Answer:
The numbers are 87 and 130
Step-by-step explanation:
Call the numbers x and y[tex]x+y=217[/tex] [1][tex]y-x=43[/tex] [2]Rearrange [2] to make y the subject[tex]y=43+x[/tex] [3]Substitute [3] into [1][tex]x+(43+x)=217[/tex][tex]2x+43=217[/tex][tex]2x=174[/tex][tex]x=87[/tex] [4]Use [4] for [2][tex]y-87=43[/tex][tex]y=130[/tex]How to graph the equation y=-x^2+6x-5 on the accompanying set of axes?
Answer: See attached
Step-by-step explanation:
Given:
y = -x² + 6x - 5
Since this is a quadratic function, we will have a parabola.
Because our x² value is negative, this parabola will be a "frowny face" instead of a "smiley face" like the parent function.
The - 5 means we shift the function 5 units to the right from the parent function.
See attached for our graph.
What parent function am I mentioning?
The parent function of y = -x² + 6x - 5 is y = x²
A college student takes the same number of credits each semester. She had 8 credits when she started, and after 7 semesters, she had 92 credits.
Which of these expresses the rate at which she is earning credits
Answer:
12 credits per semester
Step-by-step explanation:
she has 92 in the end but she started off with 8 so your first step is to subtract 8 from 92 which gives you 84 once you get 84 you divide that by 12 you get 7 which means she got 12 credits in each of her 7 semeters
Solve for 2. Round to the nearest tenth, if necessary.
B
U
67
T
x
142°
Tan(angle) = opposite/ adjacent
tan(42) = 67/x
x =67/tan(42)
X = 74.411
rounded to nearest tenth : x = 74.4
Find the mean of the data in the dot plot below. Make sure to show your work and explain the steps you took in solving the problem. please help I took a picture I just need the problem to be explained
Answer: 6.
Step-by-step explanation: To find the mean, the first step is to add all the data together. Here's how it should look:
2 + 3 + 6 + 6 + 7 + 8 + 8 + 8 = 48.
Next, you need to divide whatever you get after adding the data by how many numbers there are for your data. In this case, 48 was the answer when we added all the data. In total, you have 8 numbers in your data, so you need to divide 8 from 48. It should look like this:
48 / 8 = 6.
Therefore, the mean for this data set is 6.
Have a great day! :)
Evaluate this:
[tex]\displaystyle\rm\int_0^\frac{\pi}{2}\sqrt{\sin x}\ dx \times \int_0^\frac{\pi}{2}\frac{1}{\sqrt{\sin x}}\ dx[/tex]
Only elementary methods are allowed.
The first integral has a well-known beta function representation, so the second one should too. The beta function itself is defined as
[tex]B(x,y) = \displaystyle \int_0^1 t^{x-1} (1-t)^{y-1} \, dt[/tex]
and satisfies the identity
[tex]\displaystyle B(x,y) = \frac{\Gamma(x) \Gamma(y)}{\Gamma(x+y)}[/tex]
Later on, we'll also use the so-called reflection formula for the gamma function; for non-integer z,
[tex]\Gamma(z) \Gamma(1-z) = \dfrac{\pi}{\sin(\pi z)}[/tex]
as well as the identity
[tex]\dfrac{\Gamma(z+1)}{\Gamma(z)} = z[/tex]
Replace [tex]x\to\sin^{-1}(x)[/tex] in both integrals, so that
[tex]\displaystyle \int_0^{\frac\pi2} \sqrt{\sin(x)} \, dx = \int_0^1 \frac{\sqrt x}{\sqrt{1-x^2}} \, dx[/tex]
[tex]\displaystyle \int_0^{\frac\pi2} \frac{dx}{\sqrt{\sin(x)}} = \int_0^1 \frac{dx}{\sqrt x \sqrt{1-x^2}}[/tex]
Now replace [tex]x\to\sqrt x[/tex] :
[tex]\displaystyle \int_0^1 \frac{\sqrt x}{\sqrt{1-x^2}} \, dx = \frac12 \int_0^1 x^{-\frac14} (1-x)^{-\frac12} \, dx = \frac12 B\left(\frac34, \frac12\right) [/tex]
