Answer:
k = 10
Step-by-step explanation:
30+2k+5k=100
Combine like terms
30 + 7k = 100
Subtract 30 from each side
30+7k-30 = 100-30
7k = 70
Divide each side by 7
7k/7 = 70/7
k = 10
Answer:
k=10
Step-by-step explanation:
We are given the equation:
30+5k+2k=100
We want to find k, therefore we must isolate k on one side of the equation.
First, combine like terms on the left side of the equation. 5k and 2k can be added together.
30+5k+2k=100
30+(5k+2k)=100
30+7k=100
30 is being added to 7k. The inverse of addition is subtraction. Subtract 30 from both sides of the equation.
30-30+7k=100-30
7k= 100-30
7k= 70
k is being multiplied by 7. The inverse of multiplication is division. Divide both sides by 7.
7k/7=70/7
k=70/7
k= 10
The solution to the equation 30+5k+2k=100 is k=10
Why is it important to have a control group in an experiment of investigation?
Answer choices-
•To show what happens when the dependent variable is not changed.
•To see how the dependent variable changes the dependent variable is not involved.
•To compare the results when the independent variable is not involved.
•To allow the researchers to change the dependent variable as they wish.
Answer:
I think its A
Step-by-step explanation:
Sorry if I'm wrong
AB = 2x-5 BC = 6x AC = 27
Answer:
correct answer is x = 2.75
Step-by-step explanation:
Given;
AB = 2x-5
BC = 6x
AC = 27
Hence,
=> AC = AB + BC
=> 27 = 2x-5 + 6x
=> 27 = 8x-5
=> 27-5 = 8x
=> 22 = 8x
=> 22/8 = x
=> 11/4 = x
or
2.75 = x
which expression is equivalent to 1/2 x + (-7) -2 q/4 x - (-2) ?
Answer:
−1 /2 qx+ 1 /2 x-5
Step-by-step explanation:
Let's simplify step-by-step.
1 /2 x−7− 2q/ 4 x−(−2)
= 1 /2 x+−7+ (−1/2) qx+2
Combine Like Terms:
= 1 /2 x+−7+ (−1 /2 qx+2
=( −1 /2 qx)+( 1 /2 x)+(−7+2)
= −1 /2 qx+ 1 2x+−5
Answer:
= −1 /2 qx+ 1 /2 x-5
HOPE THIS HELPS!!!!!! :)
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Your favorite local college football team, the UCF Knights, won 35 of out 39 games over a period of 4 years. If they keep their winning pace, predict how many games you would expect them to win over the next 78 football games?
Answer:
They will win 70 games
Step-by-step explanation:
if for 39 games they won 35 of them,
for 78 they will win X
39*X= 78* 35
39X= 2730
X= 70
Pls help !!!!
A video game designer places an anthill at the origin of a coordinate plane. A red ant
leaves the anthill and moves along a straight line to (1, 1), while a black ant leaves the
anthill and moves along a straight line to (1, -1). Next, the red ant moves to (2, 2), while
the black ant moves to (-2,-2). Then the red ant moves to (3, 3), while the black ant
moves to (-3, -3), and so on. Complete the explanation of why the red ant and the black
ant are always the same distance from the anthill,
At any given moment, the red ant's coordinates may be written as (a, a) where a > 0. The
red ant's distance from the anthill is . The black ant's coordinates may be written
as (-a, -a) and the black ant's distance from the anthill is . This shows that at
any given moment, both ants are
units from the anthill.
Answer:
At any given moment, the red ant's coordinates may be written as (a, a) where a > 0. The red ant's distance from the anthill is [tex]a\sqrt{2}[/tex] . The black ant's coordinates may be written as (-a, -a) and the black ant's distance from the anthill is [tex]a\sqrt{2}[/tex] . This shows that at any given moment, both ants are [tex]a\sqrt{2}[/tex] units from the anthill.
