Answer:
[tex]x=\frac{2}{5}[/tex] or [tex]x=1[/tex]
Step-by-step explanation:
The given quadratic equation is
[tex]5x^2-7x+2=0[/tex]
Group the constant terms on the right hand side.
[tex]5x^2-7x=0-2[/tex]
[tex]5x^2-7x=-2[/tex]
Divide through by 5.
[tex]x^2-\frac{7}{5}x=-\frac{2}{5}[/tex]
Add the square of half the coefficient of x., which is [tex](\frac{1}{2}\times- \frac{7}{5})^2=\frac{49}{100}[/tex] to both sides of the equation.
[tex]x^2-\frac{7}{5}x+\frac{49}{100}=-\frac{2}{5}+\frac{49}{100}[/tex]
The left hand side is now a perfect square.
[tex](x-\frac{7}{10})^2=\frac{9}{100}[/tex]
Take the square root of both sides;
[tex](x-\frac{7}{10})=\pm \sqrt{\frac{9}{100}}[/tex]
[tex]x-\frac{7}{10}=\pm \frac{3}{10}[/tex]
[tex]x=\frac{7}{10}\pm \frac{3}{10}[/tex]
[tex]x=\frac{7-3}{10}[/tex] or [tex]x=\frac{7+3}{10}[/tex]
[tex]x=\frac{4}{10}[/tex] or [tex]x=\frac{10}{10}[/tex]
[tex]x=1[/tex] or [tex]x=\frac{2}{5}[/tex]
Answer:
[tex]x_1=1\\\\x_2=\frac{2}{5}[/tex]
Step-by-step explanation:
- You must divide the equation by 5:
[tex]x^{2}-\frac{7}{5}x+\frac{2}{5}=0[/tex]
- Add and subtract [tex](\frac{\frac{7}{5}}{2})^2[/tex]:
[tex]x^{2}-\frac{7}{5}x+(\frac{7}{10})^2+\frac{2}{5}-(\frac{7}{10})^2=0[/tex]
Therefore, you obtain:
[tex](x-\frac{7}{10})^2-0.09=0[/tex]
-add 0.09} to both sides:
[tex](x-\frac{7}{10})^2=0.09[/tex]
- Apply square root to both sides and solve for x:
[tex]\sqrt{(x-\frac{7}{10})^2}=\sqrt{\0.09}\\x-\frac{7}{10}=\sqrt{0.09}\\\\x_1=\frac{7}{10}+\sqrt{0.09}=1\\\\x_2=-\frac{7}{10}-\sqrt{0.09}=\frac{2}{5}[/tex]
Find the probability distribution for the following function: P(x) = x/10 for x = 3, 5, and 7
Answer:
3/10. 1/2 and 7/10
Step-by-step explanation:
For P(x) = x/10
When x = 3;
Then;
P(3) = 3/10
When x = 5
Then;
P(5) = 5/10
= 1/2
When, x = 7
Then;
P(7) = 7/10
Answer:
[tex]P(3)=\frac{3}{10}=0.3\\\\P(5)=\frac{5}{10}=0.5\\\\P(7)=\frac{7}{10}=0.7[/tex]
Step-by-step explanation:
Probability is the possibility of happening of some event .
Probability = [tex]\frac{No.\,\,of\,\,outcomes}{Total\,\,no.\,\,of\,\,outcomes}[/tex]
Probability distribution links each outcome of an experiment with it's probability of occurrence .
Given: [tex]P(x)=\frac{x}{10}[/tex]
To find: Probability distribution for the given function for x = 3 , 5 and 7
Solution:
For x = 3 :
On putting x = 3 in function [tex]P(x)=\frac{x}{10}[/tex] , we get
[tex]P(3)=\frac{3}{10}=0.3[/tex]
For x = 5 :
On putting x = 5 in function [tex]P(x)=\frac{x}{10}[/tex] , we get
[tex]P(5)=\frac{5}{10}=0.5[/tex]
For x = 7 :
On putting x = 7 in function [tex]P(x)=\frac{x}{10}[/tex] , we get
[tex]P(7)=\frac{7}{10}=0.7[/tex]
Find the area of the shaded segment. Round your answer than your square meter.
Answer options: 3m2, 5m2, 6m2, 4m2.
Answer:
3 m^2
Step-by-step explanation:
The shaded area = Area of Sector - Area of Triangle
First we find area of sector = [tex]\frac{\theta}{360}*\pi r^2[/tex]
We know the angle is 60° (vertical angles are equal) and the radius is 6, so we find the area of sector to be:
[tex]\frac{\theta}{360}*\pi r^2\\\frac{60}{360}*\pi (6)^2\\=18.85[/tex]
Secondly, we find area of triangle (isosceles) = [tex]\frac{1}{2}abSinC[/tex]
where
a and b are the two sides bordering the known angle, so a=b=6, and
C is the angle which is 60°
Now we find the area to be:
[tex]\frac{1}{2}(6)(6)Sin(60)\\=15.59[/tex]
Hence, area of shaded = [tex]18.85 - 15.59=3.26[/tex]
Rounding to nearest whole number, area of shaded region = 3m^2
1. For the carnival, the park rented a dunking booth shaped as a rectangular prism. The booth is 3 1/2 ft wide, 3 1/2 ft long, and 8 ft tall. (a) What is the total volume of the dunking booth? (b) If they are only going to fill the dunking booth 6/7 full, how many cubic feet of water will they need?
Answer:
a) The volume of the dunking booth = 98 feet³
b) They will need 84 feet³ of water to fill 6/7 of dunking booth
Step-by-step explanation:
* Lets talk about the rectangular prism
- It has 6 rectangular faces each two opposite faces are congruent
- It has three dimensions Length, Width and Height
- Its volume = Length × Width × height
* In our problem the dunking booth is a rectangular prism
with dimensions:
- Width = 3.5 ft
- Length = 3.5 ft
- Height = 8 ft
∴ Its volume = 3.5 × 3.5 × 8 = 98 feet³
a) The volume of the dunking booth = 98 feet³
* They want to fill 6/7 of the dunking booth with water
∴ The volume of the water will be 6/7 from the volume
of the dunking booth
∵ The volume of the dunking booth = 98 feet³
∴ The volume of the water = 6/7 × 98 = 84 feet³
b) * They will need 84 feet³ of water
a) 98
b) 84
hope this helps!
Is the sequence -1,6,-36,216 geometric and what is the common ratio
Answer:
yes, -6
Step-by-step explanation:
6/-1 = -36/6 = 216/-36 = -6
Adjacent terms have a common ratio of -6, so they comprise a geometric sequence.
I would like some help please
A triangle has sides of lengths 4, 3, and 5. Is it a right triangle?
Answer:
Yes, because 3^2 + 4^2 = 5^2
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
it doesn't have the same length so one sides gonna be longer
you have 3/4 yard of felt for a project and you use 1/8 yard. What fraction of a yard of felt do you have left over?
Answer: [tex]\frac{5}{8}[/tex] yard.
Step-by-step explanation:
You have the following information given in the problem:
- You have 3/4 yard of felt.
- You used 1/8 yard,
Therefore, to find the fraction of a yard of felt that you have left over (which you can call x), you only need to subtract 3/4yard and 1/8 yard, as you can see below:
[tex]x=\frac{3}{4}yard-\frac{1}{8}yard\\\\x=\frac{5}{8}yard[/tex]
Find the next three terms in each sequence
Answer:
10) 40,80,160
11) 64, 256, 1024
12) 5, 2.5, 1.25
Step-by-step explanation:
Hope this helps. :)
i don’t understand :(
Answer:
multiplication
Step-by-step explanation:
See what is happening to the expression x - 4 and choose the opposite operation.
x - 4 is being divided by 5.
The opposite operation to division is multiplication, so you need to use multiplication to get x - 4 alone on the left side.
the answer to the question is multiplication
7x + 2y = 4
y = x + 1
Solve the system of equations.
A. (1/3, 4/3)
B. (2/9,11/9)
C. no solution
In 1997 U.S. House of Representatives there were 222 Republicans, 204 Democrats, 2 Independents, and 7 undecided. What percentage of the total is neither Republican nor Democrat?
A.) .02%
B.) .98%
C.) 2.1%
D.) 9%
Answer:
2.1
Step-by-step explanation:
There were a total of 435 people in the House. 9 were neither Republican nor Democratic. Divide 9/435. multiply that by 100
Answer:
The answer is C.
Step-by-step explanation:
In 1997 U.S. House of Representatives there were 222 Republicans, 204 Democrats, 2 Independents, and 7 undecided.
So total number in the House = 222 + 204 + 2 + 7
= 435
Total number who is neither Republican nor Democrat = 2 + 7
= 9
Percentage of the total is neither Republican nor Democrat
= 9 / 435 * 100%
= 2.1%
Point A is located at (7, -1). After it is translated, point A' is located at (0, -1). What was the translation?
7 units to the right
7 units to the left
7 units up
7 units down
Answer:
7 units to the left
Step-by-step explanation:
Because if you move to the left you subtract 7 from the x-axis number or in this case 7, so 7-7=0.
Answer:
7 units to the left.
Step-by-step explanation:
-4(3s) + 2(-t)
if s = 1/2 and t = -3, what would the answer be?
Answer:
The expression would be = to 0.
Step-by-step explanation:
Starting with -4(3s) + 2(-t), substitute (1/2) for s and (-3) for t:
-4(3/2) + 2(+3)
This gives us:
-12/2 + 6 = 0
Answer:
-12
Step-by-step explanation:
3 times 1/2 is 1 1/2. 1 1/2 times -4 is -6. Then, -3 times 2 equals to -6. lastly -6 plus -6 equals to -12
Which comparison is not correct?
a. 6 > 5
B. -7 > -9
C. -3 < 4
D. -4 < -12
-4 < -12 would be my answer, just from looking at it. If you write it out on a number line, the number -4 is higher than -12. The higher the negative number, the lower it is on the line. So, -4 is greater than -12, not lower than.
The comparison which is not correct is Option (D) -4<-12
Concept of inequality between two numbers -The inequality, greater than or lesser than between two numbers indicate that whether one number is greater than the other number or less than the other number. The inequality is represented by ">" and "<".
How to find the comparison from the options which is not correct ?In number system, when comparing two numbers less than zero then the magnitude of smaller negative number is always greater than the magnitude of bigger negative number. Or in other words it is opposite to the positive number system .
For example, -10<-4 or -2<-1
Thus the comparison which is incorrect is Option (D) -4 < -12.
To learn more about comparison between two numbers, refer -
https://brainly.com/question/2954013
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What is a way to write 1,00,000 using exponents
Answer:
10^5
Step-by-step explanation:
100,000
= 10 x 10 x 10 x 10 x 10
= 10^5
Which of the following relations is a function click on the graph until the correct graph appears
only the last one since the others don’t pass the vertical line test
which is when you draw a straight line down your function and if it hits 2 or more points it is not a function
The correct graph should have x values that have no more than one y value.
What is function graph ?The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function.Type of function graph ?
Depending on the kind of function that is graphed, various graph types exist.
Linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal graphs are the eight most often used types.
Learn more about function graph https://brainly.com/question/9834848
here
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Which of the following could be the side lengths of a triangle?
A. 12,15,30
B. 14,16,34
C. 15,16,33
D. 17, 18, 32
Here is your answer
D. 17, 18, 32
REASON:
Sum of any two sides of a triangle is always greater than the third side.
So,
17+18= 35
35>32
In other cases
a. 12+15= 27
27 <30
b. 14+16= 30
30 <34
c. 15+16= 31
31 <33
Hence other three can't be sides of a triangle.
HOPE IT IS USEFUL
The side lengths that could represent a triangle is 17, 18, 32
What is a triangle?
A triangle is a polygon with three sides and three angles. Type of triangles are isosceles, equilateral, scalene and obtuse.
For a triangle, the sum of any two sides must be greater than the third side. Hence:
For 12, 15 , 30; 12 + 15 < 30
For 14, 16 , 34; 14 + 16 < 34
For 15, 16 , 33; 15 + 16 < 33
For 17, 18 , 33; 17 + 18 > 33
The side lengths that could represent a triangle is 17, 18, 32
Find out more on triangle at: https://brainly.com/question/17335144
An 8-car Ferris wheel is shaped like a regular octagon. Does the Ferris wheel have rotational symmetry?
Answer:
Yes, it does.
Step-by-step explanation:
Every regular shaped figure will have rotational symmetry, since they are built with identical segments all around.
To find the answer, ask yourself « If I rotate the shape, is there a time where I’ll find the exact same shape again with a different angle? »
So, a square has rotational symmetry, but not a rectangle.
A equilateral triangle has rotational symmetry, but not any other type of triangle.
Annabel uses 5 gallons of gas to drive 140 miles on the highway if she travels at the same rate how many miles can she drive on 7 gallon of gas
Answer:
196
Step-by-step explanation:
Divide 140 by 5 to find out how many miles she can drive with one gallon:
140/5 = 28
Multiply by 7:
28 x 7 = 196
hope this helps
an office building in the form of a right rectangular prism with a height of 200 m, a length of 60 and a width of 40 m. the upper quarter of each vertical face of the building must be covered with a large banner promoting a sports event. what will be the surface of the surface covered by the streamer
Final answer:
The surface area covered by the banner is 27,000 square meters. The side length of a square with the same area would be approximately 164.3 meters.
Explanation:
The office building is a right rectangular prism with a height of 200m, a length of 60m, and a width of 40m. The upper quarter of each vertical face needs to be covered with a large banner.
To find the surface area covered by the banner, we need to calculate the surface area of each vertical face. The surface area of a rectangular prism is given by the formula 2lw + 2lh + 2wh. Since we need to cover the upper quarter of each face, we can consider only three quarters of the height, resulting in a formula of 2lw + (3/4)lh + 2wh.
Plugging in the given values, we get:
Surface area = 2(60)(40) + (3/4)(200)(60) + 2(40)(200)
Simplifying the expression, we get the surface area covered by the banner to be 27,000 square meters.
If we want to represent the area as a square with the same area, we can take the square root of the surface area. In this case, the side length of the square representing the area would be approximately 164.3 meters.
Out of 2 9 15 21 is not a composite
Answer:
2
Step-by-step explanation:
2 is actually a prime number because composite numbers have more than 2 factors but prime numbers don't.
(V2.00)
Rewrite f(x) = -2(x - 3)2 + 2 from vertex form to standard form.
Answer:
The standard form of the quadratic equation is [tex]f(x)=-2x^{2}+12x-16[/tex]
Step-by-step explanation:
we know that
The standard form of a quadratic equation is
[tex]f(x)=ax^{2}+bx+c[/tex]
we have
[tex]f(x)=-2(x-3)^{2}+2[/tex]
convert to standard form
[tex]f(x)=-2(x-3)^{2}+2\\f(x)=-2(x^{2} -6x+9)+2\\f(x)=-2x^{2}+12x-18+2\\f(x)=-2x^{2}+12x-16[/tex]
2 cars are driving in a highway.car A starts 10 miles ahead of car B.Car A is driving at a speed of 55 miles per hour.car B is driving at a speed of 60 miles per hour.After how Many hours will the 2 cars be in the same location?how far will car B have driven when the 2 cars leer?
Answer:
Step-by-step explanation:
60 - 55 = 5, car B catches up to Car A 5 miles per hour, they are 5 miles closer every hour
10 / 5 = 2, 2 hours
car b would have driven 60 * 2 = 120
Please help solve this problem
Answer: OPTION A
Step-by-step explanation:
To simplify the expression you must multiply the numerator and the denominator of the expression by √3.
As all the square roots have equal index, you can multiply the radicands, which are the numbers inside of the sqaures roots.
You also must keep on mind that:
[tex](\sqrt[n]{a})^n=a[/tex]
Therefore, you obtain:
[tex]\frac{6\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}}=\frac{6\sqrt[]{6}}{3}=\frac{2\sqrt[]{6}}{3}[/tex]
Answer:
The correct answer is option B. 2√6
Step-by-step explanation:
It is given that an expression, 6√2/√3
To simplify the expression
6√2/√3
Multiplying numerator and denominator with √3
6√2/√3 = (6√2 x √3)/(√3 x √3)
= [ 6 x √(2x3)]/3) (√2 x √3 = √(2 x 3)
= 6√6/3
= 2√6
Therefore the simplified form of given expression 6√2/√3 is 2√6.
