1.
[tex]2\cdot x^2+2\cdot x^1+1\cdot x^0=25\\2x^2+2x+1=25\\2x^2+2x-24=0\\x^2+x-12=0\\x^2+4x-3x-12=0\\x(x+4)-3(x+4)=0\\(x-3)(x+4)=0\\x=3 \vee x=-4[/tex]
The base can't be negative, therefore [tex]x=3[/tex].
2.
[tex]3\cdot x^0+3\cdot x^1+4\cdot x^0-4\cdot x^1+0\cdot x^0=0\\3+3x+4-4x=0\\x=7[/tex]
3.
[tex]2\cdot x^1+3\cdotx^0=1\cdot 2^3+1\cdot2^2+1\cdot2^1+1\cdot2^0\\2x+1=8+4+2+1\\2x=14\\x=7[/tex]
The table gives the scores of 6 students from a class of 25 in a competitive exam. the point estimate of the mean score for the students is
The mean of the scores if 6 students in a competitive exam is 25 marks.
Given scores of 6 students are: 10,30,50,40,20 in a competitive exam.
We have to find out the mean of the mark of 6 students in a competitive exam.
Mean is the sum of all the values in a set of data, such as numbers, measurements, divided by the number of values. It is also known as average.
Mean=∑X/n
∑X=10+30+50+40+20
=150
N=6
Now to calculate the mean we have to divide 150 by number of students which is 6.
Mean=150/6
=25 marks.
Hence the mean of the scores of 6 students is 25 marks.
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Question is incomplete as it should include :
Marks of students =10,30,50,40,20.
help me with the fonction please im stuck U_U
Answer:
It is NOT a function
Step-by-step explanation:
No it is NOT a function.....each value of x can only have one y value....
this has two y values for x = 2 : y = 2 and 4 therefore not a function
-x+4y=9
pls find ordered pair
We can write the ordered pairs that meet this condition as:
(x, y) = (x, (9 + x)/4 )
How to find the ordered pair?An ordered pair on the X-Y plane is written as (x, y).
Here we also have the relation:
-x + 4y = 9
If we isolate y, we get:
4y = 9 + x
y = (9 + x)/4
Now, we can write the ordered pairs that meet this condition as:
(x, y) = (x, (9 + x)/4 )
To get the particular ones you can replace the value of x, for example, if x = 0, then:
(x, (9 + x)/4 ) = (0, 9/4)
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find the value of x
A. √30
B. 16
C. 2√2
D. 20
Answer:
A. √30
=================
Use the intersecting chords theorem, according to which, the products of the lengths of the line segments on each chord are equal,
or
TW × WU = CW × WVSubstitute the lengths and solve for x:
x*2x = 6*102x² = 60x² = 30x = √30The matching answer choice is A.
Rhombus wxyz is graphed on a coordinate plane. what is the area of the rhombus? 24 square units 28 square units 32 square units 48 square units
The area of the rhombus WXYZ is 48 unit².
From the diagram:
Diagonal WY = 8 units, Diagonal XZ = 6 units, hence:
Area = 8 * 6 = 48 unit².
A rhombus is a special case of a parallelogram. In a diamond, the opposite sides are parallel and the opposite sides are equal in angle. In addition, all sides of the rhombus are the same length and the diagonal bisects at right angles. Diamonds are also known as diamonds.
The diagonals of the rhombus intersect at right angles to form a non-uniform triangle. The opposite angles are equal. However, if all angles of the diamond are 90 degrees, the diamond is said to be square.
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Determine whether the geometric series 27 + 18 + 12 + 8 + ... converges or diverges, and identify the sum if it exists.
The given geometric series as shown in the question is seen to; Be converging with its' sum as 81
How to identify a converging or diverging series?We are given the geometric series;
27 + 18 + 12 + 8 + ...
Now, we see that;
First term; a₀ = 27
Second Term; a₁ = 2(27/3)
Third term; a₂ = 2²(27/3²)
Fourth term; a₃ = 2³(27/3³)
Thus, the formula is;
2ⁿ(27/3ⁿ)
Applying limits at infinity gives;
2^(∞) * (27/3^(∞)) = 0
Since the terms of the series tend to zero, we can affirm that the series converges.
The sum of an infinite converging series is:
S_n = a/(1 - r)
S_n = 27/(1 - (2/3)
S_n = 81
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Create a list of steps, in order, that will solve the following equation. (x-5)^2=25(x−5) 2 =25left parenthesis, x, minus, 5, right parenthesis, squared, equals, 25 Solution steps:
The value of x in the equation (x - 5)² = 25 is 10.
How to solve an equation?(x - 5)² = 25
Take the square root of both sides
Therefore,
√(x - 5)² = √25
x - 5 = 5
add 5 to both sides
x - 5 + 5 = 5 + 5
x = 10
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P l e a s e h e l p~!!!!!!~!!~~~!
Answer:
A. 100
Step-by-step explanation:
Angle 1 = 40
Angles 1 and 2 are equal. Add the angles 1 and 2 together.
40+40=80
The last step is to subtract 80 from 180.
180-80=100.
∠3=100
Hope this helps!
If not, I am sorry.
In the figure, POG is a diameter of the circle with centre O.
Find x° + y°.
The value of x° + y° is 216°
How to determine the angles
Note that the shape is a regular pentagon
Sum of angle in a pentagon = 540
Angle on each side = 108°
x = 108°
y = 108°
x° + y° = 108 + 108
x° + y° = 216°
Thus, the value of x° + y° is 216°
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Write a polynomial function with the real
zeros -3, 0, and 3.
[tex]f(x)=x(x-3)(x+3)[/tex]
Find the distance between the two points in simplest radical form.
(−5,−4) and (−2,−6)
Answer: [tex]\sqrt{13}[/tex] units
Work Shown:
[tex](x_1,y_1) = (-5,-4) \text{ and } (x_2, y_2) = (-2,-6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-5-(-2))^2 + (-4-(-6))^2}\\\\d = \sqrt{(-5+2)^2 + (-4+6)^2}\\\\d = \sqrt{(-3)^2 + (2)^2}\\\\d = \sqrt{9 + 4}\\\\d = \sqrt{13}\\\\d \approx 3.6056\\\\[/tex]
I used the distance formula.
A slightly alternate method is to form a right triangle and use the pythagorean theorem. The hypotenuse will have the endpoints (-5,-4) and (-2,-6).
helppp!!!
Lynn is putting tiles on her bathroom floor. Each tile measures 1 square foot each. The floor measures 4 1/2 ft by 3 3/4 ft. How many tiles will she need to cover the floor?
Considering the area of the rectangle, it is found that she will need 17 tiles to cover the floor.
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
The dimensions in feet are given as follows:
l = 4 1/2 ft = 4.5 ft.w = 3 3/4 ft = 3.75 ft.Hence the area in square feet is given by:
A = 4.5 x 3.75 = 16.875 ft².
Each tile has 1 square foot, hence, rounding, she will need 17 tiles to cover the floor.
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f(x) = 4^ x / 8
can you Graph this ?
Answer:
Graph is below
Brainliest, please :)
Write and simplify an expression to represent the area. Then determine the area when x = 3
Answer:
5*8 = 40
Step-by-step explanation:
2(3) -1 = 5
3 +5 = 8
area = 5*8 = 40
Answer:
formula-Area=l×b
Step-by-step explanation:
Length (l)=2x-1
Breadth(b)=x+5
We know that,
Area(A)=l×b
=(2x-1)×(x+1)
=(2×3-1)×(3+1)
=5×4
=20cm*2*
The angle by which turns clockwise about point b to coincide with is 63.9 degrees. if from point b, a point e is drawn directly opposite point c so that b, e, and c are on the same straight line, the angle by which turns counterclockwise to coincide with is 243.9 degrees.
AB turns clockwise to coincide with BC.
To find the angle by which turns counterclockwise to coincide with is 243.9 degrees:
An angle -
An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles formed by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles.So,
= ABD + DBC
= 33.3° + 30.6°
= 63.9°
b) If E is drawn directly opposite C.
EBC is a straight line, so the sum of angles =180°
ABE + ABD + DBC = 180°
ABE + 33.3° + 30.6° = 180°
ABE + 63.9° = 180°
ABE = 180 - 63.1
ABE = 116.9
Therefore, AB turns clockwise to coincide with BC.
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3y > 2x + 12
2x + y ≤ -5
The solution for the inequalities 3y>2x+12, 2x+y<=-5 is the value of x<-27/8 and y<7/4.
Given 3y>2x+12 and 2x+y<=-5.
We are given two inequalities 3y>2x+12 and 2x+y<=-5. Inequality are like equations but in greater than ,less than or in combination with equal to. To solve them we need to first write them properly.
2x-3y<-12
2x+y<=-5
Now assume these are equalities
2x-3y=-12
2x+y=-5
now subtract 2 from 1
2x-3y-2x-y=-12+5
-4y=-7
y=7/4
put the value of y in 2x-3y=-12
2x-3(7/4)=-12
2x-21/4=-12
2x=-12+21/4
2x=(-48+21)/4
2x=-27/4
x=-27/8
Now put the signs between the values
x<-27/8
y<7/4.
Hence the solution of the inequalities 3y > 2x + 12
2x + y ≤ -5 is the value of x<-27/8 and y<7/4.
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Write a polynomial function of least degree with integral coefficients that has the given zeros. -1/3, 2/3, -1/4
Step-by-step explanation:
"integral" means here that the factors in the polynomial are integers.
we have 3 zeros.
the least degree of a polynomial with 3 zeros is 3.
and yes, that works also for 2 zeros (the degree must be at least 2, it must be at least a quadratic equation).
or 4 zeros (at least 4th degree).
it in general n zeros (at least nth degree).
constructing this out of the given zeros is easy.
what happens, when I multiply something by 0 ? the total result will be 0.
and so, we simply multiply 3 short terms with each other, where each term turns 0 for one of the given zeros.
what expression in x turns 0, when x = -1/3 ?
well : x + 1/3 or with integers 3x + 1 (multiplied by 3)
and for x = 2/3 ?
x - 2/3 or with integers 3x - 2
and for x = -1/4 ?
x + 1/4 or with integers 4x + 1
so, our polynomial function (of at least 3rd degree) is then
(3x + 1)(3x - 2)(4x + 1)
basically this could be already the result, depending on what your teacher wants.
for the fully extended form we need to do the multiplications :
(3x + 1)(3x - 2) = 9x² - 6x + 3x - 2 = 9x²- 3x - 2
(9x²- 3x - 2)(4x + 1) = 36x³ + 9x² - 12x² - 3x - 8x - 2 =
= 36x³ - 3x² - 11x - 2
the requested polynomial function is
f(x) = 36x³ - 3x² - 11x - 2
D
Distance
ST
Speed
Time
A bus is moving at an average speed of 70 mph on the
motorway.
The journey takes 3 hours 30 minutes.
How far did the bus travel?
miles
The distance would be 231 miles.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken
Given information;
Time taken = 3 hours 30 minutes
Speed = 70 mph
We know that,
Distance = speed x time
Distance = 70 x 3.30
Distance = 231 miles
Thus, the distance would be 231 miles.
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What is the exact value
of cos
7pi/8
The exact value of cos 7pi/8 is 0. 9988
How to find the value
It is important to note that the value for pi = 3. 142
= cos 7π
Substitute value of π
= cos(7× 3. 142)
= cos 21. 994
Divide 21. 994 by 8
= 2. 740
Let's find the vale of [tex]cos \frac{21. 994}{8}[/tex]
= [tex]cos (2. 749)[/tex]
= [tex]0. 9988[/tex]
Thus, the exact value of cos 7pi/8 is 0. 9988
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A company produces candy bags that each hold about 528 cubic inches of candy. Each bag is filled with any mixture of lollipop candies and gummy bear candies. When a bag contains only lollipop candies, then it has about 361 candies. When a bag contains only gummy bear candies, then it has about 697 candies. Given any candy bag produced by this company, which of the following equations could relate the approximate number of lollipop candies, 7, in the bag and the approximate number of gummy bear candies, g, in the bag? A company produces candy bags that each hold about 528 cubic inches of candy . Each bag is filled with any mixture of lollipop candies and gummy bear candies . When a bag contains only lollipop candies , then it has about 361 candies . When a bag contains only gummy bear candies , then it has about 697 candies . Given any candy bag produced by this company , which of the following equations could relate the approximate number of lollipop candies , 7 , in the bag and the approximate number of gummy bear candies , g , in the bag ?
361 lollipop candies or 697 gummy bear candies fills the bag of volume 528 in.³, which gives the following possible equation;
1.46•l + 0.76•g = 528How can the correct equation be found?Volume of candy bag = 528 in.³
Number of lollipop candies the bag can hold = 361 candies
Number of gummy bear candies the bag can hold = 697 candies
Therefore;
[tex]1 \: lollipop = \frac{528}{361} = 1.46[/tex]
[tex]1 \: gummy \: bear = \frac{528}{697} = 0.76[/tex]
Which gives the following equation;
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Answer:
l/361 + g/697= 1
Khan Academy Sat Practice
which number produced a rational number when added to 1/5
The number that produced a rational number when added to 1/5 is D. -2/3.
