Answer:
x = 5/3Step-by-step explanation:
Guven two prime numbers to be 31/x and 71/x, if their sum is 10 as given;
3x + 71/x = 10 then to find the value of x, the following steps must be taken;
Step 1
Find the LCM of the given equation;
3x + 71/x = 10
[tex]\frac{3x^{2}+71 }{x} =10\\[/tex]
Step 2:
Cross multiplying;
[tex]3x^{2} +71=10x\\3x^{2} -10x+71 =0\\[/tex]
Using the general formula to get the value of x;
x = -b±√b²-4ac/2a
a=3, b=-10, c=71
= 10±√(-10)²-4(3)(71)/2(3)
= 10±√100-852/6
= 10±√-752/6
= 10±27.4i/6
= 10+27.4i/6 or 10-27.4i/6
x = 5/3+27.4i/6 or 5/3-27.4i/6
Since the values of x are real values then, our answer will be the real part of the complex number gotten.
x = 5/3
Which function is the result of vertically shrinking ƒ(x) = (x + 1)2 by a factor of 1∕6?
Question 6 options:
A) ƒ(x) = (6x + 1)2
B) ƒ(x) = (1∕6x + 1)2
C) ƒ(x) = 6(x + 1)2
D) ƒ(x) = 1∕6 (x + 1)2
Answer:
[tex]y=\frac{1}{6}(x+1)^2[/tex] is the result of vertically shrinking
Step-by-step explanation:
Vertical stretch or shrink
[tex]y=c \cdot f(x)[/tex]
a stretch by a factor of c if c>1
a shrink by a factor of c if c<1
c is the factor
We are given that factor = 1/6 <1
So, Vertical shrink
So, [tex]y = \frac{1}{6} \cdot f(x)[/tex]
We are given that [tex]f(x) = (x + 1)^2[/tex]
So,[tex]y=\frac{1}{6}(x+1)^2[/tex]
Option D is true
Hence [tex]y=\frac{1}{6}(x+1)^2[/tex] is the result of vertically shrinking
Answer:
ƒ(x) = (1∕6x + 1)^2
Step-by-step explanation:
PLEASE ANSWER THIS ASAP
Answer:
i really dont know
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The slope (rate of change) are 2/5 or .4 for both of them
What is the answer? Plz need help
30x and 12 have a common factor of 6. So yes, this might have been the result of distributing the 6 in
6(5x - 2)
Answer:
30x - 12 = 2(15x - 6)
30x - 12 = 3(10x - 4)
30x - 12 = 6(5x - 2)
Step-by-step explanation:
30 and 12 have these factors in common: 2, 3, 6
There are three possible answers.
30x - 12 = 2(15x - 6)
30x - 12 = 3(10x - 4)
30x - 12 = 6(5x - 2)
What is the surface area?
10 cm
8 cm
10 cm
12 cm
10 cm
square centimeters
Step-by-step explanation:
surface area = (2*0.5*12*8) + (2*10*10) + (12*10)
= 96 + 200 + 120
= 416 cm^2
A rectangular prism has a length of 12in, a height of 5in, and a width of 8in. What is its volume, in cubic in?
Answer: The volume is 480 in^3
Step-by-step explanation:
v= lwh
v= 12 * 5 * 8
v= 480 in^3
Answer:
Volume of the rectangular prism = [tex]480in.^{3}[/tex]
Step-by-step explanation:
Formula for the volume of a rectangular prism= Ah, where A= base area
& h= height
Base area(A)= Length×Width
= 12in.×8in.
= [tex]96in.^{2}[/tex]
Since height=5in.,
Volume= [tex]96in.^{2}[/tex]×5in.
= [tex]480in.^{3}[/tex]
Hope this helps!!!
Pls mark as brainliest
can net worth be negative?
Answer:
our net worth can tell you many things. If the figure is negative, it means you owe more than you own. If the number is positive, you own more than you owe. ... Negative net worth does not necessarily indicate that you are financially irresponsible; it just means that – right now – you have more liabilities than assets
Step-by-step explanation:
hope it help
Yes, of course. A good fraction of the people on earth owe more than they own, so have negative net worth.
