We have
arctan(-1) = -π/4
cos(-π/4) = 1/√2
and
arccos(√3/2) = π//6
sin(π/6) = 1/2
Then
cos(arctan(-1)) / sin(arccos(√3/2)) = (1/√2) / (1/2) = √2
The vertex form of the equation of a parabola is y=(x-4)^2 + 22,
What is the standard form of the equation?
PLEASE HELP ASAP
Answer:
[tex]y = x^2 - 8x + 38[/tex]
Step-by-step explanation:
Hello!
The standard form of a quadratic is [tex]ax^2 + bx + c[/tex].
To convert the vertex form to standard form, we have to expand the parenthesis and add the constant.
Convert:
[tex]y = (x - 4)^2 + 22[/tex][tex]y =(x -4)(x-4) + 22[/tex][tex]y = x^2 - 4x - 4x + 16 + 22[/tex][tex]y = x^2 - 8x + 38[/tex]The standard form is [tex]y = x^2 - 8x + 38[/tex]
Which of the following could be the measure of the angle below?
O -180°
O -120°
O 140°
An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and right angled.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and right angled.
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Answer:
A. -180
Step-by-step explanation:
Edge2022
The equation y = 1.99x represents the cost y for x downloaded songs. Is this equation a direct variation?
- Yes, this is a direct variation
- No, this is not a direct variation.
( Will give 20 points )
Answer:
No.
Step-by-step explanation:
To find the y value, one must replace x value, meaning that it's a multi step problem and it's not direct because y=exact value is not given
What is the experimental probability of the spinner landing on red?.
Answer:
The chances of landing on red are 1 in 4, or one fourth. This problem asked us to find some probabilities involving a spinner
I hope it helps you please mark me as brainlistalg 1 adding/subtracting with rational expression
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's evaluate ~
As the denominator of both the terms is same, we can simply perform subtraction on numerator.
That is :
[tex]\qquad \sf \dashrightarrow \: \dfrac{a - 2}{ {a}^{2} + 7a + 6 } - \dfrac{5a - 6}{ {a}^{2} + 7a + 6 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{a - 2 - (5a - 6)}{ {a}^{2} + 7a + 6 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{a - 2 - 5a + 6}{ {a}^{2} + 7a + 6 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ - 4a + 4}{ {a}^{2} + 7a + 6 } [/tex]
Answer:
-4a + 4/ a^2 + 7a +6
HELP ASAP- NO LINKS AND NO JOKES
a student solved a system of equations as shown below
3x+2y=7
5x-4y=-3
which step in the solution contains the first error
A. Step 4
B. Step 6
C. step 2
D. Step 1
Answer:
A
Step-by-step explanation:
step 3 is correct
x = 1
in step 4 the student has substituted x = 1 into y instead of x, that is
3x + 2(1) = 7 ← Incorrect substitution
Should be
3(1) + 2y = 7
3 + 2y = 7 ( subtract 3 from both sides )
2y = 4 ( divide both sides by 2 )
y = 2
Answer:
A. Step 4
Step-by-step explanation:
Identifying the error
In step 4 the value of x is supposed to be substituted into the second equation however the value of x is instead substituted for y which is the first error made
Solving it correctly and explaining each step.
We have the two equations 3x + 2y = 7 and 5x - 4y = -3
It appears that the elimination method is being used as the first step consist of multiplying the first equation by 2 so that we have the two variables -4y and 4y which can cancel out in the next step so we are going to use the elimination method as well to solve it correctly.
What is the elimination method?
The elimination method is a method used to solve a system of equations. When you have two variables that have the same coefficient ( number before variable; x or y ) but different signs ( it works if they have the same too ) you can add the two equations eliminating one of the variables. Using this method will leave you with a singular variable in which you can solve
Solving it using the elimination method
Again we have the two equations 3x + 2y = 7 and 5x - 4y = -3
(step 1) Notice how the first equation has 2y which can be multiplied by 2 resulting in us getting 4y which is opposite of -4y. This sets us up exactly for using the elimination method.
Thus the first step would be too multiply the first equation by 2
3x + 2y = 7
x2
------------------
6x + 4y = 14
Now we have the two equations 6x + 4y = 14 and 5x - 4y = -3
(step 2)Our next step would be to add the two equations so that the variable y is eliminated
6x + 4y = 14
+ 5x - 4y = -3
--------------------
11x 0 = 11
We're left with 11x = 11
(step 3)Our next step would be to solve for x
11x = 11
==> divide both sides by 11
x = 1
(step 4) Now that we have defined one of are variables we plug it in into one of the equations and solve for the other, this is step 4.
