Answer:
[tex]\sum_{n=5}^{\infty}n^2[/tex]
Step-by-step explanation:
The pattern given is:
25+36+49+64+...+n^2+...
The pattern can be written as
(5)^2+(6)^2+(7)^2+(8)^2+.....+n^2+....
The series is started with 5 and it continues up to infinity.
The summation notation for the given series is:
[tex]\sum_{n=5}^{\infty} n^2[/tex]
n= 1 and goes up to infinity and the series is made up of taking square of n,
The sum using summation notation, assuming the suggested pattern continues is :
[tex]25 + 36 + 49 + 64 + ... + n^2 + ...=\sum_{n=5}^{\infty} n^2[/tex]
Step-by-step explanation:We are given a series of numbers as
25 + 36 + 49 + 64 + ... + n^2 + ...
To write the sum using summation notation means we need to express this series in terms of a general n such that there is a whole summation expressing this series.
Here we see that each of the numbers could be expressed as follows:
[tex]25=5^2\\\\36=6^2\\\\49=7^2\\\\64=8^2[/tex]
and so on.
i.e. the series starts by taking the square of 5 then of 6 then 7 and so on.
and the series goes to infinity.
Hence, the summation notation will be given by:
[tex]25 + 36 + 49 + 64 + ... + n^2 + ...=\sum_{n=5}^{\infty} n^2[/tex]
Who was the 35th president
Answer:
John F. Kennedy
A cat keeps eating to gain weight while a dog keeps doing exercise.Later, the cat's weight increases by 20% and the dog's weight decrease such that their weights become the same. By what percentage is the cat weight less than the dog's original weight?
The feline expanded in weight compared with the canine's underlying weight which is steady with the data given.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Let c be the feline's unique weight. Let c* be the feline's new weight.
Let d be the canine's unique weight. The d* be the canine's new weight.
The equation is given as,
c = 1.2 c
d = .9 d
c = d
The other equation is given as,
p = (d - c)/d = 1 - c/d
We know that the given condition,
c = d = 0.9 d
Then the equation is written as,
p = 1 - 0.9d/d
p = 1 - 0.9
p = 0.1 or 10%.
Hence, toward the beginning, the rate contrast compared with the canine was,
q = (d - c)/d = 1 - 0.75 = 0.25 or 25%.
That is, the feline weighed not exactly like the canine toward the beginning. Since p < q, the feline expanded in weight compared with the canine's underlying weight — which is steady with the data given.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
Find the simplified product: 3 sqrt 2x^5 *3 sqrt 64x^9
Answer:
[tex]\large\boxed{4x^4\sqrt[3]{2x^2}}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{2x^5}\cdot\sqrt[3]{64x^9}\qquad\text{use}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\\\=\sqrt[3]{2}\cdot\sqrt[3]{64}\cdot\sqrt[3]{x^5x^9}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt[3]2\cdot4\cdot\sqrt[3]{x^2x^3x^9}\\\\=4\sqrt[3]2\cdot\sqrt[3]{x^2x^{12}}\\\\=4\sqrt[3]2\cdot\sqrt[3]{x^2x^{4\cdot3}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=4\sqrt[3]2\cdot\sqrt{x^2(x^4)^3}\\\\=4\sqrt[3]2\cdot\sqrt[3]{x^2}\cdot\sqrt[3]{(x^4)^3}\qquad\text{use}\ \sqrt[n]{a^n}=a\\\\=4\sqrt[3]{2x^2}\cdot x^4\\\\=4x^4\sqrt[3]{2x^2}[/tex]
Answer: it's c to put it simply
Step-by-step explanation:
What do I do for this?
if EF ≅ WV and JK is intersecting both at a right-angle, the distances OK = JP and likewise PG = GO, namely
[tex]\bf 2(4x-3)-8=4+2x\implies 8x-6-8=4+2x\implies 8x-14=4+2x \\\\\\ 6x-14=4\implies 6x=18\implies x=\cfrac{18}{6}\implies x=3[/tex]
A waitress sold 12 steak dinners and 27 grilled salmon dinners, totaling $554.98 on a particular day. Another day she sold 26 ribeye steak dinners and 9 grilled salmon dinners, totaling &584.36. How much did each type of dinner cost?
Answer:
the cost of rib eye steak dinner = $22.47
the cost of grilled salmon dinners= $10.57 .....
Step-by-step explanation:
Let x be the rib eye steak dinner.
Let y be the grilled salmon dinner.
According to the first given statement:
12x+27y= $554.98 (equation 1)
According to the second statement:
26x+9y=$584.36 ( equation 2)
Lets take a look at the 1st equation:
12x+27y= $554.98
12x=$554.98- 27y
x=$554.98- 27y/12
Now substitute the value of x in 2nd equation:
26x+9y=$584.36
26($554.98- 27y/12)+9y=$584.36
26(554.98- 27y)+9y=584.36*12
14429.48-702y=7012.32
-702y=7012.32-14429.48
-702y= -7417.16
y= 7417.16/702
y=$10.57
Now substitute the value of y in equation 1:
12x+27y= $554.98
12x+27(10.57)=554.98
12x+285.39 = 554.98
Move the constant to the R.H.S
12x=554.98-285.39
12x=269.59
Divide both the terms by 12
12x/12=269.59/12
x=$22.47
Thus the cost of rib eye steak dinner = $22.47
the cost of grilled salmon dinners= $10.57 .....
The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 242
What is the height of the cylinder?
2 units
4 units
6 units
8 units
Answer:
D
Step-by-step explanation:
Formula
Volume = pi*r^2*h
Givens
r = x
h = 3x
Volume= 242
Solution
242 = pi * x^2 * 3x
242 = 3.14 * 3x^3 Divide by pi
242/3.14 = 3.14 * 3x^3 / 3.14 Do the division
77 = 3x^3 Divide by 3
77/3 = 3x^3 /3
25.69 = x^3 Take the cube root of both sides.
2.95 = x
The height of the cylinder is 3 times that of the radius of the circle (x)
The answer is 8.85. I suppose the closest answer is 8.
Find the value of each variable.
Answer:
see explanation
Step-by-step explanation:
Using the exact values of the trigonometric ratios
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex], cos60° = [tex]\frac{1}{2}[/tex]
sin45° = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex]
Using the sine ratio on the right triangle on the left
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{4\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]
Cross- multiply
2a = 4[tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 12 ( divide both sides by 2 )
a = 6
Using the cosine ratio on the same right triangle
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{c}{4\sqrt{3} }[/tex] = [tex]\frac{1}{2}[/tex]
Cross- multiply
2c = 4[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
c = 2[tex]\sqrt{3}[/tex]
------------------------------------------------------------------------------------------
Using the sine/cosine ratios on the right triangle on the right
sin45° = [tex]\frac{a}{b}[/tex] = [tex]\frac{6}{b}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]
Cross- multiply
b = 6[tex]\sqrt{2}[/tex]
cos45° = [tex]\frac{d}{b}[/tex] = [tex]\frac{d}{6\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]
Cross- multiply
[tex]\sqrt{2}[/tex] d = 6[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
d = 6
------------------------------------------------------------------------------------------------
a = 6, b = 6[tex]\sqrt{2}[/tex], c = 2[tex]\sqrt{3}[/tex], d = 6
The solutions of the quadratic equation 0 = (x + 3)(x - 2)
are
0 -6 and 0.
04 and 3.
0-3 and 2
0 -2 and 1.
Answer:
x = -3 or x = 2
Step-by-step explanation:
It is given a quadratic equation,
(x + 3)(x - 2) = 0
To find the solution of given equation
Let (x + 3)(x - 2) 0
⇒ either (x + 3) = 0 or (x - 2) = 0
If (x + 3) = 0 then x = -3
If (x - 2) = 0 then x = 2
Therefore the solution of given equation are
x = -3 or x = 2
Whats the answer??? And how do i solve it!
Answer:
[tex]\large\boxed{3^\frac{2}{3}}[/tex]
Step-by-step explanation:
[tex]Use\\\\\sqrt[n]{a^m}=a^\frac{m}{n}\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}\\\\\bigg(\sqrt[4]{9^{15}}\cdot\sqrt{3^3}\bigg)^\frac{2}{27}=\bigg(\sqrt[4]{(3^2)^{15}}\cdot3^\frac{3}{2}\bigg)^\frac{2}{27}=\bigg(\sqrt[4]{3^{2\cdot15}}\cdot3^{\frac{3}{2}}\bigg)^\frac{2}{27}\\\\=\bigg(3^{\frac{30}{4}}\cdot3^\frac{3}{2}\bigg)^\frac{2}{27}=\bigg(3^{\frac{15}{2}}\cdot3^\frac{3}{2}\bigg)^\frac{2}{27}=\bigg(3^{\frac{15}{2}+\frac{3}{2}}\bigg)^\frac{2}{27}[/tex]
[tex]=\bigg(3^{\frac{18}{2}}\bigg)^\frac{2}{27}=\bigg(3^9\bigg)^\frac{2}{27}=3^{9\cdot\frac{2}{27}}=3^\frac{2}{3}[/tex]
Which graph below solves the following system of equations correctly?
y = three over four times x squared minus 3
y = negative three over four times x squared plus 3
A) two quadratic graphs opening up. They intersect at 0 and negative 3.
B)one quadratic graph opening up and one quadratic graph facing down. They intersect at 0, 3.
C) quadratic graph opening up and quadratic graph opening down. They intersect at 0, negative 3.
D) two parabolas one facing down with a vertex at 0, 3 and one facing up with a vertex at 0, negative 3
D) two parabolas one facing down with a vertex at 0, 3 and one facing up with a vertex at 0, negative 3
Step-by-step explanation:First of all, let's rewrite the equations in a mathematical language:
y = three over four times x squared minus 3:[tex]y=\frac{3}{4}x^2-3[/tex]
Since the leading coefficient, the number that accompanies [tex]x^2[/tex] is positive, that is, its value is 3/4, then the parabola opens upward. On the other hand, the vertex can be found as:
[tex](h,k)=\left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right) \\ \\ a=3/4 \\ b=0 \\ c=-3 \\ \\ h=-\frac{0}{2(3/4)}=0 \\ \\ k=f(0)=\frac{3}{4}(0)^2-3=-3 \\ \\ \\ \boxed{Vertex \rightarrow (h,k)=0,-3}[/tex]
y = negative three over four times x squared plus 3:[tex]y=-\frac{3}{4}x^2+3[/tex]
Since the leading coefficient is negative, that is, its value is -3/4, then the parabola opens downward. Similarly the vertex can be found as:
[tex](h,k)=\left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right) \\ \\ a=-3/4 \\ b=0 \\ c=3 \\ \\ h=-\frac{0}{2(-3/4)}=0 \\ \\ k=f(0)=-\frac{3}{4}(0)^2+3=3 \\ \\ \\ \boxed{Vertex \rightarrow (h,k)=0,3}[/tex]
Both graph are shown below and you can see that the conclusion of our problem is correct.
Need help with question number 55
Answer:
1) The profit of the company dropped by -15% compared to last year.
2) The temperature of Alaska was -5 degrees yesterday.
3) John had 1,000$ dollars deposited in the bank, and then made a poor investment, causing him to owe the bank 5,000$, making his account -4,000$
Step-by-step explanation:
With each scenario you have to try to find a new way to express a negative number which is primarily through loss. In which ways can you unique express loss of a value below zero in real world is the question, and you can do so with examples like money and temperature.
Male and female high school students reported how many hours they worked each week in summer jobs. The data is represented in the following box plots: Identify any values of data that might affect the drastically measures of spread and center.
A) The zero hour mark on both plots prevents the graphs from being balanced.
B) The median is near the center of the IQR for both males and females.
C) There is not enough evidence to see any effects on spread or center.
D) The makes have a suspected significant high outlier.
Answer:
I think the answer is d
Step-by-step explanation:
since the graph is a lot bigger than the females, but the box thing is in about the same spot as the females ( you know what i mean), but i'm not 100% sure, but i think its the safest answer
On a map, two cities are 4 and 1/4 inches apart. The scale of the map is 1/2 inch = 3 miles. What is the actual distance between the towns?
Answer:
25,5 miles
Step-by-step explanation:
4.25 inch on map
4.25/0.5 = 8,5
8,5 * 3 = 25,5 miles
Final answer:
To find the actual distance between two towns on a map, set up a proportion using the given scale. By solving the proportion, you can determine the real distance between the towns.
Explanation:
To find the actual distance between the two towns, we can set up a proportion using the given scale:
1/2 inch on the map represents 3 miles in reality.4 1/4 inches on the map represent x miles in reality.Set up the proportion: (1/2 inch) / (3 miles) = (4 1/4 inches) / (x miles).Solve for x to find the actual distance between the two towns.emily has earned the following grades A, c+, a-,b- and b+. what grade must she earn in her biology class to keep her 3.2 gpa?
Answer:
B+
Step-by-step explanation:
Grades earned in five subjects are;
A,C+,A-,B- and B+
Remaining subject is biology
Total number of subjects will be=6
3.2 gpa as a percentile =86
For her to maintain 3.2 gpa total sum of percentile in the 6 subjects should be at least
6×86=516
Emily total sum of subjects in percentile is 93+77+90+80+87=427
Find the difference , 516-427=89
89 is grade B+
Emily should earn a grade of B+ to keep her 3.2 gpa
Which of the following is a trino
Answer:
Option 1
Step-by-step explanation:
Tri means 3. An expression which has 3 terms and the terms are separated by plus or minus:
c^2+c+6
Thus option 1 is correct....
For this case we have that by definition, a trinomial is an algebraic expression formed by the sum or difference of three terms or monomials.
Example:
[tex]ax ^ 2y + cx + dy[/tex]
Thus, the correct option is option 1.
[tex]c ^ 2 + c + 6[/tex]
Three terms are observed.
Answer:
Option 1
Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 3, -2 is the only other zero, leading coefficient is 2.
f(x)=?
Can someone help?
Answer:
[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]
Step-by-step explanation:
we know that
2 is a zero of multiplicity 3 of the polynomial
so
we have that
x=2 is a solution of the polynomial
A factor of the polynomial is
[tex](x-2)^{3}[/tex] ----> is elevated to the cube because is a multiplicity 3
and the other solution is x=-2
since the polynomial is fifth degree, x=-2 must have a multiplicity 2
so
the other factor of the polynomial is
[tex](x+2)^{2}[/tex] ----> is squared because is a multiplicity 2
therefore
The polynomial is equal to multiply the factors by the leading coefficient
so
[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]
The polynomial function based on the given properties: zeros at 2 (with multiplicity 3) and -2 (with multiplicity 1), leading coefficient of 2, is f(x) = 2(x - 2)³(x + 2).
Explanation:To construct a polynomial with given zeros and multiplicities, we need to set up a product of binomial factors based on the zeros, with each binomial factor raised to the power of its respective multiplicity. The resulting polynomial is the given function f(x).
For the given properties, the roots are 2 and -2. The root 2 has multiplicity 3 and the root -2 has multiplicity 1. Also, the leading coefficient is 2. So, we can set up the polynomial function as follows:
f(x) = 2(x - 2)3(x + 2)
This represents a fifth degree polynomial function that has the zeros and multiplicities listed, with the leading coefficient of 2.
Learn more about Polynomial Function here:https://brainly.com/question/30474881
#SPJ1
What is the measure of AC?
Answer:
AC = 26
Step-by-step explanation:
AD = DC . . . . . .these segments are marked congruent
8x-1 = 6x+9 . . . substitute the given expressions
2x = 10 . . . . . add 1-6x
x = 5
__
AC = 2·AB = 2(3x-2) = 2(3·5-2) . . . . substitute into expression for AB
AC = 26
Which statement correctly describes the solution to this scenario?
Answer: Choice C
x represents time and x is positive; y value is 45 times more than the x value
==================================
Explanation:
The inequality y > 45x is the same as y > 45*x
We have y greater than 45*x meaning that y is 45 times more than the x value.
As an example, if x = 2, then 45*x = 45*2 = 90 meaning that y must be larger than 90 if you picked x = 2. In this scenario, x = 2 means that if you traveled for 2 hours then you must have gone more than 90 miles in total distance.
20 POINTS!
Use the graph of the line to answer the questions.
1. What is an equation of the line in point-slope form?
2. How can the point-slope form be written in function notation?
Answer:
[tex]y+1=\dfrac{1}{3}(x+2)[/tex] - point-slope form
[tex]f(x)=\dfrac{1}{3}x-\dfrac{1}{3}[/tex] - function notation
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points (-2, -1) and (1, 0).
Substitute:
[tex]m=\dfrac{0-(-1)}{1-(-2)}=\dfrac{1}{3}[/tex]
[tex]y-(-1)=\dfrac{1}{3}(x-(-2))[/tex]
[tex]y+1=\dfrac{1}{3}(x+2)[/tex] - point-slope form
[tex]y+1=\dfrac{1}{3}(x+2)[/tex] use the distributive property
[tex]y+1=\dfrac{1}{3}x+\dfrac{2}{3}[/tex] subtract 1 = 3/3 from both sides
[tex]y=\dfrac{1}{3}x-\dfrac{1}{3}[/tex]
Answer:
1. 3rd option
2. 2nd option
Step-by-step explanation:
(02.02LL)
If f(x) = 2(X - 5), find f(8).
Answer:
6
Step-by-step explanation:
You can see how f(x) is now f(8), this implies you have to replace any x's you see with an 8.
So f(8) = 2(8-5) = 2(3) = 6
What are the coordinates of the point 3/5 of the way from A(-9,3) to B(21, -2)
Answer: The required co-ordinates of the point are (9, 0).
Step-by-step explanation: We are given to find the co-ordinates of the point that is [tex]\dfrac{3}{5}[/tex] of the way from A(-9,3) to B(21, -2).
Let K be the required point. Then, we mus have
[tex]AK:AB=3:5\\\\\Rightarrow \dfrac{AK}{AK+BK}=\dfrac{3}{5}\\\\\\\Rightarrow 5AK=3AK+3BK\\\\\Rightarrow 2AK=3BK\\\\\Rightarrow AK:BK=3:2.[/tex]
We know that
the co-ordinates of a point that divides the line joining the points (a, b) and (c, d) in the ratio m : n are given by
[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{2}\right).[/tex]
For the given division, m : n = 3 : 2.
Therefore, the co-ordinates of the point K are
[tex]\left(\dfrac{3\times21+2\times(-9)}{3+2},\dfrac{3\times(-2)+2\times3}{3+2}\right)\\\\\\=\left(\dfrac{63-18}{5},\dfrac{-6+6}{5}\right)\\\\=\left(\dfrac{45}{5},\dfrac{0}{5}\right)\\\\=(9,0).[/tex]
Thus, the required co-ordinates of the point are (9, 0).
Building and solving an equation, it is found that the coordinates are: (9,0).
We are given two points: A(-9,3) and B(21, -2).We also want point C(x,y).C is 3/5 of the way from A to B, thus:
[tex]C - A = \frac{3}{5}(B - A)[/tex]
This is used to find both the x-coordinate and the y-coordinate of C.
First, the x-coordinate, considering [tex]C = x, A = -9, B = 21[/tex].
[tex]C - A = \frac{3}{5}(B - A)[/tex]
[tex]x + 9 = \frac{3}{5}(21 + 9)[/tex]
[tex]x = 18 - 9[/tex]
[tex]x = 9[/tex]
Then, the y-coordinate, considering [tex]C = y, A = 3, B = -2[/tex].
[tex]C - A = \frac{3}{5}(B - A)[/tex]
[tex]y - 3 = \frac{3}{5}(-2 - 3)[/tex]
[tex]y = -3 + 3[/tex]
[tex]y = 0[/tex]
Thus, the coordinates are (9,0).
A similar problem is given at https://brainly.com/question/24352869
Which expression could be used to determine the product of -4 and 3
A. (-4)(3) × (-4) 1/4
B. (-4)(3)+(-4) 1/4
C. (3)(-4)x(3) 1/4
D. (3)(-4)+(3)(1/4)
Answer ASAP!
Answer:
I think that the answer is A.
Answer:
No options is correct.
Step-by-step explanation:
Given : The product of -4 and 3.
To find : Which expression could be used to determine the product ?
Solution :
The product of -4 and 3 is [tex]-4\times 3=-12[/tex]
To know which expression we solve each options and get whose result is same as ours,
A) [tex](-4)(3)\times (-4)(\frac{1}{4})[/tex]
Solve,
[tex](-4)(3)\times (-4)(\frac{1}{4})= -12\times -1=12[/tex]
B) [tex](-4)(3)+(-4)(\frac{1}{4})[/tex]
Solve,
[tex](-4)(3)+(-4)(\frac{1}{4})= -12+(-1)=-13[/tex]
C) [tex](3)(-4)\times (3)(\frac{1}{4})[/tex]
Solve,
[tex](3)(-4)\times (3)(\frac{1}{4})=-12\times\frac{3}{4}=-9[/tex]
D) [tex](3)(-4)+(3)(\frac{1}{4})[/tex]
Solve,
[tex](3)(-4)+(3)(\frac{1}{4})=-12+\frac{3}{4}=-11.25[/tex]
From the given options, No options will get the product.
How do I solve rate of change problems? (With picture) thanks!
**please help me understand the 3 problems by explaining
5)
[tex]\bf \begin{array}{|cc|cccc|ll} \cline{1-6} sodas&x&\underline{24}&28&\underline{32}&36\\ \cline{1-6} cost&y&\underline{18}&21&\underline{24}&27\\ \cline{1-6} \end{array}~\hspace{9em} (\stackrel{x_1}{24}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{32}~,~\stackrel{y_2}{24}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{24-18}{32-24}\implies \cfrac{6}{8}\implies \cfrac{3}{4}[/tex]
6)
[tex]\bf \begin{array}{|cc|cc|ll} \cline{1-4} year&x&0&12\\ \cline{1-4} \$&y&720&1080\\ \cline{1-4} \end{array}~\hspace{10em} (\stackrel{x_1}{0}~,~\stackrel{y_1}{720})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{1080}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1080-720}{12-0}\implies \cfrac{360}{12}\implies \cfrac{30}{1}\implies 30[/tex]
7)
slope as you should already know is rise/run, or how much something moves in relation something else, namely how much the y-axis go up as the x-axis moves sideways, one moves, the other follows, but the increments will be different, sometimes the same, but usually different.
the y-intercept means, when the graph of the equation touches or intercepts the y-axis, and when that happens x = 0, or the horizontal distance is at bay.
for the slope on 6), 30 or 30/1 means, for every 1 year(x) passed, the worth(y) increased by 30, or jumped by 30 units, so as the x-axis moved 1, the y-axis moved 30. After 12 years 30 * 12 = 360, and we add the initial 720 and we end up with 1080.
the y-intercept, well, as aforementioned is when x = 0, is year 0.
Answer:
Top:
The rate change is 4.
Bottom:
The rate change is 3.
Step-by-step explanation:
24+4= 28 28+4=32 (and) 32+4=36
18+3=21 21+3=24 (and) 24+3=27
I will get back to you on the rest>
Hope this helped tho! :3
You need a 30% alcohol solution. On hand, you have a 90 mL of a 45% alcohol mixture. How much pure water will you need to add to obtain the desired solution?
You will need
_____ mL of pure water
to obtain
______ mL of the desired 30% solution.
Answer:
45ml of pure water to obtain 135ml of the desired 30% solution
Step-by-step explanation:
45% of 90 = 40.5
So, 40.5ml of alcohol in 90ml
We want 30% and therefore need a ratio of 3:7
40.5÷3=13.5
so one part of our ratio is 13.5
we then times this by 7
13.5 x 7 = 94.5
so, 94.5ml of water
to work out how much we already have, we should do 90ml- 40.5ml = 49.5ml
and then 94.5- 49.5 = 45ml
We need 45ml of water and the total mo of the desired solution will be 90+45=135ml
To dilute a 45% alcohol solution to a 30% alcohol solution by adding pure water, you will need to add 45 mL of pure water to the initial 90 mL to achieve a total volume of 135 mL with the desired 30% alcohol concentration.
To dilute a 45% alcohol solution to a 30% alcohol solution using pure water, we can use the concept of concentration dilution in chemistry. This involves calculating the amount of diluent (in this case, water) to add to an existing solution to achieve a desired concentration.
Let's denote the amount of pure water to add as x mL. The initial volume of the alcohol solution is 90 mL with a 45% concentration, meaning it contains 40.5 mL of pure alcohol. Since adding water doesn't change the amount of alcohol, the final mixture's alcohol volume remains at 40.5 mL.
To find the final volume of the solution and the amount of water needed, we use the formula for the final concentration: Final Concentration = (Volume of Solute) / (Final Volume of Solution). Substituting the given and desired values gives us 30% = 40.5 mL / (90 mL + x).
Rearranging and solving for x gives: x = (40.5 / 0.3) - 90 = 135 - 90 = 45 mL. Therefore, 45 mL of pure water must be added to the original solution to get a 30% alcohol solution.
In conclusion, adding 45 mL of pure water to the 90 mL of 45% alcohol mixture yields a total volume of 135 mL of the desired 30% solution.
Classify the following triangle. Check all that apply.
A. Right
B. Equilateral
C. Isosceles
D. Scalene
E. Obtuse
F. Acute
Answer:
This is an obtuse, isosceles triangle.
Step-by-step explanation:
The largest angle is greater than 90 degrees (obtuse), and two sides are equal as you can tell by two equal angles (isosceles).
The given triangle can be classified as isosceles and acute triangle.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
Given is a triangle.
The three angles of the triangle are 41°, 41° and 98°.
That is, two angles of the triangle are equal. So the sides opposite these two angles are also equal.
So this is an isosceles triangle.
Obtuse triangle has one of the angles greater than 90°.
Acute triangle has all the angles less than 90°.
Here all the angles are less than 90°.
So it is acute.
Hence the given triangle is acute and isosceles triangle.
Learn more about Triangles here :
https://brainly.com/question/13515945
#SPJ7
At most, how many unique roots will a third-degree polynomial function have?
Answer: 3
Step-by-step explanation: I jus got it right on a pex
One x-intercept for a parabola is at the point
(2,0). Use the quadratic formula to find the
other x-intercept for the parabola defined by
this equation:
y = 4x2 - 4x – 8
Answer:
(2,0) was already given so (-1,0) is the other one.
Step-by-step explanation:
So we are asked to use the quadratic formula.
To find the x-intercepts (if they exist) is use:
[tex]\text{ If } y=ax^2+bx+c \text{ then the } x-\text{intercepts are } (\frac{-b \pm \sqrt{b^2-4ac}}{2a},0)[/tex].
Let's start:
Compare the following equations to determine the values for [tex]a,b, \text{ and }c [/tex]:
[tex]y=ax^2+bx+c[/tex]
[tex]y=4x^2-4x-8[/tex]
So
[tex]a=4[/tex]
[tex]b=-4[/tex]
[tex]c=-8[/tex]
We are now ready to enter into our formula:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{4 \pm \sqrt{(-4)^2-4(4)(-8)}}{2(4)}[/tex]
[tex]x=\frac{4 \pm \sqrt{16+16(8)}}{8}[/tex]
[tex]x=\frac{4 \pm \sqrt{16(1+8)}}{8}[/tex]
[tex]x=\frac{4 \pm \sqrt{16}\sqrt{1+8}}{8}[/tex]
[tex]x=\frac{4 \pm 4\sqrt{9}}{8}[/tex]
[tex]x=\frac{ 4 \pm 4(3)}{8}[/tex]
[tex]x=\frac{4 \pm 12}{8}[/tex]
[tex]x=\frac{4(1\pm 3)}{8}[/tex]
[tex]x=\frac{1(1\pm 3)}{2}[/tex]
[tex]x=\frac{1 \pm 3}{2}[/tex]
[tex]x=\frac{1+3}{2} \text{ or } \frac{1-3}{2}[/tex]
[tex]x=\frac{4}{2} \text{ or } \frac{-2}{2}[/tex]
[tex]x=2 \text{ or } -1[/tex]
So the x-intercepts are (2,0) and (-1,0).
(2,0) was already given so (-1,0) is the other one.
a kids skipping rope is 210 cm long. how many ropes could i cut from a 10 meter long piece of rope?
Answer:
4 ropes.
Step-by-step explanation:
There are 100 cms in a meter.
So 10 meters = 10* 100
= 1000 cms.
1000 / 210 = 4 ropes with 160 cms remaining.
The equations y= x^2/2 - 8 and y=2x−2 are graphed below. What are the solutions to the equation x^2/2−8=2x−2
graph is attached
Please choose one answer below
x=−6 and x=10
x=−4 and x=4
x=−2 and x=6
x=−8 and x=−2
Your answer is the third option, x = -2 and x=6
We can see this because the solutions of x^2/2 - 8 = 2x - 2 are going to be where the lines y = x^2/2 - 8 and y = 2x - 2, because this is where the two equations are equal to each other.
Therefore, we can just look on the graph at where the two lines intersect, and see that it happens when x = -2 and x = 6.
I hope this helps!
Answer:
x=-2 and x=6
Step-by-step explanation:
The solution to a graph would be where the two lines intersect. When you look at the graph you plot where they connect
(-2, -6), (6, 10)
The x value is the very first variable in an ordered pair. Therefore, the solution to this graph would be x=-2 and x=6.
the length of a rectangular garden is 3 times its width. if the perimeter of the garden is 40 yards, what is the area
Answer:
75 yd^2.
Step-by-step explanation:
If the width = x yards, the length will be 3x yards.
The perimeter = 2 * length + 2 * width
= 2* 3x + 2*x = 40
6x + 2x = 40
8x = 40
x = 5
So the width is 5 and the length is 15 yards.
The area = 5 * 15 = 75 yd^2.
Answer:
75
Step-by-step explanation:
x=breadth
3x=length
perimeter=2(x+3x)=8x
40=8x
x=5
length=15
breadth=5
area=15*5=75