Step-by-step explanation:
Given:
red ant's coordinates written as (a,a)
black ant's coordinates are written as (-a, -a)
To find:
The distance of red and black ants from anthill
Solution:
Compute the distance of red ant from the anthill using distance formula
d (red ant) = [tex]\sqrt{(a-0)^{2}+ (a-0)^{2}}[/tex]
= [tex]\sqrt{a^{2} + a^{2} }[/tex]
= [tex]\sqrt{2a^{2} }[/tex]
= [tex]a\sqrt{2}[/tex]
So distance of red ant from anthill is [tex]a\sqrt{2}[/tex]
Compute the distance of black ant from the anthill using distance formula
d (black ant) = [tex]\sqrt{(-a-0)^{2}+ (-a-0)^{2}}[/tex]
= [tex]\sqrt{(-a)^{2} + (-a)^{2} }[/tex]
= [tex]\sqrt{a^{2} + a^{2} }[/tex]
= [tex]\sqrt{2a^{2} }[/tex]
= [tex]a\sqrt{2}[/tex]
So distance of black ant from anthill is [tex]a\sqrt{2}[/tex]
Hence both ants are [tex]a\sqrt{2}[/tex] units from the anthill.
What is the y-intercept of the graph? Thank you!!
Answer: 4
Step-by-step explanation: The y-intercept is a point
where a line crosses the y-axis.
All y-intercepts have an x-coordinate of zero.
The equation shown here is in slope-intercept form or y = mx + b form.
In this form, the m represents the slope and the b is y-intercept.
So here, we can tell that the y-intercept is 4.
A logarithm question: 3² +㏒₂5
Answer:11.322
Step-by-step explanation:
3^2 + log2 5 =9+(ln5/ln2)=9+2.322=11.322
I need help on this plz i don’t understand the question
We know that the area of a circle in terms of π will be πr². However the area with respect to the diameter will be a different story. The first step here is to find a function relating the area and diameter of any circle --- ( 1 )
For any circle the diameter is 2 times the radius,
d = 2r
Therefore r = d / 2, which gives us the following formula through substitution.
A = π(d / 2)² = πd² / 4
Hence the area of a circle as the function of it's diameter is A = πd² / 4. You can also say f(d) = πd² / 4.
Now we can substitute " d " as 4, solving for the area ( A ) or f(4) --- ( 2 )
f(4) = π(4)² / 4 = 16π / 4 = 4π - This makes the area of circle present with a diameter of 4 inches, 4π.
A small ball floats on the surface of the water in a wave pool. As a wave moves past the ball, the ball's
height above the bottom of the pool varies from 22 inches to 34 inches. The waves occur every
6 seconds. Which function models the distance from the bottom of the pool to the ball, as it moves
from wave crest to wave crest, as a function of t in seconds?
d(t) = 12 cos(3At) + 28
d (t) = 6 cos(3mt) + 28
34 in.
d(t) = 6 cos (+) +
+ 28
22 in
d(t) = 12 cos( 5 ) + 28
Answer:
The correct option is;
d(t) = 6·cos(π/3·t) + 28
Step-by-step explanation:
The general form of a cosine function is given as follows;
y = A·cos(B·x - C) + D
Where;
A = The amplitude = The distance from the peak to the midline = 1/2×(Maximum - minimum)
The amplitude = 1/2 × (34 - 22) = 6 inches
B = 2·π/P = 2·π/6 = π/3
P = The period = 6 seconds
C/B = The phase shift
D = The midline = Minimum + Amplitude = 22 + 6 = 28 inches
x = The independent variable
Therefore, to model the function of the wave can be given as follows;
d(t) = 6·cos(π/3·t) + 28
A function that models the distance from the bottom of the pool to the ball, as it moves from wave crest to wave crest, as a function of t in seconds is [tex]d(t)= 6cos(\frac{\pi}{3} t) + 28[/tex]
The standard wave equation is expressed as;
[tex]y=Acos(Bx-C)+D[/tex] where:
A is the amplitude
Get the amplitude:
[tex]A=\frac{1}{2}(34-22)\\A=\frac{1}{2}(12)\\A= 6\\[/tex]
If the wave occurs every 3 seconds, then:
[tex]B=\frac{2 \pi}{k} \\B=\frac{2\pi }{6}\\B=\frac{\pi}{3}[/tex]
Get the midline D
[tex]D=minimum + amplitude\\D=22+6\\D = 28[/tex]
Substitute the given parameters into the equation above to have;
[tex]y= 6cos(\frac{\pi}{3} t) + 28[/tex]
Hence a function that models the distance from the bottom of the pool to the ball, as it moves from wave crest to wave crest, as a function of t in seconds is [tex]d(t)= 6cos(\frac{\pi}{3} t) + 28[/tex]
Learn more here: https://brainly.com/question/25524388
The Trumbull Tree Farm sold 390 trees last week. All of the trees were either evergreens, oaks, or maples. Twice as many oak trees as evergreen trees were sold. 5 times as many maple trees as oak trees were sold.
