Answers
x1 = 4.8284
x2 = - 0.828
Remark
Substitute the value for y from the first equation into the second equation. Multiply by 4 and then see if it factors out. Solve for x first and then y.
Step one
Solve for y in the first equation. Subtract x from both sides.
y = 2 - x
Step Two
Equate the two ys.
2 - x = - 1/4x^2 + 3
Step Three
Bring the left side over to the right side.
0 = -1/4 x^2 + x + 3 - 2 Combine the like terms.
0 = -1/4 x^2 + x + 1
Step Four
0 = -1/4 x^2 + x + 1 Multiply through by 4
0 = - x^2 + 4x + 4
Step five
This won't factor. The only thing you can do is use the quadratic equation for roots.
a = - 1
b = 4
c = 4
[tex]\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]\text{x = }\dfrac{ -(4) \pm \sqrt{4^{2} - 4(-1)4}}{-2}[/tex]
[tex]\text{x = }\dfrac{ -(4) \pm \sqrt{16 + 16}}{-2} [/tex]
[tex]\text{x = } 2 \pm \sqrt{32 }\div -2 [/tex]
x = 2 +/- sqrt(4^2 * 2) / (- 2)
x = 2 +/- 4 sqrt(2) / - 2
x = 2 -/+ 2 sqrt(2)
x = 2 -/+ 2 *(1.414)
x = 2 -/+ 2.828
x1 = 4.8284
x2 = - 0.828
Short Answer
x1 = 4.8284
x2 = - 0.828
Remark
Substitute the value for y from the first equation into the second equation. Multiply by 4 and then see if it factors out. Solve for x first and then y.
Step one
Solve for y in the first equation. Subtract x from both sides.
y = 2 - x
Step Two
Equate the two ys.
2 - x = - 1/4x^2 + 3
Step Three
Bring the left side over to the right side.
0 = -1/4 x^2 + x + 3 - 2 Combine the like terms.
0 = -1/4 x^2 + x + 1
Step Four
0 = -1/4 x^2 + x + 1 Multiply through by 4
0 = - x^2 + 4x + 4
Step five
This won't factor. The only thing you can do is use the quadratic equation for roots.
a = - 1
b = 4
c = 4
x = 2 +/- sqrt(4^2 * 2) / (- 2)
x = 2 +/- 4 sqrt(2) / - 2
x = 2 -/+ 2 sqrt(2)
x = 2 -/+ 2 *(1.414)
x = 2 -/+ 2.828
x1 = 4.8284
I hope this helps
x = 2 +/- sqrt(4^2 * 2) / (- 2)
x = 2 +/- 4 sqrt(2) / - 2
x = 2 -/+ 2 sqrt(2)
x = 2 -/+ 2 *(1.414)
x = 2 -/+ 2.828
x1 = 4.82
Related Questions
Find the inverse function of h(x) = - 2/3x + 6.
h -1(x) = -3/2x + 9
h -1(x) = -3/2x - 6
h -1(x) = -2/3x + 9
h -1(x) = -2/3x - 6
Answers
In this triangle, side AT = 24. Please give the value for the sine, cosine, and tangent for this diagram (Which is the marked angle?). Give the value as a ratio ONLY. Make sure all ratios are in the lowest form.
Be sure to explain IN WRITING how you find sine, cosine, and tangent! If you are not sure, check the directions in this problem!
Question 1 options:
Answers
a] Sine
sin x=(opposite)/(hypotenuse)
opposite=7
hypotenuse=25
thus:
sin x= 7/25
b] Cosine
cos x=adjacent/hypotensue
adjacent=24
hypotenuse=25
cos x=24/25
Tangent
Tan x=opposite/adajcent
opposite=7
adjacent=24
thus
tan x=7/24
Which of the following types of equations have you learned to solve using algebraic methods?
[]Quadratic[]Exponential[]Radical[]Linear[]Rational
Answers
The following types of equations have you learned to solve using algebraic methods is Linear.
Quadratic equations involve a variable raised to the power of 2, and algebraic methods like factoring or using the quadratic formula are used for solving.
Exponential equations involve variables in the exponent, and logarithmic methods are employed to solve them.
Radical equations involve roots, and solving them often involves isolating the radical and squaring both sides or other methods based on the root's degree.
