Answer:
8
Step-by-step explanation:
2+6+8+12+12 is 40 divide that by 5 and it gives you 8
x = 2t
y = t + 5, -2 ≤ t ≤ 3
Can you please graph this
Answer:
See attachment
Step-by-step explanation:
The given parametric equations are;
[tex]x=2t[/tex] and [tex]y=t+5[/tex], [tex]-2\le t\le 3[/tex].
We can graph this by plotting some few points within the given range or eliminate the parameter to identify the type of curve.
Plotting points;
When [tex]t=-2[/tex],
[tex]x=2(-2)=4[/tex] and [tex]y=-2+5=3[/tex]
This gives the point (-4,3).
When [tex]t=0[/tex]
[tex]x=2(0)=0[/tex] and [tex]y=0+5=5[/tex]
This gives the point (0,5).
When [tex]t=3[/tex]
[tex]x=2(3)=6[/tex] and [tex]y=3+5=8[/tex]
This gives the point (6,8).
We plot these points and draw a straight line through them.
Eliminating the parameter.
[tex]x=2t[/tex]
[tex]y=t+5[/tex]
Make t the subject in the second equation;
[tex]t=y-5[/tex]
Substitute into the first equation;
[tex]x=2(y-5)[/tex]
This implies that;
[tex]x=2y-10[/tex]
[tex]y=\frac{1}{2}x+5[/tex]
This is an equation of a straight line with slope [tex]\frac{1}{2}[/tex] and y-intercept 5 on the interval
[tex]-4\le x \le 6[/tex]
Answer:
The answer is in attachment
Step-by-step explanation:
First step finde a function t(x) ⇒ t=x/2;
Now we need to finde the limits of that function:
if t=-2 ⇒ x=-4 and t=3 ⇒ x=6. That means -4≤x≤6
Now replace on y(t) ⇒ y(x)= x/2+5, 4≤x≤6
The function table shows the rule y = 3x + 5. Which number correctly completes the table?
Answer:
the answer is 3
Step-by-step explanation:
11-8=3
17-11=6
6/2=3
Answer:the answer is 14 just took the test
Step-by-step explanation:
Graph this line using the slope and y
-intercept:
y
=
-
1
7
x
+
8
Click to select points on the graph.
Answer:
The expression is
y = -17*x + 8
Which is already in the slope intercept form
y = m*x + b
Where m is the slope and b is the y-intercept.
The slope
m = -17
The intercept
b = 8
Please see attached picture for graph
Find the product of z1 and z2, where z1 = 2(cos 70° + i sin 70°) and z2 = 4(cos 200° + i sin 200°)
Answer:
-8i
Step-by-step explanation:
To multiply numbers is polar form
z1 = r1 ( cos theta 1 + i sin theta 1)
z2 = r2 ( cos theta 2 + i sin theta 2)
z1*z2 = r1*r2 (cos (theta1+theta2) + i sin (theta1+theta2)
z1 = 2(cos 70° + i sin 70°)
z2 = 4(cos 200+ i sin 200)
z1z2 = 2*4 (cos (70+200) + i sin (70+200)
z1z2 = 8 (cos(270) + i sin (270))
= 8 (0 + i (-1))
=-8i
The product of z1 and z2, where z1 = 2(cos 70° + i sin 70°) and z2 = 4(cos 200° + i sin 200°), is found by multiplying the moduli and adding the angles, resulting in -8i.
To find the product of z1 and z2, where z1 = 2(cos 70° + i sin 70°) and z2 = 4(cos 200° + i sin 200°), we use the properties of complex numbers in trigonometric form. According to the properties, the product of two complex numbers in this form is given by multiplying their moduli (or absolute values) and adding their angles.
The product is: |z1||z2| e[tex]^{(i(angle1+angle2)),}[/tex] where |z1|, |z2| are the moduli of z1 and z2, and angle1, angle2 are the angles of z1 and z2 respectively.
For z1 and z2, we have:
|z1| = 2Angle1 = 70°|z2| = 4Angle2 = 200°The product is:
|z1||z2| = 2 * 4 = 8
Sum of the angles: angle1 + angle2 = 70° + 200° = 270°
Therefore, z1z2 = 8(cos 270° + i sin 270°), and since cos 270° = 0 and sin 270° = -1, the product simplifies to z1z2 = 8i(-1) = -8i.
what does this number represent
answer is: a number to the third power divided by ten. pls mark brainliest!!