In the USA about 14% of the households have negative net worth. I would have guessed that credit card debt was the culprit, but it's mostly student loans that drag folks into this category.
which point is an x-intercept of the quadratic function
f(x)=(x-8)(x+9) ?
Answer:
(0, 8)
Step-by-step explanation:
i just got this question
Answer:
(-9,0)
Step-by-step explanation:
To find the x intercept, set y=0 and solve for x
f(x) = (x-8) (x+9)
0 = (x-8) (x+9)
Using the zero product property
x-8 =0 x+9=0
x=8 x=-9
(8,0) (-9,0) are the x intercepts
Evaluate the expression 3 x
{10 +1} +5.
Answer:
38
Step-by-step explanation:
3 x {10 +1} +5.
PEMDAS
Parentheses first
3 x {11} +5.
Then multiply and divide
33+5
38
Answer:
38
Step-by-step explanation:
3 x {10 +1} +5 Following PEMDAS, solve in the parentheses
3 x 11 + 5 Multiply 3 x 11
33 + 5 Add
38
13th term of 2, 10, 18, 26
Answer:
192
Step-by-step explanation:
Add 8 started from 2 and keep going till you hit 192.
Answer:
a1 = 2 d = 8
n = 13
an = a1 + d(n-1)
a(13) = 2 + 8(13-1)
2 + 8(12)
2 + 96 = 98
Step-by-step explanation:
1. identify the terms
2. write down the arithmetic sequence formula and then replace the letters with their values.
3. do parenthesis first, then multiply by d.
4. add them together to get the 13th term
Can someone please help me? I keep losing points...
CORRECT ANSWERS ONLY PLEASE!!!!
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
$93,996
Step-by-step explanation:
i = prt
i = ($53,712)(.15)(5)
i = $40, 284
$40, 284 + $53,712
$93,996
Answer:
$92996
Step-by-step explanation:
Using the given formula :
I = P × R × T
I = 53712 × 15/100 × 5
I = $40284
He has = 40284 + 53712 = $93996
If a right triangle is rotated around one of its legs for 360 degrees, what three dimensional shape is produced?
Answer:
The shape of a cone
Step-by-step explanation:
If we rotate the right triangle for 360 degrees around one leg, we will have a shape of a cone (a conical shape).
the leg we choose to rotate around will be the height of the cone.
The other leg will be the radius of the cone's base.
And the hypotenusa of the right triangle will be the slant height of the cone.
Round your answer to the nearest hundredth..
B
?
5
2
A
С
Answer: m<B = 66.42
Step-by-step explanation:
Use cosine to find the missing angle.
Cosine = adjacent/hypotenuse
cos x = 2/5
since you know the side lengths and you’re finding the angle, use inverse cosine
cos -1 (2/5) = 66.4218215...
m<B = 66.42
Hey there!
We are looking for an angle. Whenever we want to look for an angle in a right triangle given two sides, we use inverse trigonometric functions. This is basically the inverse operation of the sine, cosine, and tangent. You could use it to undo any of these in an equation. If you said that the sine of x was equal to 1/2, you would do the inverse sine of 1/2 and get that x=30.
In our case, we see that the cosine of our angle is 2/5. How do we know that?
Well, we can remember the trigonometric functions using the mnemonic "soh cah toa"
SOH
Sine= Opposite/Hypotenuse
CAH
Cosine= Adjacent/Hypotenuse
TOA
Tangent= Opposite/Adjacent
If we look at the number values we have, we have 2 (the adjacent side to the angle) and 5 (the hypotenuse). This is adjacent over hypotenuse, which is the cosine. So, the cosine of our angle is 2/5.
Now, we can put this into an equation. I will call the measure of our mystery angle Θ (theta).
cosΘ= 2/5
We want to get the theta by itself to solve the equation. To do this, we have to use the inverse cosine on both sides of the equation to cancel out our cosine and figure out the value of theta. The inverse trig functions can be found on a calculator :)
cos[tex]^-1[/tex]cosΘ=cos[tex]^-1[/tex] 2/5
Θ ≈ 66.42
I hope that this helps! Now you will be able to find any angle given two sides of a right triangle! Have a wonderful day!
