The factor of the given equation; -2x⁴-34x³-140 is (x³ + 10)(x + 7).
What is defined as factorization?Factorization is the process of dividing a large number into smaller numbers that, when multiplied together, yield the original number.
Factorization occurs when you divide a number into its factors or divisors. For example, the factorization of the number 12 could be 3 times 4.Now, as per the stated question;
Quartic Equation: The general quartic equation has an analogous formula: ax⁴ + bx³ + cx² + dx + e = 0. This really refers to four different formulas, each of which yields one root of a equation.
The given quartic equation is -2x⁴-34x³-140.
Divide the complete equation by -2.
= x⁴ + 17x³ + 70
Find the factors of 0 such that on addition it given 17.
= x⁴ + 10x³ + 7x³ + 70
Taking x common
= x(x³ + 10) + 7(x³ + 10)
Taking (x³ + 10) common,
= (x³ + 10)(x + 7)
Therefore, the factors of the given quartic equation is found as: (x³ + 10)(x + 7).
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A.Are the expressions 3(m2) + 2(m2) and 5(m2) equivalent expressions?B.in two or more complete sentences justify ur answer to A
Yes, the given expressions i.e., 3m^2+2m^2 and 5m^2 are equivalent expression.
An expression is defined as a combination of various terms or numbers that are combined by using mathematical operations in addition, subtraction, multiplication, and division.
Equivalent expressions are expressions that have similar value or worth but do not look the same. When considering if the expressions given are equivalent, at least two expressions are must.
A) Yes, by considering the above definitions we can conclude that 3m^2+2m^2 and 5m^2 are equivalent expressions.
B) Given, 3m^2+2m^2 and 5m^2
Now, solve 3m^2+2m^2 we simply get the value which is similar to other expression given to us in the question i.e., 5m^2.
Hence, 3m^2+2m^2 and 5m^2 are similar or equivalent expression.
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Simplify this expression.
2d + 1 + d-5
[?]d + []
Answer:
3d-4
Step-by-step Explanation:
2d+1+d-5 Combine like terms 2d and d together which is 3d. That leaves you with 1-5 which is -4. so then you end up with 3d-4 as your answer.
SOMEONE PLEASE HELP ME I REALLY NEED HELP ON THIS
The volume of the square frustrum, the volume of the pyramid and the volume of the obelisc are 1018791.667 ft³, 22019.625 ft³ and 1040811.292 ft³, respectively.
How to determine the volume of the Washington Monument
In this problem we must determine the volume of a obelisc, which is equal to the sum of the volumes of a square frustrum and a pyramid with a square base. First, sum the volumes of the frustrum and the pyramid:
V' = (1 / 3) · 500 · (55² + 55 · 34.5 + 34.5²)
V' = 1018791.667 ft³
V'' = (1 / 3) · (34.5)² · 55.5
V'' = 22019.625 ft³
Second, calculate the volume of the obelisc:
V = V' + V''
V = 1018791.667 ft³ + 22019.625 ft³
V = 1040811.292 ft³
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Two hikers are 11 miles apart and walking toward eachother. they meet in 2 hours. find the rate if one hiker walkers 0.3 mph faster than the other.
If two hikers are 11 miles apart and walking towards each other and they meet in 2 hours, then if one hiker walks 0.3mph faster than the other, then the rate at which the slow hiker and fast hiker walk towards each other is equal to 2.6 and 2.9 mph respectively.
Consider, the speed of the slow hiker = s
Then, the speed of the fast hiker = s + 0.3
The distance covered by both the hikers in 1 hour = 2s + 0.3 miles
The distance covered by both the hikers in 2 hours = 2(2s + 0.3) = 4s + 0.6 miles
We can find the value of s by forming an algebraic expression as follows,
4s + 0.6 = 11
4s = 11 - 0.6
4s = 10.4
s = 10.4 / 4
s = 2.6
Speed of the slow hiker = s = 2.6 mph
Speed of the fast hiker = s + 0.3 = 2.6 + 0.3 = 2.9 mph
Hence, the rate at which the slow hiker and the fast hiker walk toward each other is equal to 2.6 and 2.9 mph respectively.
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Is Figure B a scale copy of figure A?
Yes, figure B is a scale copy of figure A.
As per the question statement and its reference diagram attached thereby, we are provided with two geometrical figures of same shape but different sizes.
We are required to determine if figure B is a scale copy of figure A or not.
To solve this question, we need to carefully compare the lengths of the corresponding sides from both the figures.
We can clearly see that, the dimension of every side of figure B is twice that of the corresponding side of Figure A, i.e.,
[tex](1*2)=2\\(2*2)=4\\(3*2)=6\\(4*2)=8[/tex]
Hence, it is proved that figure B is a scale copy of figure A.
Scale copy: In geometry, a scale copy of a figure is another figure having same shape, but the dimensions of all the sides of the scale copy are equal multiples of the dimensions of the corresponding sides of the original figure.To learn more about Scale Copy, click on the link below.
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Help me solve these please
Answer:
See picture below
Step-by-step explanation:
Answer:
7. 2^-5= 1/2^5= 1/32
8. (4/5)^-3= (5/4)^3=125/64
9. 8^-4/8^-7=8^-4+(-7)=8^11=216
10. (1/3)^-2 x (1/3)^2=(1/3)^-2+2=(1/3)^0=1
solids that can made by equilateral triangle
Answer:
the tetrahedron, octahedron and icosahedron
Answer:
tetrahedron, octahedron, icosahedron
ill in the missing numbers along the sides of the triangle so that it contains each of the numbers from through exactly once. furthermore, each side of the triangle should contain four numbers whose sum is .
Each side of the triangle should contain four numbers whose sum is 28.
3+5+9+11=28
3+10+8+7=28
11+6+9+7=28
The pain of numbers that can be used for A and B is [5,9] The pain of numbers that can be used for C and D is [10,8] and the pain of numbers that can be used for E and f is [6,4].
What are the 3 sides of a triangle?The hypotenuse of a right triangle is its longest side; its "opposite" side is the one that faces the angle in question; and its "adjacent" side is the one that faces it. We use special terminology to define the sides of right triangles.
We use special terminology to define the sides of right triangles.
The side opposite the right angle is always the hypotenuse of a right triangle. It is the longest side in a right triangle.
The opposing and neighboring sides are the other two sides. The labels on these sides relate to an angle.
One side is across from another at a particular angle.
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The length of a rectangle is twice the width. The area of the rectangle is 90 square units. Note that you can divide the rectangle into squares. A. Which irrational number represents the length of each side of the square? B. Estimate the length and width of the triangle
Answer: A. [tex]3\sqrt{5}[/tex]
B. l=[tex]6\sqrt{5}[/tex], w=[tex]3\sqrt{5}[/tex]
Step-by-step explanation:
A. A=l*w
l=2w
A=2w*w
90=2w*w
w*w=45
w=[tex]\sqrt{45}[/tex]
w=[tex]\sqrt{9*5}[/tex]
w=[tex]3\sqrt{5}[/tex] ==> Square length and the rectangle width
B. 90=l*w
90=l*[tex]3\sqrt{5}[/tex]
30=l[tex]\sqrt{5}[/tex]
l=[tex]\frac{30}{\sqrt{5} }[/tex]
l=[tex]\frac{30\sqrt{5} }{5}[/tex]
l=[tex]6\sqrt{5}[/tex], w=[tex]3\sqrt{5}[/tex]
Write a program that promptsthe user for their quarterly water bill for the last four quarters. the program should find and output their average monthly water bill. if the average bill exceeds $75, the output should include a message indicating that too much water is being used. if the average bill is at least $25 but no more than $75, the output should indicate that a typical amount of water is being used. finally, if the average bill is less than $25, the output should contain a message praising the user for conserving water. also show input validation for the first entry. you may have to apply all the programming constructs that you have learned so far, as needed, to complete this exercise. (decisions, loops, input validation). sample run 1: please input your water bill for quarter 1: 300 please input your water bill for quarter 2: 200 please input your water bill for quarter 3: 225 please input your water bill for quarter 4: 275 your average monthly bill is $83.33. you are using excessive amounts of water
calculate the total of the bills= 300+200+225+275 =1000
the average monthly bill= 1000/12 = 83.333
Total =0
for i in range(4):
bill = float(input("Enter bill for quarter " + str (i+1) + ": "))
total += bill
average = total / (4 * 3)
if average > 75:
print("Average monthly bill is $" + str(average) + ". Too much water is being used")
if 25 <= average < 75:
print("Average monthly bill is $" + str(average) + ". A typical amount of water is being used")
if average < 25:
print("Average monthly bill is $" + str(average) + ". Thank you for conserving water")
calculate the total of the bills= 300+200+225+275 =1000
the average monthly bill= 1000/12 = 83.333
Total =0
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Find the values of a and b
Answer:
a=15, b=14
Step-by-step explanation:
We know all angles must add up to 360, so lets add all angles and set them equal to 360.
[tex]7a+33+3b+10a-12+6b-42=360\\17a+9b-21=360[/tex]
We also know that any angle opposite another is equal. Lets take 6b-42 and 3b and set them equal.
[tex]3b=6b-42[/tex]
Now solve for b in both equations
[tex]3b=6b-42\\-3b=-42\\b=14[/tex]
[tex]17a+9b-21=360\\9b-21=360-17a\\9b=381-17a\\b=\frac{381-17a}{9}[/tex]
Now we set the two equations equal to each other to solve for a:
[tex]14=\frac{381-17a}{9} \\126=381-17a\\-255=-17a\\15=a[/tex]
This gives a=15, b=14.
4x+3y ≥9
-3x+7y< 14
point in the solution set (x,y)
Lamar spent $34 on fruit at the grocery store. He spent a total of $40 at the store. What percentage of the total did he spend on fruit?
Answer:
85%
Step-by-step explanation:
Answer:
85%
Step-by-step explanation:
85% because, $40 X .85 = $34 which means, $34 is 85% of $40
10. The sum of the angle measures in a triangle is 180. In triangle ABC,
the measure of angle A=4x+34, the measure of angle B=7x-10, and the
measure of angle C-5x+12. Find the measure of angle A.
Answer:
Step-by-step explanation:
Angles in a triangle add up to 180 degrees.
Therefore A+B+C = 180
This means 4x+34+7x-10+5x+12 = 180
Simplies down to 16x+36 = 180
Rearrange to have 16x = 144
Divide by 16 on both side to get x = 9
Substitue the value of x back into the equation of A
A = 4(9)+34 = 70 degrees
estimation 31.5 and (-1.5)
Answer:
(30.00)
Step-by-step explanation:
(30.00) is the correct answer for your question/ statement you have asked. the answer is (30.00) again.
HELP PLS!!!!!!!!!!!!!!!!
Answer:
4x^3 (3)_/x + 10x^3 (3)_/x
Step-by-step explanation:
First lets solve the first term
When you multiply exponents you add them, so x^10 can be split into:
x^3 * x^3 * x^3 * x^1
We can then take it out.
4x^3 (3)_/x
Then for the other part we can also factor it.
2*2*2 is 8 so we can take that out and multiply it by 5 =10
You can keep x in there since you can factor it into smaller pieces.
The final answer you get when you add all of it together is :
4x^3 (3)_/x + 10x^3 (3)_/x
16 ones 24 tens 1 hundred
The standard form for given values is 12416.
What are form of numbers?A number has two form . First is standard form and another is expended form of numbers.
What is standard form?It is a form in which we write number as a whole without describing the places for the numbers.
The numbers such as 456, 17817, 9009, 32 etc all are the standard form of the numbers.
What is Expended form?In the case of expended form we generally write number with its describe places of value or with the plus (+) symbol between them.
For example, 16 ones 24 tens 1 hundred is the expended form of numbers.
In the given question the form given is :
16 ones 24 tens 1 hundred
so, we have to place 16 at ones place , 24 at tens place and 1 at hunderedth place value .
Therefore, the standard form becomes : 12416.
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The complete question is:
Convert to standard form
16 ones 24 tens 1 hundred
Calculate the volume of this regular solid. a cylinder labeled b at the top, 13 centimeters high with a radius of 4 centimeters. what is the volume of the cylinder? use the button on your calculator to complete this problem. round at the end to the nearest hundredth.
Answer:
[tex]volume = 653.71 {cm}^{3} [/tex]
Step-by-step explanation:
Volume = πr^2h
=
[tex] \frac{22}{7} \times {4}^{2} \times 13 \: c {m}^{3} [/tex]
= 22*16*13/7 cm^3
= 653.714cm^3
Rounding off = 653.71 cm^3
Answer:
653.45
Step-by-step explanation:
it told me the answer
Question: Can it be simplified? If NO, explain why. If YES, simplify completely or rewrite as a simplified radical expression. SHOW ALL WORK.
Expression: (x^4y)^2/3
Please help me with this!
Answer:
Step-by-step explanation:
1) Use multiplication distributive property [tex](xy)^a=x^ay^a[/tex]
= [tex]\frac{(x^4)^2y^2}{3}[/tex]
2) Use Power rule [tex](x^a)^b = x^{ab}[/tex]
= [tex]\frac{x^8y^2}{3}[/tex]
Question 2(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Approximate -8+√√20 to the nearest tenth.
O 4.5
03.5
O-35
O-4.5
The approximation of -8 plus the square root of 20 is given by:
-3.5.
How a number is rounded to the nearest tenth?To round a number to the nearest tenth, it will have only one decimal digit, and the rule is as follows:
If the second decimal digit is less than 5, the first decimal digit remains constant.If the second decimal digit is of 5 or greater, one is added to the first decimal digit.The square root of 20 is given by:
sqrt(20) = 4.47.
7 > 5, hence, rounded to the nearest tenth:
sqrt(20) = 4.5.
Then:
-8 + 4.5 = -3.5.
Which is the approximation.
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which is the slope of the line y=-3x+2
Answer:
3
Step-by-step explanation:
y=mx+b
m is the slope
PLEASE HELP!!! Julie is helping her mom carry groceries. The bag she is carrying has everything they need to make spaghetti for dinner tonight. It has 450 grams of spaghetti, 750 grams of tomato sauce, and 0.5 kilograms of ground beef. How many kilograms does her bag of groceries weigh?
Answer:
1.7 kilograms
Step-by-step explanation:
750 + 450 + 0.5kg ( 1kg = 1000) so 0.5 would be 500g.
=1,700g (1.7kg) :)
Hi could someone help my sister is asking me this question but I never learned this
Answer:
12 cm
Step-by-step explanation:
Volume of total shape = Volume of big rectangle - Volume of small rectangle
Volume of big rectangle = L×B×H
Volume of big rectangle = 10 cm×3 cm×2 cm
Volume of big rectangle = 60 cm
Volume of small rectangle = l×b×h
l = 10 cm - 6 cm = 4cm
Volume of small rectangle = 4 cm×3 cm×4 cm
Volume of small rectangle = 48cm³
Volume of total shape = 60cm³ - 48cm³
Volume of total shape = 12cm³
Which is a correct representation of x + 5 using algebra tiles?
The correct representation of x + 5 using algebra tiles is one green rectangle box and one small yellow box.
What are algebra tiles?Algebra tiles are the tiles or square or rectangular boxes which are use to represent the polynomial expression whether of linear , monomial or quadratic.
There are three types of algebra tiles :
Small squares : Small squares are generally use to represent a constant value which is a letter or any symbol. Rectangles : Rectangles are use to represent a monomial or linear expression such as x ,y , z etc.Large squares : They are use to represent quadratic expressions such as x^2 , y^2 , z^2 etc.All of these tiles has different color to represent positive and negative value :
Square Type Positive color Negative Color
Small squares Yellow Red
Rectangles Green Red
Large Squares Blue Red
For the given question, Expression is x + 5
that means, there is one Green rectangle and one Yellow small square.
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WILL CHOOSE THE BRAINLIEST ANSWER!!!
Answer:
A. 25°
Step-by-step explanation:
In triangle ABC:
<A + <B + <C = 180°
=> 45° + (2x - 15)° + 4x° = 180°
=> 6x° + 30° = 180°
=> 6x° = 150°
=> x° = 25°
Choose A.25°
Answer:
A. 25 degrees
x = 20
2(20) - 15 = 25 degrees
3. A local charity wants to purchase a classic 1975 Chevy Monte Carlo for use as a prize in a fundraiser.
They find the following eight prices in the paper
$18,000
$16,000
3090
$18,888
b. What is the range?
a. What is the best measure of central tendency to use to get a reasonable estimate for
the cost of the car? Explain.
Can someone please help mee (20 points + brainliest!!!)
Find the highest common factor (HCF) of 32, 48 and 72
highest common factor (HCF) of 32, 48 and 72= 8
HCF - Highest Common Factor
The Highest Common Factor (HCF) of two numbers is the highest possible number that divides both the numbers completely. The Highest Common Factor (HCF) is also called the Greatest Common Divisor (GCD).
There are many ways to find the HCF of two numbers. One of the quickest ways to find the HCF of two or more numbers is by using the prime factorization method. Explore the world of HCF by going through its various aspects and properties. Find answers to questions like what is the highest common factor for a group of numbers, easy ways to calculate HCF, HCF by division method, its relation with LCM, and discover more interesting facts around them.
HCF by Prime Factorization
In order to find the HCF of numbers by the prime factorization method, we use the following steps. Let us understand this method using the example given below.
Step 1: Find the common prime factors of the given numbers.
Step 2: Then, multiply these common prime factors to obtain the HCF of those numbers.
highest common factor (HCF) of 32, 48 and 72
32 = 2x2x2x2x2
48= 2x2x2x2x3
72= 2x2x2x3x3
highest common factor (HCF) of 32, 48 and 72 = 2x2x2= 8
highest common factor (HCF) of 32, 48 and 72= 8
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x
-3
-2
-1
0
Intro
2
f(x)
-16
-1
2
-1
-1
Analyze the table of values for the continuous function,
f(x), to complete the statements.
A local maximum occurs over the interval
A local minimum occurs over the interval
4 of 10
Done
A local maximum occurs over the interval (-2,0).
A local minimum occurs over the interval (0,2).
If the graph of the function increases first and decreases after a particular point, then the function acquires a local maximum at that point.
Similarly, if the graph of the function decreases first and then increases after a point, then the function acquires a local minimum at that point.
Here the given x and f(x) values for the continuous function f(x) are:
x f(x)
-3 -16
-2 -1
-1 2
0 -1
1 -4
2 -1
As we can see by examining the table values, the function is increasing in the intervals (-3,2) and (-2,-1).The function acquires value f(x) = 2 at x = -1 and then it starts to decrease. So this value f(x) = 2 is the local maximum and is acquired on the interval (-2,0).
The graph is then decreasing from x = -1 to x = 1. The function has the value f(x) = -4 at x = 1. Then the function starts to increase from x = 1 to x = 2. So f(x) = -4 is the local minimum of the function and is acquired on the interval (0,2).
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A random sample of 92 sophomores are asked whether they plan to attend Homecoming. Of these, 51 sophomores said they will attend. What is the margin of error at 90% confidence and its interpretation?
The margin of error at 90% confidence and its interpretation is 0.085. 90% confident that the true proportion of sophomores who will attend Homecoming is within 0.085 of the sample proportion.
The margin of error is defined as a term used in statistics to find the confidence interval. It is denoted by E.
Given, random sample of 92 .
The formula for margin of error is;
[tex]E = z(\sqrt{(p(1 - p)/n} )[/tex]
The parameters are given as;
Sample size; n = 92
Sample of success; x = 51
Sample proportion:
p = 51/92
= 0.554
z at 90% CL = 1.645
Thus;
[tex]E = 1.645(\sqrt{(0.554(1 - 0.554)/92} )[/tex]
[tex]E = 0.085[/tex]
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