The correct answer is option B. 2√6
10 points! What is answer
Answer:
B
Step-by-step explanation:
Using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex]
Hence
[tex]\frac{3^{4} }{3^{2} }[/tex] = [tex]3^{(4-2)}[/tex] = 3² = 9 → B
The answer is 9
because 3 to the power of 4 is 81 and 3 to the power of 2 is 9 so it’s 81 divided by 9 which is 9
Pls find the zeros
in 10th level
Answer:
x = - 3[tex]\sqrt{2}[/tex], x = [tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given
x² + 2[tex]\sqrt{2}[/tex] x - 6
To calculate the zeros equate to zero
x² + 2[tex]\sqrt{2}[/tex] x - 6 = 0 ( add 6 to both sides )
x² + 2[tex]\sqrt{2}[/tex] x = 6
One way is to use the completing the square method
add ( half the coefficient of the x- term )² to both sides
x² + 2[tex]\sqrt{2}[/tex] x + ([tex]\sqrt{2}[/tex])² = 6 + ([tex]\sqrt{2}[/tex])²
x² + 2[tex]\sqrt{2}[/tex] x + 2 = 6 + 2
(x + [tex]\sqrt{2}[/tex] )² = 8
Take the square root of both sides
x + [tex]\sqrt{2}[/tex] = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex]
subtract [tex]\sqrt{2}[/tex] from both sides
x = - [tex]\sqrt{2}[/tex] ± 2[tex]\sqrt{2}[/tex]
x = - [tex]\sqrt{2}[/tex] - 2[tex]\sqrt{2}[/tex] = - 3[tex]\sqrt{2}[/tex], or
x = - [tex]\sqrt{2}[/tex] + 2[tex]\sqrt{2}[/tex] = [tex]\sqrt{2}[/tex]
A bag contains an equal number of blue, green, pink, and red balls. If a ball is chosen at random 160 times, with replacement, predict the number of times the ball would be the color red.
Answer:
Step-by-step explanation:
Any one color would be 1/4 of the total. So the number of times you should get red is 1/4 of 160 = 40
Notice that this very odd problem does not depend on what the total is. It only depends on the number of times you make the draw. Unusual question.
three times the difference of 5 and a number gives 30. Find the number.
Answer:
15
Step-by-step explanation:
we need to write the equation. I came up with....
3(5 - x) = 30
so take the 3 away from the 30. I think your not supose to do the 3 because it out of the ( ). the opppisite of multiplication is division. so...
3 divided by 30 =10
rewrite
(5 - x) = 10
take the 5 away. the oppisite of subbtraction is addition.
5 + 10 = 15
check your; plug in x
3(5 - 15) = 30 This equation looks true!
Hope this helped! Please mark as brainliest! Thanks
Factor 24x^3y^2-4x^2y+84x^4 please show work
The given equation is :
[tex]24x^{3}y^{2} -4x^{2}y +84x^{4}[/tex]
Now taking [tex]4x^{2}[/tex] common from all the terms, we get
[tex]4x^{2} (6xy^{2} -y+21x^{2} )=0[/tex]
Writing the equation in standard form we get:
[tex]21x^{2} +6xy^{2} -y=0[/tex]
Now we will use the formula of quadratic equations to solve this,
[tex]x1,2 = \frac{-b+\sqrt{b^{2}-4ac }} {2a}[/tex] and
[tex]x1,2 = \frac{-b-\sqrt{b^{2}-4ac }} {2a}[/tex]
Now putting a = 21, b = 6y² and c = -y and solving the equations, we get
[tex]x=\frac{-6y^{2}+\sqrt{36y^{4}+84y }}{42}[/tex] and
[tex]x=\frac{-6y^{2}-\sqrt{36y^{4}+84y }}{42}[/tex]
Which of the following expressions are equivalent to (x + y) − z ?
A. z + (x + y)
B. x +(y − z)
C. None of the above
[tex]\huge\text{B. $\boxed{x+(y-z)}$}[/tex]
First, let's take a look at the terms in the original expression. Since its just addition and subtraction, we can get rid of the parentheses, leaving behind just [tex]x+y-z[/tex].
As long as an answer is made up of a positive [tex]x[/tex], a positive [tex]y[/tex], and a negative [tex]z[/tex], its correct!
Removing the parentheses in choice A leaves us with [tex]z+x+y[/tex], which has a positive [tex]z[/tex] rather than a negative [tex]z[/tex], so it's incorrect.
Removing the parentheses in choice B on the other hand gives us [tex]x+y-z[/tex], which means it's the correct answer! This is a good example of the associative property of addition in action.
The correct expression that is equivalent is option B. x +(y − z)
Let's simplify each expression to see if they are equivalent to (x + y) - z:
A. ( z + (x + y))
We can rearrange the terms:
z + (x + y) = (x + y) + z
This is not equivalent to (x + y) - z because the terms are added in a different order.
B. (x + (y - z))
We can expand the expression:
[tex]\[ x + (y - z) = x + y - z \][/tex]
This expression is indeed equivalent to (x + y) - z because the terms are arranged in the same order and operations are consistent.
So, the correct answer is:
[tex]\[ \text{B. } x + (y - z) \][/tex]