What is a rational number?A rational number is a number that can be written as a ratio (or fraction) of two integers.
For example, when 1/5 is added to -2/3, it produces a rational number, -7/15, that remains as a fractional value.
Thus, the number that produced a rational number when added to 1/5 is D. -2/3.
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A diagonal of a cube measures StartRoot 150 EndRoot cm. The diagonal of a face measures 10 cm.
What is the length, in centimeters, of an edge of the cube? Round the answer to the nearest tenth.
The side of the edge of the cube is 7. 07cm
How to determine the lengthGiven that a diagonal of a cube measures the square root of 150 cm and the diagonal of a face measures 10 cm.
Let's find the edge of the face
Note that the face of the cube is in the shape of square .
The diagonal of the face is 10 cm.
The formula for diagonal of square = [tex]\sqrt{2a}[/tex]
a is the side of the square face
We have that,
[tex]\sqrt{2a} = 10[/tex]
Make 'a' subject of formula
a = [tex]\frac{10}{\sqrt{2} }[/tex]
Find the surd of the equation, we have
a = [tex]\frac{10}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]
a = [tex]\frac{10\sqrt{2} }{2}[/tex]
a = [tex]5\sqrt{2}[/tex]
a = [tex]7. 07cm[/tex]
Thus, the side of the edge of the cube is 7. 07cm
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According to the rational root theorem, the numbers below are some of the potential roots of f(x) = 10x3 29x2 – 66x 27. select all that are actual roots.
The actual roots of the function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex] are -9/2, 3/5 and 1.
Given function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex].
Function is a relationship between two or more variables expressed in equal to form.
The roots of a polynomial function are the zeroes of the polynomial function. A polynomial function is a function that involves only non negative integer powers in an equation.
The polynomial function is given as:
[tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex]
factorize the above function
[tex]f(x)=(2x+9)(5x-3)(x-1)[/tex]
Now put the function f(x) equal to zero.
f(x)=(2x+9)(5x-3)(x-1)
split the function means put all the expressions equal to zero as under:
(2x+9)(5x-3)(x-1)=0
solve each for the value of x
x=-9/2,x=3/5,x=1
Hence the roots of the function [tex]f(x)=10x^{3} +29x^{2} -66x+27[/tex] are which are also the values of x are -9/2,3/5,1.
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Answer:
Step-by-step explanation:
4. A juice bottling company makes a variety pack
with 24 orange juices, 12 apple juices, and 8
grape juices. Describe the ratio of the juices to
one another (orange: apple: grape).
(A) 2:1:1
(B) 3:1:2
(C) 4:2:2
(D) 6:3:2
The ratio of orange juice to apple juice to grape juice is 6: 3 : 2
What is ratio?A ratio says how much of one thing there is compared to another thing.
Therefore, we are comparing the numbers of juice produce by a bottling company.
Hence,
number of orange juice = 24
number of apple juice = 12
number of grape juice = 8
Therefore, the ratio of orange juice to apple juice to grape juice is as follows:
ratio = 24 : 12 : 8
divide through by 4
ratio = 6: 3 : 2
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The price of an emergency light is $375 and it decreased by
2% each year. Find the exponential model representing
this situation.
The price of the light as a function of x is given by the exponential function:
[tex]p(x) = \$375*(0.98)^x[/tex]
Which exponential model represents this situation?
We know that the original price of the light is $375.
This value decreases a 2% each year, so each year we need to multiply the above price by (1 - 2%/100%) = (1 - 0.02) = 0.98
Then, if x represents the number of years, the price of the light as a function of x is given by the exponential function:
[tex]p(x) = \$375*(0.98)^x[/tex]
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Please help!
Using the graph below, which of the following equations represents the line that is parallel to line FG and passes through the (8,−3) point?
my only answers can be the ones in the attached image (just had a random one ticked)
Answer:
the second option: [tex]7x+4y=44[/tex]
Step-by-step explanation:
So when a line is parallel, it means that it has the same slope and a different y-intercept, it's important that there is a different y-intercept, otherwise it would be the same line, and the "two lines" would intersect at infinite points.