Find the sum of the finite geometric sequence
Answer:
45
Step-by-step explanation:
Use the geometric sum formula for in infinite sum. 20 terms of this basic formula is close enough The 20th term is 8.6 * 10^-10 which means this goes out to a number with 9 zeros after the decimal and before the 8.
Put another way, the tenth number of this series is the only one affected.
When you use a spreadsheet, it seems to know that the answer is 3/2 as the solution to the sum.
Solution.
Sum = a / (1 - r)
a = 1
r = 1/3
Sum = 1 / (1 - 1/3)
Sum = 1 // 2/3
sum = 3/2
Now you can worry about the 30.
30 * sum(1/3)^n = 30* 3/2 = 45
If there is something you want more information on, leave a note.
The sum of a finite geometric sequence can be calculated using the formula S = a1(1 - r^n) / (1 - r), where S is the sum, a1 is the first term, r is the common ratio, and n is the number of terms.
Explanation:The student's question pertains to the summation of a finite geometric sequence. A geometric sequence is a series of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. Considering the information provided doesn't match the exact question, we would educate the student on how to find the sum of a finite geometric sequence using the standard formula for such a sum, which is S = a1(1 - r^n) / (1 - r), where S is the sum of the sequence, a1 is the first term, r is the common ratio, and n is the number of terms.
Unfortunately, specific values were not provided in the question. Therefore, to calculate the sum, we'd need the initial term, the ratio, and the number of terms. This formula is only applicable if the common ratio r is not equal to 1. Essential to note is that if the common ratio is greater than 1, the terms in the sequence increase, and if the ratio is between 0 and 1, the terms decrease.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Solve the given system of equations.
4x-5y=10
-x-8=3y
To solve the system of equations, start by isolating one variable in one equation. Substitute the value of the variable into the other equation, and solve for the remaining variable. The solution to the system of equations is x = 118/17 and y = -42/17.
Explanation:To solve the given system of equations:
4x - 5y = 10
-x - 8 = 3y
Start by isolating one variable in one equation. Let's isolate x in the second equation.Add x to both sides: -x + x - 8 = 3y + x.Simplify: -8 = 3y + x.Rewrite the equation as x = -8 - 3y.Now substitute the value of x in the first equation.Replace x with -8 - 3y: 4(-8 - 3y) - 5y = 10.Distribute: -32 - 12y - 5y = 10.Combine like terms: -32 - 17y = 10.Add 32 to both sides: -17y = 42.Divide by -17: y = -42/17.Substitute the value of y back into x = -8 - 3y to find x.Replace y with -42/17: x = -8 - 3(-42/17).Simplify: x = -8 + 126/17.Find a common denominator for -8 and 126/17, which is 17.Convert -8 into a fraction over 17: -8/17.Add the fractions: x = (-8/17) + (126/17).Simplify: x = (118/17).Therefore, the solution to the system of equations is x = 118/17 and y = -42/17.
Final answer:
The solution to the system is x = -10/7 and y = -22/7.
Explanation:
To solve the given system of equations, 4x-5y=10 and -x-8=3y, we can use the method of substitution or elimination. Let's use the substitution method:
Step 1: Solve one equation for one variable in terms of the other. From the second equation, we can rearrange it to get x in terms of y: x = 3y + 8.
Step 2: Substitute the expression for x in terms of y into the other equation.
Substituting 3y + 8 for x in the first equation gives us 4(3y + 8) - 5y = 10.
Step 3: Simplify and solve for y.
Expanding the equation and solving for y gives us 12y + 32 - 5y = 10.
Combining like terms yields 7y + 32 = 10.
Subtracting 32 from both sides gives us 7y = -22.
Dividing both sides by 7 gives us y = -22/7.
Step 4: Substitute the found value of y back into the equation x = 3y + 8 to solve for x.
Substituting -22/7 for y gives us x = 3(-22/7) + 8.
Simplifying the expression gives us x = -66/7 + 56/7, which equals -10/7.
Therefore, the solution to the system of equations is x = -10/7 and y = -22/7.