5x - 4y = -3
==> plug in x = 1
5(1) - 4y = -3
(step 5)==> simplify
5 - 4y = -3
(step 6) ==> subtract 5 from both sides
-4y = -8
(step 7) ==> divide both sides by -4
y = 2
The real solution would be (1,2)
Order the cities according to population density (persons/sq. km), from greatest to smallest.
Answer:
Step-by-step explanation:
City Population Density (Persons/Square Mile) 2016 Population Land A...
New York, New York 28,211 8,537,673 303
Los Angeles, California 8,484 3,976,322 469
Chicago, Illinois 11,883 2,704,958 228
View 751 more rows
A box contains coins, number cubes labelled 1 to 6, and a spinner with 4 congruent sectors. Which 2 items from the box would you use to simulate a situation with 8 equally likely outcomes?
A) A number cube and a spinner
B) A coin and a number cube
C) Two number cubes
D) A coin and a spinner
Using the Fundamental Counting Theorem, it is found that a simulation with 8 equally likely outcomes would be generated from:
D) A coin and a spinner.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
The coin has 2 outcomes, hence [tex]n_1 = 2[/tex].The spinner has 4 outcomes, hence [tex]n_2 = 4[/tex].The total number of equally likely outcomes is given by:
N = 2 x 4 = 8.
Hence option D is correct.
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Srekar needs to increase the length, width, and height of the prism below by 2 inches. The original prism has a length of 3 inches, a width of 2 inches, and a height of 1 inch.
A prism has a length of 3, height of 1, and width of 2.
Which statements about the new prism are true? Select three correct answers.
The new prism will have a length of 5 because 3 + 2 = 5.
The new prism will have a width of 4 because 2 + 2 = 4.
The new prism will have a height of 2 because 1 times 2 = 2.
The volume will increase by 6 because 2 times 3 = 6 and each of the 3 dimensions is increased by 2.
Srekar could increase the volume by the same amount by just adding 6 to the height instead of 2 to each side.
The volume of the new prism will be 20 times 3 = 60 because there will be 20 cubes in each layer and the height will be 3 so there will be 3 layers of 20 cubes each.
The three correct statements are:-
The new prism will have a length of 5 because 3 + 2 = 5.The new prism will have a width of 4 because 2 + 2 = 4.The new prism will have a height of 2 because of 1 time 2 = 2.What is a rectangular prism?
A rectangular prism is a three-dimensional rectangular object having all surfaces rectangular.
It is given in the question:-
Sarkar needs to increase the length, width, and height of the prism below by 2 inches. The original prism has a length of 3 inches, a width of 2 inches, and a height of 1 inch. A prism has a length of 3, a height of 1, and a width of 2.
The solution will be:-
The new prism will have a length of 5 because 3 + 2 = 5.The new prism will have a width of 4 because 2 + 2 = 4.The new prism will have a height of 2 because of 1 time 2 = 2.
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Can you help me please?
Question 37 of 49
Which of the following is a logical conclusion to the conditional statements
below?
If it is a hamburger, then it is a sandwich.
If it is a sandwich, then it can be held in your hands.
O
A. hands -> hamburger
O
B. hands > sandwich
O
C sandwich -›hamburger
D. hamburger => hands
The logical conclusion to the conditional statements in the question is; hamburger => hands.
What is logic?Logic deals with the process of arriving at a conclusion based of certain premises. If the premises are true, then the conclusion must be true and vice versa.
Thus, in this case, the logical conclusion to the conditional statements in the question is; hamburger => hands.
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xpress the logarithm in terms of ln 2 and In 5.
In 80
Answer:
4ln 2+ln 5
Step-by-step explanation:
Write the ratio for the trig function indicated.
Answer:
cos(θ) = 3/4
Step-by-step explanation:
Since cos=adj/hyp, the Hypotenous is 24, and the adjacent is 18. We write cos(θ)=18/24, which can be simplified to cos(θ)=3/4.
Write an informal proof proving that the two triangles are congruent.
The triangle is congruent with the ASA property.The two triangles are having same sides AB = XY, BC = YZ and CA = ZX and the same angles ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z.
What is congruency?If two triangles are congruent, this means they are the same shape and the same size.
By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.
The triangle is congruent by the ASA theorem. Here in the question, we can see in the figure that two angles ∠A = ∠X and ∠B = ∠Y so the third angle must be equal so ∠C = ∠Z.
Since side XY = AB and the three angles are equal so the other two sides will also be equal for the two triangles.
Therefore triangle is congruent with the ASA property.The two triangles are having same sides AB = XY, BC = YZ and CA = ZX and the same angles ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z.
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Write an equation of the direct variation that includes the point (35, 7)
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies directly with "x"}}{y=kx}~\hfill \textit{we also know that} \begin{cases} x= 35\\ y = 7 \end{cases} \\\\\\ 7=k(35)\implies \cfrac{7}{35}=k\implies \cfrac{1}{5}=k~\hfill \boxed{y=\cfrac{1}{5}x}[/tex]
pls help me
45 points just to help me with this plsss
Answer:
64 cm²
Step-by-step explanation:
Formula(s):
Surface area = Sum of the area of the prism's facesArea of triangle: 1/2 x Base x HeightArea of square: (side)²Clearly, we can see that there are 4 triangles and a square included in the prism. Therefore,
⇒ Surface area = 4(Area of triangle) + Area of squareWe know the following:
Given height of triangle: 6 cmGiven base of triangle: 4 cmSince the base of the triangle is equivalent to the side of square (As shown in picture), the side of the square must be 4 cm.
⇒ Surface area = 4(1/2 x Base x Height) + (side)²⇒ Surface area = 4(1/2 x 4 x 6) + (4)²⇒ Surface area = 4(12) + 16⇒ Surface area = 48 + 16⇒ Surface area = 64 cm²Therefore, the surface area of the prism is 64 cm².
3 Given 7x + 2 > 58, which number is not in the solution set?
(1) 6
2: 8
(3) 10
(4) 12
Answer:
(1) 6
Step-by-step explanation:
Let's start by solving the inequality.
7x +2 > 58
Minus 2 on both sides:
7x > 58 -2
7x > 56
Divide both sides by 7:
x > 56 ÷7
x > 8
This means that the value of x has to be greater than 8. 6 is smaller than 8, and is therefore not in the solution set. Thus, option 1 is the correct answer.
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
Given 7x+2>58, which number is not in the solution set?
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer \& how to solve:-}}}\rule{50}{1}[/tex]
First, subtract 2 on both sides:-
[tex]\sf{7x > 56}[/tex]
Now divide by 7 on both sides:-
[tex]\sf{x > 8}[/tex]
Henceforth, We conclude that
[tex]\large\textsf{Numbers greater than 8 make this inequality true}[/tex].
Edit:- Option A (6) is the correct answer, since it's not greater than 8, so it doesn't satisfy the inequality.
Good luck with your studies.[tex]\rule{50}{1}\smile\smile\smile\smile\smile\rule{50}{1}[/tex]
he table shows the relationship “Mason rode 15 miles per hour on his bicycle.”
Hours (h)
Miles (m)
1
15
2
30
3
45
4
60
5
75
Which statements are correct? Check all that apply.
The variable m is the independent variable.
The number of miles increases as time increases.
The number of hours causes a change in the number of miles ridden.
The variable h is the independent variable.
The variable h is the dependent variable.
The farther Mason rides, the less time it takes.
The variable m is the dependent variable.
Answer: The number of miles increases as time increases.
The number of hours causes a change in the number of miles ridden.
The variable h is the independent variable.
The variable m is the dependent variable.
Step-by-step explanation:
John earned 2% commission on the sale of a $95,000 house. How much commission did he earn?
*
10points
Jocelyn recorded the grade-level and instrument of everyone in the middle school
School of Rock below.
Seventh Grade Students
Eighth Grade Students
Instrument # of Students
Instrument # of Students
Guitar
12
Guitar
11
Bass
3
Bass
7
Drums
10
Drums
13
Keyboard
14
Keyboard
2
Based on these results, express the probability that a student chosen at random will
play an instrument other than drums as a fraction in simplest form.
The probability that a student chosen at random will play an instrument other than drums is 31/36.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability can be defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Total number of elements of sample space is 36.
Based on these results, express the probability that a student chosen at random will play an instrument other than drums as;
31/36
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You randomly draw a marble from a bag of 72 marbles, and then replace the marble. You do this 30 times and record your results in Tally chart. Base on these results, how many marbles in the bag are grey?
Answer:
2160
Step-by-step explanation:
You just have to mutiply, 72 x 30 is 2160. So the answer is there are still 2160 marbles in the bag that are grey!
Please mark branliest!!!
Answer:
30 ≥ x ≥ 0
Step-by-step explanation:
I don't think this is the full question but if it is the answer above should be right.
Have a nice day! :)
Find the area of the rhombus. using 9cm and 6cm
Answer:
27
Step-by-step explanation:
The formula is pq/2. If you plug in your values, you will get 27.
On Monday a team of street sweepers cleaned 1 1/3 city blocks. Tuesday, the team cleaned 1/5 as many blocks as on Monday. How many city blocks did the street sweepers clean on Tuesday?
