaneously;
4x+3y=8 -----(1)
−2x−3y=−4---(2)
If we multiply equation (1) by 1 and equation (2) by (2)
We have;
4x+3y=8 -----(3)
-4y - 6x = 4 ---(4)
Adding equation (3) and (4)
-3x = 12
x= -4
Substitute x = -4 into equation (1)
4(-4) + 3y = 8
-16 + 3y = 8
3y = 8 + 16
y= 24/3
y= 8
Hence;
x= -4 and y =8
identify the equation of the line graphed below
Two square based pyramids are joined, total volume is 2700mm, perpendicular height of top pyramid is 16mm, perpendicular height of bottom pyramid is 20mm, length and width of joint base area both x, find x. Please help me
Answer: 15 m
Step-by-step explanation:
Given
Total volume of the combined pyramid is [tex]V=2700\ mm^3[/tex]
Height of top and bottom pyramid is
[tex]h_t=16\ mm[/tex]
[tex]h_b=20\ mm[/tex]
If the base has a side length of x, its area must be [tex]x^2[/tex]
Volume of square prism is given by
[tex]\Rightarrow V=\dfrac{1}{3}Bh\quad [\text{B=base area}]\\\\\text{Total volume will be the sum of the two pyramids}\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times 16+\dfrac{1}{3}\times x^2\times 20\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times (16+20)\\\\\Rightarrow x^2=225\\\Rightarrow x=15\ mm[/tex]
Thus, the value of [tex]x[/tex] is 15 m.
Calculate the average rate of change of a function over a specified interval. Which expression can be used to determine the average rate of change in f(x) over the interval 2, 9?
Given:
The interval is [2,9].
To find:
The average rate of change in f(x) over the interval [2,9].
Solution:
The average rate of change in f(x) over the interval [a,b] is defined as:
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
In the interval [2,9], the value of a is 2 and the value of b is 9.
Using the above formula, the average rate of change in f(x) over the interval [2,9] is:
[tex]m=\dfrac{f(9)-f(2)}{9-2}[/tex]
[tex]m=\dfrac{f(9)-f(2)}{7}[/tex]
Therefore, the required expression for the average rate of change in f(x) over the interval [2,9] is [tex]\dfrac{f(9)-f(2)}{9-2}[/tex], it is also written is [tex]\dfrac{f(9)-f(2)}{7}[/tex].
Answer:
D
Step-by-step explanation:
right on edge
Find the first five terms of the sequence described.
Answer:
I dont think i dont know this but its 10?
Tickets to a football final are selling well. On Thursday, 47 of the tickets are sold. On Friday, 14 of the tickets are sold. What fraction of tickets are available to sell on Saturday?
The question seems incomplete ; as the total number of tickets to be sold isn't given.
Answer:
61 / X
Step-by-step explanation:
Let's take the total Number of tickets to be sold as : X
Number of tickets sold on Thursday = 47
Number sold on Friday = 14
Fraction of tickets available for sale on Saturday :
(Total number of tickets already sold) / Total number of tickets to be sold
(Thursday + Friday sales) / total number of tickets to be sold
Fraction available for sale on Saturday = (47+14) / X
Fraction available for sale on Saturday = 61 / X
Kindly put value of x = total number of tickets available for sale to get the exact fraction.
A circle is centered at the point (5,-4) and passes through the point (-3, 2). what is the equation of this circle?
Answer:
(x-5)² + (y+4)² = 100
Step-by-step explanation:
The formula for calculating the equation of a circle is expressed as;
(x-a)² + (y-b)² = r² where:
(a,b) is the centre of the circle
r is the radius
Get the radius using the distance formula;
r = √(2-(-4))²+(-3-5)²
r = √6²+(-8)²
r = √36+64
r =√100
r² = 100
Since a = 5 and b = -4, on substituting into the formula;
(x-5)² + (y+4)² = 100
This gives the required equation
Answer:
(x-5)² + (y+4)² = 100
Step-by-step explanation:
Just got it correct on Edmentum test.
Triangle ABC is congruent to LMN. Find the value of x. Please and thank you!
Warning: if you give an answer that is NOT related to the question at all then I will report you - FIND THE VALUE OF X
Answer:
x = 9
Step-by-step explanation:
The ratios of corresponding sides are equal, that is
[tex]\frac{BC}{MN}[/tex] = [tex]\frac{AB}{LM}[/tex] , substitute values
[tex]\frac{x}{15}[/tex] = [tex]\frac{6}{10}[/tex] ( cross- multiply )
10x = 90 ( divide both sides by 10 )
x = 9
I NEED HELP!!! Can someone please help me
Answer:
x = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Here you have to use the Pythagorean Theorem.
Pythagorean Theorem: a^2 + b^2 = c^2
STEP 1: Define your variables
a and b are the legs of the triangle, and c is the hypotenuse
a = 7
b = x
c = 9
STEP 2: Plug the variable into the equation
7^2 + x^2 = 9^2
STEP 3: Solve
7^2 + x^2 = 9^2
49 + x^2 = 81
49 - 49 + x^2 = 81 - 49
[tex]\sqrt{x}[/tex]^2 = [tex]\sqrt{32}[/tex]
x = [tex]\sqrt{32}[/tex]
STEP 4: Simplify
Since the questions asks you to put it in simplified radical form, you do not have to approximate the answer, but you do have to simplify the radical.
x = [tex]\sqrt{32}[/tex]
x = [tex]\sqrt{16}[/tex] * [tex]\sqrt{2}[/tex]
x = 4[tex]\sqrt{2}[/tex]
Hope this helps
Using trial and improvement, find the solution between 5 and 6 for the following equation:
x
2
=
27
Give your answer rounded to 1 DP.
Answer:
2
Step-by-step explanation:
that is √ 14 which is 27 ×>44.2177
PLEASE ASAP
c) Next, you will make a scatterplot. Name a point that will be on your scatterplot and describe what it represents.
d) Using the regression calculator in your tool bar, create a scatterplot using your data set from step 1. Insert a screenshot of your scatterplot, or recreate it below.
The data is in the pic below
If u want more points for the answer, pls answer the previous question (same one) in my profile worth 30 points)
THX
Answer:
C)Ok i pick the point (18,4)
this point represents that if this person studied from 18 hours they got a GPA of 4.0
D) the chart below is the scatter plot
Hope This Helps!!!
Determine the simplest expression for the area of shaded region below
Answer:
5x^2+3x^2+(3x+1)^2+(2x-4)^2
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle .
Answer:
these points lie INSIDE THE CIRCLE
Hope it helps
have a nice day
A taxi firm charges a fixed cost of $10 together with a variable cost of $3 per mile. (a) Work out the average cost per mile for a journey of 4 miles. (b) Work out the minimum distance travelled if the average cost per mile is to be less than $3.25
Answer:
$5.5 per mile
40 miles
Step-by-step explanation:
Given :
Fixed cost = $10
Variable cost = $3
For a journey of 4 miles ;
Cost = fixed cost + Variable Cost
Cost = $10 + $3x
x = number of miles
Cost = $10 + $3(4)
Cost = $10 + $12 = $22
Average cost per mile for a journey of 4 miles
Cost / number of miles
$22 / 4 = $5.5 per mile
Minimum distance if average per mile is to be less Than 3.25
$3.25 = (10 + 3x) / x
3.25x = 10 + 3x
3.25x - 3x = 10
0.25x = 10
x = 10 / 0.25
x = 40 miles