Let's call the two numbers we're trying to find x and y. We know that x + y = 12 and xy = 23. From the first equation, we can solve for one of the variables in terms of the other. So if we subtract x from both sides, we get y = 12 - x. Now we can substitute this expression for y into the second equation to get x(12 - x) = 23. Expanding this out, we get 12x - x^2 = 23. Rearranging, we get x^2 - 12x + 23 = 0. This quadratic equation can be factored as (x - 2)(x - 10) = 0. So either x = 2 and y = 10, or x = 10 and y = 2.
Answer:
The two numbers are 2 and 10.
Use properties of exponents to verify that 2s − 1 and _1
2 (2)
s
are equivalent.
The properties of the exponents are solved and the expression is given by the relation ( 2s )⁻¹ = 1 / 2s
Given data ,
Let the expression be represented as A
Now , the value of A is
( 2s )⁻¹ = 1 / 2s
From the laws of exponents , we get
m⁻ᵃ = ( 1 / mᵃ )
So , on simplifying , we get
( 2s )⁻¹ = 1/ ( 2s )
On further simplification , we get
1/ ( 2s ) = ( 2s )⁻¹
Hence , the expression is ( 2s )⁻¹ = 1/ ( 2s )
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The complete question is attached below :
Use properties of exponents to verify that ( 2s )⁻¹ = 1/ ( 2s ) are equivalent.
A cone has a diameter of 16 cm and a height of 35 cm. What is its volume?
Answer: if with 3.14 v= 37512.5333
if with pi v= 37531.56
Step-by-step explanation:
the formula is 1/3hπr^2
r= 2d so radius is 32
plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)
Which of the points below correctly plots the point (4,π/3)?
Answer: The correct answer is B
Step-by-step explanation:
Remember that the coordinates (4,π3) tell us the radius r=4 and the angle θ=π3. So the point should be on the circle labeled 4 and form an angle of π3 with the positive x-axis. Point B is the correct point
hey guys, im b-o-r-e-d in class... what should i do?
Answer:
Do whatever you want, but paying attention would really help you.
Step-by-step explanation:
If you find yourself bored in class, consider the following options to make the most of your time and stay engaged:
1. Actively participate: Ask questions, contribute to discussions, and try to engage with the material. Active participation can make the class more interesting and help you retain the information better.
2. Take notes: Focus on taking detailed notes, even if you think you understand the material. This will help you stay engaged and make it easier to review the content later.
3. Find connections: Try to relate the class material to your interests or real-world applications. This can make the content more engaging and relevant.
4. Set learning goals: Set specific learning objectives for each class, and try to achieve them during the session. This can help you stay focused and motivated.
5. Practice active listening: Pay attention to the teacher and try to understand the main points they are making. This can help you stay focused and better comprehend the material.
6. Break down the material: Divide the content into smaller chunks and focus on understanding each part. This can make the material more manageable and engaging.
7. Speak with your teacher: If you're consistently bored in class, consider discussing your concerns with your teacher. They may be able to offer suggestions or modify their teaching approach to better suit your learning style.
Remember, it's essential to stay engaged in class to maximize your learning experience and make the most of your education.
Answer:
watch RUN BTS EPISODE simple
find the polar coordinates of a point with Cartesian coordinates (x,y)=(5√3/2,−5/2).Select the correct answer below:
(5,5π/6)
(10,4π/3)
(5,11π/6)
(10,5π/6)
(5,4π/3)
(10,11π/6)
Answer: The correct answer is (5, 11π/6). or C
Step-by-step explanation:
The polar coordinates of the point (x, y) = (5√3/2, -5/2) are (r, θ) = (5, 11π/6).
Explanation:
Using the formulas for converting Cartesian coordinates to polar coordinates:
r = √(x^2 + y^2)
θ = atan2(y, x)
Plugging in the given values:
r = √((5√3/2)^2 + (-5/2)^2)
= √(75/4 + 25/4)
= √(100/4)
= 5
θ = atan2(-5/2, 5√3/2)
≈ 11π/6 radians
So, the correct polar coordinates of the point (5√3/2, -5/2) are (r, θ) = (5, 11π/6).
Faster please!! thanks!! 30 points + brainliest!!
Which is an example of simple random sampling created from each given population?