A factory uses 3/4 of a barrel of raisins in each batch of granola bars. Yesterday, the factory
used 1 1/2 barrels of raisins. How many batches of granola bars did the factory make
yesterday?
Answer:
Step-by-step explanation:
3/4 * 2 = 1 1/2
The factory made two batches of granola bars.
If angle AOC = 40 degrees, how many degrees is angle ABC?
80........................
3. Nine books are to be bought by a student. Some
cost $6 each and the remainder cost $6.50 each.
If the total amount spent was $56, how many
books at each price are bought?
Answer:grjjrd
Step-by-step explanation:fdfgdjj
Eric created a rectangular patio 1 ft.² paving stones which are sold in batches by a dozen the patio measures 7‘ x 8‘ how many batches of Pavingstone did Eric need
Answer:
The number of batches of paving stones Eric needs is 5 batches
Step-by-step explanation:
Here we have the size of of one paving stone = 1 ft²
The dimensions, size, of one patio = 7 ft × 8 ft = 56 ft²
Therefore, the number of paving stones Eric needs per patio is given by the relation;
[tex]Number\, of\ paving\ stones \ required =\frac{size\, of \, one\, patio}{size \, of \, one\, paving\, stone} = \frac{56 \, ft^2}{1 ft^2/(paving \, stone)} = 56 \, paving \, stones[/tex]
Since the paving stones are sold in batches of one dozen, we have ;
4 batches = 48 paving stones and 5 batches = 60 paving stones
Therefore, the number of batches of paving stones Eric needs = 5 batches.
a1 = 92 cm
b1 = 66.7 cm
a2 = 38 cm
b2 = 53.42 cm
h = 52 cm
Answer:
area=250.12. perimeter=3380
Step-by-step explanation:
Justin earned $25.67 one week and $37.85 the next
week. He also purchased a DVD for $19.99 and gas for
his car for $22.07. He started with a zero balance in his
checking account. Justin recorded all of these
transactions in his checkbook and ended up with a
balance of $105.58. Was his balance correct? If it was,
write an equation to support the answer.
Answer:
No, Justin isn't correct
Step-by-step explanation:
Because Justin added everything even the money he spent, and when he spent the money meaning subtracting them, he should get $21.46.
($25.67+$37.85)-($19.99+$22.07)=$21.46
↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑
Money earned Money spend Money left
You're playing a game where you defend your village from an orc invasion. There are 3 characters (elf, hobbit, or human) and 555 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from.
If you randomly choose your character and tool, what is the probability that you won't be a hobbit or use an umbrella?
Answer:
There is a 1/3 chance of getting a hobbit, and a 0.1/11 chance of getting an umbrella.
Factor the following polynomial:
5x(a - b) – 2y(a - b)
Answer:
(a - b)(5x - 2y)
Step-by-step explanation:
5x(a - b) – 2y(a - b) =
The factors in parentheses (shown in bold) are a common factor.
Factor (a - b) out from both terms.
= (a - b)(5x - 2y)
Sorin hits a cricket ball straight up into the air. After 1.5s, the ball is falling straight down with a speed of 6.5 m/s. We want to find the initial vertical velocity of the ball. We can ignore air resistance. Which kinematic formula would be most useful to solve for the target unknown?
Step-by-step explanation:
We have, Sorin hits a cricket ball straight up into the air. After 1.5 s, the ball is falling straight down with a speed of 6.5 m/s.
We want to find the initial vertical velocity of the ball.
The relation between initial speed, final speed, acceleration and time is given by using first equation of kinematics. Let v₀ is the initial speed. So,
[tex]v=v_o +at[/tex]
Here, v = -6.5 m/s, t = 1.5 s and a = -g
[tex]v_o=v-at\\\\v_o=v+gt\\\\v_o=-6.5+9.8\times 1.5\\\\v_o=8.2\ m/s[/tex]
So, the initial velocity of the ball is 8.2 m/s and the formula used is (1).
So do i divide by 2 each time?