[tex]\displaystyle \int_0^1 \frac{dx}{\sqrt x \sqrt{1-x^2}} = \frac12 \int_0^1 x^{-\frac34} (1-x)^{-\frac12} \, dx = \frac12 B\left(\frac14, \frac12\right)[/tex]
So, the original integral (which I condense here to a double integral) is
[tex]\displaystyle \int_0^{\frac\pi2} \int_0^{\frac\pi2} \sqrt{\frac{\sin(x)}{\sin(y)}} \, dx \, dy = \frac14 B\left(\frac34, \frac12\right) B\left(\frac14, \frac12\right)[/tex]
[tex]\displaystyle = \frac14 \frac{\Gamma\left(\frac14\right) \Gamma\left(\frac34\right) \Gamma\left(\frac12\right)^2}{\Gamma\left(\frac54\right) \Gamma\left(\frac34\right)}[/tex]
[tex]\displaystyle = \frac14 \frac{\Gamma\left(\frac14\right) \Gamma\left(\frac34\right) \Gamma\left(\frac12\right)^2}{\frac14 \Gamma\left(\frac14\right) \Gamma\left(\frac34\right)}[/tex]
[tex]\displaystyle = \Gamma\left(\frac12\right)^2 = \frac{\pi}{\sin\left(\frac\pi2\right)} = \boxed{\pi}[/tex]
On Monday the postman brought two checks, one for $56.00 and one for $10.00. Assuming you
have no other money in the world, what is your financial situation after this delivery?
Answer: $66.00
Step-by-step explanation:
56 + 10 = 66
Find the greatest common factor of 8 and 24.
Answer:
8
Step-by-step explanation:
Factors of 8: 1, 2, 4, 8
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
They do share a few factors but the greatest one shared between the two is 8
Looking for the best answer
Answer:
4x - 5 - 3
Step-by-step explanation:
the 3rd is the best answer i think
50 PTS PLS HELP! Michael works at a furniture store. He makes a commission for every piece of furniture he sells. He sold a couch for $1245 he got a check for $62.25. What was the % of the commission he made?
Answer:
11% yan po answer hehehe tama yan
a 8 1/2 foot board Is cut Into 2 1/2 foot lengths. how many sections will you have
Answer:
3 whole but 3.4 as a decimal
Step-by-step explanation:
Look at this rectangle. Find the value of u.
Answer:
1 inch
Step-by-step explanation:
We know that opposite sides of a rectangle are equal to each other.
Given that,
Perimeter = 30 in
Therefore,
u + u + 14 + 14 = 30
2u + 28 = 30
2u = 30 - 28
2u = 2
Divide both sides by 2.
u = 1 in
What is the area of this trapezoid?
Answer:
The area is [tex]80[/tex]
Step-by-step explanation:
rectangle in the middle; 24
both triangles on the side; 56
In total; 80
0.7 is equivalent to what fraction
Answer:
7/10
Step-by-step explanation:
Fractional form of 0.7 is 7/10.
Ellie left her house and drove to the store. She stopped and went inside. From
there, she drove in the same direction until she got to the bank. She stopped
and went inside the bank. Then she drove home. The graph below shows the
number of blocks away from home Ellie is x minutes after she left her house,
until she got back home.
Answer:
Ellie spent 21 minutes after she left her house until she got back home
Which real-world scenario involves a right triangle?
Answer:
There are a few different scenarios
Step-by-step explanation:
Bathroom Tiles,Kitchen flooringTriangle Backsplash ( tile behind your sink in kitchenDrywall work if you need right edges, you will need a right triangleFinally any sort of contracting and Deck workFROM- THE GENIUS ANSWERER
what is this number? 1,010,020,030,040,050,060,070,080,090,010,020,030,040,050,060,070,080,090,010,020,030,040,050,060,070,080,090,010,020,030,040,050 WILL MARK BRAINLIEST
Answer:
that isn't a number
Step-by-step explanation:
please show your work, tysm :D
~giving brainliest!~
Answer:
1/16th
Step-by-step explanation:
You can write this problem as a function of time.