An example of simple random sampling is given as follows:
C. In a bag of more than 500 marbles, reaching the hand into a bag and drawing 25 of them.
How are samples classified?Samples may be classified as:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.Hence the samples for this problem are classified as follows:
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The average temperature for a dog is 101.8° F, but it can vary by as much as 0.7° F. Write an inequality to represent the normal temperature range of a dog, where t represents body temperature.
|t − 101.8| ≥ 0.7
|t − 101.8| ≤ 0.7
|t − 0.7| ≥ 101.8
|t − 0.7| ≤ 101.8
The correct inequality to represent the normal temperature range of a dog is |t − 101.8| ≤ 0.7. So, correct option is B.
Here, |t - 101.8| represents the absolute value of the difference between the body temperature of the dog (t) and the average temperature of dogs (101.8° F). The inequality states that this absolute value must be less than or equal to 0.7° F, which is the maximum amount that the temperature of a dog can vary from the average.
If the temperature of a dog is within this range, it is considered to have a normal body temperature. If the temperature is outside this range, it may indicate an underlying health issue or illness.
The other answer choices are incorrect because they do not accurately represent the relationship between the body temperature of a dog and the normal temperature range. For example, |t - 0.7| ≥ 101.8 makes no sense in the context of the problem, as there is no logical reason to subtract 0.7 from the body temperature.
So, correct option is B.
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Write a two-column proof for the following information. Upload your proof below.
Given: M is the midpoint of CD; CM = 5x – 2; MD = 3x + 2
Prove: x = 2
The required two column proof is explained below.
What is a midpoint?A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.
The two column proof for the information is given as:
M is the midpoint of CD (Given)
CD = CM + MD (addition property of a line segment)
CM = MD (definition of a midpoint)
So that;
5x – 2 = 3x + 2 (Definition of midpoint)#
Then,
5x - 3x = 2 + 2 (collecting like terms)
2x = 4
x = 2
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13x−6y=22
x=y+6
Please help first come first surve
Answer:
The answer is
x= -2
y= -8
Step-by-step explanation:
x=y+6
substitute into equation 1
13(y+6)-6y=22
13y+78-6y=22
13y-6y=22-78
7y=-56
divide both sides by 7
7y/7= -56/7
y= -8
x=y+6
x= -8+6
x= -2
I need help please !!
Answer:A,D
Step-by-step explanation:
y = [5.3, 27]
x= [-1,3]
Gretta travels 77 miles per hour for 5 hours, find the distance traveled in miles
Answer: 358 miles
Step-by-step explanation:
Answer: 385
Step-by-step explanation: 77x5
1. Simplify(3mks)
a + b / 2 - 2A - b / 3 =
Determine the equation of the circle with center (0,−1) containing the point ( − 8 , 10 )
To find the equation of the circle with center (0, −1) that contains the point (−8, 10), we can use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Since the center of the circle is given as (0, −1), we have:
(x - 0)^2 + (y + 1)^2 = r^2
We still need to find the radius, r. We know that the circle passes through the point (−8, 10), so we can substitute these values for x and y and solve for r:
(-8 - 0)^2 + (10 + 1)^2 = r^2
64 + 121 = r^2
r^2 = 185
So the equation of the circle is:
x^2 + (y + 1)^2 = 185
Alternatively, we can expand the equation to get it in standard form:
x^2 + y^2 + 2y + 1 = 185
x^2 + y^2 + 2y - 184 = 0
So another form of the equation is:
x^2 + (y + 1)^2 = 185
Solve for BC: 3√2 A B C
Sides AB = 3√2 and BC = 6.
The given triangle ABC is a right-angled triangle, as ∠BAC = 90°.
In the given right triangle ABC,
Hypotenuse of the triangle = BC
Base and height = AC and AB.
Also, we see from the diagram that ∠ACB and ∠ABC are equal.
∴ Triangle ABC is isosceles, with sides AC = AB = 3√2.
Now, by Pythagoras' theorem,
Hypotenuse² = Base² + Height²
Or, BC² = AC² + AB²
Or, BC² = (3√2)² + (3√2)²
⇒ BC² = 36
Or, BC = 6
Hence, sides AB = 3√2 and BC = 6.
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TONS OF POINTS - please help
The Cannon: Ernest's friend Nik is about to be shot out of a cannon. The path he will
travel follows a parabolic arch that can be described by this polynomial.
f(x) = -0.05(x2-26x-120)
He is supposed to land on a safety net 30 feet away. Does the function give you
enough information to tell you where he will land? If so, how far from the cannon will he land?
Make Sense of the Problem
3 points: 1 point for each answer.
-What do you know?
-What do you want to find out?
-What kind of answer do you expect?
1. The function f(x)=-0.05(x2-26x-120)
Represents the path coming out of the cannon. If x is the horizontal distance from the cannon, what does f(x) represent
2.what do the zeros of this function represent? Remember the zeros are where f(x)=0
3. Will the zeros tell you where the net should be placed? Why or why not?
4.to find zeros, set the function equal to 0, and then factor the polynomial start by setting the function equal to 0
5. Next factor the polynomial x2-26x-120. To identify the factors, complete the table: note this does not contain all the factors of -120, but it has enough to let you factor the polynomial
(I tried to type out the table )
pqp+q
P. q. p. |
————————— |
10. | 12 | blank. |
—————————.|
-10 | 12 |. Blank. |
—————————.|
30. |. -4. |. Blank. |
—————————-|
4. |. 30. | blank. |
—————————.|
6. Which values of p and w give the correct factors
7. Factor the polynomial completely
0=-0.05(x2 - 26x -120)
8. Find the roots of equation by setting each factor equal to 0 and solving for x.
Hint: there are three factors, but the constant factor, -0.05, does not equal zero
Solve for x with the other two factors
9. Identify the roots
Answer:
Step-by-step explanation:
2344
Hello, I hope you are having a great day so far, I was wondering if someone ca (seriously) help me and not play around. I really need an Answer asap as soon as possible
PLEASE HELP (I NEED AN ANSWER QUICK!)
Answer:
the corresponding sides are proportional
According to your graphing calculator what is the approximate solution to the trigonometric inequality tan(x/4)<1/5 over the interval 0<= x<=2pi radians 
The approximate solution to the trigonometric inequality tan(x/4) < 1/5 over the interval 0 <= x <= 2π radians is 0 <= x <= 0.75. Option 1 is correct.
To solve the trigonometric inequality tan(x/4) < 1/5 over the interval 0 <= x <= 2π radians, we can use a graphing calculator and follow these steps:
Press the "mode" button on the calculator and make sure it is in radian mode.Enter the function "tan(x/4)" into the calculator.Press the "y=" button and enter "1/5" as the second function.Press the "graph" button to plot both functions on the same graph.Use the "trace" function or the cursor to find the points where the two graphs intersect.Check the values of x for which the tan(x/4) function is less than 1/5.Using this method, we can see that the two graphs intersect at approximately x = 0.75, x = 4.6, and x = 8.4 (or their equivalents within the interval 0 <= x <= 2π). We can also see that the tan(x/4) function is less than 1/5 between the first two intersection points (0 <= x <= 0.75 and 4.6 <= x <= 2π), but not between the second and third intersection points. Hence Option 1 is correct.
Note: Since we are rounding to the nearest degree, the approximate values may not be exact and may need to be adjusted slightly to ensure accuracy.
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The Bayview Community Pool has a snack stand where Juan works part-time. He tracked his total sales during each shift last month. This box plot shows the results. Total sales per shift ($) 100 150 Submit 200 250 300 What fraction of Juan's shifts had total sales of $225 or more? 350
It looks like there are five data points in the box plot, representing Juan's total sales during each shift. The third data point is $200, which is the median value. Since there are an odd number of data points, we know that the median is exactly in the middle of the data set. This means that two of the data points are less than $200, and two of the data points are greater than $200.
The last data point is $300, which is the maximum value. So we know that only one of the data points is between $200 and $300. Therefore, the fraction of Juan's shifts that had total sales of $225 or more is 1/5, or 20%.
Answer:
Step-by-step explanation:
Suppose you invest $5,000 in an account earning 4.71% APR compounded
monthly. How much money will be in the account after 15 years?
$9,664.47
After 15 years the account will have $9,664.47
solve 5 to the power of x+2 is less than or equal to 3 to the power of x
Step-by-step explanation:
5^(x+2) <= 3^x
5^x * 5^2 <= 3^x
25 <= 3^x / 5^x
25<= (3/5)^x LOG both sides
log 25 <= x log (3/5)
log 25 / log (3/5) <= x
- 6.3 <= x
Correct answer gets brainliest
Answer:
C. Points have no size and no dimensions.
Answer:
I think it is choice A and choice C
Cole and his sister took part in a canned food drive. Cole brought in 21 cans of food. His sister brought in 7 fewer cans than he did. Together, how many cans did they bring in?
If Cole brought 21 cans and his sister brought 7 cans less, then the total number of cans brought by them is 35 cans.
The number of cans which Cole brought = 21 cans of food.
His sister brought in 7 fewer cans than he did, which means she brought in:
⇒ 21 - 7 = 14 cans of food,
Let the total number of food-cans be = "f",
So, the equation to find the number of cans is written as :
⇒ x = 21 + 14,
On adding the number of cans,
We get,
⇒x = 21 + 14 = 35,
Therefore, together they brought in 35 cans of food.
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SOS need help on this math project with all the work
To perform this and any other construction in math, you need to use the right tools which include a compass, your drawing board or paper, and a clear understanding of the instruction.
How to construct the shapes and anglesA key to getting the shape and angles of any construction includes knowing what is required of you and implementing these in your construction. In the second slide, you are told to use the segment tool to create segment AB. This tool will be a scale and the measurement will be that of a line AB.
Next, identify the radius of the circle. This is the point from the center of the circle to any line on the circle. Understanding the instructions is key to bisecting the segment and completing the other activities.
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In an ossicles triangle the base is 65 which of the following expressions is a way to calculate the measure of the third triangle
The measure of the third angle in an isosceles triangle can be expressed using the expression of option c. 180° - 2(65°).
In an isosceles triangle,
Measure of the base angles is equal to 65°.
Let us consider the measure of the third angle in an isosceles triangle is equal to x degrees.
The two base angles are congruent.
Since each base angle measures 65°, the sum of the base angles is.
65° + 65° = 130°
The sum of the angles in any triangle is 180°.
This implies,
The measure of the third angle in the isosceles triangle is equal to,
x° + 130° = 180°
⇒ x° = 180° - 130°
⇒ x° = 50°
Therefore, the correct expression to calculate the measure of the third angle in an isosceles triangle is option (c) 180° - 2(65°).
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The above question is incomplete, the complete question is:
In an isosceles triangle, the base angles measure 65°. Which of the following expressions is a way to calculate the measure of the third angle?
a. 180° - 65°
b. 180°+ 65°
c. 180° - 2(65°)
d. 180° + 2( 65°)
the surface area of a rectangular prism is 1,648 inches, the width is 16 inches and the hight is 20 inches. What is the length
Answer:
14
Step-by-step explanation:
l = length, w = width, h = height.
The surface area of a rectangular prism is:
2lw + 2wh + 2lh.
If the total surface area is 1648, your equation will be:
2lw + 2wh + 2lh = 1648.
lw + wh + lh = 824.
Plug in your width and height values.
16l + 16*20 + 20l = 824.
36l = 504.
Length = 14.
[tex]\boxed{\sf l=14(in)}.[/tex]
Step-by-step explanation:1. Write the surface area equation for rectangular prisms.[tex]\sf SA=2(wl+hl+hw)[/tex]
2. Substitute the variables by the given values in the formula.Surface area (SA)= 1,648 inches;
Width (w)= 16 inches;
Height (h)= 20 inches.
[tex]\sf 1648(in)=2((16(in))l+(20(in))l+(20(in))(16(in)))[/tex]
3. Simplify the expression.Let's remove the units for these steps to make the algebra a little bit easier to understand.
[tex]\sf 1648=2(16l+20l+320)\\ \\1648=2(36l+320)[/tex]
Here, we apply the distributive property of multiplication. Check attached image 1.
[tex]\sf 1648=(2)(36l)+(2)(320)\\\\1648=72l+640[/tex]
Now solving the equation for "l" to find its value.4. Subtract "640" from both sides of the equation.[tex]\sf 1648-640=72l+640-640\\ \\1008=72l\\ \\72l= 1008[/tex]
5. Divide both sides by "72".[tex]\sf \dfrac{72l}{72} = \dfrac{1008}{72} \\ \\\\ \boxed{\sf l=14(in)}.[/tex]
6. Verification.If you want to verify this answer simply take the surface area formula for rectangular prisms and calculate the value for the SA using these values of lengh, width and height:
[tex]\sf SA=2((16)(14)+(20)(14)+(20)(16))=\boxed{\sf 1648}. That's\,correct![/tex]
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Callie uses leather cord to make necklaces. She has a pieces of leather cord that has a length of 4 yards. Each necklace will have a length of 28 inches. How many necklaces can Callie make? Show your work.
Callie can make 5 necklaces.
What is the formula for yards to inches?So to convert from a value in inches to one in yards, we need to divide by 36. To convert a value in yards to inches, we need to multiply by 36.
Now, She has a pieces of leather cord that has a length of 4 yards.
Each necklace will have a length of 28 inches.
We have to determine the how many necklaces can Callie make?
We know that :
1 yard= 36 inches
So, Multiply by 36 into 4 yards
4 yards= 36x4= 144
Length of leather cord is 4 yards
144/4 = 5.14
Callie can make 5 necklaces.
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Someone rolls a die 180 times.
Given: 1. She can expect to see 30 aces in 180 rolls (aces means one spot) and 2. The give or take number for this result is 5 (standard deviation).
Question: What are the chances she gets between 20 and 40 aces? (inclusive of the endpoints 20 and 40)
The chances of rolling between 20 and 40 aces (inclusive) in 180 rolls is approximately 0.9544 or 95.44%.
How to solve for the probabilityWe can first standardize the values of 20 and 40 using the formula:
z = (x - μ) / σ
where x is the value we want to standardize (20 or 40), μ is the expected value (30), and σ is the standard deviation (5).
For x = 20, we get:
z = (20 - 30) / 5 = -2
For x = 40, we get:
z = (40 - 30) / 5 = 2
probability of getting a z-score between -2 and 2.
Using a standard normal distribution table or calculator, we find that the probability of getting a z-score between -2 and 2 is approximately 0.9544.
Therefore, the chances of rolling between 20 and 40 aces (inclusive) in 180 rolls is approximately 0.9544 or 95.44%.
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hi how to integrate this
Integration of [tex]\int\limits^6_0 {\frac{8}{1+74e^{-0.3t} } } \, dt[/tex] is 2.199.
We can solve this integral using the substitution method, where u = 1 + 74[tex]e^{-0.3t}[/tex] . Taking the derivative of both sides, we have du/dt = -222[tex]e^{-0.3t}[/tex] .
We can rewrite the integral in terms of u:
∫[8/(1+74[tex]e^{-0.3t}[/tex] )]dt = ∫[8/u * (-1/222) * (-222[tex]e^{-0.3t}[/tex] )]du
Simplifying this expression, we have:
= (-8/222) ∫[1/u] du
= (-4/111) ln|u| + C
where C is the constant of integration.
Substituting back for u, we have:
= (-4/111) ln|1 + 74[tex]e^{-0.3t}[/tex] | + C
To evaluate the definite integral from 0 to 6, we plug in the limits of integration:
= (-4/111) [ln | 1 + 74[tex]e^{-0.3(6)}[/tex] | - ln | 1 + 74[tex]e^{-0.3(0)}[/tex] |]
= (-4/111) [ln|1 + 74[tex]e^{-1.8}[/tex]| - ln75]
≈ 2.199
Therefore, the value of the definite integral is approximately 2.199.
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A scientist has 68 lbs of a material. In 40 years , there is 63.3 lbs left. How much will be there be left in 200 years?
Evaluating the exponential decay we can see that 200 years, there will be 47.43 pounds left of the material.
How much will be there be left in 200 years?A general exponential decay is:
f(x) = A*(b)^x
Where A is the initial value, b is the rate of decay, x is the variable.
We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:
63.3 = 68*(b)^40
Where b defines how it decays, we can solve that equation for b to get:
(63.3/68)^(1/40) = b
0.9982 = b
Then the decay is:
f(x) = 68*(0.9982)^x
The amount left after 200 years will be:
f(200) = 68*(0.9982)^200 = 47.43
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Contrary to common belief, the price of a single item as listed in the CPI (Consumer Price Index) does not always rise and fall in tandem with the price of the same item in the PPI (Producer Price Index). Which of the following is not a reason that makes this so?
a.
Imports are excluded from PPI, but included in CPI.
b.
Taxes paid as part of the purchase are not included as part of the PPI but are included in the CPI.
c.
The PPI includes the prices of goods purchased by other producers while the CPI includes only the prices of goods purchased by consumers.
d.
Since the PPI measures the change of the price the producer receives for their product and the CPI measure the change of the price the consumer pays for the product, one should rise while the other will fall.
What does not make the context given as such is since PPI measures the change of the price the producer receives for their product and the CPI measure the change of the price the consumer pays for the product, one should rise while the other will fall. The Option D is correct.
Why does the price not always rise and fall in tandem?This is because two indexes measure different things. The PPI measures change in prices of goods and services at the producer level while CPI measures the change in prices of goods and services at the consumer level.
That tells us PPI assess prices producers receive for their goods while CPI assess prices consumers pay for those same goods. So, while we have overlap between them, they are measuring different aspects of the economy and their trends may not always move in lockstep with each other.
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