Step-by-step explanation:
sin(theta)=4/7
cos(theta)=√1-sin²theta
=√1-(4/7)²
=√1-16/49
=√(49-16)/49
= √33/49
=(√33)/7
(08.01)
A new video game is expected to sell 120 copies the first hour at a local game store. After that, the sales will follow the function s(x) = 15(=
1) where x is the number of hours. What is the function that shows total sales, including the first hour?
Answer:
f(x)=15x+120
Step-by-step explanation:
trust
it is about Name the property of the rational numbers in each of the following
The property of each given rational number operation are respectively; Commutative Property; Closure Property; Associative Property; Closure Property; Distributive Property
What is the property of the rational number?The main properties of rational numbers are:
Commutative property.Associative Property. Distributive Property.Closure property.a) The property used here is commutative property which says that;
a + b = b + a.
This tallies with the operation used on the rational numbers.
b) The property used here is called Closure Property. This is because for two rational numbers say a and b, the results of addition, subtraction and multiplication operations gives a rational number.
c) The property used here is called associative property because it states that; a * (b * c) = (a * b) * c.
d) The property used here is called Closure Property. This is because for two rational numbers say a and b, the results of addition, subtraction and multiplication operations gives a rational number.
e) The property used here is called distributive property because it states that; a * (b * c) = (ab * ac)
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For every 10 yards on a football field, there is a boldly marked line labeled with the amount of yards.
There are two parallel sidelines on each side of the field. If the 50 yard line is perpendicular to one of the
sidelines, what is its relationship to the other sideline?
Answer:
Same, because they are parallel.
Step-by-step explanation:
Kevin and Randy Muise have a jar containing 65 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $8.65 .How many of each type of coin do they have?
what is the equation?
3 + 5(2 + 7n) = 258
Answer:
n = 7
Explanation:
[tex]\rightarrow \sf 3 + 5(2 + 7n) = 258[/tex]
apply distributive method: a(b + c) = ab + ac
[tex]\rightarrow \sf 3 + 10 + 35n = 258[/tex]
simply add the numbers
[tex]\rightarrow \sf 13 + 35n = 258[/tex]
subtract both sides by 13
[tex]\rightarrow \sf 13-13 + 35n = 258-13[/tex]
simplify the following
[tex]\rightarrow \sf 35n = 245[/tex]
divide both sides by 35
[tex]\rightarrow \sf n = 7[/tex]
Answer:
n = 7
Step-by-step explanation:
1) Subtract 3 from both sides.
5(2 + 7n) = 258 - 3
2) Simplify 258 - 3 to 255.
5(2 + 7n) = 255
3) Divide both sides by 5.
2 + 7n = 255/5
4) Simplify 255/5 to 51.
2 + 7n = 51
5) Subtract 2 from both sides.
7n = 51 - 2
6) Simplify 51 - 2 to 49.
7n = 49
7) Divide both sides by 7.
n = 49/7
8) Simplify 49/7 yo 7.
n = 7
Write and solve a proportion to complete the statement. Round to the nearest hundreth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
The conversion of the following units are done below.
6 km = 3.72 miles2.5 L = 0.65 gallons90 lb = 40.5 kgWhat is conversion?Conversion means to convert the same thing into different units.
We know the following unit's conversion.
1 km = 0.62 miles
6 km = 3.72 miles
1 L = 0.26 gallons
2.5 L = 0.65 gallons
1 lb = 0.45 kg
90 lb = 40.5 kg
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The terms of a particular sequence are determined according to the following rule: If the value of a given term $t$ is an odd positive integer, then the value of the following term is $3t -9$; if the value of a given term $t$ is an even positive integer, then the value of the following term is $2t -7$. Suppose that the terms of the sequence alternate between two positive integers $(a, b, a, b, \dots )$. What is the sum of the two positive integers
More plainly, the sequence is defined recursively by
[tex]a_{n+1} = \begin{cases} 3a_n - 9 & \text{if } a_n \text{ is odd} \\ 2a_n - 7 & \text{if } a_n \text{ is even} \end{cases}[/tex]
and some starting value [tex]a_1[/tex].
We're given that the sequence alternates between two constants, [tex]a[/tex] and [tex]b[/tex], so that [tex]a_1 = a[/tex].
• If [tex]a[/tex] is even, then the second term [tex]b[/tex] must be odd, since
[tex]a_2 = 2a_1 - 7[/tex]
by the given rule, and 2×(even) - (odd) = (odd). So
[tex]a_2 = 2a-7 = b[/tex]
In turn, the third term is even, since we jump back to [tex]a[/tex]. From the given rule,
[tex]a_3 = 3a_2 - 9[/tex]
and so
[tex]3b-9 = 3(2a-7)-9 = a \implies 6a-30=a \implies 5a=30 \implies a=6[/tex]
[tex]3b-9 = 6 \implies 3b = 15 \implies b = 5[/tex]
Then the sum of the two integers is [tex]a+b=\boxed{11}[/tex]
• You end up with the same answer in the case of odd [tex]a[/tex], so I'll omit this part of the solution. (It's almost identical as the even case.)
