Answer:
The numbers can be written as x and x + 1. Set the product of the numbers equal to 1,332 to get x(x + 1) = 1,332. You can solve the quadratic equation by using the quadratic formula, completing the square, or factoring. When you solve the quadratic equation, you find that x = –37 and 36. Since the question asked for positive integers, the only viable solution is x = 36. To solve for the larger integer, you add 1 to 36 to get an answer of 37.
Step-by-step explanation:
sample response
The first consecutive number is 36 and the second consecutive number is 37.
What are the consecutive numbers?Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.
Let the first consecutive number be x and the second consecutive number be (x+1).
The product of two consecutive positive integers is 1,332.
[tex]\rm x\times (x+1)=1332\\\\x^2+x=1332\\\\x^2+x-1332=0\\\\x^2+37x-36x-1332=0\\\\x(x+37)-36(x+37x)=0\\\\(x+37)(x-36)=0\\\\x+37=0, \ x=-37\\\\x-36=0, \ x=36[/tex]
(Ignoring the negative value of x).
The first consecutive number = x = 36
The second consecutive number = x+1 = 36 + 1 = 37
Hence, the first consecutive number is 36 and the second consecutive number is 37.
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Find (x^4 − 5x^3 + 17x + 3) divided
by (x − 3).
Answer:
the division of (x^4 − 5x^3 + 17x + 3) by (x − 3) is equal to x^3 - 3x^2 + 4x - 3, with a remainder of 0.
Step-by-step explanation:
To divide (x^4 − 5x^3 + 17x + 3) by (x − 3), we can use polynomial long division. This involves dividing the polynomial by the divisor (x - 3) and expressing the result as a quotient plus a remainder. The remainder will be a polynomial of degree less than the degree of the divisor.
Here is how the division would look:
x -3 x^4 -5x^3 17x 3
--- ----- ---- ----- --- ---
x -3 x^3 -5x^2 17 0
x^3 -3x^2 -2x^2 3
0 -2x^2 -2x^2 0
0 0 -4x^2 3
0 0 -4x^2 -9
0 0 0 -9
0 0 0 0
From this division, we can see that the quotient is x^3 - 3x^2 + 4x - 3, and the remainder is 0. Therefore, we can express the division as:
(x^4 − 5x^3 + 17x + 3) / (x − 3) = (x^3 - 3x^2 + 4x - 3) + 0
This means that the division of (x^4 − 5x^3 + 17x + 3) by (x − 3) is equal to x^3 - 3x^2 + 4x - 3, with a remainder of 0.
Given equation= (x^4 - 5 x^3 + 17 x + 3)/(x - 3)
alternate form-x^3 - 2 x^2 - 6 x - 1 (for x!=3)
expanded form-x ((x - 2) x - 6) - 1 (for x!=3)
x^4/(x - 3) - (5 x^3)/(x - 3) + (17 x)/(x - 3) + 3/(x - 3)
quotient form and reminder-x^4 - 5 x^3 + 17 x + 3 = (x^3 - 2 x^2 - 6 x - 1)(x - 3) + 0.
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How do you find the duplicate number on a given integer array in Python?
The duplicate number on a given integer array in Python can be found through two loops.
How do you find the duplicate number on a given integer array in Python?We need to print the duplicate elements present in the array. This can be done through two loops. The first loop will select an element and the second loop will iteration through the array by comparing the selected element with other elements. If a match is found, print the duplicate element.
ALGORITHM:
STEP 1: Declare and initialize an array.
STEP 2: Duplicate elements can be found using two loops. The outer loop will iterate through the array from 0 to length of the array. The outer loop will select an element. The inner loop will be used to compare the selected element with the rest of the elements of the array.
STEP 3: If a match is found which means the duplicate element is found then, display the element.
PYTHON PROGRAM:
#Initialize array
arr = [ ];
print("Duplicate elements in given array: ");
#Searches for duplicate element
for i in range(0, len(arr)):
for j in range(i+1, len(arr)):
if(arr[i] == arr[j]):
print(arr[j]);
The duplicate number on a given integer array in Python can be found through two loops.
