Answer:
If you're trying to find x or y, you cannot find the exact value since there is one equation. If there was, for example, 2 equations, [a system of equations] you could solve that. But here we only have one equation.
So, if you're trying to solve for x;
x = 7 - 3y
And if you're trying to solve for y;
y = 7/3 - x
How long is the second hand to the nearest tenth if it moves 2cm in 15 seconds?
let's recall that a circular clock has 360° and 60 seconds per minute.
the seconds hand does 60 seconds in one go-around, and if it has covered 15 seconds on the clock, that gives us an angle of 90°, 15 is one quarter of 60, so in 15 seconds it has covered one quarter of the full circle or 90°.
we also know it covered 2cm, namely the arc's length on the 15 seconds is 2cm.
[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =90\\ s=2 \end{cases}\implies 2=\cfrac{(90)\pi r}{180}\implies 2=\cfrac{\pi r}{2} \\\\\\ 4=\pi r\implies \cfrac{4}{\pi }=r\implies 1.27\approx r[/tex]
Mr. Jones asks his students to generate the next two numbers in the sequence beginning –5.5, 11, ....
Taquan suggests that the sequence is geometric and the next two numbers are –22 and 44. Julia suggests that the sequence is arithmetic and the next two numbers are 27.5 and 44.
Which best explains which student is correct?
Taquan is correct. When the signs change in a sequence, the sequence is geometric. Each successive term is generated by multiplying by –22 .
Julia is correct. When the numbers alternate between decimals and whole numbers, the sequence is arithmetic. Each successive term is generated by adding 16.5.
Both students could be correct about the types of possible sequences. However, one student made a computational error because it is not possible to arrive at a fourth term of 44 in two different ways.
Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.
Answer:
D
Step-by-step explanation:
Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.
A sequence could either be arithmetic or geometric. The truth statement about the correct student is:
Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.
Given that:
[tex]-5.5, 11, .....[/tex]
If the sequence is arithmetic, then the common difference is
[tex]d = 11 --5.5[/tex]
[tex]d = 16.5[/tex]
So, the next two elements are:
[tex]T_3 = 11 + 16.5 =27.5[/tex]
[tex]T_4 = 27.5 + 16.5 =44[/tex]
If the sequence is geometric, then the common ratio is
[tex]r =\frac{11}{-5.5}[/tex]
[tex]r= -2[/tex]
So, the next two elements are:
[tex]T_3 = 11 \times -2 = -22[/tex]
[tex]T_4 = -22 \times -2 = 44[/tex]
Based on the above computations, both students are correct.
Read more about sequence at:
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Identify the parent function of the equation below.
Answer:
y = x² ⇒ answer C
Step-by-step explanation:
* Lets explain the problem
∵ The function is y = 1/2 x² + 3 , that means the parent function is
transformed by some transformation
- If the parent function is y = x²
- y = x² is a quadratic function represented graphically by upward
parabola with vertex (0 , 0)
∵ y = x² changed to y = 1/2 x² that means we multiply each
y-coordinates of the points on the graph of the function by 1/2
∴ The graph of the function is compressed vertically by scale
factor 1/2
- That means the graph is squeezing toward the x-axis
∵ y = 1/2 x² changed to y = 1/2 x² + 3 that means we add each
y-coordinates of the points on the graph of the function by 3
∴ The function translated 3 units up
- That means the vertex of the parabola changed to (0 , 3)
∴ The new function is y = 1/2 x² + 3
* The parent function of y = 1/2 x² + 3 is y = x²
# Look to the attached graph for more understand
- y = x² ⇒ the red graph (parent function)
- y = 1/2 x² + 3 ⇒ the blue graph
Help asap
Congruent Angle pairs
Answer:
Option A ∠RWQ, ∠WPS and ∠PWU
Step-by-step explanation:
we know that
Two angles are supplementary if their sum is equal to 180 degrees
Part 1)
∠OPW+∠WPS=180° ------> by supplementary angles
we have
∠OPW=110°
substitute
110°+∠WPS=180°
∠WPS=180°-110°=70°
Part 2) we know that
∠RWQ+(50°+60°)=180° ------> form a linear pair
∠RWQ=180°-(50°+60°)=70°
so
∠OPW+∠RWQ=180° -----> by supplementary angles
Part 3) we know that
∠PWU=∠RWQ -------> by vertical angles
so
∠OPW+∠PWU=180° -----> by supplementary angles
therefore
The angles that are supplements to angle ∠OPW are
∠WPS, ∠RWQ and ∠PWU
If LMNO is a rectangle, and m_MON = 30°, what is the value of x?
Answer:
120
Step-by-step explanation:
a pex
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
The slope is the change in Y over the change in x:
Using the two points shown on the graph:
(1,7) and (0,0)
Slope = (7-0) / (1-0)
Slope = 7/1
Slope = 7
The number if front of the x would be the slope
The answer would be D. y = 7x
a watch is getting slow by 2 minutes for each hour in a day . if it shows 10 am now. what shall be the time after 12hours
Answer:
9:36 p.m.
Step-by-step explanation:
10 am + 12 hours = 10:00 pm
2 minutes every hour
12 hours x 2 = 24 minutes
12*2=24
10:00+12:00-0:24=21:36
How can you tell whether a counting problem is a permutation or combination problem? Give examples to support your answer
Answer:
Step-by-step explanation:
Permutation is the ways in which a fixed group or members that can be arranged or ordered and combinations are used when a smaller group has to be chosen from a larger group.
Examples:
Permutation: How many unique combinations of the word MAHNOOR can be formed when the letters will be scrambled
2. In what order or arrangements five people can be seated in the front row?
The number of people are fixed, we have to find the order.
Combination: Choosing two cards from a deck of 52 cards. We are choosing a small group from a larger group of all cards.
2. Choosing 4 students from a class to take part in the competition.
The selection can be made in multiple ways ..
Answer:
Permutation - requires to arrange order with quantities
Combination - order is not required
Step-by-step explanation:
If a question demands you to select as well as arrange the given quantities then it means that it is a problem of permutation.
While on the other hand, a problem of combination would only ask you to select the quantities and not their order.
So with practice, you get to know how exactly it works.
Use synthetic division to solve (x4- 1) = (x - 1). What is the quotient?
x3 -x2+x-1
O x3
x+x2+x+1
x3-2
Answer:
The quotient is x³+x²+x+1
Step-by-step explanation:
=(x^4-1) ÷ (x-1)
=(x^4-1)/ (x-1)
Solve the numerator by using perfect square formula:
⇒x^4-1 = (x²-1)(x²+1)
=(x²-1)(x²+1)/(x-1)
Further solve the numerator by using perfect square formula:
=(x+1)(x-1)(x²+1)/(x-1)
Cancel the like terms of numerator and denominator
We get;
=(x+1)(x²+1)
Multiply the terms:
=x³+x+x²+1
Re-arrange the terms:
=x³+x²+x+1
Hence the quotient is x³+x²+x+1....
Answer:
C
Step-by-step explanation:
A city determines that a planned community must have at least 4 acres of developed and open space, and the difference between the number of developed acres, y, and the number of open acres, x, can be no more than 1. Which graph represents the system of inequalities for this scenario? x + y ≤ 4 y – x ≥ 1
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x ----> the number of open acres
y ----> the number of developed acres
we know that
[tex]x+y \geq 4[/tex] -----> inequality A
The solution of the inequality A is the shaded area above the solid line [tex]x+y=4[/tex]
[tex]y-x\leq 1[/tex] -----> inequality B
The solution of the inequality B is the shaded area below the solid line [tex]y-x=1[/tex]
so
The graph in the attached figure
Answer:
Option B.
Step-by-step explanation:
Let x be the number of open acres and y be the number of developed acres.
It is given that a community must have at least 4 acres of developed and open space.
[tex]x+y\geq 4[/tex]
The difference between the number of developed acres, y, and the number of open acres, x, can be no more than 1.
[tex]y-x\leq 1[/tex]
The relative equations of both inequalities are
[tex]x+y=4[/tex]
[tex]y-x=1[/tex]
The table of values
For line 1 For line 2
x y x y
0 4 0 1
4 0 -1 0
Plot these ordered pairs on a coordinate plane and draw both lines.
The related line of first inequality is a solid line and shaded area lies above the line because the sign of inequality is ≥.
The related line of second inequality is a solid line and shaded area lies below the line because the sign of inequality is ≤.
Therefore, the correct option is B.
Find the measure of C in the picture please
Answer:
Option A. The measure of angle C is 140°
Step-by-step explanation:
see the attached figure with letters to better understand the problem
we know that
The triangle OAB is an isosceles triangle
Because
OA=OB=radius
m∠BAO=m∠ABO=20°
Find the measure of angle C
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
so
m∠BAO+m∠ABO+m∠C=180°
substitute the given values
20°+20°+m∠C=180°
m∠C=180°-40°=140°
I don’t get this question
[tex]\text{Use pythagorean theorem}[/tex]
[tex]$a^2 + b^2 = c^2 \longrightarrow a^2 +6^2=9^2 \longrightarrow a^2 =45\longrightarrow a =6.7082\longrightarrow a = 6.71$[/tex]
[tex]\textbf{a = 6.71}[/tex]
This is a right triangle and to solve this you must use Pythagorean theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
a and b are the legs (the sides that form a perpendicular/right angle)
c is the hypotenuse (the side opposite the right angle)
In this case...
a = 6
b = x
c = 9
^^^Plug these numbers into the theorem
[tex]6^{2} +x^{2} =9^{2}[/tex]
simplify
36 + [tex]x^{2}[/tex] = 81
Now bring 36 to the right side by subtracting 36 to both sides (what you do on one side you must do to the other). Since 36 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.
36 - 36 + [tex]x^{2}[/tex] = 81 - 36
0 + [tex]x^{2}[/tex] = 45
[tex]x^{2}[/tex] = 45
To remove the square from x take the square root of both sides to get you...
x = √45
x ≈ 6.71
(choice A)
Hope this helped!
~Just a girl in love with Shawn Mendes
A music store owner noted that CD sales had dropped 29% from one quarter to the next. If the owner sold 570 units in the first quarter, how many did she sell in the next quarter?
Answer:
About 405
Step-by-step explanation:
570 CDs were sold the first quarter.
The second quarter CDs had dropped 29% from the first quarter (570).
Dropped, you should think you are subtracting.
So we need to
simplify 570-.29(570):
570(1-.29)
570(.71)
404.7
404.7 --> 405 (when rounded)
Step-by-step explanation:In order to find the answer to your question, we would need to find how much of 570 is 29%, and subtract that number to 570.
The reason why we would do this is because in the question, it says that the sales dropped 29% for one quarter to the next. This means that the next quarter would drop 29%.
We know that they sold 570 units, so we would use 570 in our calculations.
We know that the sales decrease by 29%, so we would multiply 570 by 0.29 to find how much of 570 is 29%.
[tex]570*0.29=165.3[/tex]
29% of 570 is 165.3
What we would do now is subtract 570 by 165.3 in order to fin how much sales they made in the next quarter.
[tex]570-165.3=404.7[/tex]
Once you're done solving, you would get the answer of 404.7
This means that they sold 404.7 (405 when rounded) CDs in the next quarter.
I hope this helps you out.Good luck on your academics.Have a fantastic day!The area of a rectangular back yard is 55 square meters. The length of the yard is one meter greater than twice the width.
What is the width of the yard in meters?
Provide your answer below:
Step-by-step explanation:
Area of a rectangular backyard is given as 55 m²
the length is 1 m greater than the twice the width
=>l=2w+1---(say A)
we know that
Area of a rectangle is always length * width=A=l*w
Divide both sides by w
A/w=l
put this value of l in (A)
A/w=2w+1
multiply both sides by w
A=w(2w+1)
55=2w²+w
subtract 55 from both sides
2w²+w-55=0
2w²-10w+11w-55=0
2w(w-5)+11(w-5)=0
(2w+11)(w-5)=0
(2w+11=0 , w-5=0
2w=-11. , w=5
w=-11/2 m
width can never be a negative integer so we omit -11/2
we will consider w=5m
put this in (A)
l= 2(5)+1
l=10+1
l=11m
checking ,
A=lw
A=(11m)(5m)
A=55m²
Answer:
5
Step-by-step explanation:
Area= 55
width=y(unknown)
length=1+2y(given)
formula for finding A.=l*b
(1+2y)(y)= y+2y^2
y+2y^2=55
2y^2= 55-y
y=5
verification
2*5^2=55-5
2*25=55-5
What are the measures of angles Q and R
Angle Q = 93° & angle R = 87°
What is the relation between adjacent sides of parallelogram ?
The sum of any two adjacent angles of a parallelogram is equal to 180°, i.e. they are supplementary angles.
What are the values of required angles ?In parallelogram QRST,
∠Q= (9x-6)° & ∠R= (8x-1)°
Here, angle Q & angle R are adjacent angles of the parallelogram QRST.
∴ ∠Q+∠R = 180°
⇒ (9x-6)+(8x-1)= 180
⇒ 9x-6+8x-1 = 180
⇒ 17x-7= 180
⇒ 17x = 180+7
⇒ 17x = 187
⇒ x = 187/17
⇒ x = 11
So, ∠Q= (9x-6)° = {(9×11)-6}° = (99-6)° = 93°
& ∠R= (8x-1)° = {(8×11)-1}° = (88-1)°= 87°
Learn more about measuring angle here :
https://brainly.com/question/331095
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What is the area of the sector having ....
Answer:
D) 160π/3 units²
Step-by-step explanation:
Step 1: Write the formula for area of sector
Area of sector = 1/2 x r² x angle in radians
Step 2: Substitute values in the formula
Area of sector = 1/2 x 8² x 5π/3
Step 3: Solve to find the value of area of sector
Area of sector = 160π/3 units²
Therefore, the correct option is D
!!
How do you do 6 divided by 11 bus stop method, please explain the steps?
Which one of the following numbers is an irrational number?
A. 8.234234…
B. 123⁄455
C. 3.131131113…
D. 5.364
Answer:
C. 3.131131113…
Step-by-step explanation:
Irrational numbers cannot be written as a ratio of two integers and irrational numbers can have decimal that goes on forever without repeating
C. 3.131131113…
It's a decimal which is not repeating, therefore it's an irrational number.
what will be the circumference of a circle if the area is 64cm
Given that area of circle is 64cm we can assume we will need to first find radius and then calculate circumference.
First we know that area of a circle is [tex]A=\pi r^2[/tex] hence [tex]r=\sqrt{\dfrac{A}{\pi}}[/tex]
We can now put in our area,
[tex]r=\sqrt{\dfrac{64}{\pi}}\approx20.37[/tex]
Then we use the formula for circumference,
[tex]C=2\pi r\Longrightarrow C=2\pi\cdot20.37\approx\boxed{128\mathbf{cm}}[/tex]
Hope this helps.
r3t40
A school district needs 3 teachers for every 70 students. They expect to have 14,700 in the district next year. At this time they have 612 teachers. How many more teachers are needed.
Answer:
18
Step-by-step explanation:
We can use a proportion to find out the number of teachers that are needed.
3/70 = x/14,700
70x = 3 * 14,700
70x = 44,100
x = 630
630 teachers are needed altogether. Since there are already 612 teachers, the number of more teachers who are needed is the difference between 630 and 612.
630 - 612 = 18
Answer: 18
PLEASE HUREY IXL QUESTION
Answer:
5 12/24 -> -0.5 -> -5 6/20
Step-by-step explanation:
Negatives are lasts and positive goes first! Since the order is greatest to least.
-5 6/20 is less than -0.5 because *think of a number line -5 6/20 will be all the way to the left because it large in negative value
What is the slope of the line?
y+5=2(x+1)
A. 1/5
B. 2/5
C. 2
D. 1/2
Rewrite the equation in slope-intercept form:
y+5=2(x+1)
Use the distributive property:
y+5 = 2x +2
Subtract 5 from each side:
y = 2x -3
The slope is the value with the X
The slope = 2
Answer:
2.5
Step-by-step explanation:
2(x+1)=y+5
2x+1=y+5
y+5=6
in addtion y can be add
so we have now...
2x+1=6
minus 1 from 6 and get 5
2x=5
5 divide by 2 = 2/5
Hope it helps
3 radical 12 times 5 radical 2
Answer:
Step-by-step explanation:
3*√12 * 5*√2
15 √24
15 √(2*2*2*3)
15*2 √6
30√6
What is the solution set for x-4>2?
Answer:
(6,∞)
x > 6
Step-by-step explanation:
Solve by adding 4 to both sides.
[tex]x-4>2\\x>6[/tex]
To put this in interval notation for your solution set, consider your sign.
You have a greater than sign, which means that 6 is not a solution. In interval notation, that means that you should use parentheses " ( " instead of brackets " [ ".
Your solution set goes on infinitely, and infinity also uses parentheses rather than brackets.
You can write your solution set in interval notation as follows:
(6, ∞)
Find the measure of b in the picture please
Answer:
The correct answer option is B. 126°.
Step-by-step explanation:
We are given a figure where triangle within a triangle is inscribed in a circle and we are to find the measure of angle b.
From the given figure, we can see that the angle b is at the center of the circle. So this must be an isosceles with two sides equal to each other.
If that is the case, then angle a must be equal to 27° so we can find the measure of angle b.
∠b = 180° - (27° + 27°)
∠b = 126°
If p(x)=2x^2 -4 and q(x)=x-3, what is (p*q)(x)
Answer:
2x^3 - 6x^2 - 4x + 12.
Step-by-step explanation:
(p*q) (x) = (2x^2 - 4)(x - 3)
= 2x^3 - 6x^2 - 4x + 12.
For this case we have the following functions:
[tex]p (x) = 2x ^ 2-4\\q (x) = x-3[/tex]
We must find [tex](p * q) (x).[/tex] For definition, we have to:
[tex](p * q) (x) = p (x) * q (x)[/tex]
So:
[tex](p * q) (x) = (2x ^ 2-4) (x-3)[/tex]
We apply distributive property:
[tex](p * q) (x) = 2x ^ 3-6x ^ 2-4x + 12[/tex]
Answer:
[tex](p * q) (x) = 2x ^ 3-6x ^ 2-4x + 12[/tex]
Simplify cos[arccsc((2/3)/3)].
A)no solution
B)sqrt3/2
C)1/2
Answer:
1/2
Step-by-step explanation:
We have [tex]\cos(\arccsc(\frac{2\sqrt{3}}{3}))[/tex].
Let [tex]u=\arccsc(\frac{2\sqrt{3}}{3})[/tex].
This implies [tex]\csc(u)=\frac{2\sqrt{3}}{3}[/tex].
Use that sine and cosecant are reciprocals.
[tex]\sin(u)=\frac{3}{2\sqrt{3}}[/tex]
Now I'm going to rationalize the denominator there by multiply numerator and denominator by [tex]\sqrt{3}[/tex]:
[tex]\sin(u)=\frac{3\sqrt{3}}{2(3)}[/tex]
[tex]\sin(u)=\frac{3\sqrt{3}}{6}[/tex]
Reduce the fraction:
[tex]\sin(u)=\frac{\sqrt{3}}{2}[/tex]
Now I'm going to use a Pythagorean Identity: [tex]\cos^2(u)+\sin^2(u)=1[/tex].
This will give me the value of cos(u) which would give me the answer to my question if it exists.
Replace [tex]\sin(u)[/tex] with [tex]\frac{\sqrt{3}}{2}[/tex] in:
[tex]\cos^2(u)+\sin^2(u)=1[/tex]
[tex]\cos^2(u)+(\frac{\sqrt{3}}{2})^2=1[/tex]
[tex]\cos^2(u)+\frac{3}{4}=1[/tex]
Subtract 3/4 on both sides:
[tex]\cos^2(u)=\frac{1}{4}[/tex]
Square root both sides:
[tex]\cos(u)=\pm \frac{1}{2}[/tex] (since 1/2*1/2=1/4 or -1/2*-1/2=1/4)
Now we must decide between the positive or the negative.
It depends where u lies. What quadrant? Hopefully it lays between 0 and [tex]\pi[/tex]. Otherwise, it doesn't exist (unless you have a different definition for arc function).
So u led to this equation earlier:
[tex]\sin(u)=\frac{\sqrt{3}}{2}[/tex]
arcsin( ) only has outputs between [tex]\frac{-\pi}{2}[/tex] and [tex]\frac{\pi}{2}[/tex].
This would have to be in the first quadrant because we have only positive sine values there.
So this means cos(u)=1/2 and not -1/2 because we are using that u is in the 1st quadrant.
Remember u was [tex]\arccsc(\frac{2\sqrt{3}}{3})[/tex].
So we have actually evaluated
[tex]\cos(\arccsc(\frac{2\sqrt{3}}{3}))[/tex] without a calculator.
The value is 1/2.
Emily was going to sell all of her stamp collection to buy a video game. After selling half of them she changed her mind. She then bought seventeen more. If she started with 46 stamps, how many does she have now?
Answer:
starts wuth 46, and sells half, so she has 23. then when she buys 17 more she then has 40.
if you are asked to show work its 46/2=23, then 23+17=40!
Answer:
40 stamps
Step-by-step explanation:
She started with 46 stamps.
She sold half of them
46*1/2 = 23
She sold 23 46-23 = 23
So she has 23 stamps
Then she bought 17
23+17 = 40
She now has 40 stamps
Which of the following are solutions to the equation below. Check all that apply
Answer:
B. -2√2 - 5
C. 2√2 - 5
Step-by-step explanation:
The left side of the equation is already a perfect square.
Let us factorize it first.
x²+10x+25=8
x(x+5)+x(x+5)=8
(x+5)²=8
Let us take the square roots of both sides.
x+5=±√8
But √8=±2√2
Therefore in surd form, the two solutions become:
x+5=2√2 or x+5=-2√2
Therefore x= 2√2-5 and -2√2+-5
Simplify (1 − cos x)(1 + cos x). (2 points)
Answer:
sin²x
Step-by-step explanation:
we have
(1 − cos x)(1 + cos x)=1-cos²x
Remember that
sin²x+cos²x=1 ------> i-cos²x=sin²x
therefore
(1 − cos x)(1 + cos x)=sin²x
Answer:
[tex]sin^2x[/tex]
Step-by-step explanation:
Given expression,
[tex](1 - cos x)(1 + cos x)[/tex]
By using [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex](1 - cos x)(1 + cos x)=1^2 - cos^2x = 1 - cos^2x[/tex]
[tex]\because sin^2x+cos^2x=1[/tex]
[tex]\implies (1 - cos x)(1 + cos x)=sin^2x+cos^2x - cos^2x=sin^2x[/tex]
Since, further simplification is not possible,
Hence, the simplified form of the given expression is [tex]sin^2x[/tex]