Answer:
[tex]x_1=1\\x_2=\frac{1}{2} =0.5[/tex]
Step-by-step explanation:
Given a equation of the form:
[tex]ax^2+bx+c=0[/tex]
The roots of this equation can be found using the quadratic formula which is given by:
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
In this case we have this equation:
[tex]2x^2-3x+1=0[/tex]
So:
[tex]a=2\\b=-3\\c=1[/tex]
Using the the quadratic equation :
[tex]x= \frac{-(-3)\pm\sqrt{(-3)^{2}-4(2)(1) } }{2(2)} = \frac{3\pm\sqrt{9-8 } }{4}=\frac{3\pm 1}{4}[/tex]
Therefore the two roots would be:
[tex]x_1=\frac{3+ 1}{4}=\frac{4}{4}= 1\\x_2=\frac{3- 1}{4}=\frac{2}{4}=\frac{1}{2}=0.5[/tex]
find the difference 6x^2-14x+4/x(x-2) - 6x-1/x+1
Final answer:
To find the difference between two expressions in the given question, you need to simplify each expression first and then subtract them. The steps involve simplifying each expression separately and then performing the subtraction.
Explanation:
To find the difference 6x² - 14x + 4 / x(x - 2) - 6x - 1 / x + 1, you need to first simplify each expression and then subtract them from each other.
Step 1: Simplify each expression separately.
6x² - 14x + 4 / x(x - 2) = (3x - 2)(2x - 1) / x(x - 2) = 3(2x - 1) / x
- 6x - 1 / x + 1 = -6 - 1 / x + 1 = -7 / (x + 1)
Step 2: Subtract the two simplified expressions: 3(2x - 1) / x - 7 / (x + 1).
PART A: All but two of the pyramids built by the ancient Egyptians have faces inclined at 52 degree angles. Suppose an archaeologist discovers the ruins of a pyramid. Most of the pyramid has eroded, but the length of a side of the square base is 82 meters. How tall was the pyramid, assuming its faces were inclined at 52 degrees? Round your answer to the nearest meter.
25 m
32 m
52 m
105 m,
In the problem, we were asked to compute for the height of the pyramid. Given are the base of the pyramid which is 82 m and the angle of 52°.
If given an illustration, the height is opposite to the angle and the adjacent side is given by half the base.
Based on the mnemonics of trigonometry (SOH CAH TOA), the function to be used is tangent.
The computation is as follows:
Let h = height of pyramid (m)
tan52 = h/41
h = 41tan52
h ≈ 52.5 m
Hence, the height of the pyramid is approximately 52.5.
However, the closest answer based on the choices you provided is 52 m.
If arc SQ = 92° and arc QR = 86°, what is the measure percent of ∠RPS
The answer is 45°. First combine arc SQ and QR: 178°. Then subtract that from the whole circle (360°) and that will give us 182°. Now subtract arc SQ from it and divide the difference (90°) by two.
What is the probability of drawing a diamond from a standard deck of cards on a second draw, given that a diamond was drawn on the first draw and not replaced?
twelve over fifty one
one over fifty two
one over fifty one
thirteen over fifty two,
Write the equation of the circle with center (0, 0) and (5, 2) a point on the circle.
Which expression can be used to find the value of X?
Mrs. Gomez is sewing a dress for each of her four daughters. Each dress uses 2.25 yards of fabric, and the fabric costs $4.15 per yard. What will be the cost for fabric for all four dresses? Show your work, including labeling your answer with the appropriate units of measure.
Answer:
The cost for fabric for all four dresses is $37.35
Step-by-step explanation:
Each Dress requires fabric = 2.25 yards
Fabric required for 4 dresses = [tex]2.25 \times 4[/tex]
= [tex]9yards[/tex]
Cost of 1 yard fabric = $4.15
Cost of 9 yard fabric = [tex]4.15 \times 9[/tex]
= $37.35
Hence the cost for fabric for all four dresses is $37.35
Four times the larger of two numbers is equal to seven times the smaller. the sum of the numbers is 22. what are the numbers?
The larger is 14 the smaller is 8
Explanation:Let the larger number be L and the smaller be S
So we know that
1) L+S=22
And
2)4L=7S
From equation 1) we get L=22-S
Substitute this into equation 2) to get 4(22-S)=7S
88-4S=7S
88=11S
S=8. The smaller number is 8
As they total 22 the larger number is 14.
Check: 4x14=7x8. Yes
Solution 2:
Let x= larger number
And let y= smaller. umber
Now we are told that:
4x=7y--------eq1
We are also told that:
x + y=22-----eq2
Substitution method looks easier.
From eq1 x=(7/4)y. Substitute this into eq2
(7 /4)y +y=22
(7/4)y+(4/4)y=22
(11/4)y=22 multiply each side by 4
11y=88
y=8
From eq2, x+8=22
x=14
Hope this helps
Final answer:
To find the two numbers where four times the larger is equal to seven times the smaller, and the sum is 22, we set up a system of equations and solve them. We find that the larger number is 14 and the smaller number is 8.
Explanation:
To solve the question "Four times the larger of two numbers is equal to seven times the smaller. The sum of the numbers is 22. What are the numbers?", we use a system of equations. First, we assign variables to the unknowns: let x be the larger number and y be the smaller number. According to the problem, we have two equations:
4x = 7y (because four times the larger number is equal to seven times the smaller)
x + y = 22 (because the sum of the numbers is 22)
Now, we can solve for one of the variables. Let's isolate y in the second equation:
y = 22 - x
Substitute this expression for y into the first equation:
4x = 7(22 - x)
Expand and solve for x:
4x = 154 - 7x
11x = 154
x = 14
Then we find y by substituting x back into the equation y = 22 - x:
y = 22 - 14
y = 8
Therefore, the larger number is 14 and the smaller number is 8.
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 190 grams of a radioactive isotope, how much will be left after 4 half-lives?
4. find the real number roots. sqrt-0.25
Given is square root of a negative real number, i.e. [tex] \sqrt{-0.25} [/tex]
When we find square root of positive real numbers, we get Real answers.
But when we find square root of negative real numbers, we get Imaginary answers. To solve them, we can split the given negative number into product of -1 and the number itself but with positive sign. e.g. -4 = -1 x 4.
For square root of -1, we use english letter 'i' called Imaginary unit i.e. [tex] \sqrt{-1} = i [/tex]
Now we can use -0.25 = -1 x 0.25
[tex] \sqrt{-0.25} =\sqrt{-1*0.25} \\\\
\sqrt{-0.25} =\sqrt{-1}*\sqrt{0.25} \\\\
\sqrt{-0.25} =i*0.5 \\\\
\sqrt{-0.25} =0.5i [/tex]
Hence, "0.5i" is the final answer.
The square root of -0.25 is not a real number because the square root of a negative number is not defined within the set of real numbers.
The square root of a negative number is not a real number. In the case of √(-0.25), the expression is undefined within the set of real numbers because taking the square root of a negative number results in a complex number. The square root of a negative number is typically represented using the imaginary unit "i" in the complex number system. Therefore, √(-0.25) is not a real number.
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SOMEONE HELP ME PLEASE MY LAST DAY TO TURN THIS IN!
Solving Systems of Equations by Elimination
1) 5x + 2y= 21
-x - y= -9
2) 3x + 2y= -13
3x+4y= 1
3) 7x + 3y= 22
4y= 20
4) -2x + y= 10
4x - y= -14
after examining the figure shown here, Daniel determines that FG/TU= EF/ST wich theorem or collary allowed him to draw that conclusion?
A. Side-splitting theorem
B. two- transversal proportionality corollary
C.Proportional Altitudes theorem
D. Proportional Medians Theorem
The Proportional Medians Theorem states:If two triangles are similar, then the ratio of the lengths of two corresponding medians is the same as the ratio of the lengths of two corresponding sides.
A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.
It is given the two triangles are similar.FG and TU are the medians of the triangle .
By Proportional Medians Theorem ratio of the lengths of two corresponding medians is the same as the ratio of the lengths of two corresponding sides.
So [tex] \frac{FG}{TU} =\frac{EF}{ST} [/tex]
Option D. Proportional Medians Theorem is the right answer.
please help me !!!!!!!
Express the fractions 3/4, 7/16, and 5/8with the LCD.
A. 24/32, 14/32, 24/32 B. 12/16, 7/16, 10/16 C. 9/16, 49/16, 36/16 D. 3/4, 2/4, 3/4
You bought jeans last week for $55. Today you see that the jeans are on sale for $40. What is the percent decrease of the price? (Explain please!)
Which of the following forms of bonds has the least risk
Municipal bonds
Below investment grade bonds
Corporate bonds
Treasury bonds
Treasury Bonds is the correct answer.
Treasury Bonds has the least risk as these bonds are issued and backed by the United States federal government. They are credit-risk free as they have practically no default risk and thus the safest bonds to buy. These are issued by the government to finance its budget deficits.
two line segments ab and cd, have end points at A ( -5,11) , B( 3,5) , C (9,3) and D (2,10) which of the two lines segments is longer ?
Line segment AB is longer than segment CD.
What is distance between two points?The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}
Two line segments AB and CD have endpoints at A (-5, 11), B(3, 5), C (9, 3) and D (2, 10).
To find the distance:
The distance of two points
= √ {(x₂-x₁)² + (y₂-y₁)²}
The distance of segment AB
= √ {(3+5)² + (5-11)²}
= √ {(8)² + (-7)²}
= √(64 + 49)
= √(64 + 49)
= √113
= 10.63 unit.
The distance of segment CD
= √ {(2-9)² + (10-3)²}
= √ {(-7)² + (7)²}
= √(49 + 49)
= √98
= 9.9 unit.
Clearly, distance of AB > distance of CD
Therefore, distance of AB > distance of CD.
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By what factor does the y-value change for y = 4x?
Answer:
the answer is 4
Step-by-step explanation:
What is the measure of ∠D ?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
m∠D=
°
Answer:
[tex]m\angle D=29.05[/tex]
Step-by-step explanation:
We have been given an image of a right triangle and we are asked to find the measure of angle D.
We can see from our given triangle that the opposite side of angle D measures 25 ft and adjacent side of angle D is 45 ft.
Since we know that tangent represents the relation between the opposite and adjacent sides of a right triangle.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
Upon substituting our given values in above formula we will get,
[tex]\text{tan}\angle D=\frac{25}{45}[/tex]
[tex]\angle D=\text{tan}^{-1}(\frac{25}{45})[/tex]
[tex]\angle D=29.054604099077[/tex]
Upon rounding our answer to nearest hundredth we will get,
[tex]\angle D\approx 29.05[/tex]
Therefore,the measure of angle D is 29.05 degrees.
Simplify using the distributive property.
8(y + 12)
8y + 12
20y
20 + y
8y + 96
The expression 8(y + 12) simplifies to 8y + 96 using the distributive property, which involves multiplying 8 by both y and 12.
The question asks us to simplify the expression using the distributive property. The expression given is 8(y + 12). To simplify, we apply the distributive property by multiplying 8 with both y and 12.
So, we have:
8(y) + 8(12) = 8y + 96.
Therefore, the simplified form of the expression 8(y + 12) is 8y + 96.
Factor completely. 12x^4+18x^3+45x^2
Answer: so is the answer 3^2 or the other?
Step-by-step explanation:
well anyway but what I know the answer should be the second thing because you want the numbers to be the LCM which for this it would be (4x^2 + 6x + 15) but not 100% bout this
What is the value of b in the equation (yb) 4= 1/y24
Answer:
The value of b is [tex]\frac{1}{y^7}[/tex].
