Answer:
a21 = -61
Step-by-step explanation:
[tex]a_{n}=a_{1}+(n-1)d[/tex]
[tex]-19=a_{1}+(7-1)d[/tex]
[tex]-28=a_{1}+(10-1)d[/tex] (subtract to eliminate a₁)
9 = -3d
d = -3
-19 = a₁ + (6)(-3)
-1 = a
a21 = -1 + (21 - 1)(-3)
= -61
Answer:
-61 (Answer D)
Step-by-step explanation:
The general formula for an arithmetic sequence with common difference d and first term a(1) is
a(n) = a(1) + d(n - 1)
Therefore, a(7) = -19 = a(1) + d(7 - 1), or a(7) = a(1) + d(6) = -19
and a(10) = a(1) + d(10 - 1) = -28, or a(1) + d(10 - 1) = -28
Solving the first equation a(1) + d(6) = -19 for a(1) yields a(1) = -19 - 6d. We substitute this result for a(1) in the second equation:
-19 - 6d + 9d = -28. Grouping like terms together, we get:
3d = -9, and so d = -3.
Going back to an earlier result: a(1) = -19 - 6d.
Here, a(1) = -19 - 6(-3), or a(1) = -1.
Then the formula specifically for this case is a(n) = -1 - 3(n - 1)
and so a(21) = -1 - 3(20) = -61 (Answer D)
Use the distributive property to rewrite the given expression without parentheses.
7(x+2)
7(x+2) =
Answer:
7x+14
Step-by-step explanation:
The distributive property is when you multiply the number on the outside of rhe parenthesis with the numbers on the inside.
In this case it will be 7×x and 7×2
7(x+2)=7x+14
equation y = (2x)/(x-1), how do I get -0.5 as the x intercept ???
Answer:
( 0,0) is the x intercept
Step-by-step explanation:
y = (2x)/(x-1),
To find the x intercept set y = 0 and solve for x
0 = (2x)/(x-1)
Multiply by x-1 on each side assuming x does not equal 1
0 = 2x
x = 0
The x intercept is 0
( 0,0) is the x intercept
5x -2 ( 2x-2)= 2(3x-1)+7/2
Answer:
x = 1/2 or 0.5
Step-by-step explanation:
5x - 2(2x-2) = 2(3x - 1) + 7/2
= 5x - 4x + 4 = 6x - 2 + 7/2
= 5x + 4 = 10x - 2 + 7/2
= 5x + 6 = 10x + 7/2
= 5x + 2.5 = 10x
= 2.5 = 5x
Thus, x = 1/2 or 0.5
Hope this helps!
Given an angle of a triangle and the opposite side length; which trigonometric function would you use to find the hypotenuse? a TAN b COS c SIN d Not enough information
Answer:
Sin
Step-by-step explanation:
Sin < = opposite/hypotenuse
PLEASE ANSWER !! WILL GIVE BRAINLIEST! Consider the exponential functions f, g, and h, defined as shown. Place the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval [0, 3].
Answer: g(x) f(x) h(x)
Step-by-step explanation:
The order of the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval [0, 3] is is g(x) >f(x) > h(x)
What is Function?A function from a set X to a set Y assigns to each element of X exactly one element of Y.
What is Exponential function?A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.
What is average rate of change?It is a measure of how much the function changed per unit, on average, over that interval.
Given,
[tex]f(x) = 16(\frac{1}{2})^{x}[/tex]
interval = [0,3]
[tex]f(0)= 16(\frac{1}{2})^{0} =16 \\f(3)= 16(\frac{1}{2})^{3} =2[/tex]
Average rate of change = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Average rate of change= [tex]\frac{2-16}{3-0}=-4.67[/tex]
Consider the function g(x)
g(0)=21
g(3)=1
Average rate of change = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Average rate of change =[tex]\frac{1-27}{3-0}=-8.67[/tex]
Consider the exponential function
at x=0 the exponential function h =4
at x=0 the exponential function h =-3
Average rate of change = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Average rate of change =[tex]\frac{-3-4}{3-0}=-2.33[/tex]
Hence, the order of the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval [0, 3] is g(x) >f(x) > h(x)
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The cost of milk is modeled by a linear equation where four quarts (one gallon) costs $3.09 while two quarts
(half-gallon) costs $1.65. Write the linear equation that expresses the price in terms of quarts. How much would
an eight-quart container of milk cost?
Answer:
linear equation to express the price is:
y=0.72x+0.21
An eight quarts will cost : $5.97
Step-by-step explanation:
linear equation represent y=mx+b
let x=quarts ( x=4, x=2)
y= price (3.09 and y=1.65 )
two points (4,3.09) and (2,1.65)
need to find the slope m:
y2-y1/x2-x1
(1.65-3.09)/(2-4) ⇒ m=0.72
y=0.72x+b find b at point (2,1.65)
1.65=0.72(2) +b ⇒ b=0.21
y=0.72x +0.21
check : point (4,3.09)
y=0.72(4) +0.21
y=3.09 ( correct)
An eight quarts will cost :
y=0.72(8)+0.21
y=5.97 dollars
Select all transformations that carry rectangle
ABCD onto itself.
A. Rotate by 90 degrees clockwise using center P.
B. Rotate by 180 degrees clockwise using center P.
C. Reflect across line m.
D. Reflect across diagonal AC
.
E. Translate by the directed line segment from A to B.
THIS HAS MULTIPLE QUESTIONS PLEASE ANSWER ASAP
Question 1 Solve the inequality. |d + 2| ≥ 6
Question 2 Solve the equation. If there is no solution, select no solution. 5|x+3/4|=10
Question 3 Solve the inequality. –2 < 4 x – 10 < 6
Answer:
Question 1: d ≥ 4 or d ≤ -8
Step-by-step explanation:
Question 1 Solve the inequality. |d + 2| ≥ 6
d + 2 ≥ 6 or d + 2 ≤ -6
d ≥ 4 or d ≤ -8
Plot the image of quadrilateral ABCD under a reflection across the x-axis.
Answer:
The points for this will be:
A: (1, -4)
B: (-4, -2)
C: (-5, 4)
D: (-2, 1)
Step-by-step explanation:
If we reflect a shape over the x-axis, all of it’s points y values will be negated.
So, (1, 4) becomes (1, -4)
(-4, 2) becomes (-4, -2)
(-5, -4) becomes (-5, 4)
and (-2, -1) becomes (-2, 1)
Hope this helped!
New coordinates of the quadrilateral are A' is (1, -4), B' is (-4, -2), C' is (-5, 4) and D' is (-2, 1)
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The coordinates of quadrilateral ABCD are A is (1, 4), B is (-4, 2), C is (-5, -4) and D is (-2, -1)
After reflecting across the x-axis , the x-coordinates of the vertices will remain the same, but the signs of their y-coordinates will change.
Therefore, the new coordinates of the vertices will be:
A' is (1, -4)
B' is (-4, -2)
C' is (-5, 4)
D' is (-2, 1)
Hence, new coordinates of the quadrilateral are A' is (1, -4), B' is (-4, -2), C' is (-5, 4) and D' is (-2, 1)
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If x = 7, what is the value of 4(x - 5)
Answer:
8
Step-by-step explanation:
Because if x=7 then it would be 7-5 which equals 2 then you would times 2 and 4 together which equals 8 then you would have your answer which is 8.
Answer:
its 8
Step-by-step explanation:
x= 7
so replace the x with the value of 7
4(7-5)
7 minus 5 is 2
4·2
4 multipied by 2 is 8
so the answer is 8
Use distributive property to simplify the following expression. 2(4+9w)
Answer:
18w+8
Step-by-step explanation:
[tex]2(4 + 9w) \\ = 2(4) + 2(9w) \\ 8 + 18w \\ = 18w + 8[/tex]
Answer:
8+18w [tex]\huge\checkmark[/tex]
Step-by-step explanation:
Hi! Hope you are having an amazing day! :)
Distribute 2 by multiplying everything inside the parentheses by 2:
[tex]\huge\mathrm{2(4+9w)}[/tex]
[tex]\huge\mathrm{8+18w}[/tex] (Answer)
Hope you find it helpful.
Feel free to ask if you have any doubts.
[tex]\bf{-MistySparkles^**^*}\star[/tex]
please helppp ill give brainliest the question is attached below
Answer: It is false, the diameter is not 16 m.
Step-by-step explanation:
P 4m are 8 m are 32 m away. The diameter= 32 m.
(I hope its rights!!!)