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pls help me due asap
Answer:
iam think that y=2x cause curve y have two curve x
find the limit of the points specified
Find the product:
[2 1 0] x [1 -1 2] = [a b c]
[-1 -2 1]
[0 1 1]
Step-by-step explanation:
the multiplication result is found by row×column multiplications.
1st row × 1st column = a
2×1 + 1×-1 + 0×0 = 2 - 1 = 1 = a
1st row × 2nd column = b
2×-1 + 1×-2 + 0×1 = -2 + -2 = -4 = b
1st row × 3rd column = c
2×2 + 1×1 + 0×1 = 4 + 1 = 5 = c
The population of a city has decreased by 35% since it was last measured. If the current population is 20,800, what was the previous population?
help pls
The previous population of the city was 32,000.
What is percentage?Percentage is a measurement to find value of given number out of hundred.
Given that,
The current population of the city = 20,800.
Let the previous population was 100%.
Since, The population of the city decreased by 35%,
So, the current population of the city = 100 - 35 = 65%
According to given condition,
65 % = 20800
1 % = 20800 / 65
1 % = 320
100% = 320 x 100
= 32,000
Hence, the initial population was 32,000.
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lins family had completed 60% of a trip. they have traveled 30 miles. how many miles is the trip
Lin's family make a trip of length 50 miles.
What is a trip?
People move between far-off geographic regions when they travel. Travel can be done with or without luggage, on foot, by bicycle, car, rail, boat, airline, ship, or by another mode of transportation. It can also be one way or round trip.
Given that Lin's family had completed 60% of a trip.
Thus they have to travel (100 - 60)% = 40% of the trip.
Also given that, they have traveled 30 miles..
Therefore,
60% of the trip is equal to 30 miles.
1% of the trip is equal to 30/60% miles.
100% the trip is equal to (30× 100%)/60% miles.
= 50 miles.
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megan wants to test her assumption on the amount of sleep students are getting. she decides to focus her efforts on examining if students are getting less than eight hours of sleep. what should megan state for the null hypothesis and alternative hypothesis?
Your research question can also be answered by the alternative hypothesis (Ha). The populace, according to the assertion, is affected.
What is an alternative hypothesis?Your alternate theory and research hypothesis are frequently same. It is the assertion that you anticipate or hope will be accurate, to put it another way.The complementary idea to the null hypothesis is the alternative theory. The extensive nature of the null and alternative hypotheses ensures that they account for every scenario. As only one of them may be true at once, they are also mutually exclusive.When writing a research paper or thesis, use caution when describing the findings of a statistical test. When the null hypothesis is rejected, the alternative hypothesis is said to be supported. Conversely, if you are unable to disprove the null hypothesis, you can conclude that the alternative hypothesis is unsupported. Never assert that a theory has been supported or refuted.Alternative hypotheses frequently make use of words like "an effect," "a difference," or "a relationship." A mathematical inequality (often, but occasionally or >) is always included in alternative hypotheses. The formulation of an alternative hypothesis can be expressed in a variety of ways, just like null hypotheses.To Learn more About alternative hypothesis refer to:
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Is physics science hard?
Yes, it is hard but with a lot of practice and putting effort one can also find it easy.
Why physics is hard?Physics requires the ability to solve problems, which can only be acquired via practice. In addition to these difficult ideas, there are theoretical concepts, mathematical calculations, and laboratory experiments.
How to deal with physics?It is better to comprehend the derivations than to memorise the formulas. Making a mess of several formulas will just increase your anxiety over the topic. Instead, if you strive to comprehend where they originate, you will begin to appreciate physics and its applications.
Physics is a difficult topic since it combines science and arithmetic, which may be challenging for the best of us. Nevertheless, despite how difficult it is, you can achieve if you follow a few simple guidelines and put yourself through some practice.
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Which system of equations can be used to find the roots of the equation 4x 5 12x?
The system of equations that can be used to find the roots of the equation 4x 5 12x is:x = -5/8
1. Set up the equation: 4x - 12x = 5
2. Simplify the equation on the left side: -8x = 5
3. Solve for x: x = -5/8
To find the roots of the equation 4x - 12x = 5, we must first set up the equation. On the left side of the equation, we can simplify it to -8x = 5. Then, we can solve for x by dividing both sides by -8, giving us x = -5/8. This is the solution to the system of equations, and the root of the original equation.
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jksjsisks 78i2o
[tex]32. \frac{33}{31?} [/tex]
Answer:
34.064516129
Step-by-step explanation:
[tex]32 \times \frac{33}{31} = \frac{1056}{31} [/tex]
[tex] = 34.064516129[/tex]
i hope this helps
A box is dragged without acceleration in a straight-line path across a level surface by a force of 100 n. What is the frictional force between the box and the surface?.
The frictional force between the box and the surface is 100 newtons .
Since the body being dragged across the surface is not accelerating, the acceleration of the body is 0m/s².
From Newtons second law of motion, F = ma where;
F is the sum of the forces acting on the body
m is the mass of the body
a is the acceleration
If the box is dragged along a straight line by a force of 100 N, its moving force (Fm) is 100 N and the frictional force (Ff) will act opposite to this force.
Resultant force acting on the box along the horizontal will be Fm+(-Ff)
Therefore;
Fm+(-Ff) = ma
Fm-Ff = ma
Since a = 0m/s²
Fm-Ff = m(0)
Fm-Ff = 0
Fm = Ff
This shows that for a static body, the moving force acting on the body will be the same as the frictional force. Since Fm = 100 N
Frictional force (Ff) = 100 N
Therefore, the frictional force between the box and the surface is 100 N
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What is the median of the sample 5 5 11 9 8 5 8?
The median for the next batch of observations is 8.
What is median?The median is the value in the middle of a data set, which indicates that 50% of the data points have a value less than or equal to the median, and 50% have a value greater than or equal to the median. The median is the number in the middle of a set of numbers. The median represents the 50th percentile of the set of numbers. In other words, the median is the value in the center of a set of numbers where half are less than the median and half are more than the median.
Here,
given set of observation,
= 5,5,5,8,8,9,11
n=7
median=(7+1)/2
=4th term
=8
The median for following set of observation is 8.
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Alexa is trying to pick out an outfit for the first day of school. She can choose from 8 pairs of pants, 6 t-shirts, 6 sweaters or hoodies, and 2 pairs of shoes. How many different outfits does Alexa have to choose from?
The number of different outfits is 576
How to determine the number of different outfits?From the question, we have the following parameters that can be used in our computation:
8 pairs of pants, 6 t-shirts, 6 sweaters or hoodies, and 2 pairs of shoes
The number of different outfits is the products of the count of each apparel
This is represented as
Different outfits = Pants * T-shirts * Sweaters or hoodies * Pairs of shoes
Substitute the known values in the above equation
Different outfits = 8 * 6 * 6 * 2
Evaluate
Different outfits = 576
Hence, there are 576 different outfits
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a number m is either less than 2 or greater than 9
What is the solution to the system of equations?
x-y+2z=9
3x+y=z=2
2x-y+z=8
Answer:
x=8/7, y=-25/7, z=15/7
Step-by-step explanation:
x-y+2z=9 ==> equation 1
3x+y=z=2 ==> equation 2
2x-y+z=8 ==> equation 3
3x+y+z=2
+ (2x-y+z=8)
3x+2x + y+(-y) + z+z = 2+8 ==> add equation 2 and 3 to eliminate y
5x + 2z = 10 ==> equation 4
x-y+2z=9
- (2x-y+z=8)
x - 2x + (-y)-(-y) + 2z-z = 9-8 ==> subtract equation 1 and 3 to eliminate y
-x + 0 + z = 1 ==> Let's say -y=a. (-y)-(-y) = a-a = 0.
(-x + z = 1)*2 ==> multiply by 2 to get z to become 2z
-2x + 2z = 2 ==> equation 5
5x + 2z = 10
- (-2x + 2z = 2)
5x-(-2x) + 2z-2z = 10-2 ==> subtract equation 4 and 5 to solve for x
5x+2x = 8
7x = 8 ==> divide both sides by 7 to isolate x
x = 8/7
-2(8/7) + 2z = 2 ==> plugin x into equation 5 to solve for z
-16/7 + 2z = 2 ==> simplify
(-16/7 + 2z = 2)*7 ==> multiply the equation by 7 to eliminate fractions
-16 + 14z = 14
14z = 30 ==> add 16 on both sides to isolate z
z = 30/14 ==> divide each side by 14
z = 15/7 ==> simplify
2(8/7)-y+(15/7)=8 ==> plugin x = 8/7 and z = 15/7 into equation 3
16/7 - y + 15/7 = 8
(16/7 + 15/7 - y = 8)*7 ==> multiply the equation by 7 to remove fractions
16 + 15 - 7y = 56
31 - 7y = 56
-7y = 25 ==> subtract 31 on both sides to isolate y
7y = -25
y = -25/7
Answer: (x=8/7, y=15/7, z=-25/7)
Is there a calculator that solves algebra?
Answer:
yes
Step-by-step explanation:
do you want names for online ones
Please someone help me with this!
A projectile is fired from the ground at an angle of 30 degrees above the horizon with an initial velocity of 960 ft/sec. If the height as a function of time t is given by h(t)=480t-16t^2, find,
The time when the projectile hits the ground
The maximum height
I think
h(t)=480t–16t^2
Max height is the vertex of the parabola at t = -b/2a
t = -480/-32 = 15 seconds
--> h(15)
I think of a number, double it, then subtract 7. The result is 10.
Find the number.
Answer:
17/2
Step-by-step explanation:
Work backwards. you have 10, then opposite of subtract 7 is add 7 which gives you 17. then opposite of double is half getting you 8.5 or 17/2
Answer:
Your number is 8.5 or 17/2
Step-by-step explanation:
Let's say your number is equal to the variable n.
Then we can set up an equation for this scenario: 2n - 7 = 10
Now, we need to use algebra to solve:
2n - 7 = 10 → add 7 to both sides
2n = 17 → divide both sides by 2
n = 17/2 = 8.5
Thus, the number you were thinking of was 8.5, or 17/2
Fill in the blanks to complete the proofs
Answer:
Look at the image I attached to my response.
Step-by-step explanation:
For proof #3, I did it according to the way I was taught how to do proofs in my state/school, so what you wrote could be correct.
if I bought a $40 basket and it was on sale for 50% off but added 10% sales tax how much is it
Answer:
$24
Step-by-step explanation:
50% of 40 = 20
10% of 40 = 4
20+4=$24
the equation of a line is y equals 4 over 3 x minus 5 over 3. what would be the slope of a line perpendicular to this line?
The slope of the line perpendicular to the given line is calculated by taking the negative reciprocal of the given slope.The slope of the given line is 4/3. The slope of the line perpendicular to the given line is -3/4.
To find the slope of a line perpendicular to the given line, we need to take the negative reciprocal of the slope of the given line. The equation of the given line is y = 4/3x - 5/3. To calculate the slope, we need to rearrange the equation to the form y = mx + b, where m is the slope and b is the y-intercept. Rearranging the equation to the form y = mx + b, we get y = 4/3x - 5/3 which can be written as 4/3x - y = 5/3. The slope of the given line is 4/3. To find the slope of the line perpendicular to the given line, we take the negative reciprocal of 4/3 which is -3/4. Therefore, the slope of the line perpendicular to the given line is -3/4.
y = 4/3x - 5/3
4/3x - y = 5/3.
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Where is the domain and range of a function?
On solving the provided question we can say that - The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,∞)
What is Domain?The range of values that may be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while employing a value for x to that end, then the selected x-value is said to belong to the domain of f.
f(x)= -3x-2 x <4
3/4x-1 x [tex]\geq[/tex] 4
Domain =
The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,∞).
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Benjamin bought two pounds of strawberries for 12.80. What is the price, in dollars per ounce of strawberries?
Answer: 6.4
Step-by-step explanation:
divide in half
N
A city has a population of 360,000 people. Suppose that each year the population grows by 3%. What will the population be after 13 years?
Use the calculator provided and round your answer to the nearest whole number.
Answer:
528,672
Step-by-step explanation:
A=P(1+r)^t
360,000(1+.03)^13 = 528,672.1368
Rounded: 528,672
What is the value of the following expression 20 19 − 5 7?
The value of the expression after simplification is found as 415.
What is meant by the term simplification?To simplify simple means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.
Calculations and problem-solving techniques simplify the issue.
We can —
By eliminating all common elements from the numerator and denominator and putting the fraction through its simplest/lowest form, fractions can be made simpler.By combining and grouping like terms, mathematical expressions can be made simpler. This makes the phrase simple to comprehend and to solve.The given expression is-
= 20 x 19 + 5 x 7
Applying the BODMAS, multiply the numbers.
= 380 + 35
Add the values,
= 415
Thus, the value of the expression after simplification is found as 415.
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The correct question is-
What is the value of the following expression 20 x 19 + 5 x 7?
Need help (100 easy points)
Answer:
Step-by-step explanation:
What is the relationship between a scalene triangle and
the location of its centroid? Explain.
O A. The centroid will always be inside the scalene
triangle, since the centroid is always inside
any type of triangle.
O
O
O
B. The centroid will always be outside the
scalene triangle, since the centroid is always
outside any type of triangle.
C.
The centroid will always be on the scalene
triangle, since the centroid is always on a
triangle with no congruent side lengths.
D.
The centroid will be inside, on, or outside the
scalene triangle, depending on whether it is
acute, right, or obtuse, respectively. The
number of congruent sides does not affect
the location of the centroid.
The relationship between a scalene triangle and the location of its centroid is; A: The centroid will always be inside the scalene
triangle, since the centroid is always inside any type of triangle.
What is the location of the centroid of the triangle?A scalene triangle is a triangle in which all three sides have different lengths. Also the angles of a scalene triangle have different measures.
Some right triangles can be a scalene triangle when the other two angles or the legs are not congruent.
Now, a centroid of a triangle is defined as the point formed by the intersection of the medians of the triangle. Now, the medians of a triangle always lie within a triangle. This means that their intersection point which is the centroid of a triangle always lies inside a triangle.
Thus, the centroid of the scalene triangle can be concluded to always lie inside the triangle.
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5 ≤ y + 2 ≤ 11 find the compound inequality
Answer:jkd
Step-by-step explanation:
d
A covered Bridge is 8 yards long. In a photograph for sale at a gallery The Bridge is 5/12 foot-long which statements are true?
1. One yard of the covered Bridge is represented by 1.6 inches in the photograph
2. One inch on the photograph represents 1.6 yards of the real bridge.
3. A tree that is 3 inches tall in the photograph is 4.8 yards tall.
4. The people walking over the bridge are about 2.5 inches tall in the photograph.
5. A river that is 12 yards wide is 7.5 inches wide in the photograph.
(PLEASE EXPLAIN)
Answer:
2. One inch on the photograph represents 1.6 yards of the real bridge.
Step-by-step explanation:
1 yd = 36 in.
8 yd = 36 in./yd × 8 yd = 288 in
1 ft = 12 in.
5/12 ft × 12 in./ft = 5 in.
5 in. in the picture equals 288 inches real.
1 in. in the picture equals 57.6 inches real.
57.6 in. × (1 yd)/(36 in.) = 1.6 yd
1 in. in the picture equals 1.6 yd real
Answer:
2. One inch on the photograph represents 1.6 yards of the real bridge.
Which of the following is equal to (x^4 + 4x^3 − 3x^2 − 12x) divided by (x + 4)?
F x^3 − 3x G x3 + 3x
H x^3 − 2x^2 − 3x
G x^3 + 3x
J x^3 + 2x^2 − 3x
Answer:
F
Step-by-step explanation:
[tex]x^4+4x^3-3x^2-12x=x^3(x+4)-3x(x+4)=(x^3-3x)(x+4) \\ \\ \therefore \frac{x^4+4x^3-3x^2-12x}{x+4}=x^3-3x[/tex]