Answer:
eqn 1. ( k + a = 500 )
Step-by-step explanation:
In eqn. 1 , both 'k' & 'a' have co-efficient as 1. But in eqn. 2 , 'k' has co-efficient as 3 & 'a' has co-efficient as 10.
I WILL MARK YOU BRAINLIEST Juvi is baking chocolate chip cookies today! To make 4 batches of chocolate chip cookies, Juvi needs 45 of a cup of sugar. Her sister Evi wants to make 8 batches of chocolate chip cookies. How much sugar does Evi need to make 8 batches of chocolate chip cookies?*
Answer:
90 cups
Step-by-step explanation:
First, let's calculate how much cups of sugar we need for 1 batch of chocolate chip.
45 / 4 = 11.25
So, now we know that we need 11.25 cups of sugar to make 1 batch of chocolate chip.
Therefore, we know we need 90 cups of sugar for 8 batches because
11.25 * 8 = 90
Hope this helps ^^
Simplify: 80÷4−2(2+1)2
Answer:
8
Step-by-step explanation:
Applying the PEDMAS rule, the expression 80÷4−2(2+1)² would be simplified as: 80÷4−2(2+1)² = 2.
What is the PEDMAS Rule?The PEDMAS rule guides the order of operation when solving a math problem with several operations.
P - parenthesis, E - exponent, D - division, M - multiplication, A - addition, S - subtraction.
To simplify 80÷4−2(2+1)², apply PEDMAS rule:
Solve parenthesis
80÷4−2(3)²
Solve exponent
80÷4−2(9)
Divide
20 −2(9)
Multiply
20 − 18
Subtract
= 2
Therefore, 80÷4−2(2+1)² = 2
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missing angle for triangle
Answer:
86
Step-by-step explanation:
33+61=94
180-94=86
Find the focus and directrix of the parabola y= 1/2 (x+2)^2 - 3 A. The focus is at (–2,–2) and the directrix is at y = –4. B. The focus is at (–2,–3) and the directrix is at y = –5. C.The focus is at (–2,–2 1/2) and the directrix is at y = –3 1/2. D. The focus is at (–2,–1 1/2) and the directrix is at y = –2 1/2.
Answer:
C. The focus is at [tex](-2,-2 \frac{1}{2})[/tex] and the directrix is at [tex]y = -3\frac{1}2.[/tex]
Step-by-step explanation:
First of all, let us learn about the formula to find Focus and Directrix from the standard equation of a parabola.
Standard form of a parabola is given as:
[tex](x - h)^2 = 4p (y - k)[/tex]
where the focus is [tex](h, k + p)[/tex] and
the directrix is [tex]y = k - p[/tex]
Now, we are given the equation of parabola as:
[tex]y= \dfrac{1}2 (x+2)^2 - 3[/tex]
Let us try to convert it to standard form:
[tex]\Rightarrow y+3= \dfrac{1}2 (x+2)^2 \\\Rightarrow 2(y+3)= (x+2)^2 \\\Rightarrow (x+2)^2 = 2(y+3)\\\Rightarrow (x+2)^2 = 4\times \frac{1}{2}(y+3)[/tex]
Comparing the above with standard equation of parabola [tex](x - h)^2 = 4p (y - k)[/tex]:
[tex]h = -2, p = \frac{1}{2}, k = -3[/tex]
So, Focus is at [tex](h, k + p)[/tex]
[tex]k + p = -3+\frac{1}{2} = -2\frac{1}{2}[/tex]
Focus is at [tex](-2, -1\frac{1}2)[/tex].
Equation of directrix:
[tex]y = k - p=-3-\frac{1}{2}\\\Rightarrow y = -3\frac{1}{2}[/tex]
Also, please refer to the attached image for the diagram of given parabola, focus and directrix.
So, the answer is:
C. The focus is at [tex](-2,-2 \frac{1}{2})[/tex] and the directrix is at [tex]y = -3\frac{1}2.[/tex]
(1 point) Find the antiderivative F of f(x)=4−3(1+x2)−1 that satisfies F(1)=−3.
The value of antiderivative F will be;
⇒ F = 4x - 3 arc tan x - 7 + 3π/4
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ f (x) = 4 - 3 (1 + x²)⁻¹
Now,
Since, The function is,
⇒ f (x) = 4 - 3 (1 + x²)⁻¹
Hence, The antiderivative F of f (x) is,
⇒ F = ∫ (4 - 3 (1 + x²)⁻¹ ) dx
⇒ F = ∫ 4 dx - 3 ∫ (1 + x²)⁻¹ dx
⇒ F = 4x - 3 arc tan x + c
Where, c is constant of integration.
Here, The antiderivative of f (x) is satisfy F(1) = - 3,
So, Substitute x = 1, F = - 3
⇒ F = 4x - 3 arc tan x + c
⇒ - 3 = 4×1 - 3 arctan (1) + c
⇒ - 3 = 4 - 3π/4 + c
⇒ - 3 - 4 + 3π/4 = c
⇒ c = - 7 + 3π/4
Thus, The antiderivative F of f (x) is,
⇒ F = 4x - 3 arc tan x - 7 + 3π/4
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What is the simplified form of the following expression
Parallel Lines /\/\/\
Answer:
its also again 40
Step-by-step explanation:
its L angle
Answer:
40°
Step-by-step explanation:
∠1 and ∠2 are corresponding angles. Corresponding angles have the same measurement. This means that:
m∠1 = m∠2
Therefore, the measure of ∠2 would be the same as the measure of ∠1.
m∠2 = 40°
Hope this helps.
There are 7 books on the floor. The number of books on the shelf is 2 more than 3 times the number of books on the floor.
150 students in 3 classes
Answer:
50 if you're asking for dividing
Step-by-step explanation:
if you're dividing then it's 50 hopefully this is the answer your asking
If y varies directly as x and y=5 when x=8 find y when x=4
Answer:
2.5
Step-by-step explanation:
x=8 x=4
y=5 y=2.5
is ratio problem
If y varies directly with x and y = 5 when x= 8 . then the value of y when x = 4 is 2.5
What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called constant of proportionality.
If y varies directly with x and y = 5 when x= 8 . then we need to find y when x = 4
Therefore, y = kx
k = y/x
k = 5/8
Then y = kx
y = (5/8)4
y = 5/2
y = 2.5
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The sum of a number and 5
Help
Hey there! I'm happy to help!
Let's call our number n.
The word sum means to add.
Therefore....
n+5
Have a wonderful day! :D
PLS HELP simplify (2b^3)^2
Answer: 4b^6
Remember if theres a bracket you multiply the power instead of adding
For example if it was 2b^3 x 2b^2 then the answer would be 4b^5 instead according to indices law, read up on it if you havent yet itll help a bunch! :)
A factory makes 300 sheets of construction paper per hour. How many sheets of construction paper will the factory make in 9 hours?
Answer:
2700
Step-by-step explanation:
One hour is 300 sheets. We need to find 9 hours,
so 300*9= 2700
idk what this is
pls help
Answer:
Coplanar points
Step-by-step explanation:
Coplanar points are three or more points that lie in the same plane.
7x-6y=11 solve for y
Answer:
7x+11 = 6y
(7x+11)/6 = y
7x/6= y-11
There are multiple answers for this
Step-by-step explanation:
A driver education course
costs $45 but saves those
under 25 years old 10% of their annual insurance premiums until they are 25. Dan has just
turned 18, and his insurance is $100 per month.
1. When will the amount saved from insurance equal the price of the course?
2. Including the cost of the course, when Dan turns 25, how much will he have saved?
Answer:
after 4.5 months (or 5)$795Step-by-step explanation:
10% of $100 per month is $10 per month.
1. By saving $10 per month on insurance cost, Dan's savings after 4.5 months will be equal to the $45 cost of his course. (If billing is monthly, he won't experience any net gain from the course until the 5th insurance payment--after 5 months.)
__
2. In 7 years, the savings on insurance costs will total ...
(7 years)×(12 months/year)×($10 /month) = $840
His cost for the course is $45, so his net saving is ...
$840 -45 = $795 . . . net saving by age 25
7x(15+4) = (7x ) + (7+4)
Find square of -9.2
Answer:
84.64.
Step-by-step explanation:
(-9.2)^2
= (9.2)^2
= 84.64.
A crowd of people stood on both sides of the street to view a 4th of July Parade.
The length of the parade was 3 miles long and 15 feet deep on each side of the street.
If 5 people can fit into a 25 ft^2 area.
Estimate the size of the crowd.
(1mile = 5280ft)
Given :
Length of parade , [tex]L = 3\ miles=3\times 5280\ miles = 15840\ miles[/tex] .
Breadth of parade , [tex]B=2\times 15=30\ ft[/tex] .
5 people can fit into a [tex]25\ ft^2[/tex] area.
1 mile = 5280 ft .
To Find :
The size of the crowd.
Solution :
Area of parade ,
[tex]A=15840\times 30\ ft^2\\\\A=475200\ ft^2[/tex]
Also , 5 people can fit in [tex]25\ ft^2[/tex] area .
So , number of people fit in A is :
[tex]n = \dfrac{475200\times 5}{25}\\\\n=95040[/tex]
Therefore , 95040 can fit in the parade .
Hence , this the required solution .
Find the Cardinal number of the set of all solutions to x^2=100
Answer: 2
Step-by-step explanation:
this is the answer knewton alta said
The Cardinal number of the set of all solutions to x²=100 is 2.
What is Number system?A number system is defined as a system of writing to express numbers.
Cardinal numbers are natural numbers or positive integers. The smallest cardinal number is 1.
We have to find the Cardinal number of the set of all solutions to x²=100
To find the solution of the equation we have to take square root on both the sides' x=10, -10
The set of solutions will be {-10, 10}
It has two terms. Hence cardinal number is 2.
Hence, the Cardinal number of the set of all solutions to x²=100 is 2.
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Solve for w . p=w/t
Answer:
w = pt
Step-by-step explanation:
[tex]p=\frac{w}{t}\\\\p*t=\frac{w}{t}*t\\\\pt=w\\\\\boxed{w=pt;t\neq 0}[/tex]
Hope this helps.
please help asap, and if you can explain why after the answer, please and thank you❤️
Samantha conjectures that for x < - 1 it is true that x ^ 5 - 2 > x her conjecture correct? Why or why not?
Answer:
Incorrect
Step-by-step explanation:
Given
[tex]x < -1[/tex]
[tex]x^5 - 2 > x[/tex]
Required
Determine if the conjecture is true
To determine if it's true or not, we have to substitute the values of x in [tex]x^5 - 2 > x[/tex]
In the first inequality, we have that [tex]x < -1[/tex]
This means that the values of x are: -2. -3, -4......
Substitute -2 for x in [tex]x^5 - 2 > x[/tex]
[tex](-2)^5 - 2 > -2[/tex]
[tex]-32 - 2 > -2[/tex]
[tex]-34 > -2[/tex]
Her conjecture is incorrect because the inequality is not true for x = -2
5. A six sided number cube is tossed onto a table 25 times. The results are shown below.
Number on die
Number of times
rolled out of 25
1
.
OWN
III
MINI
11
What is the theoretical probability of a 5 or 6?
_Answer as a fraction. (5 pts)
What is the experimental probability 5 or 6?
Answer as a fraction. (5 pts)
Answers:
Theoretical probability of 5 or 6 is 1/3
Experimental probability of 5 or 6 is 9/25
======================================================
Explanation:
For the theoretical probability, we ignore the table of values. We assume the cube will land on any of the 6 sides with equal probability.
So landing on any given side has probability 1/6. Landing on 5 or 6 has probability 2*(1/6) = 2/6 = 1/3.
---------
For the experimental probability, we use the table. We see that '5' shows up twice, and '6' shows up seven times. In total, those values show up 2+7 = 9 times out of 25 total.
So that's how I got 9/25.
Solve the inequality. Then graph the solution set. 1 < 3x + 4 < 13
Answer:
Step-by-step explanation:
1 - 4 < 3x < 13 - 4
-3 < 3x < 9
-1 < x < 3
Please please please help me with this please and i will give you a brainlist and 10 points
how can simplify 5x-4=6
What is the range of the given function?
{(-2, 0), (-4, -3), (2, -9), (0, 5), (-5, 7)}
оооо
О{x | x = -5, -4, -2, 0, 2}
{y | y = -9, -3, 0, 5, 7}
{x | x = -9, -5, -4, —3, -2, 0, 2, 5, 7}
О{y | y = -9, -5, -4, -3, -2, 0, 2, 5, 7}
Answer:
Step-by-step explanation:
the range of the given function is:
{0, -3, -9, 5, 7}= y
answer is B
PLEASE HELP ME
A map has a scale of
2 in. = 18 mi. If you measured the distance between two cities to
be 16 in. on the map, how many miles would it actually be?
Answer:
it would be 144 miles
Step-by-step explanation:
We start by a ratio of map to mile = 2:18
if we see that the map distance is 16, 16:?
We divide 16 by 2 to get 8, so we enlarge the 2, 8 times, and we get 16
the 18, also has to be enlarged, so 18x8 = 144
on 8(x - 2) + 3 = -61?
Answer:
Hey there!
8(x-2)+3=-61
8(x-2)=-64
x-2=-8
x=-6
Let me know if this helps :)
Answer:
X=-6
Step-by-step explanation:
8(x - 2) + 3 = -61
8X-16+3=-61
8X-13=-61
8X=-61+13
8X=48
X=[tex]\frac{48}{8}[/tex]
X=-6
HAVE A NICE DAY £$