Let x be the amount of acetaminophen that you start off with.
Let n be the amount of 2.5 hour intervals that have passed
x*0.5^n
The reason this function works is because with each 2.5 hour interval, you multiply the total product by another 1/2.
Plugging in 4(because 4 2.5 hour intervals in 10 hours), you get:
x*0.5^4,
which is x/16.
This shows that 1/16th of the acetaminophen is left in the body after 10 hours.
Find the arc length of the partial circle.
Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.
Explanation:
A full circle of radius r has a circumference of 2pi*r which is the perimeter aka distance around the circle's edge.
We divide that by 4 to get the arc length of the quarter circle and we'd get to (2pi*r)/4 = 0.5pi*r
Plug in r = 1 and pi = 3.14
0.5*pi*r = 0.5*3.14*1 = 1.57
Solve the system of equations.
Answer:
3x+2y=24
Y=3
Substitute in the equation
3x+2(3)=24
3x+6=24
3x=24-6
3x=18
X=18/3
X=6
1
C
2
3
✓4
5
7
8
✓ 10
A car travels at an average speed of 56 miles per hour. How many miles does it travel in 4 hours and 45 minutes?
mites
x
5
?
I
Answer:
266 miles
Step-by-step explanation:
Given statement
4 hours and 45 minutesClearly, 45 is 3/4th of an hour. Thus, this statement can also be written as:
⇒ 4 hours and 3(Hour)/4 minutes⇒ 4 hours + 3(Hour)/4 minutes⇒ 4 hours + 0.75(Hour)⇒ 4.75 hoursWe are given that:
56 miles per hourWhen we convert this statement into an equation, we get:
⇒ 56 miles = 1 hourMultiply both sides by 4.75 to obtain the distance in 4.75 hours.
⇒ 56 × 4.75 miles = 1 hour × 4.75⇒ 266 miles = 4.75 hourswhat is the inverse of f(x)=2(3^x)
If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then by definition
[tex]f\left(f^{-1}(x)\right) = x[/tex]
so that
[tex]2 \times 3^{f^{-1}(x)} = x[/tex]
Solve for [tex]f^{-1}(x)[/tex] :
[tex]3^{f^{-1}(x)} = \dfrac x2[/tex]
[tex]\log_3\left(3^{f^{-1}(x)}\right) = \log_3\left(\dfrac x2\right)[/tex]
[tex]f^{-1}(x) \log_3(3) = \log_3\left(\dfrac x2\right)[/tex]
[tex]\boxed{f^{-1}(x) = \log_3\left(\dfrac x2\right)}[/tex]
Lucas bought a package of baseball cards for $0.70. His friend bought 3 times as many packages. How much did his friend spend?
$2.10
$2.50
$2.80
$3.10
Answer: $2.10
Step-by-step explanation:
It took Theo 18 minutes to count his cards and he finished at 4:45
p.m. What time did Theo start counting?
4:27
Step-by-step explanation:
just subtract 45 and 18. common sense
50 points+ Brainliest PLEASE SHOW WORK!!!!
(i can only give brainliest if at least 2 people answer)
Answer:
here
Step-by-step explanation:
we can do it by using the formula like
mean; efx÷n
median =n+1÷2
mode =which is more
range=highest-smallest
Answer:
Step-by-stwe can do it by using the formula like
mean; efx÷n
median =n+1÷2
mode =which is more
range=highest-smallestep explanation:
PLEASE HELP PLEASE HELP
Answer:
B
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The Square Pyramid Has 5 Vertices.