How many oak trees were sold last week?
Answer:
60
Step-by-step explanation:
We can use x to represent the number of oak trees.
This means evergreen trees will be 1/2x and 5x will be the maple trees.
Set up an equation:
x + 1/2x + 5x = 390
6.5x = 390
x = 60
So, 60 oak trees were sold last week.
can u do question b pls
Answer: a) $481.62 b) $16,569.76
Step-by-step explanation:
The formula for compound interest is: [tex]A = P(1 + r)^t[/tex] where
A is the accrued amount (balance)P is the principle (initial deposit)r is the rate (convert percentage into a decimal)t is the time (number of years)Given: P = 3000, r = 1.15% (0.015), t = 10
[tex]A = 3000(1 + 0.015)^{10}\\\\\\A = 3000(1.015)^{10}\\\\\\A = 3,481.62[/tex]
Interest Earned = accrued amount - principle
= 3,481.62 - 3,000
= 481.62
******************************************************************************************
I couldn't remember the formula so I created a table:
[tex]\begin{array}{c||l|c||r}\underline{Jan\ 1}&\underline{Interest\ Earned}&\underline{Deposit}&\underline{Balance}\\2019&0&3000&3,000.00\\2120&3000(1.015)&1200&4,245.00\\2121&4245(1.015)&1200&5,508.68\\2122&5508.68(1.015)&1200&6,791.31\\2123&6791.31(1.015)&1200&8,093.17\\2124&8093.17(1.015)&1200&9,414.57\\2125&9414.57(1.015)&1200&10,755.79\\2126&10755.79(1.015)&1200&12,117.13\\2127&12117.13(1.015)&1200&13,498.88\\2128&13498.88(1.015)&1200&14,901.37\\2129&14901.37(1.015)&1200&16,324.89\\\end{array}[/tex]
2130 || 16324.89(1.015) | 0 || 16,569.76
need help ASP .find the universe function of f(x)=1/2x+3
Answer:
f (1) = 1/ 2(1) + 3
= 1/2 + 3
= 1/5
pls solve with workings
Answer:
2a). Height = 2 cm
2b). Surface area = 395.84 cm²
Step-by-step explanation:
2a). Volume of the cylinder = 308 cm³
Radius of the base of the cylinder = 7 cm
Formula to get the volume of a cylinder = πr²h
308 = π(7)²h
h = [tex]\frac{308}{49\pi }[/tex]
h = 2 cm
Therefore, height of the cylinder will be 2 cm.
2b). Formula to calculate the surface area of the cylinder = [tex]2\pi r(r + h)[/tex]
By substituting the values in the given formula,
S.A. = 2π(7)(7 + 2)
= 395.84 cm²
Therefore, Surface area of the cylinder is 395.84 cm².
Popular magazines rank colleges and universities on their ""academic quality"" in serving undergraduate students. Describe two categorical variables and two quantitative variables that you might record for each institution.
Answer:
Quantitative: i) The number of students in the school vis - a - vis the number of classes in the school. In order words, simply number of students per class
ii) The rate of graduation of students.
