To solve the given polynomial addition and subtraction question, combine like terms. The z4 terms combined are -7z4 and the z2 terms are 5z2, resulting in the simplified expression 5z2 - 7z4.
Explanation:To add or subtract the polynomials 7z2 − 2z4 − 2z2 − 5z4, you'll want to combine like terms. Like terms are terms that have the same variables raised to the same power.
Here, z2 and z4 are like terms, so you can combine them separately.
Starting with the z4 terms:
-2z4 and -5z4 combine to give you -7z4. They both have the same variable z raised to the fourth power, so you just add the coefficients, keeping the exponent the same.
Then, combine the z2 terms:
7z2 and -2z2 combine to give you 5z2.
Similarly, these terms have the same variable z raised to the second power.
Now, putting it all together, you get:
5z2 − 7z4
This is the simplified version of the polynomial after combining like terms.
I’m too sure how to do this?
Answer:
x= -12/5 y+2
y=3/2y+-35/2x=
Step-by-step explanation:
The center of a circle is located at (3, -4). The radius of the circle is 6.
What is the equation of the circle in general form?
x2 + y2 + 6x − 8y − 11 = 0
x2 + y2 − 6x + 8y − 11 = 0
x2 + y2 + 6x − 8y + 19 = 0
Answer:
B
Step-by-step explanation:
The equation of a circle in standard form is [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h, k) is the center and r is the radius. The general form is simply the expanded form of the standard. Let's first write the standard form.
Here, the center is (3, -4) and the radius is r = 6, so:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](x-3)^2+(y+4)^2=6^2[/tex]
Now expand:
x² - 6x + 9 + y² + 8y + 16 = 36
x² + y² - 6x + 8y - 11 = 0
The answer is B.
Answer:
x² + y² - 6x + 8y - 11 = 0
Step-by-step explanation:
Equation of a circle:
(x - h)² + (y - k)² = r²
(x - 3)² + (y + 4)² = 6²
x² - 6x + 9 + y² + 8y + 16 = 36
x² + y² - 6x + 8y - 11 = 0
Sam cleaned of his house in 50 minutes. How many hours will it take him to clean his entire house?
Answer:
20min
Step-by-step explanation:
Y varies inversely with x, when y is 48 when x is 1/3 .which equation represents this situation?
a) Y=16/x
b) Y=16x
c) Y=144x
d) Y= 144/x
Answer:
A
Step-by-step explanation:
Given that y varies inversely with x then the equation relating them is
y = [tex]\frac{k}{x}[/tex]
To find k use the condition y = 48 when x = [tex]\frac{1}{3}[/tex], thus
k = yx = 48 × [tex]\frac{1}{3}[/tex] = 16
y = [tex]\frac{16}{x}[/tex] ← equation of variation
what is first even number that is a multiple of 5 and 7?
Answer:
I think its 35
Step-by-step explanation:
Answer:
70
Step-by-step explanation:
The least common factor of 5 and 7 is 35. We multiply it by two because it is not even.
Simplifty (x - 4)(x +8)
Answer: x² + 4x - 32
Step-by-step explanation: So to multiply these two binomials together, let's use the F.O.I.L. method.
Remember, F.O.I.L. stands for First, Outter, Inner, Last.
This is because we start with the product of the first terms which is x², then we add the product of the outer terms which is 8x, then we add the middle terms which is -4x, and then we add the product of the last terms which is -32.
So we have x² + 8x + -4x + -32.
Combining the like terms 8x + -4x, our final answer is x² + 4x - 32.
which type of event is thought to have caused most species on earth to have become extinct?
A) volcanic eruptions
B) human activity
C) air pollution
D) climate change
Answer:
D because climate change can kill people
Answer:
I agree with lazarbeam profile man
Step-by-step explanation:
reeeeeeeeeeEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A triangle has a height of 22 and a base of 10. What is the area (in square units)?
options:
a)110
b)55
c)168
d)220
Answer:
110
Step-by-step explanation:
solve for x.
A. x = √55
B. x = √73
C. x = 4√7
D. x = √130
Answer:
C. x = 4√7
Step-by-step explanation:
This is a right triangle
The hypotenuse is 3+8 (the radius is 3 and the exterior length is 8)
We can use the Pythagorean theorem
a^2 +b^2 = c^2
3^2 + x^2 = 11^2
9+x^2 = 121
Subtract 9 from each side
9-9 + x^2 = 121-9
x^2 = 112
Take the square root of each side
sqrt(x^2) = sqrt(112)
x = sqrt(16*7)
x = 4 sqrt(7)
What is bigger 0.2 or 0.125
Answer:
0.2 is bigger than 0.125.
please help its math
Let the length of the radius = r feet.
Diameter = 2r = 2 x 6.8 = 13.6 feet
Circumference = 2[tex]\pi[/tex]r = 2 x 3.14 x 6.8 = 42.704 feet = approx. 42.7 feet
The diameter is 13.60 feet.
The circumstance is approximately 42.70 feet.
Look at the attached picture
Hope it will help you
alice is playing checkers against a computer and has won 8 games out of the 12 she’s played so far
I do not know what kind of answer you may want but here is a few you might be asking for
(1). Every 12 games Alice wins 8 games and looses 4. ( 8/12 )
(2). Alice wins 2/3 games against a computer. ( 8/12 )
(3). Alice wins 66% of games she plays against a computer.
There you go.
Alice's win ratio for playing checkers against a computer is 8 wins out of 12 games, which simplifies to 2/3.
Alice has played 12 checker games against a computer and has won 8 of them. To understand her win ratio, we simply divide the number of games won by the total number of games played. This gives us a ratio or fraction of 8/12, which can also be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4, resulting in 2/3. Therefore, Alice has a winning ratio of 2 wins for every 3 games played. Understanding win ratios is an essential part of probability and statistics, a key area within mathematics dealing with the analysis of numerical data.
A circle with area \blue{9\pi}9πstart color #6495ed, 9, pi, end color #6495ed has a sector with a central angle of \purple{60^\circ}60 ∘ start color #9d38bd, 60, degrees, end color #9d38bd. What is the area of the sector?
Answer:
The area of the sector is 3pi/2
Step-by-step explanation:
A sector is that part of a circle bounded by 2 radii and an arc
The circle has an area of 9 pi with a central angle of 60 degrees.
Now the area of the sector is pretty much straight forward to calculate. Since it is a circle, the total angle we have is 360.
Now the sector subtends an angle of 60 degrees at the centre. What this means is that the sector is exactly 1/6 of the circle. meaning that cutting the circle into 6 slices will give the sector.
Thus, the area of the sector is one-sixth the area of the circle.
The area of the sector is thus 1/6 * 9pi = 9pi/6 = 3pi/2 or 3/2 pi
2. If one angle of a parallelogram is 70°, find
the degrees in the remaining 3 angles.
Answer:
The remaining three angles would be 70°, 110°, and 110°.
Step-by-step explanation:
A parallelogram has a measurement of 360° with two pairs of congruent opposite angles/sides.
Work out the surface area of this solid prism.
The surface area of the solid rectangular prism is 408 square meters.
To find the surface area of a solid rectangular prism, you can use the formula:
Surface Area = 2lw + 2lh + 2wh
Where:
l = length
w = width
h = height
In your case, the dimensions of the prism are:
Length (l) = 9 meters
Width (w) = 10 meters
Height (h) = 6 meters
Now, plug these values into the formula:
Surface Area = 2(9m)(10m) + 2(9m)(6m) + 2(10m)(6m)
Surface Area = 180m^2 + 108m^2 + 120m^2
Now, add these areas together:
Surface Area = 180m^2 + 108m^2 + 120m^2 = 408m^2
So, the surface area of the solid rectangular prism is 408 square meters.
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Gwen has a £5 note and a £2 coin. A litre of cola costs £1.25. Gwen buys as many litre bottles of cola as she can. How much money will she have left over?
Gwen can buy 5 bottles of cola with her £7 and will have £0.75 left over.
Explanation:Gwen has in total £7 (£5 note + £2 coin). A litre of cola costs £1.25. To find out how many bottles of cola Gwen can buy, we need to divide the total amount Gwen has by the cost of one bottle of cola.
Divide the total amount of money (£7) by the cost of one litre of cola (£1.25).£7 ÷ £1.25 = 5.6. Gwen can buy 5 bottles because she cannot buy a fraction of a bottle.Multiply the number of bottles she can buy (5) by the cost per bottle (£1.25) to find out the total cost. 5 × £1.25 = £6.25.Subtract the total cost of the cola (£6.25) from the total amount of money Gwen has (£7). £7 - £6.25 = £0.75.
Therefore, Gwen will have £0.75 left over after buying as many bottles of cola as she can.
if y varies directly as x and y = 34 when x = 8, determine an equation to represent this relation.
Answer:
y = 4.25x
Step-by-step explanation:
Given that y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 34 when x = 8, thus
34 = 8k ( divide both sides by 8 )
k = [tex]\frac{34}{8}[/tex] = 4.25
y = 4.25x ← equation of variation
Find the volume. *
30 ft
.
24 ft
Volume =
steps to solve -3x-2=13
Answer:
X=-5
Step-by-step explanation:
1.) Add 2 to 13, then you have -3x=15
2.) Divide 15 by -3 to get the solution. x=-5
Sample response: Start by calculating the volume of the original prism. The area of the base, B, is 4(6) = 24 m2. Multiply that by the height to get the volume: 24(10) = 240 m3. Now, if you double all of the dimensions, you would have a rectangular prism with a base that is 8 m by 12 m and a height of 20 m. The area of the base, B, is 8(12) = 96 m2. Multiply that by the height to get the volume: 96(20) = 1,920 m3. To compare, look at the ratio of the original prism to the new prism: 96/1,920 = 1/8. The volume increases by 8 times the original volume.
Check all that you included in your response.
Find the original volume. The area of the base, B, is 4(6) = 24 m2. Multiply that by the height to get the volume: 24(10) = 240 m3.
If you double all of the dimensions, you would have a rectangular prism with a base that is 8 m by 12 m and a height of 20 m.
Find the new volume. The area of the base, B, is 8(12) = 96 m2. Multiply that by the height to get the volume: 96(20) = 1,920 m3.
The volume increases by 8 times the original volume.
Answer:
Step-by-step explanation:
Antonio was visiting three cities that lie on a coordinate grid at A(4, 5), B(-1, 3) and C(-3, -4). If he visited the cities and ended up where he started, how many miles did he travel?
Answer:
24.065 miles
Step-by-step explanation:
Antonio visited three cities on the coordinate grid at A(4, 5), B(-1, 3) and C(-3, -4), he visited the cities and ended up where he started. That means he moved from point A to B to C and back to A.
The distance (d) between two points (x₁, y₁) and (x₂, y₂) can be given as:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore distance between AB = [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(-1-4)^2+(3-5)^2}=\sqrt{25+4}=5.385[/tex]
distance between BC = [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(-3-(-1))^2+(-4-3)^2}=\sqrt{4+49}=7.28[/tex]
distance between CA = [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(4-(-3))^2+(5-(-4))^2}=\sqrt{49+81}=11.4[/tex]
The total distance = AB + BC + AC = 5.385 + 7.28 + 11.4 = 24.065 miles
Find (2x^2 + 2) + (x^2-4) – (3x^2 + 1)
Step-by-step explanation:
hope this is right I got this answer on one my fav website tiger
Answer:
[tex] - 3[/tex]
Step-by-step explanation:
[tex]2 {x}^{2} + 2 + ( {x}^{2} - 4) - (3 {x}^{2} + 1) \\ 2 {x}^{2} + 2 + {x}^{2} - 4 - 3 {x}^{2} - 1 \\ 2 {x}^{2} + {x}^{2} - 3 {x}^{2} + 2 - 4 - 1 \\ = - 3[/tex]
Para iniciar un negocio, una pareja pide $5.500.000 para comprar equipo y suministros. Si el préstamo tiene una tasa de 14% de interés. ¿Cuánto deben pagar al final de un período de 90 días?
Answer:
They will have to pay $5,692,500 in 90 days.
Deben pagar $5,692,500 pagar al final de un período de 90 días.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time, in years..
After t years, the total amount of money is:
[tex]T = E + P[/tex].
In this question:
[tex]P = 5500000, I = 0.14[/tex]
3 months is 3/12 = 1/4 = 0.25 of an year. So [tex]t = 0.25[/tex]
Then the interest accrued is:
[tex]E = P*I*t = 5500000*0.14*0.25 = 192500[/tex]
What they will have to pay:
[tex]T = 192500 + 5500000 = 5692500[/tex]
They will have to pay $5,692,500 in 90 days.
Deben pagar $5,692,500 pagar al final de un período de 90 días.
What is the answer for 4t≤13
Step-by-step explanation:
4t < 13
t < 13/4
I think this should be the answer
Answer: T<13/4
Step-by-step explanation: See below
can u round this number?
2.29885057471
Answer:
no
Step-by-step explanation:
you can round it to 2.3 but depending on what place you are asked to round to it is still just 2
Find the missing side. Round to the nearest tenth.
A) 25.7
B) 15.5
C) 12.6
D) 31.8
Answer:
i think 40
Step-by-step explanation:
Answer:
C. 12.6
Step-by-step explanation:
That is the answer when correctly put into a calculator.
In a race in which eleven automobiles are entered and there are no ties, in how many ways can the first three finishers come in?
Answer:
990 ways
Step-by-step explanation:
The total number of automobiles we have is 11.
Now, what this means is that for the first position , we shall be selecting 1 out of 11 automobiles, this can be done in 11 ways( 11C1 = 11!/(11-1)!1! = 11!/10!1! = 11 ways)
For the second position, since we have the first position already, the number of ways we can select the second position is selecting 1 out of available 10 and that can be done in 10 ways(10C1 ways = 10!9!1! = 10 ways)
For the third position, we have 9 automobiles and we want to select 1, this can be done in 9 ways(9C1 ways = 9!/8!1! = 9 ways)
Thus, the total number of ways the first three finishers come in = 11 * 10 * 9 = 990 ways
find the surface area of the square pyramid if the slant height is 13mm and the base length is 11mm
a) 264mm squared
b) 286mm squared
c) 335.5mm squared
d) 407mm squared
To find the surface area of a square pyramid, you need to calculate the lateral area and the area of the base. The lateral area can be found using the formula (1/2) × perimeter of the base × slant height. The base area is equal to the side length squared. To find the total surface area, you add the lateral area and the base area.
Explanation:Surface Area of Square PyramidTo find the surface area of a square pyramid, we need to calculate the lateral area and the area of the base.
Lateral Area
The lateral area of a square pyramid can be found using the formula:
Lateral Area = (1/2) × perimeter of the base × slant height
In this case, the slant height is given as 13mm and the base length is given as 11mm, so we have:
Lateral Area = (1/2) × 4 × 11mm × 13mm = 286mm2
Base Area
The base of the square pyramid is a square with side length 11mm. Therefore, the area of the base is:
Base Area = side length × side length = 11mm × 11mm = 121mm2
Total Surface Area
To find the total surface area, we add the lateral area and the base area:
Total Surface Area = Lateral Area + Base Area = 286mm2 + 121mm2 = 407mm2
Therefore, the surface area of the square pyramid is 407mm2.
Which of the following equations matches the graph above?
A.
y=2x-1
B.
y=2/5x-1
C.
y=2/5x+1
D.
y=5x-1
it will be A. y=2x-1
hope this helps
Write −0.258 as a fraction in simplest form
Answer:
57/200
Step-by-step explanation:
285/1000 The fraction is not reduced to lowest terms. We can reduce this fraction to lowest
terms by dividing both the numerator and denominator by 5.
Why divide by 5? 5 is the Greatest Common Divisor (GCD)
or Greatest Common Factor (GCF) of the numbers 285 and 1000.
So, this fraction reduced to lowest terms is
57/200
So your final answer is: 0.285 can be written as the fraction 57/200
−0.258 written as a fraction in its simplest form is [tex]-\frac{129}{500}[/tex]
To write a given decimal as a fraction in its simplest form,
We will first express the decimal as a fraction and then reduce it to its lowest form.
The given decimal is −0.258
−0.258 written in fraction is [tex]-\frac{258}{1000}[/tex]
Now, we will reduce [tex]-\frac{258}{1000}[/tex] to its lowest form
First, we will divide both the numerator and denominator by 2 (Since 2 is a common factor)
We get
[tex]-\frac{258}{1000} = -\frac{258 \div 2}{1000 \div 2} = -\frac{129}{500}[/tex]
Since the fraction cannot be reduced further, then −0.258 as a fraction in its simplest form is [tex]-\frac{129}{500}[/tex]
Hence, −0.258 written as a fraction in its simplest form is [tex]-\frac{129}{500}[/tex]
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