Simply the expression given below. x^2+x-2/x^3-x^2+2x-2
Answer:
Step-by-step explanation:
(x-1)(x+2)/x^2(x-1)+2(x-1)
(x-1)(x+2)/(x-1)(x^2+2)
(x+2)/(x^2+2)
Answer:
[tex]\frac{(x+2)}{(x^2+2)}[/tex]
Step-by-step explanation:
[tex]\frac{x^2+x-2}{x^3-x^2+2x-2}[/tex]
To simplify the given expression , factor both numerator and denominator
Numerator : [tex]x^2+x-2[/tex]
Product is -2 and sum is +1. factors are 2 and -1
[tex]x^2+x-2=(x+2)(x-1)[/tex]
Denominator : [tex]x^3-x^2+2x-2[/tex]
Group first two terms and last two terms
Factor out GCF from each term
[tex](x^3-x^2)+(2x-2)[/tex]
[tex]x^2(x-1)+2(x-1)[/tex]
[tex](x^2+2)(x-1)[/tex]
Replace the factors in the given expression
[tex]\frac{(x+2)(x-1)}{(x^2+2)(x-1)}[/tex]
Cancel out x-1 at the top and bottom
[tex]\frac{(x+2)}{(x^2+2)}[/tex]
3v/7=6, then v=
a) 1-2/3
b) 2-4/7
c) 14
d) 42
Answer:
c) 14
Step-by-step explanation:
The given equation is [tex]\frac{3v}{7}=6[/tex].
We need to solve this equation for v, so we multiply both sides of the equation by the multiplicative inverse of [tex]\frac{3}{7}[/tex] which is [tex]\frac{7}{3}[/tex] to obtain;
[tex]\frac{7}{3} \times \frac{3v}{7}=6\times \frac{7}{3}[/tex].
We simplify to obtain;
[tex]v=2\times 7[/tex]
[tex]v=14[/tex]
The correct choice is C.
Answer: option c
Step-by-step explanation:
To solve this problem you must apply the following proccedure:
- Multiply both sides of the equation by 7.
- Divide both sides of the equation by 3.
Therefore, keeping the steps above on mind, you obtain the result shown below:
[tex]\frac{3v}{7}=6\\\\(7)\frac{3v}{7}=6(7)\\\\3v=42\\\\\frac{3v}{3}=\frac{42}{3}\\ v=14[/tex]
The volume of a rectangular prism is (x3 – 3x2 + 5x – 3), and the area of its base is (x2 – 2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?
Answer:
height = (x^3 – 3x^2 + 5x – 3) / (x^2 – 2)
Step-by-step explanation:
We know that the volume of a rectangular prism is the product of its base area and height
Volume_prism = area_base * height
height = Volume_prism / area_base
Volume_prism = (x^3 – 3x^2 + 5x – 3)
area_base = (x^2 – 2)
height = Volume_prism / area_base
height = (x^3 – 3x^2 + 5x – 3) / (x^2 – 2)
Please see attached image
Answer:
The answer is A
Step-by-step explanation:
The way that you get this answer is by divided x2 to x3 and you get x and then you multiply x to x2-2 and you get x3-2x and the you subtract that from x3-3x2+5x-3 and then you repeat that process and the final answer is x-3 + 7x-9/x2-2
A $1508 award is shared equally by 8 people. What is each persons share of the award
Answer:
$188.50
Step-by-step explanation:
i got this answer by dividing $1,508 by 8 and you would get 188.5 which would turn into $188.50 and that is how much each person would get.
I hope this helps.
is 0.64 rational ....
yes, 0.64 is a rational number. it can be expressed as the fractions 64/100, 32/50, 16/25.
Answer:
yes 0.64 is a rational number
Step-by-step explanation:
1) 0.64 = 64/100
2) Divide by 4
64 divided by 4 is 16 (Numerator)
100 divided by 4 is 25 (Denominator)
3) 16/25
It is a rational number because it can be written as a fraction.
Hopes this helps!
What is the answer to number 1
what is the area of this figure enter your answer in the box.
PLEASE HELP ME!?
Answer:
its 18 inchs in diamatr
Step-by-step explanation:
The area of the figure is 400 in.
a) As x decreases within bound, f(x) increases without bound.
b) As x decreases without bound,f(x) approaches zero
c) as x increases without bound,f(x) approaches the line y = - 4
d) as x decreases without bound,f(x) approaches the line y = - 4
Answer:
a) As x decreases within bound, f(x) increases without bound.
c) as x increases without bound,f(x) approaches the line y = - 4
Step-by-step explanation:
From the graph, we can see, as x becomes more negative, y gets larger and larger.
As x→ -∞, y → ∞
As x decreases without bound, y increases without bound
We can also see as x gets larger and larger, y gets closer to -4
As x →∞, y → -4
As x increases without bound, y approaches -4
As x decreases within a limit, f(x) increases without bound.
Explanation:The correct statement in this question is a) As x decreases within bound, f(x) increases without bound.
To understand this concept better, we can look at the graph of the function y = 1/x. As x approaches zero (within the bound), the value of y increases without bound, meaning it becomes very large and approaches infinity.
Other functions can also exhibit similar behavior where as x decreases within a limit, the corresponding values of f(x) increase without bound.
Learn more about Functions here:https://brainly.com/question/21145944
#SPJ3
How to do this question?
Answer:
D
Step-by-step explanation:
The answer is D, since there is no correlation in the data (meaning that it is scattered all over the plot with no pattern or anything).
The vertex of this parabola is at (-1,-3). Which of the following could be it’s equation?
Answer:D
Step-by-step explanation: The vertex is (-1, -3), and since it's in terms of y, the y-coordinate is in the parentheses. D is the only choice with -3 as the y-coordinate.
The equation of the parabola with vertex (-1, -3) is y = a(x + 1)^2 - 3.
Explanation:The equation of a parabola in vertex form is y = a(x - h)^2 + k, where the vertex is (h, k). In this case, the vertex is (-1, -3), so the equation could be y = a(x + 1)^2 - 3. The coefficient a determines the shape of the parabola.The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape. If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “ U ”-shape.
Learn more about Parabola equation here:https://brainly.com/question/11911877
#SPJ3
All possible solutions for -6k < -12
ANSWER
All possible solutions are
[tex]k \: > \: 2[/tex]
EXPLANATION
The given inequality is
[tex] - 6k \: < \: - 12[/tex]
Divide both sides by -6 and reverse the inequality sign.
[tex] k \: > \: \frac{ - 12}{ - 6} [/tex]
[tex]k \: > \: 2[/tex]
All real numbers greater than 2.
the area of a parallelogram is 36x^6y^5. if the base of the parallelogram is 3xy^2 units,what is the height of the parallelogram
Answer:
h = 12x^5y^3
Step-by-step explanation:
The area of a parallelogram is found using A = b*h. Substitute the values given and solve for h.
A = b*h
36x^6 y^5 = 3xy^2 * h
36x^6 y^5 ÷ 3xy^2 = h
12x^5y^3 = h
Select all the correct locations on the table
Answer:
(i) Exponential Decay
(ii)linear
(iii)Exponential Growth
Step-by-step explanation:
(i)
Cost of the van=$25,000.
After 2 years, value of van=$17,500.
After 4 years, value of van = $12,250.
Its a decay but to be a exponential decay it must have constant rate.
As its known the exponential decay formula is [tex]C=C_{0} e^{-kt}[/tex]
Now substitute the values in the above formula
[tex]17500=25000 e^{-k*2}[/tex]
Now on simplification, we get
[tex]k=0.1783[/tex]
Now again apply the same formula for the next time interval
[tex]12250=25000 e^{-k*4}[/tex]
Now on simplification, we get
[tex]k=0.1783[/tex]
Since the value of k is constant for both the time interval. Hence the decays is exponential.
(ii)
At the beginning, battery life=100%.
After 3 Hours, battery life=60%.
After 6 Hours, battery life = 20%.
Since the value of battery life decreases by 40% in each interval. Hence the decay of battery life is linear.
(iii)
Initial population=20.
After 5 years, population=30.
After 10 years, population = 45.
Its a growth but to be a exponential growth it must have constant rate.
As its known the exponential growth formula is [tex]P=P_{0} e^{kt}[/tex]
Now substitute the values in the above formula
[tex]30=20 e^{-k*5}[/tex]
Now on simplification, we get
[tex]k=-0.081[/tex]
Now again apply the same formula for the next time interval
[tex]45=20 e^{-k*10}[/tex]
Now on simplification, we get
[tex]k=-0.081[/tex]
Since the value of k is constant for both the time interval. Hence the decays is exponential.
find the area of each figure. round to the nearest tenth if necessary .
We first would divide the Pentagon into two shapes, one a square and the other a triangle. To find the height of the triangle we must minus the 15cm to the 10cm, which gives us 5cm.
5cm= height of triangle
7cm= base of triangle
Then, apply the area of triangle formula
which is: A=(b×h)÷2
so the area would be 17.5cm squared.