Categorical:i) Courses being taken by students
ii) Region of country of students.
Step-by-step explanation:
To answer this question effectively, it's important for us to know that a quantitative variable usually has numerical values, and also have units of measure as well while categorical variables simply places each student into a specific category.
Now, the two quantitative variables we will consider are;
i) The number of students in the school vis - a - vis the number of classes in the school. In order words, number of students per class
ii) The rate of graduation of students.
Also, the two categorical variables we will consider are;
i) Courses being taken by students
ii) Region of country of students
-1+(-4)= -1-___ can you please help
Answer: -1+(-4)=-1-4
Step-by-step explanation:
-1+(-4)=-1-4
------------------
numbers after (+) sign, no need to change signs
the number after (+) is -4, so we keep the (-) sign, which will be:
-1+(-4)=-1-4
Hope this helps!! :)
Add brackets to the following equation to make it time. 1 + 72 ÷4 × 2 =10
Answer:
1 + 72 ÷4 × 2 =10 with brackets it equals 10
1 + (72 ÷ (4 × 2)) =10
Step-by-step explanation:
Skate station charges a flat rate of $5.00 for skate rental plus $2.00 per hour of skating. If the number of hours is represented by "h," which algebraic expression represents the overall rate for "h" hours of skating?
Answer:
The answer is 5+2h because it is $2 per hour so 2h and $5 per day. it does not have a variable for $5 per day
an article bought for rs 550 is sold at a profit of purchased at rs 20 percentage find the selling price
Answer:
cp is rupees 5000
Step-by-step explanation:
11x/10 -21x-/20= 250
then do lcm and answer will come x= 5000
how would i simplify the expression?
What is the area of the triangle given below?
5
14
A. 70 sq. units
B. 38 sq. units
C. 19 sq. units
D. 35 sq. units
Answer:
35
Step-by-step explanation:
6. Simplify: i) (a + b)(5a – 3b) + (a – 3b)(a – b) ii) (a – b) (a2 + b2 + ab) – (a + b) (a2 + b2 – ab) iii) (b2 – 49) (b + 7) + 343 okay, I know I posted this question before but, if you're giving your answers, please explain how you got it,
Answer:
Step-by-step explanation:
6. I will multiply then I respect the sign rules
- * - = +
- * + = -
I will atach the file immediately.
I multiplied the paranthesis and then I added the results
Answer:
i)6a^2-2ab-6b^2
ii)ab^2-1a^2b
iii)b^3-42b
Step-by-step explanation:
Use distributive property
Collect like terms
(a+b)(5a-3b)+(a-3b)(a-b)
(a+b)(5a-3b)---- Distributive property
5a^2-3ab+5ab-3b^2
5a^2+5ab-3ab-3b^2
5a^2+2ab-3b^2
(a-3b)(a-b)
a^2-ab-3ab-3b^2
a^2-4ab-3b^2
So,
5a^2+2ab-3b^2+a^2-4ab-3b^2---Collect like terms
5a^2+a^2+2ab-4ab-3b^2-3b^2
6a^2-2ab-6b^2
(a–b)(a^2+b^2 +ab)–(a + b)(a^2+b^2 –ab)
(a–b)(a^2+b^2 +ab)----Distributive property
a^3 since a^(1+2)=a^3
a^3+ab^2+a^2b-ba^2-b^3-ab^2
a^3+ab^2-ab^2+a^2b-ba^2-b^3
a^3+a^2b-a^2-b^3
a^3-b^3
(a+b)(a^2+b^2-ab)
a^3+ab^2-a^2b+ba^2+b^3-a^2b
a^3+ab^2+ba^2+b^3-a^2b-a^2b
a^3+ab^2+ba^2+b^3-2a^2b
So,
a^3-b^3-a^3+ab^2+ba^2+b^3-2a^2b--Collect like terms
a^3-a^3-b^3+b^3+ab^2-2a^2b+a^2b
ab^2-1a^2b
(b^2–49)(b + 7)+343---Distributive property
b^3+7b-49b-343+343---Collect like terms
b^3-49b+7b
b^3-42b
Hope this helps ;) ❤❤❤
Find the midpoin, M, of AB
Answer:
11
Step-by-step explanation:
The midpoint of AB is half the distance from A to B. Here that distance is 22. Thus, the midpoint of AB is 11.
Answer:
Hey there!
The answer is 11. We can use the midpoint formula, but since this is a number line, we can easily see that 11 is half of 22.
Let me know if this helps :)
Need Help PLEASE Ex 1:A scale model of a human heart is 196 inches long. The scale is 32 to 1. how many inches long is the actual heart? (can someone explain to me how to do this i have many other questions like this)
Answer: The actual heart is approximately 6.125 or rounded to 6
Step-by-step explanation: Divide the scale model 196 inches by 32 (the scale)
dante’s cell phone company charges $45 per month for unlimited calls and internet use and $0.25 per text message. his last cell phone bill was $60.50. how many text messages did he send last month. write an equation.
Answer:
242 text messages.
Step-by-step explanation:
60.50 / 0.25 = 242
60.50 being the phone bill.
0.25 being each text message.
/ stands for ' divided by '.
Answer:
62 text messages
Step-by-step explanation:
Let the number of text messages be x,
Then the required equation:
0.25x + 45 = 60.50Solution:
0.25x = 60.50 - 450.25x = 15.50x = 15.50/0.25x = 62Answer is: 62 text messages
Please help as soon as possible Will mark brainliest
Answer: 18
Step-by-step explanation: The formula for circumference is 2piR. Since 2piR = 36pi, you can cancel out the pi's which makes it 2r = 36. Divide by 2 on both sides and you get r = 18.
What is 0.6 as a simplified fraction?
Answer
3/5
0.6 / 1 = 6 / 10 = 3/5
Answer:
3/5
Step-by-step explanation:
0.6=6/10
[dividing through by two]
=3/5
can someone help me? “Fond the measure of the missing angle” pleaseee
Answer:
It's Below.
Step-by-step explanation:
1) 180° - 124° = 56°
2) 90° - 58° = 32°
3) 90° - 34° = 56°
4) 180° - 107° = 73°
Don't forget to put the degrees symbol! :)
caley is making some punch for her birthday party.She mixes 1/2 litre of cranberry juice,1/1/2 litres of apple juice,2/3 litre of orange juice and 4/5 litres of pineapple juice.She has a bowl that will hold 4 litres.Will this be enough to contain all of the punch?
Answer:
yes it will contain it
Step-by-step explanation:
.5 + 1.5 + .66 + .8 = 3.46
5 solve the literal equation 2y = x+3 for x
Answer:
[tex]x=2y-3[/tex]
Step-by-step explanation:
So we have the equation:
[tex]2y=x+3[/tex]
And we want to solve it for x. In other words, we want to isolate the x-variable. To start, first subtract 3 from both sides. The right side cancels:
[tex](2y)-3=(x+3)-3\\2y-3=x[/tex]
And, that's it :)
If preferred, we can also switch the equation around using the symmetric property:
[tex]x=2y-3[/tex]
Answer:
[tex]\Large \boxed{\sf{x=2y-3}}[/tex]
Step-by-step explanation:
[tex]\sf We \ have \ the \ equation: \\ \\ 2y = x+3 \\ \\ We \ need \ x \ on \ one \ side \of \ the \ equation. \\ Solve \ for \ x. \\ \\ Subtract \ 3 \ from \ both \ sides. \\ \\ 2y-3=x+3-3 \\ \\ Simplify \ the \ equation. \\ \\ 2y-3=x[/tex]
Which expression is equivalent to 36 + 12? 9(4+3) 10(26+2) 12(3+1) 6(30+6)
Answer:
12(3 + 1)
Step-by-step explanation:
if you distribute the 12:
12 x 3 = 36
12 x 1 = 12
= 36 + 12