If a(x) = 3x + 1 and (x)= x-4, what is the domain of (boa)(x)?
I am assuming you meant to write b(x) = x-4.
[tex](b \circ a)(x)=b(a(x))=b(3x+1)=(3x+1)-4=\boxed{3x-3}[/tex]
Since this is a linear function, the domain is all real numbers.
A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won 4 games, Ines won 3 games, Janet won 2 games, Kendra won 2 games and Lara won 2 games, how many games did Monica win
Monica win 2 games.
What is Expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
According to the question,
First we look from the perspective of one player.
How many games does this person play? 5.
Now, each or the 6 people in the tournament played 5 games,
SO,
[tex]^{6} C_{2} = \frac{6!}{2! * 4!} = \frac{6*5}{2} = 15[/tex]
Therefore,
We know that there were a total of 15 games played.
This means, there were 15 losses, and more importantly, 15 wins.
Not counting Monica, there were:
4 + 3 + 2 + 2 + 2 = 13 wins.
This leaves,
15 − 13 = 2 wins for Monica.
Hence, 2 games won by monica in a tournament.
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Which number line represents the solution set for the inequality 3(8-4x) < 6(x - 5)?
[tex]3(8 - 4x) < 6(x - 5) \\ 24 - 12x < 6x - 30 \\ 24 + 30 < 6x + 12x \\ 54 < 18x \\ \frac{54}{18} < \frac{18x}{18} \\ x > 3[/tex]
Solution : ] 3 , + ♾️ [
PLEASE GIVE BRAINLIEST
8y and y are like terms
true
or
false
Answer:
True
Step-by-step explanation:
Hope this helps :)
HELPPPPP PLSSSS I ONLY HAVE A FEW MINUTES LEFT
Answer:
6
Step-by-step explanation:
The second rational number equals 2 1/3.
Adding the mixed numbers:
[tex]3 \frac{2}{3} + 2 \frac{1}{3} = 5 \frac{3}{3} = 6 [/tex]
the equation below describes a circle. what are the coordinates of the circle?
(x+5)^2 + (y+7)^2 = 21^2
Answer:
center = (-5, -7)
radius = 21
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusGiven equation:
[tex](x+5)^2 + (y+7)^2 = 21^2[/tex]
Comparing the given equation with the standard equation of a circle:
center = (-5, -7)radius = 21Hence, the coordinates of centre is (-5,-2).
What is circle ?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.
The given equation of circle,
(x+5)² + (y+7)² = 21²
We know that,
Equation of a circle is:
(x-a)² + (y-b)² = r²
where:
(a, b) is the center
And r is the radius
Comparing with the given equation we have,
center = (-5,-7)
And radius = 21 units
Thus,
Coordinates = (-5,-7).
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Can someone help with this pls
Answer:
This is C
Step-by-step explanation:
The slope is 4, meaning the integers are 4, 8, 12, 16, 20 etc. But then the last point is seen to be 40, meaning the answer is C because it is from 0-40 with a slope of 4.
can someone please help mee(20 points and i will give brainliest!!!)
Answer:
vertex: (3,1)
y-intercept = (0,-8)
x-intercept- Smaller=2 Larger=4
Domain= all real numbers, identity, infinite
Range= 1 is greater than or equal to y
axis of symmetry=3
Step-by-step explanation:
What is the value of x in the triangle?
Answer:
45 degree=√2/2
√2/2=12√2
we use criss-cross method
√2x/√ 2=12√2/√ 2
×=24
Step-by-step explanation:
if it confused you this is (/)is dividing
hope I helped
please mark me as brainlyst
1) Which statement is needed to fill in the blank in this syllogism? If two lines are parallel, then ____________________. If the lines never intersect, then the lines have the same slope. Therefore, if two lines are parallel, then the lines have the same slope.
A) the lines have the same slope
B) the lines never intersect
C) the lines have the same equation
D) the lines are continuous
Answer:
B) the lines never intersect
Step-by-step explanation:
okay essentially, syllogism is formatted in a repetitive way
it's something like:
if "a" are "b"
and "b" are "c"
then "a" are "c"
(a = b
b = c
logically, c = a)
(idea, thing related to idea, conclusion relating the two)
hope this helps!!
Answer:
the lines never intersect
Step-by-step explanation:
Syllogisms are connected by a shared statement that connects a hypothesis to a different conclusion.
PLEASE HELP FAST!!!
The measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees
Angle of elevation and depressionFrom the question given, we have the following parameters
Base of the building = 7feet
Height of the building = 18 feet
Required
angle of elevation
Using the SOH CAH TOA identity
tanФ = opp/adj
tanФ = 18/7
Ф = 68.73 degrees
Hence the measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees
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Question:
A ladder leans against a building. The top of the ladder reaches a point on the building, which is 18 feet above the ground. The foot of the ladder is 7 feet from the building. Find the measure of the angle of elevation from the ground to the top of the ladder.
Solve this system of equations algebraically:
y – 10 = 11x + x2
y – 12x = 30
The first solution is (–4, –18).
The second solution is (
,
).