A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same base and half the height of the prism is placed inside the prism, as shown in the figure
The answer is 200 cm³
The volume of the rectangular prism (V1) is:
V1 = l · w · h (l - length, w - width, h - height)
It is given:
h = 12 cm
w = l = 5 cm (since it has a square base which all sides are the same size).
Thus: V1 = 12 · 5 · 5 = 300 cm³
The volume of pyramid (V2) is:
V2 = 1/3 · l · w · h (l - length, w - width, h - height)
It is given:
h = 12 cm
w = l = 5 cm (since it has a square base which all sides are the same size).
V2 = 1/3 · 12 · 5 · 5 = 1/3 · 300 = 100 cm³
The volume of the space outside the pyramid but inside the prism (V) is a difference between the volume of the rectangular prism (V1) and the volume of the pyramid (V2):
V = V1 - V2 = 300 cm³ - 100 cm³ = 200 cm³
Find the GFC of 20 and 16
Solve the inequality 2x-5 is less than or equal to -x+12 . Give your answer as an interval.
Answer:
[tex]\Large \boxed{\mathrm{( - \infty, \frac{17}{3}) }}[/tex]
Step-by-step explanation:
[tex]2x-5\leq -x+12[/tex]
Add x and 5 on both parts.
[tex]2x+x\leq 12+5[/tex]
Combine like terms.
[tex]3x\leq 17[/tex]
Divide both parts by 3.
[tex]\displaystyle x \leq \frac{17}{3}[/tex]
an equation uses the symbol
Answer:
The '=' sign.
Step-by-step explanation:
The equals sign ( = ). for example:
3x + 1 = 8.
The equals sign was invented by Robert Recorde of Tenby, South Wales, UK in the early part of the 16th century.
Solve for y in the following system of equations: −x+y=0 −2x+y=−5 1. 5 2. 7 3. 6 4. 5
Answer:
y = 5
Step-by-step explanation:
−x+y=0 −2x+y=−5
Multiply the first equation by -2
-2(-x+y=0)
2x-2y =0
Add this to the second equation
2x-2y =0
−2x+y=−5
-------------------
0x -y = -5
-y =-5
Multiply by -1
y = 5
For each function, determine if it intersects or is parallel to the line y = -1.5x. If it
intersects the line, find the intersection point.
y =0.5x +4
PLEASE ANSWER I HAVE 25 MINUTES LEFT PLEASE
Answer:
Intersects; intersection point: (-2,3)
Step-by-step explanation:
Substitute -1.5x for y into y=0.5x+4:
-1.5x = 0.5x +4
-1.5x - 4 = 0.5x
-4 = 2x
x = -2
Plug in -2 for x into y=-1.5x
y = -1.5(-2)
y = 3
Organize the x and y values into an ordered pair:
(-2,3)
Answer:
y=0.5x+4 intersects y=-1.5x.
The intersection point is (-2,3)
Step-by-step explanation:
First, note that if two lines are not parallel, then they must intersect eventually in one way or another. Note that since these are two lines, they will only have one intersection points.
So we have the equation:
[tex]y=-1.5x[/tex]
Parallel lines have the same slope. Therefore, a line parallel to this line also has a slope of -1.5
The equation given to us is:
[tex]y=0.5x+4[/tex]
As we can see, this does not have a slope of -1.5. Therefore, the given equation is not parallel to y=-1.5x. However, this does mean that it will intersect y=-1.5x.
To find the x-value of their intersection, simply set the equations equal to each other and solve for x.
[tex]-1.5x=0.5x+4\\-2x=4\\x=-2[/tex]
Now, plug -4 into either of the equations:
[tex]y=-1.5(-2)=3\\y=0.5(-2)+4=-1+4=3[/tex]
Therefore, the point of intersection is (2,3).
WILL GIVE BRAINLIEST!!!
Help Someone please!! Given the following perfect square trinomial, find the missing term: 4x2 + ___x + 49 7 14 28 36
Answer:
28
Step-by-step explanation:
[tex]4 {x}^{2} + - - x + 49 \\ this \: is \: the \: expanded \: form \: of \\ {(2x + 7)}^{2} = 4 {x}^{2} + 28x + 49[/tex]
Answer:
[tex]\huge \boxed{28}[/tex]
Step-by-step explanation:
The trinomial is a perfect square.
Take the square root of the first term and the last term.