Step-by-step explanation:
Here the given expression is,
[tex](yb)^4=\frac{1}{y^{24}}[/tex]
[tex]y^4b^4=\frac{1}{y^{24}}[/tex] ( Using [tex](ab)^m=a^mb^m[/tex] on left side )
[tex]y^4b^4y^24 = 1[/tex] ( By cross multiplication )
[tex]y^{4+24}b^4=1[/tex] ( Using [tex]a^ma^n=a^{m+n}[/tex] on left side )
[tex]y^{28}b^4=1[/tex]
[tex]b^4=\frac{1}{y^{28}}[/tex]
[tex]b=(\frac{1}{y^{28}})^{\frac{1}{4}}[/tex] ( [tex]a^m=b^n\implies a=b^\frac{n}{m}[/tex] )
[tex]b=\frac{1^{\frac{1}{4}}}{(y^{28})^\frac{1}{4}}[/tex] ( [tex](\frac{a}{b})^m=\frac{a^m}{b^m}[/tex] )
[tex]b=\frac{1}{y^{28\times \frac{1}{4}}}[/tex] ( [tex](a^m)^n=a^{m\times n}[/tex] )
[tex]b=\frac{1}{y^7}[/tex]
Answer:
It is -6
Step-by-step explanation:
The number of animals in a population is 775, and it increases by of 51% each year.
a. Model the situation with an exponential function.
b. Find how many animals there will be in 10 years.
c. How many years will it take for the population to become 1150.
Show all work!
Answer(a):
Exponential growth formula is given by
[tex]A=P(1+r)^t[/tex]
Where preset population = P= 775
Rate of increase = r = 51% = 0.51
t= number of years
A= Future value.
Plug these values into above formula:
[tex]A=775(1+0.51)^t[/tex]
[tex]A=775(1.51)^t[/tex]
Hence required exponential function is [tex]A=775(1.51)^t[/tex]
Answer(b):
plug t=10 years
[tex]A=775(1.51)^t=775(1.51)^{10}=775(61.6267795034)=47760.7541151[/tex]
which is approx 47761.
Answer(c):
Plug A=1150
[tex]1150=775(1.51)^t[/tex]
[tex]\frac{1150}{775}=(1.51)^t[/tex]
[tex]\ln(\frac{1150}{775})=t*\ln(1.51)[/tex]
[tex]0.394654192004=t*0.412109650827[/tex]
0.957643654334=t
Which is approx 1 year.
Find the first four terms of the given sequence tn = (-1)n(n).
A.
-1, -2, -3, -4
B.
-1, 2, -3, 4
C.
1, ½, 2/3, ¾
D.
1, 2, 3, 4
Find the volume of the sphere with a radius of 9. Express your answer in terms of π.
Find the measure of each angle please?
What does the 80 inches represent in an 80" TV
The 80 inches on an 80" TV refers to the diagonal measurement of the screen, which determines the size of the TV. This measurement is essential for potential buyers to know to match the TV to their space and optimal viewing distance. Other factors like screen resolution and whether to choose plasma or LCD also influence the viewing experience and cost.
When we refer to an 80" TV, the 80 inches represents the diagonal measurement of the screen. This measurement is taken from one corner to the opposite corner of the screen, not horizontally or vertically, which is the standard for sizing televisions and monitors. The importance of considering screen size arises from the need to match the viewer's space and viewing distance to optimize the viewing experience. With larger screens, such as an 80-inch TV, viewers can enjoy a more immersive viewing experience, especially when watching sports, movies, or DVDs. However, depending on the resolution, like 1080p for full HD or 768p for a lower resolution, the quality of the image may affect the perceived difference in quality, especially on smaller screens in which it might not be distinguishable to the nak.ed eye.
Which rational number represents a decrease in water level from 8 feet to 6 feet?
Tough one!
For what values of a and b is the following equation true?
limx->0 ((sin2x)/x^3)+a+(b/x^2)) = 0
@Calculus1,
Write an exponential function that passes through the points (0, 3) and (-1, 6)