:)
i would really like some help, factoring trinomials if you want an extra 50-100 points you could help with a previous question on my profile lol
Answer:
[tex]g) \left(5x-2\right)\left(3x+2\right)[/tex]
[tex]h)2\left(8a-9\right)\left(a-2\right)[/tex]
[tex]i)3\left(21n^2+42n+16\right)[/tex]
Step-by-step explanation:
Starting with g) [tex]15^2+4x-4[/tex]
Break the expression into group
[tex]=\left(15x^2-6x\right)+\left(10x-4\right)[/tex]
Now, Factor out [tex]3x[/tex] from [tex]15x^2-6x[/tex] which is now is [tex]3x(5x-2)[/tex]
Next, Facotr out [tex]2[/tex] from [tex]10x-4[/tex] which is now is [tex]2(5x-2)[/tex]
Thus,
[tex]=3x\left(5x-2\right)+2\left(5x-2\right)[/tex]
Factor common term 5x -2
[tex]\left(5x-2\right)\left(3x+2\right)[/tex]
-------------------------------------------------------------------------------------------------------------
Next we have [tex]h)16a^2-50a+36[/tex]
Factor out common term thus we have [tex]2(8a^2-25a+18)[/tex]
Factor again: [tex]8a^2-25a+18[/tex] now turn into [tex](8a-9)(a-2)[/tex]
[tex]=2\left(8a-9\right)\left(a-2\right)[/tex]
-------------------------------------------------------------------------------------------------------------
Lastly we have [tex]i)63n^2+126n+48[/tex]
Rewrite the following:
63 as 3 * 21
126 as 2 * 42
48 as 3 * 16
[tex]63n^2+126n+48[/tex]
Now cut out common term:
[tex]=3\left(21n^2+42n+16\right)[/tex]
-------------------------------------------------------------------------------------------------------------
~lenvy~
Answer:
(g) [tex](5x-2)(3x+2)[/tex]
(h) [tex](16a-18)(a-2)[/tex]
(i) [tex]3(21n^2+42n+16)[/tex]
Step-by-step explanation:
To factor a quadratic in the form [tex]ax^2+bx+c[/tex]
Find 2 two numbers ([tex]d[/tex] and [tex]e[/tex]) that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]Rewrite [tex]b[/tex] as the sum of these 2 numbers: [tex]d + e = b[/tex]Factorize the first two terms and the last two terms separately, then factor out the comment term.Question (g)
[tex]15x^2+4x-4[/tex]
[tex]\implies ac=15 \cdot -4=-60[/tex]
[tex]\implies d+e=4[/tex]
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Therefore, the two numbers (d and e) that multiply to -60 and sum to 4 are:
10 and -6
Rewrite [tex]4x[/tex] as [tex]+10x-6x[/tex]:
[tex]\implies 15x^2+10x-6x-4[/tex]
Factories first two terms and last two terms separately:
[tex]\implies 5x(3x+2)-2(3x+2)[/tex]
Factor out common term [tex](3x+2)[/tex]:
[tex]\implies (5x-2)(3x+2)[/tex]
Question (h)
[tex]16a^2-50a+36[/tex]
[tex]\implies ac=16 \cdot 36=576[/tex]
[tex]\implies d+e=-50[/tex]
Factors of 576: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
Therefore, the two numbers that multiply to 576 and sum to -50 are:
-32 and -18
Rewrite [tex]-50a[/tex] as [tex]-32a-18a[/tex]:
[tex]\implies 16a^2-32a-18a+36[/tex]
Factories first two terms and last two terms separately:
[tex]\implies 16a(a-2)-18(a-2)[/tex]
Factor out common term [tex](a-2)[/tex]:
[tex]\implies (16a-18)(a-2)[/tex]
Question (i)
[tex]63n^2+126n+48[/tex]
Factor out common term 3:
[tex]\implies 3(21n^2+42n+16)[/tex]
This cannot be factored any further.
if two angles at the base of an isosceles triangle are 50, the other angle is _____because_____________________________________________.
please helpp
Simplify
2 × (3 – 1) + 3
Answer:
If you put this in the calculator, the answer would be 7
I will give you 100 points and a Brainliest if you can help me with this question.
Complete the calculations so that each shows the correct difference.
Answer:
0.671
0.985
0.137
Step-by-step explanation:
ABove is answer
Answer:
0.671
0.985
0.137
Step-by-step explanation:
Now you could give the person above me brainliest
Which expression is equivalent to -8(x+2)-(x+4)
Answer:
-8x+-16-(-8x)+(-32)
Step-by-step explanation: