Answer:
Add the equations to eliminate x
Step-by-step explanation:
Let's go through each of these statements
1) Add the equations to eliminate x
y = x + 10
+
y = -x + 3
_______
2y = 13
This works!
Answer:
Add the equation to eliminate x.
Step-by-step explanation:
Add the equation to eliminate x.
Let's actually do the work!
y = x + 10
y = −x + 3
------------------
2y = 13, so y = 6.5.
Subbing 6.5 for y in either of the equations above lets us calculate y. For example, in the second equation, 6.5 = -x + 3, or 3.5 = -x, or x = -3.5.
The solution is (-3.5, 6.5).
Given cos theta = √3/4 and sin theta < 0. What is the value of sin theta?
Answer:
[tex] \sqrt{ \frac{13}{16} } [/tex]
Step-by-step explanation:
[tex]cos \: theta = \frac{ \sqrt{3} }{4} \\ sin \: theta = \sqrt{1 - {cos}^{2} theta} \\ = \sqrt{1 - {( \frac{ \sqrt{3} }{4} ) }^{2}} \\ = \sqrt{1 - \frac{3}{16}} \\ = \sqrt{ \frac{13}{16} } [/tex]
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
• sin²x + cos²x = 1 ⇒ sin x = ± [tex]\sqrt{1-cos^2x}[/tex]
Since sinΘ < 0 , then
sinΘ = - [tex]\sqrt{1-(\frac{\sqrt{3} }{4})^2 }[/tex]
= - [tex]\sqrt{1-\frac{3}{16} }[/tex]
= - [tex]\sqrt{\frac{13}{16} }[/tex] = - [tex]\frac{\sqrt{13} }{4}[/tex]
thorium -228 is a radioactive substance that decays 50% every 1.9 years. How much of a 50 gram sample will exist after 22.8 years? Round to 3 decimal places. Use the formula A=A0e^ -kt.
A.) 19.34 grams
B.) 30.32 grams
C.) 0.124 grams
D.) 12.4 grams
E.) 7.48 grams
The amount of Thorium-228 left after 22.8 years of decay from an initial 50 gram sample, given its half-life of 1.9 years, is 0.124 grams.
Explanation:In this problem of thorium -228 decay, we apply the formula for exponential decay which is A=A0e^-kt. 'A0' represents the initial amount, which in this case is 50 grams. 'A' is the final amount after 't' years, and 'k' is the decay constant. To find the decay constant first, we note that thorium-228 decays to 50% of its initial quantity in 1.9 years. Therefore, we can write the equation 0.5=A0e^-1.9k. Solving for 'k', we get k = ln(2)/1.9, which allows us to derive the time constant for the decay.
Now we use this value of 'k' to find out the amount of thorium-228 left after 22.8 years. Plugging the values into our formula, we get: A = 50e^((ln2/1.9)*-22.8). Solving this yields a value of 0.124 grams, which means option C is correct.
Learn more about Radioactive Decay here:https://brainly.com/question/1770619
#SPJ12
To find the amount of thorium-228 remaining after 22.8 years, we can use the formula A = A0e -kt. The correct answer is B) 30.32 grams.
Explanation:To solve this problem, we can use the formula A = A0e-kt where A is the amount of the substance at a given time, A0 is the initial amount, k is the decay constant, and t is the time elapsed.
In this case, we are given that thorium-228 decays 50% every 1.9 years.
This means that the decay constant k = ln(2)/1.9. We can substitute the values into the formula and solve for A: A = 50 * e(-ln(2)/1.9)*22.8 = 30.32 grams.
Therefore, the correct answer is B) 30.32 grams.
Learn more about Decay of radioactive substances here:https://brainly.com/question/13702907
#SPJ12
Write the coordinate pairs of 3 points that can be connected to construct a line that is 5 1/2 units to the right of and parrallel to the y-axis.
Answer:
(5 1/2, 1), ( 5 1/2, 2) and (5 1/2, 3).
Step-by-step explanation:
The x coordinates will all be 5 1/2 so we could have 3 points with coordinates:
(5 1/2, 1), ( 5 1/2, 2) and (5 1/2, 3).
1. Solve the quadratic equation x^2+8x=-15 by factoring
What are the solutions to the equations
A. X=3 and x=5
B. X=-3 and x=5
C. X=-3 and x= -5
2. What are the solutions to the equation -3(x-2)^2=-27?
(Select TWO that apply)
A. X=9
B. X=-5
C. X=-1
D. X= 5
3. Use the ZERO product property to find the solutions to the quadratic equation 5x^2-15x=0
(select TWO that apply)
A. X=3
B. X=0
C. X=-3
4. One solution of a quadratic equation is x=-3+2 divided by 5
Which is the exact value of the other solution
A. X=-3-2 divided by 5
B. X=2-3 divided by 5
C. X=3-2 divided by 5
I got you fam!
Here's what I worked out for you:
1. Answer is C (-3, -5)
2. Answers are C and D (5, -1)
3. Answers are A and B (0, 3)
I'm one Brainliest away from ranking up, so one would be super appreciated! Thanks and good luck!
Cara os making potato salad for a cook out. One serving of potato salad has 1 1/2 cups of cooked potatoes and 1/4 cup of mayonnaise. How many cups of potatoes would be needed if cara uses 3 1/4 cups of mayonnaise?
Answer:
19.5
Step-by-step explanation:
just look at the equation like this
1 1/2 - 1/4
???? - 3 1/4
divide 3 1/4 by 1/4 and multiply the result by 1 1/2
or just treat it as a ratio
1.5/x=.25/3.25
Need help with the question at the top
Thanks
First we must find area of a single square.
Meaning we divide total area of 80 centimetres squared by 5 since we have 5 squares in the shape.
[tex]A_{square}=\frac{A_{shape}}{5}=\underline{16}[/tex]
Now from the picture we can see that the perimeter of shape is combined by 4 times 3 times the length of side of 1 square.
So we need to find side of 1 square.
[tex]a=\sqrt{A_{square}}=\sqrt{16}=\underline{4}[/tex]
As we stated before the formula for perimeter of this shape is:
[tex]P=4(3\cdot a)=4(3\cdot4)=4\cdot12=\boxed{48}[/tex]
The perimeter of shape is 48 centimetres.
Hope this helps.
r3t40
Can someone please just give me a formula for solving this? Thank you.
When baking a cake, you have a choice of the following pans: a round cake pan that is 2 inches deep and has a 7 inch diameter.
a 6 inch x9 inch rectangular cake pan that is 2 inches deep.
A. which of these pans has the larger value? Justify your answer
Since you're looking for the volume of each...
Circle: you want to find the area (πr^2) times height
Rectangle: l×w×h
Can someone help me with this
Answer:
8 laps
Step-by-step explanation:
Assuming in the equation given than n represents the number of laps run and t represents the time in minutes, when we plug in 16 in for t and simplify we get:
n=5/10*16
n=1/2*16 (Simplify the fraction by dividing top and bottom by 5)
n=16/2 (Multiply the fractions together by writing 16 as 16/1 and multiplying straight across)
n=8
Answer:
8
Step-by-step explanation:
This question is a bit of a guess. You have to assume that n is in laps and that t is in minutes.
n = (5/10) * t Reduce 5/10 to 1/2
n = 1/2 * 16
n = 8
So if the assumptions are correct, he should be able to do 8 laps.
find the midpoint of the segment with the given end points D(5,1) and E(13,11)
Answer:
The midpoint is (9,6)
Step-by-step explanation:
The midpoint is just the average of the two end points.
x: (5 + 13)/2 = 18/2 = 9
y: (1 + 11)/2 = 12/2 = 6
The midpoint is (9,6)
Here's a question that I'm having trouble with. Please help, thanks!
Answer:
a . is the right answer
trust me
Jordan is making a beaded necklace two thirds of the beads she uses are red and 4/21 of the beads are blue she wants the rest to be white what fraction of the beads should be white
2/3 - Red
4/21 - Blue
Change the red fraction so both fractions will have the same denominator
2/3 change to 14/21
Add blue and red together
14/21 + 4/21 = 18/21
Then subtract it from the total to get the white beads
21/21 - 18/21 = 3/21
Simplify it to get 1/7
Ans : 1/7
Fraction of white beads used is 1/7.
What is fraction?A number expressed as a quotient, in which a numerator is divided by a denominator.
Given:
red beads used = 2/3 = /1
blue beads used = 4/21
Total beads other than white
=14/21 + 4/21
= 18/21
N/ow, fraction of the beads should be white
=1- 18/21
=21/21 - 18/21
=3/21
=1/7
Learn more about fraction here:
https://brainly.com/question/10354322
#SPJ2
6x(x − 4) − 16x2 − (9x − 1)?
A.
-10x2 − 33x + 1
B.
10x2 − 33x + 1
C.
-10x − 33x + 1
D.
-10x2 + 33x + 1
Answer:
[tex]\large\boxed{A.\ -10x^2-33x+1}[/tex]
Step-by-step explanation:
[tex]6x(x-4)-16x^2-(9x-1)\qquad\text{use the distributive property}\\\\=(6x)(x)+(6x)(-4)-16x^2-9x-(-1)\\\\=6x^2-24x-16x^2-9x+1\qquad\text{combine like terms}\\\\=(6x^2-16x^2)+(-24x-9x)+1\\\\=-10x^2-33x+1[/tex]
The expression simplifies to -10x^2 - 33x +1, following the distribution and combination of like terms.
The given question asks to simplify the expression 6x(x − 4) − 16x2 − (9x − 1). To solve, we follow these steps:
Distribute the 6x across the (x-4) to get 6x2 - 24x.Combine like terms: 6x2 - 24x - 16x2 - 9x + 1.Simplify the expression to -10x2 - 33x + 1.Therefore, the correct option is A. -10x2 − 33x + 1.
4 glue sticks cost $7.76
In form of equation how will be the cost of 13
Answer:
7.76(x) / 4 = Total cost
$25.22
Step-by-step explanation:
Given in the question that,
number of glue sticks that cost $7.76 = 4
To find the cost of 13 glue sticks first we need to find the cost of one glue stick, for that we will need cost of 4 sticks with 4
4 ----> $7.76
1 ----> $7.76/4
$1.94
Multiply the cost of 1 glue with 13
3 -----> $1.94x13
$25.22
Equation
7.76x/4 = Total costwhere x represent number of glue sticks
You are trying out for the school play. The probability that you are chosen to be in the play is 0.4. The probability that you get the lead role is 0.1. What is the probability that you get a lead role, given that you are chosen to be in the play?
I think the answer is 3/10
The probability that we will get a lead role, given that we are chosen to be in the play is 0.5.
What is probability?Probability is the ratio that shows the likelihood of an event occurring from a given set of possible events.
We can find the required probability below:The probability that we will be chosen for the play is 0.4.
The probability that we will get the lead role is 0.1.
We have to find the probability that we get a lead role, given that we are already chosen to be in the play.
In this situation, the probability can be found by adding the probability of being chosen and the probability that we will get the lead role.
This can be done as shown below:
The probability that we get a lead role, given that we are already chosen to be in the play = The probability that we will be chosen for the play + The probability that we will get the lead role
= 0.4 + 0.1
= 0.5
The probability of us getting a lead role given that we have already been chosen for the play is found to be 0.5. The correct answer is option D.
Learn more about probability here: https://brainly.com/question/25870256
#SPJ2
An ordinary Fair die is a cube with the numbers 1 through 6 on the sides represented by painted spots imagine that such a die is rolled twice in succession and that the face values of the two roles are added together the sum is recorded as the outcome of a single trial of the random experiment.
Compute the probability of each of the following events:
Event A: The sum is greater than 6
Event B: The sum is an odd number.
Answer:
P(A)= 21/36
P(B)=1/2
Step-by-step explanation:
Given:
An ordinary Fair die is a cube with the numbers 1 through 6 on the sides represented by painted spots imagine that such a die is rolled twice
So the sample space of rolling two dices is:
(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)
(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)
(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)
(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)
(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)
(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)
Total number of sets=36
1)Now Finding probability of
Event A: The sum is greater than 6
From the above sample space sets that have the sum >6 are
(6,1)
(5,2) (6,2)
(4,3) (5,3) (6,3)
(3,4) (4,4) (5,4) (6,4)
(2,5) (3,5) (4,5) (5,5) (6,5)
(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)
there are 21 sets
hence probability of Event A= 21/36
P(A)= 21/36
2) Now Finding probability of
Event B: The sum is an odd number
From the above sample space sets that have the sum an odd number are
(2,1)(4,1) (6,1)
(1,2)(3,2) (5,2)
(2,3) (4,3)(6,3)
(1,4) (3,4) (5,4)
(2,5) (4,5) (6,5)
(1,6) (3,6) (5,6)
there are 18 sets
hence the probability of Event B = 18/36
P(B)= 1/2 !
The figure below is a right rectangle prism. Which expression represents the volume of the prism ?
Answer:
The expression that represent the volume of the prism is [tex]\frac{1}{2}x^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the prism is equal to
[tex]V=LWH[/tex]
In this problem we have
[tex]L=x\ units[/tex]
[tex]W=x\ units[/tex]
[tex]H=(1/2)x\ units[/tex]
substitute
[tex]V=(x)(x)(1/2)x=\frac{1}{2}x^{3}\ units^{3}[/tex]
Answer:
Its the first one
Step-by-step explanation:
Can y’all answer the question for me please thank you
Answer: 544 ft²
Step-by-step explanation: 17*32=544 and ft*ft=ft² so it is 544 ft²
a roller coaster has a height of 325 feet before it's first hill, and the bottom of the hill is thirty feet off the ground. what is the height of the drop?
Subtract the 30 feet from the overall height:
325 - 30 = 295
The height of the drop is 295 feet.
Answer:
295 hope this helps!!
Step-by-step explanation:
what is the solution to the system of equations y = -4x - 19 and y = 2x - 1 in (a, b) form
For this system of equation I used substitution:
Step 1: Every time you see a y in the equation y = 2x - 1 replace it with -4x - 19
-4x - 19 = 2x - 1
Step 2: Isolate x
(-4x + 4x) - 19 = (2x + 4x) - 1
-19 = 6x - 1
-19 + 1 = 6x + (- 1 + 1)
-18 = 6x
x = -3
Step 3: To solve for y replace x in the equation y = 2x - 1 with -3
y = 2(-3) - 1
y = -6 - 1
y = -7
(-3, -7)
Check:
-7 = -4(-3) - 19
-7 = 12 - 19
-7 = -7 --------------------------------> Correct!
-7 = 2(-3) - 1
-7 = -6 - 1
-7 = -7 --------------------------------> Correct!
Hope this helped!
PLEASE HELP RIGHT AWAY
Answer:
29000, with the margin of error of ±5000
Step-by-step explanation:
Margin of error is the amount of error that can be caused due to variation, change of circumstances or any miscalculation.
In given case value of college student's debt can be between
24000 and 34000
Finding mid-point
(24000+34000)/2
29000
Now finding deviation of 29000 from 24000 and 34000
24000-29000= -5000
34000-29000= 5000
Hence
29000, with the margin of error of ±5000 !
What type of association does the graph show between x and y? (4 points)
Linear positive association
Nonlinear positive association
Answer:
Linear Positive Association
Step-by-step explanation:
Question 7
Which shape is a rectangle?
A rectangle is a 4-sided flat shape with straight lines where all interior angles are rights angles (90°)
A shape that has two long sides &’ two short sides .
18 lemons are required to make 15 cups of lemonade. how many lemons are being used for each cup
We find out the number of lemons needed per cup by dividing the total number of lemons by the total number of cups. In this case, 18 lemons divided by 15 cups gives us the number of lemons used per cup of lemonade.
Explanation:This question is asking how many lemons are required for each cup of lemonade if 18 lemons are used to make 15 cups of lemonade. This is a simple proportional math problem. To solve this, we divide the total number of lemons by the total number of cups.
Step 1: Identify the total number of lemons and cups, which are 18 and 15 respectively.
Step 2: Divide the total number of lemons by the total number of cups (18 lemons / 15 cups).
Step 3: The solution will show the number of lemons used per cup of lemonade.
Learn more about Proportional Math here:https://brainly.com/question/28979975
#SPJ12
Given y=x2 + 9x + 20 find the zeroes.
Answer:
x=-5 x=-4
Step-by-step explanation:
y=x^2 + 9x + 20
We need to factor the equation
What 2 numbers multiply to 20 and add to 9
4*5 = 20
4+5 =9
y=(x+5) (x+4)
To find the zero's we set the equation equal to zero
0= (x+5) (x+4)
Using the zero product property
x+5 = 0 x+4=0
x=-5 x=-4
How much interest does a $482 investment earn at 5% over 3 years?
Hi there! The answer you're looking for is $72.30. Simply multiply $482 by 0.05 (5%) and multiply that answer by three (three years) to get $72.30! Let me know if this helps! <3
Answer: $72.30
Step-by-step explanation: To solve this problem, first begin with the interest formula.
Formula: Interest = principal × rate × time
In this problem, we are solving for the interest.
The principal is the amount invested which in this case is $482. The rate is 5% which we can write as .05 and the time is 3 years.
Interest = (482)(.05)(3)
Interest = 72.3
This means that the interest earned is $72.30.
Graph linear equation -3y=2x-7
Answer:
Find the attached
Step-by-step explanation:
We are given the following linear equation;
-3y = 2x - 7
In order to graph it, we need to determine at least 3 pairs of points that lie on the line;
we first solve for y by dividing both sides of the equation by -3;
y = (-2/3)x + 7/3
let x be 3;
y = (-2/3)*3 + 7/3
y = 1/3
(3, 1/3)
let x be 6;
y = (-2/3)*6 + 7/3
y = -5/3
(6, -5/3)
let x be 9;
y = (-2/3)*9 + 7/3
y = -11/3
(9, -11/3)
Using the three set of points we graph our linear function. Find the attached;
3x-7y=14
What is the slope of the line given by the linear equation above?
A. 3/7
B. -3/7
C. 7/3
D -7/3
Answer:
A. [tex]\frac{3}{7}[/tex]
Step-by-step explanation:
The given equation is
[tex]3x-7y=14[/tex]
We solve for y by subtracting 3x from both sides to obtain;
[tex]-7y=14-3x[/tex]
We now divide through by -7 to get;
[tex]y=\frac{-3}{-7}x+\frac{14}{-7}[/tex]
This simplifies to;
[tex]y=\frac{3}{7}x-2[/tex]
This equation is now in the form y=mx +c, where [tex]m=\frac{3}{7}[/tex] is the slope.
A used-car dealer has a vehicle on the lot with a sticker price of $5999. If the
dealer markup on used vehicles is 20%, how much did the dealer pay for the
car?
Answer:
$4999
Step-by-step explanation:
Let the cost of the car be x
Then considering 20% markup, the sticker price is:
x + 20% = 5999Since 20% of x is 20/100x = 0.2x,
x+ 0.2x = 59991.2x = 5999x = 5999/1.2x ≈ $4999So dealer paid $4999 for the car
In a kitchen there are three containers that can hold different quantities of water, as shown in the figure below:
Three containers of the same shape but different sizes are shown, starting with the shortest and ending with the longest. The following quantities are written below the containers. x minus 10 liters below the first, x minus 5 liters below the second, and x liters below the third.
How many liters of water can the three containers hold in all?
x − 15
3x − 15
x3 + 50
3x3 − 15
Answer:
3x-15
Step-by-step explanation:
(x-10)+(x-5)+(x)=3x-15
3x - 15
Simply add the different container sizes together. The first container holds x - 10 liters, the second holds x - 5 liters, and the third holds x liters.
(x - 10) + (x - 5) + x
Because of the associative property of Addition, we can remove the parentheses.
x - 10 + x - 5 + x
Because of the communicative property of addition, we can reorder the terms so that the like terms are next to each other.
x + x + x - 10 - 5
Now, combine the x’s.
3x - 10 - 5
Finally, subtract -10 minus - 5.
3x - 15
If y varies directly as x, and y is 180 when x is n and y is n when x is 5, what is the value of n?
For this case we have that if "y" varies directly with "x", we can propose:
[tex]y = kx[/tex]
Where "k" represents the constant of proportionality.
According to the data:
[tex]180 = kn\\n = k5[/tex]
We substitute the second equation in the first:
[tex]180 = k * k5\\180 = 5k ^ 2\\k ^ 2 = \frac {180} {5}\\k ^ 2 = 36[/tex]
We apply root:
[tex]k = \pm \sqrt {36}\\k = \pm6[/tex]
If k = 6, then[tex]n = 6 * 5 = 30[/tex]
Answer:
[tex]n = 30[/tex]
Answer:
EDGE 2020
Step-by-step explanation:
C) 30
trust me