Linear equations involve variables raised to the power of 1, and solving them uses standard algebraic techniques like isolating the variable.
Rational equations involve ratios of polynomials and are solved by methods such as clearing denominators and factoring.
If 7 is subtracted from the product of 3 and a number, the result is 5 more than the number.
Answers
Please help me, if you'd be so kind.
A right rectangular prism is shown.
What is the length of DH¯¯¯¯¯¯ to the nearest tenth of an inch?
Drag and drop the answer into the box.
Answers
What is 3 to the 100th power?
Answers
3 to the 100th power is a very large number with over 47 digits, symbolizing the potential of exponential growth.
Explanation:The question is asking for the computation of the number 3 raised to the 100th power. In mathematics, exponents are used in expressions such as 'a to the power of n', written as an. Here, 'a' is the base and 'n' is the exponent, indicating how many times 'a' is multiplied by itself.
In our case, we have '3' as the base and '100' as the exponent. However, calculating 3100 directly is quite impractical due to the vast result it produces. However, we do know that it's a very large (over 47 digits!) number which could be useful for illustrating the power of exponential growth in mathematical or scientific contexts.
Learn more about Exponents here:https://brainly.com/question/33831961
#SPJ2
Twenty different statistics students are randomly selected. for each of them, their body temperature ( degrees °c) is measured and their head circumference (cm) is measured. if it is found that r=0, does that indicate that there is no association between these two variables?
Answers
The letter r represents the sample correlation coefficient .The Pearson product-moment correlation coefficient, also known as r, R, or Pearson's r, is a measure of the strength and direction of the linear relationship between two variables that is defined as the covariance of the variables divided by the product of their standard deviations.
The sample correlation coefficient value r is 0 given,so there is no linear relationship between the 2 variables that is the body temperature and head circumference.
Factor the trinomial below.
9x2 + 6x + 1
A. (3x + 1)(3x – 1)
B. (9x + 1)(x – 1)
C. (9x + 1)(x + 1)
D. (3x + 1)(3x + 1)
Answers
Answer: D. (3x + 1)(3x+1)
Step-by-step explanation:
9x² + 6x + 1
find two factor of 9 such that its product gives 9 and its sum gives 6 (3 and 3, 3×3 = 9 , also 3+ 3=6)
we are going to replace 6x by 3x + 3x
9x² + 6x + 1
9x² + 3x +3x + 1
3x(3x + 1) + 1(3x+ 1)
(3x + 1)(3x+1)
The correct factorization of the trinomial 9x² + 6x + 1 is (3x + 1)(3x + 1) or (3x + 1)². option D.
How do we identify the correct option when the trinomial is factorized?The trinomial 9x² + 6x + 1 is a perfect square trinomial, which can be factored as the square of a binomial.
Let's find the correct answer from your options:
(A) (3x + 1)(3x - 1): The difference of squares isn't the correct form for our trinomial.
(B) (9x + 1)(x - 1): Expanding this will not give us the original trinomial.
(C) (9x + 1)(x + 1): Expanding this will not give us the original trinomial.
(D) (3x + 1)(3x + 1): When expanded, this gives us 9x^2 + 3x + 3x + 1, which simplifies to 9x² + 6x + 1.
Therefore option D (3x + 1)(3x + 1) is correct
Find more exercises on trinomial ;
https://brainly.com/question/16347049
#SPJ6
Circle J has center J (4,-3) and radius 5 What is the measure, in degrees, of the arc with endpoints A (9,-3) and B (4,2)?
Explain the process you used (in words) and include the work you did to find this answer.
Answers
To find this, we can find the measure of the central angle that intercepts the arc.
The endpoints of the arc are at (9, -3) and (4, 2).
The slope of the line that passes through the endpoint (9, -3) and the center (4, -3) is given by
m=(-3--3)/(9-4) = 0/5 = 0.
Since the slope is 0, this tells us it is a horizontal line.
The line that passes through the endpoint (4, 2) and the center (4, -3) has a slope that is undefined; it is a vertical line at x=4. Numerically the slope is given by
m=(2--3)/(4-4) = 5/0, which is undefined.
These slopes are negative reciprocals of one another; 5/0 and 0/5 (0 has no sign). This means that these two lines would form a right angle, so the central angle of the circle is a right angle.
The intercepted arc has a measure equal to that of the central angle, so the arc is also 90°.
Use complete sentences to explain how the coordinate plane is a useful tool for geometric proofs.
Answers
Coordinate geometry proofs employ the use of formulas such as the Slope Formula, the Midpoint Formula and the Distance Formula, as well as postulates, theorems and definitions.
The method usually involves assigning variables to the coordinates of one or more points, and then using these variables in the midpoint or distance formulas .
The facilitate verification is a proof of a geometric hypothesis which utilizes "summed up" indicates on the Cartesian Plane make a contention.
The strategy for the most part includes doling out factors to the directions of at least one focuses, and afterward utilizing these factors in the midpoint or separation equations .
For instance, the accompanying is an arrange evidence of the Triangle Midsegment Theorem , which expresses that the fragment interfacing the midpoints of two sides of a triangle is parallel to the third side and precisely a large portion of the length.
The coordinate plane is an essential tool in geometry, allowing for a visual representation of shapes and aiding in geometric proofs, such as the Pythagorean Theorem. It allows abstract geometric concepts to be more concrete and easier to understand.
Explanation:The coordinate plane is a pivotal instrument in the field of Mathematics for conducting geometric proofs. The coordinate plane enables us to visually represent geometric shapes and articulate the different points, distances, and areas which helps us in proving geometric theorems and statements.
For instance, the Pythagorean Theorem, a fundamental theorem in Geometry can be illustrated efficiently and proven right on the coordinate plane. By placing a right-angled triangle on the coordinate plane, the lengths of the sides can be calculated using the coordinates of the vertices. Then, by applying the theorem, we can demonstrate that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Overall, the coordinate plane provides a graphical representation of the geometric shapes, making the abstract ideas more concrete and easier to understand, thus aiding in geometric proofs.
Learn more about Coordinate Plane here:https://brainly.com/question/31180198
#SPJ6
WILL GIVE BRAINLIEST PLZ HURRY!!!!!!!!Woodland High School recently won the state Academic Bowl Championship. The medal counts for the 7 members of the team are listed in the table. Which statement is true about the data shown in the table?
A) The range is less than the mode.
B) The mode is greater than the median.
C) The mean is greater than the median.
D) The median is greater than the mode.
Answers
Answer: B = The range is greater than the mean.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
The mean is greater than the median
Find the surface area of the cylinder in terms of π.
See picture
a) 1008π in.2
b) 522π in.2
c) 360π in.2
d) 396π in.2
Answers
Which of the following is an undefined term?
Angle
Circle
Plane
Ray
Answers
Answer:
Plane is an undefined plane
Step-by-step explanation:
Hi, there are three undefined terms in geometry: point, line, and plane.
Point: has no size, only location . It can be named with a capital letter.
Plane: a flat surface that has no thickness, that extends infinitely n every direction. Is named by a single letter or by three coplanar, but non-collinear, points.
Line: Set of points extending in either direction infinitely.
Angle, circle, and ray are not undefined terms. are not Plane.
Help needed soon. please
Answers
x = daisies flowers
y = roses flowers
We write the system of equations:
x + 2y = 33
x = y + 3
Solving the system we have:
x = 13
y = 10
Therefore, the cost of roses is:
2 * y = 2 * 10 = 20 $
Answer:
Roses = $ 20
I really need help
What is the equation of a circle with its center at(10,−4) and a radius of 4?
(x−10)2+(y+4)2=4
(x+10)2+(y−4)2=16
(x−10)2+(y+4)2=16
(x+10)2+(y−4)2=2
(x−10)2+(y+4)2=2
(x−10)2+(y+4)2=8
(x+10)2+(y−4)2=8
(x+10)2+(y−4)2=4
Answers
(x-10)²+(y+4)²=16
The equation of any circle is
(x – h)² + (y – k)² = r²
(h,k) is the center point and r is the radius
There are five red marbles eight blue marbles and 12 Green marbles in a bag. What is the theoretical probability of randomly drawing a red marble and then a green marble
Answers
Multiply: (2x2 − 5x)(4x2 − 12x + 10)
Answers
The answer is 60x^2 - 138x + 72
Hope this helps!
Answer:
[tex]8x^4-44x^3+80x^2-50x[/tex]
Step-by-step explanation:
The given expression is
[tex](2x^2-5x)(4x^2-12x+10)[/tex]
Using distributive property we get
[tex]2x^2(4x^2-12x+10)-5x(4x^2-12x+10)[/tex]
[tex]2x^2(4x^2)+2x^2(-12x)+2x^2(10)-5x(4x^2)-5x(-12x)-5x(10)[/tex]
On simplification we get
[tex]8x^4-24x^3+20x^2-20x^3+60x^2-50x[/tex]
On combine like terms.
[tex]8x^4+(-24x^3-20x^3)+(20x^2+60x^2)-50x[/tex]
[tex]8x^4-44x^3+80x^2-50x[/tex]
Therefore the product of two polynomials is [tex]8x^4-44x^3+80x^2-50x[/tex].
Tina can paint a room 1.5 times faster than Joey can. If they work together, they can paint a room in 6 hours. How long would it take the slower person working alone to paint the room?
Answers
1/n + 1/1.5n = 1/6
We'll make the denominator 3n:
3/3n + 2/3n = 1/6
5/3n = 1/6
Cross multiply:
3n = 30
n = 10
It will take the slower person 10 hours to complete the room.
A train travels at a constant speed. What is the train's speed between checkpoints, expressed as a unit rate? Use the information given in the picture to help you.
Answers
where
[tex]S[/tex] is the speed of the train
[tex]d_{i}[/tex] is the initial distance
[tex]d_{f}[/tex] is the final distance
[tex]t_{i}[/tex] is the initial time
[tex]t_{f}[/tex] is the final time
Since checkpoint A is the initial checkpoint, we can infer that [tex]d_{i}=105[/tex] and [tex]t_{i}=2[/tex]. Similarly, since checkpoint B is the final checkpoint, we can infer that [tex]d_{f}=285[/tex] and [tex]t_{f}=5[/tex]. Lets replace the values in our kinematic euation:
[tex]S= \frac{d_{f}-d_{i}}{t_{f}-t_{i}} [/tex]
[tex]S= \frac{285-105}{5-2} [/tex]
[tex]S= \frac{180}{3} [/tex]
[tex]S=60[/tex] mph
We can conclude that the train's speed between checkpoints is 60 mph.
which transformation can verify congruence by flipping a triangle over the y-axis?
A. Dilation
B. Translation
C. Reflection
D. Rotation
Answers
Answer: C. Reflection
Step-by-step explanation:
There are three rigid transformations which create congruent figures :
a)reflections, b) rotations, c) translations
A reflection is a transformation that flips a figure on the coordinate plane across a given line without changing the shape or size of the figure.
A translation moves a shapes by a particular distance.
A rotation rotates a shape around a fix point by an angle .
Therefore, the transformation can verify congruence by flipping a triangle over the y-axis is reflection.
The frequency of F3 is 174.61 Hz. What is the frequency of the note that is a perfect fifth below f3?
A) 43.6525 Hz
B) 87.305 Hz
C) 116.407 Hz
D) 261.915 Hz
Answers
174.61 Hz × 2/3 = 116.407 Hz
The appropriate choice is ...
C) 116.407 Hz
A license plate has 3 letters and 3 digits in that order. a witness to a hit-and-run accident saw the first 2 letters and the last digit. if the letters and digits can be repeated, how many license plates must be checked by the police to find the culprit?
Answers
Hope this helped!
The police must check 2600 possible license plates, calculated by multiplying 26 possibilities for the third letter not seen by the witness with 100 possibilities for the two digits also not seen.
To determine how many license plates the police must check to find the culprit, we consider the information that the witness saw the first two letters and the last digit. Since letters can be repeated, there are 26 possibilities for each of the two letters the witness saw. For the last digit, which the witness also saw, there are 10 possibilities (0 through 9). The third letter and the other two digits, which the witness did not see, each have the following number of possibilities: 26 for the third letter, and 10 for each of the two remaining digits.