Anyways by looking at the graph you have two points (-8, 5) and (-4, -2). So the run in this case was 4 and the rise was -7. This is a slope of -7/4. So we have the equation: [tex]y=-\frac{7}{4}x+b \text{ where b}\ne-9}[/tex]. Since it passes through the point (8, -3) we can plug that in as (x, y) to solve for b (the y-intercept)
Plug in (8, -3) as (x, y)
[tex]-3=-\frac{7}{4}(8)+b[/tex]
Multiply the -7/4 and 8
[tex]-3 = -14+b[/tex]
add 4 to both sides
[tex]11 = b[/tex]
So this gives us the equation:
[tex]y=-\frac{7}{4}x+11[/tex]
Since it's asking for it in standard form you move the 7/4 x to the other side
Add 7/4x to both sides
[tex]\frac{7}{4}x+y=11[/tex]
Multiply both sides by 4 to cancel out the fraction
[tex]7x+4y=44[/tex]
Consider the line y=3x-3.
Find the equation of the line that is perpendicular to this line and passes through the point (4, 5)
Find the equation of the line that is parallel to this line and passes through the point (4, 5).
Answer:
Perpendicular: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]
Parallel: [tex]y=3x-7[/tex]
Step-by-step explanation:
So when two lines are perpendicular, that means the the slope is the reciprocal with the opposite sign so: [tex]\frac{a}{b} \text{ has a slope perpendicular to } -\frac{b}{a}[/tex]. In this case we have the equation in slope-intercept form, so it's easy to determine the slope, it's 3. So that means the perpendicular line will have a slope of: [tex]-\frac{1}{3}[/tex]. Since you have a slope of 3/1 which becomes 1/3 and also an opposite sign. This gives you the equation: [tex]y=-\frac{1}{3}x+b[/tex]. We can solve for b, by plugging in a coordinate it passes through. This is given in the problem, with it being (4, 5) = (x, y). So plugging these values in as (x, y) gives you the equation: [tex]5=-\frac{1}{3}(4)+b\implies\frac{15}{3}=-\frac{4}{3}+b\implies\frac{19}{3}=b[/tex]. This gives you the complete equation: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]
So when two lines are parallel, that means they have the slope, and a different y-intercept. This is because if they had the same y-intercept, then the two lines would be the same exact line. We already know the slope, it's 3. So we have the general equation: [tex]y=3x+b\text{ where b}\ne-3[/tex]. The restriction on b, was explained on the previous sentence, if b=-3, then we have the same equation, which is not parallel, they would be the same line, meaning they would intersect at infinite points, which is completely different than two lines that never intersect. So now we can plug in the given point (4, 5) to solve for b. Plugging these coordinates in gives you: [tex]5=3(4)+b\implies5=12+b\implies-7=b[/tex]. This gives you the complete equation: [tex]y=3x-7[/tex]
Norman makes $15 commission for selling $200 in merchandise. he makes $37.50 commission for selling $500 in merchandise. assuming that the variables are directly related and norman wants to make $150 in commission, what is the total value of merchandise he needs to sell?
So he needs to sell $2,000 in merchandise.
what is the total value of merchandise he needs to sell?
We can assume that we have a proportional relation:
y = k*x
Where y is the commission and x is what Norman sells, then:
$15 = k*$200
k = $200/$15 = 0.075
$37.50 = k*$500
k = $500/$37.50 = 0.075
Then the relation is:
y = 0.075*x
If he wants a commission of $150, then:
$150 = 0.075*x
$150/0.075 = x = $2,000
So he needs to sell $2,000 in merchandise.
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Given that f(x)=x2−4 and g(x)=x+3 , what are all the values of x for which f(g(x))=0 ?
Answer:
the answer is (x )
math way helps
Step-by-step explanation:
The requried function of function f(g(x)) is given as x² + 6x +5.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
Given functions,
f(x)=x²−4 and g(x)=x+3
In order to form a function of function we have to function g(x) in function f(x)
Now,
f(g(x)) = f(x)=(g(x))²−4
f(g(x)) = f(x)=(x+3)²−4
f(g(x)) = x² + 6x + 9 -4
f(g(x)) = x² + 6x +5
Thus, the requried function of function f(g(x)) is given as x² + 6x +5.
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A support wire that is attached from the top of an observation tower to 20 meters away on the ground. if the support wire and the ground form an angle of 46 degrees, what is the length of the support wire?
Trigonometric ratios are defined as the ratio of different sides of a right angle triangle with respect to one angle of the right angled triangle.
Length of the wire = Hypotenuse of the triangle = X
Base of the triangle = Distance from the bottom of the tower to the point where wire is attached on ground = 20 m
Angle b/w Hypotenuse and Base of triangle = 46°
cos(θ) = Base / Hypotenuse
cos(46) = 20 / X
X = 20 / cos(46)
X = 28.79 m
Hence, the length of the wire is 28.79 m.
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