[tex](\sqrt{4x^2}+\sqrt{49})^2[/tex]
[tex]\sqrt{4x^2}=2x\\ \sqrt{49} =7[/tex]
[tex](2x+7)^2[/tex]
Expand to find the second term of the trinomial.
[tex](2x+7)(2x+7)\\2x(2x+7)+7(2x+7)\\4x^2 +14x+14x+49\\4x^2 +28x+49[/tex]
The second term of the trinomial is 28x.
What is the center of a circle with the equation (x - 6)2 + (y + 2)2 = 9?
A)
(6,2)
B)
(6,-2)
0)
(-6, 2)
D)
(-6, -2)
Answer:
B. (6,-2)
Step-by-step explanation:
The equation of a circle is (x-h)^2+(y-k)^2=r^2
The center of the circle is (h,k)
So, in this problem, h is 6 and k is -2, so the center of this circle is (6,-2).
What is the domain of F(x) = In(x)?
Answer as an inequality: [tex]x > 0[/tex]
Answer in interval notation: [tex](0, \infty)[/tex]
Answer in words: Set of positive real numbers
All three represent the same idea, but in different forms.
======================================================
Explanation:
Any log is the inverse of an exponential equation. Consider a general base b such that f(x) = b^x. The inverse of this is [tex]f^{-1}(x) = \log_b(x)[/tex]
For the exponential b^x, we cannot have b^x = 0. We can get closer to it, but we can't actually get there. The horizontal asymptote is y = 0.
Because of this, [tex]\log_b(x)[/tex] has a vertical asymptote x = 0 (recall that x and y swap, so the asymptotes swap as well). This means we can get closer and closer to x = 0 from the positive side, but never reach x = 0 itself.
The domain of [tex]\log_b(x)[/tex] is x > 0 which in interval notation would be [tex](0, \infty)[/tex]. This is the interval from 0 to infinity, excluding both endpoints.
------------------------
The natural log function Ln(x) is a special type of log function where the base is b = e = 2.718 approximately.
So,
[tex]\log_e(x) = \text{Ln}(x)[/tex]
allowing all of what was discussed in the previous section to apply to this Ln(x) function as well.
------------------------
In short, the domain is the set of positive real numbers. We can't have x be 0 or negative.
M1: L12a: Solving Equations Exit Ticket Determine which of the following equations have the same solution set. Must show work. 1. 3y + 8 = -10 - 3y 2. 6r+ 7 = 13 + 7r 3. 13 - 4m = 1 - m 4.-8-h=-3h 5. 38+7f=8f + 32 6. -6n + 20 = -14n - 4
determine which of the following has the same solution set must show work
Answer:
uhfcytuyyytt ryffffffffgtgghhh
The length of a rectangle is 5/6 feet. The width is 3/8 feet. How much greater is the length of the rectangle than the width?
Answer:
0.46 feet
Step-by-step explanation:
Length = 5/6 feet (or 0.254 m)
Width = 3/8 feet (or 0.114 m)
(5/6 - 3/8) feet = 11/24 feet or 0.46 feet (0.140 m)
Tricks for solving trigonometry proof question easily ??
Answer: do do that you need a firm understanding of trig. once you do, you can see all the steps and solve a trig proof problem easily. So go back to solving regular trig questions, and keep asking yourself why this formula works. once you have understanding of that, you can solve trig proof problems with ease.
Step-by-step explanation:
PLEaSE HELP!!!!!! will give brainliest to first answer
Answer:
The coordinates of A'C'S'T' are;
A'(-7, 2)
C'(-9, -1)
S'(-7, -4)
T'(-5, -1)
The correct option is;
B
Step-by-step explanation:
The coordinates of the given quadrilateral are;
A(-3, 1)
C(-5, -2)
S(-3, -5)
T(-1, -2)
The required transformation is T₍₋₄, ₁₎ which is equivalent to a movement of 4 units in the leftward direction and 1 unit upward
Therefore, we have;
A(-3, 1) + T₍₋₄, ₁₎ = A'(-7, 2)
C(-5, -2) + T₍₋₄, ₁₎ = C'(-9, -1)
S(-3, -5) + T₍₋₄, ₁₎ = S'(-7, -4)
T(-1, -2) + T₍₋₄, ₁₎ = T'(-5, -1)
Therefore, the correct option is B
thank you theta upon sin theta cos cos theta + sin thank you theta + cos cube theta upon sin theta + cos theta + sin theta minus cos theta upon sin theta minus cos theta is equal to
Answer:
Hey... Ans is in the pic..
Hope it helped u if yes mark me mark me BRAINLIEST!
Tysm!
:)
If 4SINB=3SIN(2A+B) :
Prove that:7COT(A+B)=COTA
Answer:
Step-by-step explanation:
Given the expression 4sinB = 3sin(2A+B), we are to show that the expression 7cot(A+B) = cotA
Starting with the expression
4sinB= 3sin(2A+B)
Let us re write angle B = (A + B) - A
and 2A + B = (A + B) + A
Substituting the derived expression back into the original expression ww will have;
4Sin{(A + B) - A } = 3Sin{(A + B)+ A}
From trigonometry identity;
Sin(D+E) = SinDcosE + CosDSinE
Sin(D-E) = SinDcosE - CosDSinE
Applying this in the expression above;
4{Sin(A+B)CosA - Cos(A+B)SinA} = 3{Sin(A+B)CosA + Cos(A+B)sinA}
Open the bracket
4Sin(A+B)CosA - 4Cos(A+B)SinA = 3Sin(A+B)CosA + 3Cos(A+B)sinA
Collecting like terms
4Sin(A+B)CosA - 3Sin(A+B)cosA = 3Cos(A+B)sinA + 4Cos(A+B)sinA
Sin(A+B)CosA = 7Cos(A+B)sinA
Divide both sides by sinA
Sin(A+B)CosA/sinA= 7Cos(A+B)sinA/sinA
Since cosA/sinA = cotA, the expression becomes;
Sin(A+B)cotA = 7Cos(A+B)
Finally, divide both sides of the resulting equation by sin(A+B)
Sin(A+B)cotA/sin(A+B) = 7Cos(A+B)/sin(A+B)
CotA = 7cot(A+B) Proved!
At a school carnival is the diameter of the map of a trampoline has 12 feet and the diameter of the metal frame is 14 feet what is the length in feet of the metal frame that's around the trampoline use 3.14 for pie and round the answer to the nearest 10th
Answer:
The length of the steel frame will be approximately 44 feet
Step-by-step explanation:
We can solve this problem by calculating the circumference of the steel frame. We are working with the fact that the steel frame was welded into a circular shape.
The circumference of the steel frame can be calculated using
[tex]circumference = \pi \times d[/tex]
where d diameter of the steel frame = 14 feet
[tex]circumference = 3.14 \times 14=43.96ft[/tex]
Therefore, the length of the steel frame will be approximately 44 feet
What is the surface area of the sphere below?
Hey there! I'm happy to help!
To find the surface area of a sphere, here is what you do.
You square the radius.
4²=16
You multiply by 4.
16×4=64
And you multiply by pi!
64×π=64π
Therefore, the surface area of the sphere is A. 64π units². It's that easy!
Now you can find the surface area of a sphere! Have a wonderful day! :D
Question :-
What is the surface area of the sphere that has a radius of 4 units?Answer :-
The surface area of the sphere is 64π units².[tex] \rule{180pt}{3pt}[/tex]
Diagram :-
[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{4 \: units}}\end{picture}[/tex]
Solution :-
As per the provided information in the given question, we have been given that the radius of the sphere is 4 units. We have been asked to find or calculate the surface area of the sphere.
To calculate the surface area of the sphere, we will use the formula below :-
[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}[/tex]
Substitute the given values into the above formula and solve for surface area:
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4 \times \pi \times (4 \: units)^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4 \: units)^2 \times 4 \times \pi[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 16 \: units^2 \times 4 \times \pi[/tex]
[tex]\sf:\implies \bold{Surface \: Area_{(Sphere)} = 64\pi \: units^2}[/tex]
Therefore :-
The surface area of the sphere is 64π units².[tex]\\[/tex]
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Have a great day! <33
idk know the answer i really need help
Answer:
37x - 13
Step-by-step explanation:
Hello!
The product of 37 and x mean multiply so we can write it as
37x
13 less means subtract so we put that at the end
37x - 13
The answer is 37x - 13
Hope this helps!
Answer:
37 * x - 13
This answer is here according to your question It said that 37*x - 13 Please mark this answer The brainliest one