But The aquarium charges $12 per ticket for adults and $5per ticket for children. A group of 90 children and adult chaperones visited the aquartum on a held trip. If the total cost of their tickets was $548, how mamy chaperones were there?
Answer:
There were 76 childrens and 14 adults.
Step-by-step explanation:
Since the group has a total of 90 children and adults, then the sum of the number of adults with the number of children must be equal to 90 as shown below:
children + adults = 90
Since the total cost for their tickets was 548 then the number of children multiplied by the price of their ticket summed by the number of adults multiplied by the price of their ticket must be equal to that. We have:
5*children + 12*adults = 548
With these two equations we have a system of equations shown below:
children + adults = 90
5*children + 12*adults = 548
In order to solve this we will multiply the first equation by -5, and sum both equations we have:
-5*children - 5*adults = -450
5*children + 12*adults = 548
7*adults = 98
adults = 98/7 = 14
children + 14 = 90
children = 90 - 14 = 76
There were 76 childrens and 14 adults.
The measure of an angle is 17°. What is the measure of its complementary angle?
Answer:
73°
Step-by-step explanation:
the measure of two complementary angles add up to 90
so We need to solve this equation to get the measure of its complementary angle :
x + 17 = 90
then
x = 90 - 17
= 73
Today, everything at a store is on sale. The store offers a 20% discount.If the regular price of an item is x dollars, what is the discount price in dollars? Type the correct expression in the box below.
Answer:
0.80x dolllars
Step-by-step explanation:
20% discount of the total amount is
0.20 * x dolllars
So if you start with x dollars you need to subtract the discount to get the new (lower ) price.
x - (0.20 * x) dolllars
1* x - 0.20 * x
x * 1 - 0.20 * x
x * ( 1 - 0.20 )
x * ( 0.80 )
0.80x dolllars
What two numbers have a sum of 191 and a difference of 63
Answer:
Step-by-step explanation:
a+b=191
a-b=63
i sum these
a+b+a-b=191+63
2a=254
a=254/2
a=127
b=191-127
b=64
Answer:
127 and 64
Step-by-step explanation:
To solve this, we can set up a system of equations.
We can name the first number x and the second number y.
x+y=191
x-y=63
We can use elimination to eliminate the y variable.
We do this by adding the equations together
x+y=191
+ x-y=63
_________
2x=254
Divide both sides by 2.
x=127
Now we can plug that in to find y.
x+y=191
127+y=191
Subtract 127 from both sides.
y=64
So our two numbers are 127 and 64.
What is the circumference of the circle? Use 3.14 for pi r=6.4 cm circle
So the right answer is of option B.
Look at the attached picture
Hope it will be helpful to you..
Good luck for your test...
Please answer i'll give brainlist
AD and BE are diameters. What is the measure of arc EDC
A. 125 degrees
B. 145 degrees
C. 235 degrees
D. 215 degrees
Answer:
a
Step-by-step explanation:
what’s the missing number ?
Answer:
84
Step-by-step explanation:
One way to solve proportions is to cross multiply. If we name the unknown value x, then we can see that:
2x = 12(14)
2x = 168
x = 84
Another way to solve proportions is to ask, what number did you multiply the first numerator by to get the second numerator. In this case, what do you have to multiply 2 with to get 14. The answer is 7, so that means you must also multiply the first denominator by 7 to get the second denominator, or in this case, the unknown value. 12 x 7 = 84, so the missing number is 84.
Hope this helped! :)
(4x2 - 10x + 9) + (6x - 2) =
A) 4x2 - 4x + 7
B) 4x2 - 4x + 11
C) 4x2 - 16x - 7
D) 4x2 - 16x + 11
Answer:
4x^2−4x+7
Step-by-step explanation:
Let's simplify step-by-step.
4x^2−10x+9+6x−2
=4x^2+−10x+9+6x+−2
Combine Like Terms:
=4x^2+−10x+9+6x+−2
=(4x^2)+(−10x+6x)+(9+−2)
=4x^2+−4x+7
Answer:
=4x^2−4x+7
Answer:
A
Step-by-step explanation:
