Answer:
[tex]y=x^{2} -\frac{48}{7}x+\frac{64}{7}[/tex]
Step-by-step explanation:
step 1
Find the roots of the quadratic equation
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} -6x+7=0[/tex]
so
[tex]a=1\\b=-6\\c=7[/tex]
substitute in the formula
[tex]x=\frac{6(+/-)\sqrt{-6^{2}-4(1)(7)}} {2(1)}[/tex]
[tex]x=\frac{6(+/-)2\sqrt{2}} {2}[/tex]
[tex]x=3(+/-)\sqrt{2}[/tex]
[tex]x1=3(+)\sqrt{2}[/tex]
[tex]x2=3(-)\sqrt{2}[/tex]
The roots of the equation are a and b
so
[tex]a=3(+)\sqrt{2}[/tex]
[tex]b=3(-)\sqrt{2}[/tex]
step 2
Find a quadratic equation with roots a+1/b and b + 1/a
so
[tex]a+\frac{1}{b} =(3+\sqrt{2})+\frac{1}{3-\sqrt{2}} =\frac{9-2+1}{3-\sqrt{2}} =\frac{8}{3-\sqrt{2}}=\frac{8}{3-\sqrt{2}}*(\frac{3+\sqrt{2}}{3+\sqrt{2}})=\frac{8}{7}(3+\sqrt{2})[/tex]
[tex]b+\frac{1}{a} =(3-\sqrt{2})+\frac{1}{3+\sqrt{2}} =\frac{9-2+1}{3+\sqrt{2}} =\frac{8}{3+\sqrt{2}}=\frac{8}{3+\sqrt{2}}*(\frac{3-\sqrt{2}}{3-\sqrt{2}})=\frac{8}{7}(3-\sqrt{2})[/tex]
The quadratic equation is equal to
[tex]y=(x-\frac{8}{7}(3+\sqrt{2}))(x-\frac{8}{7}(3-\sqrt{2}))[/tex]
[tex]y=x^{2} -\frac{8}{7}(3-\sqrt{2})x-\frac{8}{7}(3+\sqrt{2})x+\frac{64}{49}(7)[/tex]
[tex]y=x^{2} -\frac{48}{7}x+\frac{64}{7}[/tex]
In simplified form, V18 is
Answer: 4.24264069
Step-by-step explanation: I think you mean the square root?
Which of the following lists of ordered pairs is a function?
A. (1, 2), (1,-2), (3, 2), (3, 4)
B. (1,6), (2, 7),(4,9), (0,5)
C. (0, 2), (2,3), (0, -2), (4,1)
D. (2, 4), (0, 2), (2, - 4), (5,3)
Answer:
B
Step-by-step explanation:
A. (1, 2), (1,-2), (3, 2), (3, 4)
B. (1,6), (2, 7),(4,9), (0,5)
C. (0, 2), (2,3), (0, -2), (4,1)
D. (2, 4), (0, 2), (2, - 4), (5,3)
Theres no repeating x value.
B. (1,6), (2, 7),(4,9), (0,5) this ordered pairs is a function.
What is a mathematical function?
In mathematics, an expression, rule, or law defines the relationship between one variable (independent variable) and another (dependent variable). Functions are ubiquitous in mathematics and are essential for formulating the physical relationships of the natural sciences.
The types of functions can be broadly classified into four types. Based on elements: one-to-one function, many-to-one function, on-function, one-to-one and on-function, in-function. You can set the relationship as a table of ordered pairs. Then test that each element in the domain exactly matches one element in the range. If so, you have the feature!
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If you divide-16 in 5 equal parts how much is each part equal to
Answer:
-3.2
Step-by-step explanation:
Solve the equation 9b2 + 30b + 25 = 0.
A. b = –5⁄3
B. b = –3⁄5, b = 3⁄5
C. b = –5⁄3, b = 5⁄3
D. b = 5⁄3
caroline can sketch 2 cartoon strips in 5 hours. how long will it take her to sketch 4 strips
Answer:
10 hours.
Step-by-step explanation:
2 cartoon strips takes 5 hours
divide 5 by 2 to give us how much time is used for 1 strip
5/2 = 2.5 which is equal to 1 strip
Now the question is asking you how much will time for 4 strips?
Take 4 and multiply it by 2.5
4x2.5 = 10
Caroline sketches at a rate of 2 strips in 5 hours, so to sketch 4 strips, which is twice as many, it will take her twice the time, resulting in 10 hours.
Explanation:To calculate how long it will take Caroline to sketch 4 cartoon strips, we first determine her rate of sketching, which is 2 strips in 5 hours. Therefore, her rate is 2/5 strips per hour. To find out how long it takes to sketch 4 strips, we can set up a proportion where the number of strips is directly proportional to the hours spent. Since she sketched 2 strips in 5 hours, sketching 4 strips will be twice the amount of strips, thus it should take her twice the time, hence 5 hours times 2. Therefore, Caroline will take 10 hours to sketch 4 strips.
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The width of a rectangle is 30% of the length. The perimeter of the rectangle is 338 ft. Find the length and width of the rectangle
Answer:
L=130 while W=39
Step-by-step explanation:
Let's setup some equations.
W=.3L from first sentence
2L+2W=338 from second sentence
I'm going to plug equation 1 into equation 2:
2L+2[.3L]=338
2L+.6L=338
2.6L=338
L=338/2.6
L=130
so W=.3L=.3(130)=39
Answer L=130 while W=39
Length of the rectangle = 130
Width of the rectangle = 39.
How to find the length and width of the rectangle?Given: that the width of a rectangle exists 30% of the length.
Where Perimeter = 338 ft
Width of the rectangle = 0.3L
Perimeter = 2(Length + Width)
Substitute the value of perimeter in the above equation, we get
2L + 2W = 338
2L + 2[0.3L] = 338
2L + 0.6L=338
2.6L = 338
L = 338/2.6
L = 130
Length of the rectangle = 130
So, Width of the rectangle = 0.3L
= 0.3(130) = 39
The length of the rectangle is 130 and the width of the rectangle is 39.
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Which equation is equivalent to
Answer:
Simplifying the equation:
[tex]\frac{2}{3} x - \frac{5}{6} = -\frac{5}{12} x + \frac{1}{4}[/tex]
Grouping like terms:
[tex]\frac{2}{3} x + \frac{5}{12} x= \frac{1}{4} + \frac{5}{6}[/tex]
⇒ [tex]\frac{39}{36} x=\frac{26}{24}[/tex]
Solving for 'x', we have:
⇒ [tex]x=\frac{26}{24}\frac{36}{39}=1[/tex]
For this case we place the terms with "x" on the left side of the equation, and the terms without "x" on the right side:
[tex]\frac {2} {3} x + \frac {5} {12} x = \frac {1} {4} + \frac {5} {6}[/tex]
We add similar terms:
[tex]\frac {24 + 15} {36} x = \frac {6 + 20} {24}\\\frac {39} {36} x = \frac {26} {24}[/tex]
We simplify both sides:
[tex]\frac {13} {12} x = \frac {13} {12}[/tex]
Dividing by [tex]\frac {13} {12}[/tex] on both sides of the equation:[tex]x = 1[/tex]
Answer:
[tex]x = 1[/tex]
lynomials and Linear Factors
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Write the polynomial function y = (x + 5) (x - 1)(x - 2) in
standard form.
Answer:
y = x³ + 2x² - 13x + 10
Step-by-step explanation:
Given
y = (x + 5)(x - 1)(x - 2) ← expand (x - 1)(x - 2)
= (x + 5)(x² - 2x - x + 2)
= (x + 5)(x² - 3x + 2)
Multiply each term in the second factor by each term in the first factor
= x(x² - 3x + 2) + 5(x² - 3x + 2) ← distribute both parenthesis
= x³ - 3x² + 2x + 5x² - 15x + 10 ← collect like terms
y = x³ + 2x² - 13x + 10
write the standard equation of a circle with the center at (-1,-4) that passes through the point (-1,-1)
Answer:
(x+1)^2+(y+4)^2=9
Step-by-step explanation:
First equation in what I like to call center-radius form is (x-h)^2+(y-k)^2=r^2 where (h,k) is center and r is radius.
So we are given (h,k)=(-1,-4) so we have so far that
(x+1)^2+(y+4)^2=r^2
Passes through the point (-1,-1) means at some point (x,y) takes on the point (-1,-1) so guess what we are going to find r^2 by plugging in that point where x and y are.
(-1+1)^2+(-1+4)^2=r^2
(0)^2+(3)^2=r^2
9=r^2
so the equation of the circle is (x+1)^2+(y+4)^2=9
Answer:
(x + 1)² + (y + 4)² = 9
Step-by-step explanation:
The equation of a circle is:
(x - h)² + (y - k)² = r²
where (h, k) is the center and r is the radius.
The center is (h, k) = (-1, -4). The radius is the distance from the center to any point on the circle. (-1, -1) is 3 units above the center, so r = 3.
(x + 1)² + (y + 4)² = 9
What is the range of y =|3x + 1|?
Answer:
[0,∞), {y|y≥0}
Step-by-step explanation:
The graph of y =|3x + 1| is attached.
By observation, we can see that the the least y-value that the graph can take is y =0 (i.e the x-axis) and the greatest y-value that the graph can take is positive infinity.
Hence the range is [0,∞), {y|y≥0}
Final answer:
The range of the function y = |3x + 1| is [0, infinity), as absolute value functions always yield non-negative values.
Explanation:
The range of the function y = |3x + 1| can be determined by understanding the behavior of absolute value functions. The absolute value function |x| always yields a non-negative value. Therefore, for any real number x, |3x + 1| will also be non-negative. Hence, the range of y = |3x + 1| is [0, ∞), meaning that y can be any real number greater than or equal to zero.
Find the sum
3a/bc+2b/ac
Answer:
3a^2 + 2b^2
= ----------------------
abc
Step-by-step explanation:
3a 2b
------- + ----------
bc ac
3a^2 + 2b^2
= ----------------------
abc
The solution to the system of equation below is (−2, −1).
2x − 3y = −1
11x − 9y = −13
When the first equation is multiplied by −3, the sum of the two equations is equivalent to 5x = −10.
Which system of equations will also have a solution of (−2, −1)?
Answer:
x = -2, y = -1 → (-2, -1)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x-3y=-1&\text{multiply both sides by (-3)}\\11x-9y=-13\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-6x+9y=3\\11x-9y=-13\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad5x=-10\qquad\text{divide both sides by 5}\\.\qquad x=-2\\\\\text{put the value of x to the first equation:}\\\\2(-2)-3y=-1\\-4-3y=-1\qquad\text{add 4 to both sides}\\-3y=3\qquad\text{divide both sides by (-3)}\\y=-1[/tex]
Answer:
A on edge
Step-by-step explanation:
What is the axis of symmetry of the function below?
Answer:
A
Step-by-step explanation:
Between 4 and 5 where the vertex is. The axis of symmetry is a line going through the vertex. For a while it will be of the form x = a
In this case, the axis of symmetry is x = 4.5
someone please help. I can’t figure this out: (m+18)/m=5/2
Answer:
m = 12
Step-by-step explanation:
[tex]\frac{m+18}{m}[/tex]=[tex]\frac{5}{2}[/tex]
2(m+18) = 5(m)
2m + 36 = 5m
2m - 5m = -36
-3m = -36
m = 12
Answer:
Step-by-step explanation:
(m + 18) / m = 5/2
Do you know what cross multiplication is for a proportion? It means that you take the top of one fraction and multiply it by the bottom of the other fraction.
So for this question
5 (top right) * m (bottom left)
and put an equal sign
5*m =
Now take the top left and multiply by the bottom right.
2 * (m + 18)
Now equate the two results.
5m = 2*(m + 18) Remove the brackets.
5*m = 2*m + 2*18 Combine the right.
5m = 2m + 36 Subtract 2m from both sides.
5m-2m=2m-2m+36 Combine
3m = 36 Divide both sides by 3
3m/3 = 36/3
m = 12
Eggs are purchased at rs.120per dozen and are sold out at rs.130per dozen.find profit or loss
Answer:
10rs
Step-by-step explanation:
C.P. - 120
S.P. - 130
cp < sp
120 < 130
so , profit = sp - cp
= 130-120
= 10 rs.
Profit=10rs
please mark me brainiest
Find he volume and surface area of the figure. Round to the nearest one hundredth when necessary. Explain please if you can.
Answer:
[tex]\large\boxed{V=3780\ in^3}\\\boxed{S.A.=1827\ in^2}[/tex]
Step-by-step explanation:
The formula of a volume of a prism:
[tex]V=BH[/tex]
B - base area
H - height
In the base we have the right triangle. The formula of an area of a right triangle:
[tex]A=\dfrac{(a)(b)}{2}[/tex]
a, b - legs
We have a = 14in and b = 22.5in. Substitute:
[tex]B=\dfrac{(14)(22.5)}{2}=157.5\ in^2[/tex]
H = 24in.
Calculate the volume:
[tex]V=(157.5)(24)=3780\ in^3[/tex]
The Surface Area:
We have
(1) two right triangles with area 157.5 in²
(2) three rectangles 24 in × 14 in, 24 in × 22.5 in, 24 in × 26.5 in.
Calculate the areas of the rectangles:
[tex]A_1=(24)(14)=336\ in^2\\\\A_2=(24)(22.5)=540\ in^2\\\\A_3=636\ in^2[/tex]
The Surface Area:
[tex]S.A.=2B+A_1+A_2+A_3\\\\S.A.=(2)(157.5)+336+540+636=1827\ in^2[/tex]
What is the measure of STR?
The term STR is not sufficiently defined in the question. It could represent a mathematical concept, an angle in geometry, or a term in physics or engineering. Without any context, it's not possible to give a precise answer.
Explanation:It appears that there is some confusion in your question, as the term STR is not sufficiently defined. In general, STR could refer to a mathematical concept, a geometric angle, or a term in engineering. However, without context, it's challenging to provide a correct answer.
If STR represents 'Stress', 'Tensile Ratio', or 'Tensile Strength Ratio' in an engineering sense, it would refer to a measure of deformation due to tension. If STR stands for an angle in a triangle, it would need the triangle's full details to be calculated properly. It would be more beneficial if you could provide added context, so I could give you a more accurate response.
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What property was applied to solve the equation below?
0.36x=-1.8
0.36(= 0.36)x=-1.8(+0.36)
X=-5,
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Answer:division property of equality
Step-by-step explanation: Because 0.36x divided by 0.36 is 1x. -1.8 divided by 0.36 is -5. Couuld you give me brainleist
Answer:
Division Property of Equality
Step-by-step explanation:
Addition Property of Equality :
a = b ⇒ a + c = b + c
Subtraction Property of Equality
a = b ⇒ a - c = b - c
Multiplication Property of Equality :
a = b ⇒ ca = cb,
Division Property of Equality :
[tex]a=b\implies \frac{a}{c}=\frac{b}{c}[/tex],
Here, the given equation is,
0.36x=-1.8,
For finding the value of x we need to isolate x,
For this we must divide both sides by 0.36,
That is, we were applied 'Division Property of Equality'.
Jerry has 48 inches of string. He cuts the string into 8 inch pieces. The letter y shows how many pieces of string he has.
y□8=48
Which operation would complete the equation to model the problem?
Answer:
y = 6 (pieces)
Step-by-step explanation:
y = (48 inches) / (8 inches per piece) = 6 pieces.
y = 6 (pieces)
Jerry will have to grow 24 more inches in order to reach his max Hight of 72 inches. If you put this into a inequality it would be 48 plus a number is greater that or equal to 72.
48+X_>72
What is the value of x?
Answer: x = 7
`Step-by-step explanation:
Because the figure shows two triangles that are similar. we can write and solve an equation of ratios:
9 cm 72 cm
----------- = -----------
3x - 20 56 cm
Cross-multiplying, we get (3x - 20)(72 cm) = (9 cm)(56 cm) = 504 cm²
Dividing both sides by 72 cm, we get:
3x - 20 = (504 cm²) / (72 cm) = 7
Then 3x - 20 = 7, and 3x = 27. Then x must be 9.
The value of x in the triangle with parallel lines is 9.
To find the value of x in the equation involving a triangle with parallel lines, we can start by simplifying the equation and then solve for x.
The given equation is:
9/72 = (3x - 20)/56
Let's first simplify the left-hand side of the equation:
9/72 = 1/8
Now, the equation becomes:
1/8 = (3x - 20)/56
To isolate x, we can cross-multiply:
1 * 56 = 8 * (3x - 20)
56 = 24x - 160
Next, add 160 to both sides of the equation:
56 + 160 = 24x
216 = 24x
Finally, divide both sides by 24 to solve for x:
x = 216/24
x = 9
So, the value of x in the given equation is 9.
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A scientist is trying to determine whether the use of cell phone contributes to brain cancer. For his study, he compares the medical records of subjects who have been diagnosed with brain cancer to the records of healthy subjects. What is the most significant weakness in this type of study?
The test groups must be unusually large to generate significant data.
The relationship between cell phone use and cancer is difficult to determine.
This type of study is expensive, and the data are difficult to analyze.
This type of study must rely on medical records, which are inaccurate.
Answer:
The relationship between cell phone use and cancer is difficult to determine.
Step-by-step explanation:
Its pretty difficult to determine the relationship between using your phone and cancer, and how they correspond to each other.
Answer:
The relationship between cell phone use and cancer is difficult to determine.
Step-by-step explanation:
There has been always a conflicting conclusions whether there is a relationship between a cell phone and the cause of brain cancer. Many years of studies by the scientist and the neurologist on the relation on cellphones and cancer have resulted in controversial arguments.
Thus, the most significant weakness in this type of study is the relationship between cell phone use and cancer is difficult to determine.
What is the area of parallelogram ABDC
Answer:
9 cm
Step-by-step explanation:
Find the area of the 1st triangle
A=1/2 b*h
1/2 3*3
1/2 9
4.5
Find the area of the 2nd triangle
A=1/2 b*h
1/2 3*3
1/2 9
4.5
Both triangles have an area of 4.5
To find the area of the parallelogram you have to add the area of the triangles
4.5+4.5=9
A= 9 cm
Plz help help me sombody help
Answer:
2/3
Step-by-step explanation:
We can find the slope of the line by using points
We have 2 points (-2,0) and (1,2)
Using the formula for slope
m = (y2-y1)/(x2-x1)
= (2-0)/(1--2)
= 2/(1+2)
= 2/3
what is the y-intercept of the line y= -6x -3?
Answer:
y = -3 or (0,-3)
Step-by-step explanation:
y intercept is when x is 0 so substitute 0 for x:
y=-6(0)-3=0-3=-3
y = -3
In order to find the y intercept you must substitute 0 for x and solve for y, and also simplify if needed.
[tex]y=-6x-3[/tex]
[tex]y=-6\times0-3[/tex]
[tex]-6\times0-3[/tex]
[tex]y=0-3[/tex]
[tex]-6\times 0 = 0[/tex]
[tex]0-3=-3[/tex]
[tex]= -3[/tex]
[tex]y = (0,-3)[/tex]
Therefore your answer is " y = (0,-3)."
Hope this helps.
Please help I’m terrible at math
Answer:
1.25
Step-by-step explanation:
Calculate the scale factor as the ratio of corresponding sides of the image to the original.
here the corresponding sides are
image = 5 and original = 4
scale factor = [tex]\frac{5}{4}[/tex] = 1.25
Anyone know what the area would be?
Answer:
Step-by-step explanation: The first step is to divide this shape into multiple other shapes. First, let's start with the smaller rectangle. It has a height of 10 centimeters and a width of 9 centimeters, giving us 90 centimeters in total.
Now, lets do the bigger rectangle. The height is 12 centimeters, and the width is 24 centimeters. [tex]12*24=288[/tex]
[tex]288+90 = 378[/tex], so our answer will be 378.
What is the slope of a line that is perpendicular to the line 2y - 3x = 87
Answer:
-2/3
Step-by-step explanation:
We need to put in slope intercept form..
Once we identify the slope of the line given, we can find the slope of the perpendicular line which is the opposite reciprocal of the slope for the given equation:
Let's do this:
2y-3x=86
add 3x on both sides to get 2y by itself
2y=3x+86
divide both sides by 2
y=3/2 x+43
So the slope is 3/2
The opposite reciprocal of 3/2 is -2/3 .
The answer is -2/3
Fill in the blank.in the triangle below,z degrees=___
Answer:
Z°= 88.36
Tan-1×35=88.36
Answer:
z = 38 degrees
Step-by-step explanation:
As we can see in the picture that the triangle is a right angle triangle and two of the angles are known.
We also know that the sum of internal angles of a triangle is 180 degrees.
We know that one angle is 90 degrees and second is 52 degrees.
So,
Sum of three angles = 180 degrees
90 + 52 + z = 180
z = 180 - 90 - 52
z = 38 degrees ..
Please help me solve this problem, and someone please clearly explain to me how to solve it.
1.) Use the value of the discriminant to determine if the given trinomials has 2 real solutions, 1 real solution, or no real solutions.
a. x2 − 4x − 7 = 0
b. 4r2 + 11r − 3 = 0
c. 3m2 + 7 = 0
d. t2 + 2t + 1 = 0
Step-by-step explanation:
For a trinomial ax² + bx + c = 0, the discriminant is b² − 4ac.
If the discriminant is positive, there are 2 real solutions.
If the discriminant is 0, there is 1 real solution.
If the discriminant is negative, there are no real solutions.
a) x² − 4x − 7 = 0
Here, a = 1, b = -4, and c = -7.
b² − 4ac = (-4)² − 4(1)(-7) = 44
The discriminant is positive, so there are 2 real solutions.
b) 4r² + 11r − 3 = 0
Here, a = 4, b = 11, and c = -3.
b² − 4ac = (4)² − 4(11)(-3) = 148
The discriminant is positive, so there are 2 real solutions.
c) 3m² + 7 = 0
Here, a = 3, b = 0, and c = 7.
b² − 4ac = (0)² − 4(3)(7) = -84
The discriminant is negative, so there are no real solutions.
d) t² + 2t + 1 = 0
Here, a = 1, b = 2, and c = 1.
b² − 4ac = (2)² − 4(1)(1) = 0
The discriminant is zero, so there is 1 real solution.
solve for x in the diagrams above.
Answer: [tex]x=2[/tex]
Step-by-step explanation:
According to the Intersecting Secants Theorem, when two secants intersect each other outside a circle, then the products of their segments are equal.
Based on this, we can write this expression:
[tex](3)(3+5)=(4)(4+x)[/tex]
Knowing this, we can solve for "x". Therefore, this is:
[tex](3)(8)=(4)(4+x)\\\\24=16+4x\\\\24-16=4x\\\\8=4x\\\\\frac{8}{4}=x\\\\x=2[/tex]