Answer:
(-4,-18) and (5,90)
Step-by-step explanation:
I'll assume the first equation is supposed to be y – 10 = 11x + x^2
This is a parabola. The second equation is a straight line:
y – 12x = 30
We want to find the points at which these lines intersect. They will intersect for any (x,y) that
Let's rearrange the second equation to isolate y:
y – 12x = 30
y = 30 + 12x
Now we can take the this value of y and substitute it into the first equation:
y – 10 = 11x + x^2
(30 + 12x) – 10 = 11x + x^2
20 + 12x = 11x + x^2
0 = x^2 -x -20
We can factor this into (x+4)(x-5)
That means x can be either -4 or 5.
Find the value of y using these values of x in both original equations:
For x = -4
y – 10 = 11x + x^2
y = 11x + x^2 + 10
y = 11(-4)+(-4)^2 +10
y = -44 + 16 + 10
y = -18 The point both lines meet is at (-4, -18) which was already given in the problem.
For x = 5
y – 10 = 11x + x^2
y = 11x + x^2 + 10
y = 11(5) + (5)^2 + 10
y = 55 + 25 + 10
y = 90
The second point both lines meet is (5,90).
We should use both solutions in the second equation to verify these values, but I'll graph them, instead. See the attached graph to prove these points are correct.
2
3
4
5
6
7
8
O They have the same slope.
O They have the same y-intercept.
9
10
TIME REMAINING
55:24
Suppose a system of two linear equations has one solution. What must be true about the graphs of the two equations
O They intersect at one point.
O They intersect at two points.
Answer:
72
Step-by-step explanation:
yhsvybybyvyyvtvvyyvvt
Answer:
number 9 is the answer for this question
Which of the following is most likely the next step in the series?
Answer:
I think the answer is B
Step-by-step explanation:
which property is illustrated for all expressions a and b if a=b then b=a
Answer:
Symmetric property
Find the distance between the pair of points given on the graph. Distance = √ (blank)
Answer:
√2.236
Step-by-step explanation:
(2,0) (5,-2). 2 - 5 = -3. 0 - -2 = 2. -3 squared = -9. 2 squared = 4. -9 + 4 = -5. Square root of -5 = 2.236, so the distance would be √2.236
Charlie is installing new carpet in his rectangular living room, which is 5 feet longer than it is wide. He has received quotes for the total
installation costs from two different contractors for the same style of carpet.
Contractor A charges an installation fee of $125 plus $2 per square foot for the carpet.
Contractor B charges an installation fee of $75 plus $2.50 per square foot for the carpet.
Based on this information, which system of equations could be used to determine the width of the living room, x, in feet, at which the
quote for the installation costs, y, is the same for both companies?
Considering the area of a rectangle, the equation that could be used to determine the width for which the costs are the same is:
125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)
What is the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of dimensions, that is:
A = lw
In this problem, the dimensions are given as follows:
w = x, l = x + 5.
Hence the area in square feet is:
A = x(x + 5) = x² + 5x.
Then the costs are given as follows:
A(x) = 125 + 2(x² + 5x).B(x) = 75 + 2.5(x² + 5x).The costs will be equal when:
A(x) = B(x)
125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)
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Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5cm². calculate correct to 3 Significant figures, the base radius, r ,height h Volume of the cone [take π 22/7]
The volume of the cone is V = 381.15 cu.cm
What is the Curved Surface Area of the cone ?The curved surface area of the cone is given by
A = πrl
The slant height given in the question is
l = 10.5 cm
A = 115.5 sq.cm
radius = ?
Height = ?
Volume = ?
Using the Curved Surface Area Formula
115.5 = π * r * 10.5
taking π = 22/7
r = 3.5 cm
The slant height is given by
[tex]\rm l = \sqrt{ r^2 + h^2}[/tex]
Therefore the height is
[tex]\rm h = \sqrt{ 10.5^2 -3.5^2}[/tex]
h = 9.9 cm
The volume of the cone is
V = π r²h
V = (22/7) * 3.5 * 3.5 * 9.9
V = 381.15 cu.cm
The volume of the cone is V = 381.15 cu.cm
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HELP ASAP/NOW...NO LINKS OR JOKING PLS
Answer:
D. 0 < x < 20
Explanation:
Domain is in the x axis, Range lies in the y axis.
Here it is seen that function's domain lies between 0 to 20.
Open circle's are used for '<' and '>'Closed circle's are used for '≤' and '≥'Here, as the circle's are open. Domain: 0 < x < 20
Additionally,
Range: -10 < f(x) < 06root27+root243 simplify
Answer:
6√27 + √243
6√9 x 3 + √81 x 3
6 x 3 √3 + 9√3
18√3 + 9√3
27√3
$50 item discounted 30%
Answer:
$15 is the answers
Step-by-step explanation:
please mark me as brainlest
Answer:
$ 35.00 is what you pay $15.00 off original price
Step-by-step explanation:
30 % discount means you pay 70 %
$ 50 * .70 = $ 35 .00
What is the original price of an item that is being charged a tax of 20%, and
the total price is $144?
Points 1
If a point is reflected over the y-axis, then the coordinates of (x, y) are changed to ______________.
Answer:
its opposite
Step-by-step explanation:
