Answer:
Step-by-step explanation:
tan 45=1
[tex]tan 2\alpha =\frac{2tan\alpha}{1-tan^2\alpha } \\put~\alpha =22.5\\2\alpha =2 \times 22.5=45\\tan~2\alpha =tan~45=1\\1=\frac{2tan \alpha }{1-tan^2\alpha} \\1-tan^2\alpha =2 tan\alpha \\ tan^2\alpha +2tan \alpha -1=0\\tan\alpha =\frac{-2 \pm\sqrt{4+4} }{2} \\=-1\pm\sqrt{2} \\\alpha =22.5\\so ~tan~\alpha ~is~positive.\\so ~tan~\alpha =\sqrt{2} -1[/tex]
A pair of parallel lines is cut by a transversal:
A pair of parallel lines cut by a transversal is shown. The inside bottom right angle is labeled 85 degrees. The alternate interior angle is cut by a ray and is labeled as x on one side and 25 degrees on the other.
What is the measure of angle x?
50 degrees
55 degrees
60 degrees
80 degrees
Answer:
60
Step-by-step explanation:
1. parallel angle = 85
2. 180 - 85 = 95
3. 180 - (95+25) = 60
(c) Given that the average speed for the entire journey was 80 km/h, form an equation in x and solve the equation.
Answer:
80x = y
Step-by-step explanation:
Which of the following is equivalent to 8-3x > 2(3x - 5) ?
A. 18>9x
B. 9x<13
C. 11>9x
D. -8x>2
Answer:
A
Step-by-step explanation:
Given:
[tex]8-3x > 2(3x-5)[/tex]
Simplify by distributing:
[tex]8-3x > 6x-10[/tex]
Add 10 to left side and add 3x to the right side:
[tex]18 > 9x[/tex]
The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows: y = 4 + 2x What does the slope of this function represent? (1 point) a The original height of the plant was 4 mm. b The original height of the plant was 2 mm. c The height of the plant increases by 2 mm for every hour of sunlight it receives. d The height of the plant increases by 4 mm for every hour of sunlight it receives.
The correct answer is option C which is the height of the plant increases by 2 mm for every hour of sunlight it receives.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Given equation is as follows:-
y = 4 + 2xHere x is the variable which depends on the amount of sunlight and 4 is the original height of the plant so as the sunlight varies the value of x changes and it increases the height of the plant by 2 mm.
The graph of the equation is also attached with the answer. Therefore the correct answer is option C which is the height of the plant increases by 2 mm for every hour of sunlight it receives.
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How to write a two column proof for number 12?
1) [tex]\overline{EJ} \parallel \overline{KF}, \overline{JG} \parallel \overline{KH}, \overline{EF} \cong \overline{GH}[/tex] (given)
2) [tex]\overline{FG} \cong \overline{FG}[/tex] (reflexive property)
3) [tex]\overline{EG} \cong \overline{FH}[/tex] (segment addition postulate)
4) [tex]\angle JEF \cong \angle KFG, \angle JGE \cong \angle KHF[/tex] (if two parallel lines are cut by a transversal, the corresponding angles are congruent)
5) [tex]\triangle EJG \cong \triangle F\text{ }KH[/tex] (SAS)
Find The Distance Between4.5 And -1.4. ( i Need A Answer Right Now Pleaseeeeee!!!!!!
Answer:
5.9
Step-by-step explanation:
The distance between a point A and a point B is A-B. (4.5) - (-1.4) is the same as 4.5 + 1.4 so your answer is 5.9
Answer:
Step-by-steDistance between
(
−
4.5
,
−
4.5
)
and
(
3.5
,
3.5
)
is
8
√
2p explanation:
Hence distance between
(
−
4.5
,
−
4.5
)
and
(
3.5
,
3.5
)
is given by
√
(
3.5
−
(
−
4.5
)
)
2
+
(
3.5
−
(
−
4.5
)
)
2
=
√
8
2
+
8
2
=
√
64
+
64
=
√
128
=
√
8
2
×
2
=
8
√
2
This image of a physics problem shows a block resting on a ramp, . ∠P is the angle between the ramp and the horizontal, and is oriented vertically. Which quantity is equal to cos W?
A. sin p
b. cos p
c. 1 - sin p
d. 1 - cos p
Based on the image description, the quantity that is equal to cos W is sin P.
What is the image about?The image is known to be showing an object on a ramp. Based on it, we can therefore take the angle a to the complementary angle of angle w.
Note that the angle w and angle b are said to be the same via alternate interior angles. Therefore, the quantity that is equal to cos W is sin P.
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which expressions are equivalent to this exponential expression?
6-10/6-4
A. 6-^6
B. 6^6
C. 1/6^6
D. 1/36
Step-by-step explanation:
Hi There! Let me help you :)
Known
[tex] = \frac{ {6}^{ - 10} }{ {6}^{ - 4} } [/tex]
[tex] \: [/tex]
Asked
Simplify form.
[tex] \: [/tex]
Answer
[tex] = \frac{ {6}^{ - 10} }{ {6}^{ - 4} } [/tex]
[tex] = {6}^{ - 10 - ( - 4)} [/tex]
[tex] = {6}^{ - 6} [/tex]
[tex] = {6}^{ - 6} \: \text{or} \: \frac{1}{ {6}^{6} } [/tex]
There are 2 answers, it's A and C.
The coefficient of 2(3)(6)Q is
The coefficient of the variable Q is 36 , Option A is the correct answer.
The complete question is
The coefficient of 2(3)(6)Q is _____. a.36 b.18 c.12
What is a Coefficient ?Coefficient is the constant term written in front of variable in an expression.
The expression given in the question is
2(3)(6)Q
The coefficient is 2 * 3 * 6 = 36
Therefore , the coefficient of the variable Q is 36 , Option A is the correct answer.
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PLEASE HELP !! In this table, the input and output values are
related. If you know the input, you can predict
the output. Which rule describes how the
output depends on x?
Click on the correct answer.
10x² +7
10x + 7
7x + 10
Answer:10X^2 +7
Step-by-step explanation:
What additional information could be used to prove that the triangles are congruent using aas or asa?.
Answer:
Two angles and a side
Step-by-step explanation:
In order to prove triangles congruent, you'd have to either have an angle, angle, and then a side in that exact order for AAS or you can have two angles and a side in the middle of them for ASA.
4
Drag each response to the correct location on the table. Each response can be used more than once, but not all responses will be used.
Consider the two exponential equations shown. Identify the attributes for each equation to complete the table.
250
111%
89%
Growth 11% 8.9%
40
Decay
250 (0.89)*
250 = 40(1.11)
40 =
Initial Value::
Growth or Decay::
Growth/Decay Rate::
Reset
Initial Value::
Growth or Decay:
Growth/Decay Rate::
Next
First function; Initial value = 250; Decay; Decay rate = 11%
Second function; Initial value = 40; Growth; Decay rate = 11%
How to solve exponential decay functions?
1) The first function is;
40 = 250(0.89)^(x)
y = 250 (initial value)
Decay because 0.89 < 1
Thus;
Decay rate: (1 - 0.89) * 100 = 11%
2) The second function is;
250 = 40(1.11)^(x)
y = 40 (initial value)
Growth because 1.11 > 1 so growth
Growth rate: (1.11 - 1) * 100 = 11%
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f(x)=|3x +5| +6
g(x) = 7
Find (f + g)(x).
Answer:
(f+g)(x)
= |3x+5| + 13
Step-by-step explanation:
(f+g)(x) means
f(x) + g(x)
so you add the functions together.
|3x+5| + 6 + 7
And simplify.
|3x+5| + 13
Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive. Mr. McMillan has already taught his class 8 letters. The students in Ms. Burke's class, who started the unit later, currently know how to write 12 letters. Mr. McMillan plans to teach his class 4 new letters per week, and Ms. Burke intends to cover 3 new letters per week. Eventually, the students in both classes will know how to write the same number of letters. How long will that take? How many letters will the students know?
The number of weeks by which the students in both classes will know how to write the same number of letters will be 4 weeks.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive.
Mr. McMillan has already taught his class 8 letters.
The students in Ms. Burke's class, who started the unit later, currently know how to write 12 letters.
Mr. McMillan plans to teach his class 4 new letters per week.
Ms. Burke intends to cover 3 new letters per week.
Eventually, the students in both classes will know how to write the same number of letters.
Then the number of weeks by which the students in both classes will know how to write the same number of letters will be
Let x be the number of the weeks and y be the total number of the letters.
Then the equation will be
y = 4x + 8 …1
y = 3x + 12 …2
Then by solving the equations 1 and 2, we have
x = 4 and y = 24
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A line segment has endpoints Q(-16, -12) and R(21, -8).
What is the midpoint of the line segment?
02¹-201
Answer:
(2.5, - 10 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = (- 16, - 12 ) and (x₂, y₂ ) = (21, - 8 ) , then
midpoint = ( [tex]\frac{-16+21}{2}[/tex] , [tex]\frac{-12-8}{2}[/tex] ) = ( [tex]\frac{5}{2}[/tex], [tex]\frac{-20}{2}[/tex] ) = (2.5, - 10 )
Answer: c - (2 1/2 - 10)
Step-by-step explanation:
-4 1/2 x (-1 3/8)
please help
Answer:
The answer is 33.31
Step-by-step explanation:
-41/2 ×-13/8
-41×-13 = 533
2×8=16
therefore, 533/16
ans= 33.31
I hope this helps.
Solve the following by completing the square y=x^2+10
The resulting equation on using the completing the square is y = (x+5)² - 25
Completing the square methodThe quadratic equation has a leading degree of 2. Given the equation below;
y = x^2+10x
Add the square of the half of coefficient of x to have;
y = x^2+10x + (10/2)²- (10/2)²
y = x^2 + 10x + 5² - 5²
y = x^2 + 10x + 25 - 25
y = (x+5)² - 25
Hence the resulting equation on using the completing the square is y = (x+5)² - 25
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The product (
[tex](a+b)(a-b) = a^2 - ab + ba - b^2 = a^2 - b^2[/tex]
Since the middle terms cancel each other out, what is left is the difference of two squares.
In your example (x+6)(x-6) = x² -36
Which is the graph of the system of inequalities y 2x-and y ≤ 2x + 6
4x
2
ANVA
-6-4-22 26
-6-4-
-6-4
2
246
O
246
2
O
x
246
Answer: Option 1
Step-by-step explanation:
The second and third options do not contain the line y = 2x+6, so they can be eliminated.
Between the first and fourth options, only the first option shows the line y=2x+6 being shaded below, so it is the answer.
The graph of the inequality is graph A
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
y ≥ ( 1/5 ) ( 4x - 1 ) be equation (1)
y ≤ 2x + 6 be equation (2)
Now , To graph the system of inequalities, we can start by graphing the boundary lines for each inequality and then determine which region of the coordinate plane satisfies both inequalities.
For the first inequality, y >= (1/5)(4x-1), we can start by graphing the line y = (1/5)(4x-1), which has a y-intercept of -1/5 and a slope of 4/5. We can draw this line as a solid line, since the inequality includes the "or equal to" condition:
And , for the second inequality, y <= 2x+6, we can graph the line y = 2x+6, which has a y-intercept of 6 and a slope of 2. We can also draw this line as a solid line, since the inequality includes the "or equal to" condition:
Hence , the inequality is solved and the solution to the system of inequalities is the shaded region above the line y = (1/5)(4x-1) and below the line y = 2x+6, including the boundary lines.
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Let a and b be real numbers where a . Which of the following functions could represent the graph below?
f(x) = x(x – a)3(x – b)3
f(x) = (x – a)2(x – b)4
f(x) = x(x – a)6(x – b)2
f(x) = (x – a)5(x – b)
It can be deduced that the option that represents the graph is B. f(x)=(x-a)²(x-b)⁴
How to solve the graph?From the graph, a and b be real numbers where a = b = 0. In this case, zero is not a root of the polynomial function
When the graph touches the x-axis at two point l, it implies that means that both the roots of the polynomial equation are of even degree.
Thus, the correct option B. i.e. f(x)=(x-a)²(x-b)⁴
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Sam calculated (2.6 × 10 -2 )(1.5 × 10 -4 ) in his calculator. Which of the following results could be displayed on the calculator screen? Select all that apply.
3,900,000
0.0000039
3.9E6
3.9 × 10 -6
3.9E-6
The results that could be displayed are 3.9 ×10⁻⁶, 3.9 E-6 OR 0.0000039
Evaluating an expressionFrom the question, we are to determine the results that could be displayed on the calculator screen
The given expression is
(2.6 × 10⁻²)(1.5 × 10⁻⁴)
= 2.6 × 1.5 × 10⁻²× 10⁻⁴
= 3.9 ×10⁻²⁺⁻⁴
= 3.9 ×10⁻²⁻⁴
= 3.9 ×10⁻⁶
= 3.9 E-6 OR 0.0000039
Hence, the results that could be displayed are 3.9 ×10⁻⁶, 3.9 E-6 OR 0.0000039
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maths uhhhhhhh?????????????????????????????
Answer: 68.852459016393 or 68.9 if you round up
Step-by-step explanation:
If you add all the students subjects together you get a total of 41. Then if you add up the total of students who study physics, chemistry, and both you get 20. Then I put those numbers is a percentage calculator then boom you got your answer.
An equation that defines y as a function of x is given. a. solve for y in terms of x and
replace y with the function notation f(x) . b. find f(3).
6x-3y=2
Answer:
f(x) = 2x -2/3f(3) = 5 1/3Step-by-step explanation:
We solve an equation for a specific variable by using inverse operations to undo what is done to the variable. The resulting function is evaluated by substituting the given value for the variable.
__
a.We are given the equation ...
6x -3y = 2
Solving for y, we get ...
6x -2 = 3y . . . . . add 3y-2 to both sides
2x -2/3 = y . . . . . divide by 3
f(x) = 2x -2/3 . . . . write using functional notation
__
b.To find f(3), we use x=3 in the function.
f(3) = 2(3) -2/3 = 6 -2/3
f(3) = 5 1/3
QUESTION 10, 11, 12 and 13, 40 POINTS FOR CORRECT AWNSER AND WILL BE BRAINLIEST PLS BE FAST!! I WILL DO ANYTHING U WANT
10. The missing conversion is 20.32 inches
11. Total number of red cars is 34
12. Total number of blue cars is 36
13. Total number of silver cars is 70
What is Ratio?Ratio is the number of times a quantity is contained more or less than another in a whole.
Analysis:
10. If 1 inch = 2.54cm
Then 8 inches = 8 x 2.54cm = 20.32 cm
First car park: Total number of cars = 60
ratio of red:blue:silver = 1:2:3
Total ratio = 1+2+3 = 6
number of red cars = 1/6 x 60 = 10
number of blue cars = 2/6 x 60 = 20 cars
number of silver cars = 3/6 x 60 = 30
second car park: Total number of cars = 80
ratio of blue: red: silver = 2:3:5
total ratio = 2+3+5 = 10
number of red cars = 3/10 x 80 = 24
number of blue cars = 2/10 x 80 = 16
number of silver cars = 5/10 x 80 = 40
11. Total number of red cars = 10+24 = 34
12. Total number of blue cars = 20+16 = 36
13. Total number of silver cars = 30+40 = 70
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what is half of 10,000
Answer:
5000
Step-by-step explanation:
1000/2=5000
Find the measure of x.
Answer:
25.99
Step-by-step explanation:
SOH CAH TOA
(sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent)
For the angle measurement provided (38 degrees), we know the opposite leg value, and we need to find the hypotenuse
the measurement of sin (opposite / hypotenuse) relates these two measurements
we can plug in our known values into sin:
sin = opposite / hypotenuse
sin (38) = 16 / x
(note: sin 38 = 0.61566147532, which we can round to 0.61566)
0.61566 = 16 / x
· x ·x {multiply both sides by x to get rid of fraction}
0.61566(x) = 16
÷ 0.61566 ÷0.61566 {divide both sides by 0.61566 to isolate 1x}
x = 25.9883702043
{round to nearest hundredth}
x = 25.99
so, the measure of x is 25.99 {rounded to the nearest hundredth}
hope this helps!! have a lovely day :)
Answer:
cosx=adjacent/hypotenuse
triangle angle =180-(90+38)
=52°
cos(52°)=16/x
x=16/cos52
x≈23.373
A girl travels from garage a for 59km ti garage b on a bearing of 037degree and then turn right through 90degree and travels for 119km to garage c what is the bearing frim c from a if ac is 138km
The bearing from C to A of the given travel path is gotten as; 100.63°
How to calculate the bearing?From the bearing image attached, we can use trigonometric ratios to get;
tanx = opp/adj
x = 53 + θ ---------- eqn(1)
opp = 119
adj = 59
Thus;
tan x = 119/59
tan x = 2.0169
x = tan⁻¹(2.0169)
x = 63.63°
From eqn (1), we have;
θ = x - 53
θ = 63.63 - 53
θ = 10.63°
Thus, the bearing from C to A = 90 + 10.63 = 100.63°
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4. The term containing the highest power of x in the polynomial f(x) is 4x^4. Given that f(x) = 0
has 2 roots -2 and 3, and that 2x² + 3x + 2 is a quadratic factor of f(x),
(a) express f(x) as a polynomial in descending powers of x,
We're given [tex]f(x) = 0[/tex] when [tex]x=-2[/tex] and [tex]x=3[/tex], so both [tex]x+2[/tex] and [tex]x-3[/tex] divide [tex]f(x)[/tex]
We're also told [tex]2x^2+3x+2[/tex] divides [tex]f(x)[/tex]. This quadratic does not have roots at -2 or 3, so we can factorize [tex]f(x)[/tex] as
[tex]f(x) = 2 (x + 2) (x - 3) (2x^2 + 3x + 2)[/tex]
where the leading coefficient is 2 because the full expansion should have a leading term of [tex]4x^4[/tex].
Now just expand [tex]f(x)[/tex] :
[tex]f(x) = 2 (x + 2) (x - 3) (2x^2 + 3x + 2)[/tex]
[tex]f(x) = 2 (x^2 - x - 6) (2x^2 + 3x + 2)[/tex]
[tex]f(x) = 2 (2x^4 + x^3 - 13x^2 - 20x - 12)[/tex]
[tex]f(x) = \boxed{4x^4 + 2x^3 - 26x^2 - 40x - 24}[/tex]
Find the average rate of change of each function over the interval [0, 2]. Match each representation with its respective average rate of change.
The average rate of change is 4.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The rate of change in interval [0, 2]
r=[h(2)-h(0)]/2
h(2)=(2)²+2(2)-6
h(2)=4+4-6
h(2)=2
h(0)=(0)²+2(0)-6
h(0)=0+0-6
h(0)=-6
So, r=[h(2)-h(0)]/2
r=[2-(-6)]/2
r=(8)/2
r=4
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What is the probability of rolling an even number on a number cube and spinning red or yellow on the spinner shown?
The probability of rolling an even number on a number cube and spinning red or yellow on the spinner will be 1/4 or 0.25.
The complete question is given below.
I rolled a number cube and spun a spinner. The number cube is numbered 1 to 6. The spinner has 4 equal parts: red, blue, yellow, and green. What is the probability of rolling an even number on a number cube and spinning red or yellow on the spinner?
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Then the probability of rolling an even number on a number cube and spinning red or yellow on the spinner will be
The probability of getting even number on dice will be
Total event = 6 {1, 2, 3, 4, 5, 6}
Favorable events = 3 {2, 4, 6}
P₁ = 3/6
P₁ = 1/2
The probability of getting red or yellow will be
Total event = 4 {red, blue, yellow, green}
Favorable events = 2 {red, yellow}
P₂ = 2/4
P₂ = 1/2
Then the both event occur simultaneously, then we have
P = P₁ × P₂
P = 1/2 × 1/2
P = 1/4
P = 0.25
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1 / 12
Hope this helps, have a great day!