Calculating the number of possible combinations:
First two letters (seen by the witness): 26 * 26 = 676 possibilitiesLast digit (seen by the witness): 10 possibilitiesThird letter (not seen by the witness): 26 possibilitiesThe two remaining digits (not seen by the witness): 10 * 10 = 100 possibilitiesTherefore, the total number of license plates the police must check is the product of the possibilities for the parts the witness did not see:
26 (third letter) * 100 (two remaining digits) = 2600 possible license plates.
What is the value of b?
Answers
d° + c° = 2 · 68° = 136°
b° = 360° - (136° + 104°) = 360° - 240° = 120°
A rectangle has a length of 4 feet and a perimeter of 14 feet. what is the perimeter of a similar rectangle with a width of 9 feet?
a. 36 ft
b. 108 ft
c. 42 ft
d. 126 ft
Answers
Second Rectangle: P= ?, L= ?, W= 9
STEP 1:
solve for the width in the first rectangle using perimeter formula
Perimeter= 2L + 2W
14= 2(4) + 2W
14= 8 + 2W
subtract 8 from both sides
6= 2W
divide both sides by 2
3= W
STEP 2:
Since the two rectangles are similar, they may be different sizes, but they have corresponding angles. We can set up a ratio to compare width and length.
First Rectangle: P= 14, L= 4, W= 3
Second Rectangle: L= ?, W= 9
length/width= length/width
4/3= L/9
cross multiply
4 * 9= 3 * L
36= 3L
divide both sides by 3
12= L
STEP 3:
find perimeter of second rectangle; use length from step 2
Perimeter= 2L + 2W
=2(12) + 2(9)
=24 + 18
=42 feet
ANSWER: (C) 42 feet
Hope this helps! :)
Please help me I’m about to cry
Answers
A-Blue
B-Green
C=yellow
D=Grey
E=maroon
Triangle E is not the same as triangle C. This means she was wrong.
Please refer to the attached figure for the drawings, the colors represent the triangles in the order above.
A feed bucket holds 12 quarts. How many cups of feed does the bucket hold?
Answers
12 quarts x 4 (cups per quart) = 48 Cups
How many arrangements are possible using the letters in the word fuzzy if each letter "z" is distinctly different than the other? how many arrangements are possible if the letter "z" is interchangeable with the other? explain your reasoning?
Answers
[tex]P\left(5,5\right)=5!=5\cdot 4\cdot 3\cdot 2\cdot 1=120[/tex]
If the z's are interchangeable, the number of different arrangements is given by
[tex]\frac{5!}{2!}=5\cdot 4\cdot 3=60[/tex]
When each letter "z" is distinctly different, there are 60 possible arrangements.
When the letter "z" is interchangeable with the others, there are 24 possible arrangements.
1. When each letter "z" is distinctly different from the others:
- The word "fuzzy" has 5 letters in total, including 2 "z" letters.
- To calculate the number of arrangements, we use the formula for permutations with repeated elements:
- The formula is: n! / (n1! n2! ... * nk!)
- n is the total number of letters in the word (5 in this case).
- n1, n2, ... are the number of repetitions of each distinct letter.
- Calculating: 5! / (1! 2! 1! * 1!) = 120 / 2 = 60 arrangements.
2. When the letter "z" is interchangeable with the other letters:
- In this case, there are 4 distinct letters in the word "fuzzy" (f, u, z, y).
- The total number of arrangements can be calculated using the formula for permutations of distinct items.
- Calculating: 4! = 24 arrangements.
In summary:
- When each letter "z" is distinctly different, there are 60 possible arrangements.
- When the letter "z" is interchangeable with the others, there are 24 possible arrangements.
Four golf balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 4cm.
What is the volume of the cylinder rounded to the nearest cubic centimeter?
What is the total volume of the four balls rounded to the nearest cubic centimeter?
What percent of the volume of the container is occupied by the four balls?
Answers
Please, see the attached files.
Thanks.
Suppose that a small town has seven burger shops whose respective shares of the local hamburger market are (as percent- ages of all hamburgers sold): 23 percent, 22 percent, 18 percent, 12 percent, 11 percent, 8 percent, and 6 percent. what is the four-firm concentration ratio of the hamburger industry in this town
Answers
Solve each of the following right triangles. Round angle measures to the nearest degree and segment lengths to the nearest tenth. Angle C is the right angle of the triangle
Answers
AC=23.
BA=55.2