For the square, 10= height and the 7=base
The formula for rectangles is:
A=b×h
so, the area is 70cm squared.
if you want the total area add the two area together, which equals 87.5cm squared.
I hope this helps.
To find the area of each figure, we can use different formulas depending on the shape. If the figure is a square or rectangle, we can use the formula A = length x width. If the figure is a circle, we can use the formula A = πr², where r is the radius.
Explanation:To find the area of each figure, we can use different formulas depending on the shape. If the figure is a square or rectangle, we can use the formula A = length × width. If the figure is a circle, we can use the formula A = πr², where r is the radius. For triangles, we can use the formula A = ½base × height. For irregular shapes, we can approximate the area by breaking it down into simpler shapes and summing up their areas.
Let's say we have a square with side length 5 cm. Using the formula A = length × width, the area would be A = 5 cm × 5 cm = 25 cm². If we have a circle with a radius of 2 cm, using the formula A = πr², the area would be A = 3.14 × 2 cm × 2 cm = 12.56 cm² (rounded to the nearest tenth).
What is the domain of the function y=2 sqrt x-6 ?
Answer
Domain of the function:
In interval notation: [6, ∞)
In set notation: {x: x∈R, x≥6}
Explanation
Remember that the the domain of the square root function are all the values such is is bigger than zero. We can express the later in set notation: {x: x∈R, x≥0}, or in interval notation: [0, ∞)
This is because the square root is not defined, in the real numbers, for negative values.
So, to find the domain of our function, we just need to set the thing inside the radical grater or equal than zero and solve for x:
The domain of the function is all the numbers bigger than 6, including 6.
Answer:
[6, infinity (use the symbol)
Step-by-step explanation:
i got this answer by graphing
The rectangular octogon shown is enlarged.........................help please
Answer:
it is b
Step-by-step explanation:
B.) The area is 3 times greater I think
A woman wants to make a 4 inch wide copy of a drawing that is 5 inch wide. On the photo copier, what percent setting should she use to make a copy this size
A 5%
B 80%
C 90%
D 125%
Answer:
B 80 %
Step-by-step explanation:
She wants to reduce the size of the drawing, so the setting should be a proper fraction.
Setting = 4/5
Multiply numerator and denominator by 20 = 80/100
Convert to percent = 80 %
The setting should be 80 %.
Answer:
80%
Step-by-step explanation:
4/5 multiply them together and it equals 20
then multiply 4 and 5 by 20 which will get you
80/100 so.. convert it to percentage and you get...
80%
Please help!! I’ll mark brainliest
The triangle was only rotated. The size did not change, so the corresponding angles would remain identical.
Because C is 28 degrees C' would also be 28 degrees.
Solve the equation 2 cos ( x ) + 1 = 0 2 cos x + 1 = 0 , 0 ≤ x ≤ 2 π 0 ≤ x ≤ 2 π . Show all of your work
Answer:
2π/3, 4π/3
Step-by-step explanation:
I interpret your question as asking us to solve the equation
2cos(x) + 1 = 0
2cos(x) = -1
cos(x) = -½x
x = arccos(-½), 0 ≤ x ≤2π
Since the cosine is negative, x must be in the second or third quadrant.
Referring to the unit circle, we find that
x = 2π/3 (120°) or x = 4π/3 (240°)
Which range is the best estimate for capacity in the fluid ounces of a water bottle
Answer:
K is the best estimate.
Step-by-step explanation:
This is just common sense, not much math.
J: No, that is smaller than an essential oils bottle, which is as tall as a finger.
K: Probably, the range is from the size of a medicine bottle to a small/medium water bottle.
L: No, that much is the size of a bottle of detergent.
M: No, that much water is 6 kg.
Find the missing measurement. Round your answer to the nearest tenth.
A: 9.1 mi
B: 7.3 mi
C: 5.2 mi
D: 10.2 mi
The answer is 7.3 mi I think
help me with this I really need help
Answer:
i think it is 19 is the whole number 9/40 is the remainder
Step-by-step explanation:
Solve x^2+5x=-6 please solve this using quadratics
x2 + 5x + 6 = 0
(x + 2)(x + 3) = 0
x = -2 or -3
Answer:
x = - 3, x = - 2
Step-by-step explanation:
Given
x² + 5x = - 6 ( add 6 to both sides )
x² + 5x + 6 = 0 ← in standard form
(x + 3)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x + 2 = 0 ⇒ x = - 2