Answer: 4/15
Step-by-step explanation:
1. Change 1/3 to 4/3 by multiplying the numerator by 3 and adding one.
2. Multiple 4/3 by 1/5 to get 4/15.
x^2 - 3 = 1
Please help me with this I need a answer and explanation so I can do this on my own asap!
Answer:
x=2
x=-2
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x^2-3-(1)=0
1.1 Factoring: x2-4
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 4 is the square of 2
Check : x2 is the square of x1
Factorization is : (x + 2) • (x - 2)
Equation at the end of step
1
:
(x + 2) • (x - 2) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : x+2 = 0
Subtract 2 from both sides of the equation :
x = -2
Solving a Single Variable Equation:
2.3 Solve : x-2 = 0
Add 2 to both sides of the equation :
x = 2
PLEASE HELP!
Before you answer:
-No spam (Will be reported)
-No incorrect answers (Will be reported)
-Correct answers and explanations will be mark as BRAINLIEST
Answer:
Step-by-step explanation:
Cone:diameter = 12 cm
r = 12 ÷ 2 = 6 cm
h = 6 cm
[tex]\sf \boxed{\text{\bf Volume of cone = $\dfrac{1}{3} \pi r^2h$ }}[/tex]
[tex]\sf = \dfrac{1}{3}*3.14*6*6*6\\\\ = 226.08 \ cm^3[/tex]
To find the surface area, we need to find the slant 'l'
[tex]\sf l = \sqrt{h^2+r^2}\\\\ =\sqrt{6^2+6^2}\\\\ = \sqrt{36+36}\\\\ =\sqrt{72}\\\\= 8.49 \ cm[/tex]
[tex]\sf \boxed{\text{\bf Total surface area of cone = $\pi r(r+l)$}}[/tex]
= 3.14 * 6 * (6 + 8.49)
= 3.14 * 6 * 14.49
= 273 cm²
If data set A has a larger standard deviation than data set B, data set B is
more spread out than data set A.
REST
TE
TER
O A. True
B. False
Reason:
Data set A has the larger standard deviation, so it is more spread out.
Randy works 50 weeks a year, averaging $500 a week in wages. He is offered a salaried position at $27,500 a year. If he accepts it, he will make ______. a. less money b. more money c. the same amount d. can’t tell
Answer:
b. more money
Step-by-step explanation:
Randy's original position lets him make:
50*500 = $25,000
The new position will let him make:
$27,500
Therefore,
original position < new position = $25,000 < $27,500
(using tables of x- and y-values).
x² - 3= 2x
a. X= -1 or x = 3
C. X = -3 or x = -3
b. x= 2 or x = -3
d.x=1 or x = -1
I need help with this plss
Answer:
a
Step-by-step explanation:
x² - 3 = 2x ( subtract 2x from both sides )
x² - 2x - 3 = 0 ← in standard form
consider the factors of the constant term (- 3) which sum to give the coefficient of the x- term (- 2)
the factors are - 3 and + 1 , since
- 3 × + 1 = - 3 and - 3 + 1 = - 2 , then
x² - 2x - 3 = (x - 3)(x + 1) = 0 ← in factored form
equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x - 3 = 0 ⇒ x = 3
What is the sum for 5x + 3x = 28x
Answer:
5x + 3x = 28x
8x = 28x
x must be 0
Determine the number of real number solutions for the equation 2^2-2x+6=0
Answer:
Step-by-step explanation:
x=(1-sqrt(13))/2=-1.303
x=(1+sqrt(13))/2=2.303
steps
(2x2 - 2x) - 6 = 0
step 2 pull out like terms
2x2 - 2x - 6 = 2 • (x2 - x - 3)
step 2 continued
3.2 Factoring x2 - x - 3
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3
Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -1 .
-3 + 1 = -2
-1 + 3 = 2
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
step 3
2 • (x2 - x - 3) = 0
Step 4
4.2 Find the Vertex of y = x2-x-3
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 0.5000
Plugging into the parabola formula 0.5000 for x we can calculate the y -coordinate :
y = 1.0 * 0.50 * 0.50 - 1.0 * 0.50 - 3.0
or y = -3.250
step 4
4.4 Solving x2-x-3 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -1
C = -3
Accordingly, B2 - 4AC =
1 - (-12) =
13
Applying the quadratic formula :
1 ± √ 13
x = —————
2
√ 13 , rounded to 4 decimal digits, is 3.6056
So now we are looking at:
x = ( 1 ± 3.606 ) / 2
Two real solutions:
x =(1+√13)/2= 2.303
or:
x =(1-√13)/2=-1.303
concluision
x =(1-√13)/2=-1.303
x =(1+√13)/2= 2.303
