The zeros of the function algebraically, by using these values we get, {x = -3/5, x = 3/5}
What are the zeros of the function algebraically?
The zeros of a function are the points at which the function's value is zero. These are obtained algebraically by setting the function to zero and solving the quadratic.
We have,
f(x) = -25x⁴ + 9x²
= (25 • (x⁴)) - 32x²
= (5)²x⁴ - (3)²x²
= 25x⁴ - 9x²
= x² • (25x²- 9)
25x² - 9
A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
25 is the square of 5
9 is the square of 3
x² is the square of x¹
Factorization is (5x + 3) • (5x - 3)
x² * (5x+3) * (5x-3)
x = -3/5, x = 3/5
Hence, the zeros of the function algebraically, by using these values we get, {x = -3/5, x = 3/5}
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Jermaine plots the point (0,0)and (4,11) on a graph to represent a proportional relationship. Which of the following equation represents the relationship between the x and y values
A)y=4 x. b)y=2.75x c)y=0.36x d)11y=4x
-----
11
The equation represents the relationship between the x and y values is y = 2.75x
The first point = (0,0)
The second point = (4,11)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line m = (11-0) / (4-0)
= 11 / 4
= 2.75
The slope intercept form is
y = mx + b
m is the slope of the line
b is the y intercept
The equation will be
y = 2.75x
Hence, the equation represents the relationship between the x and y values is y = 2.75x
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Explain how you found your answer.
Answer: First, I substituted x for 11. -2 times 11 = -22. -22 + 5 equals -17. Therefore, f(11) or y, is equal to -17.
Step-by-step explanation:
Functions can be defined using graphs, tables, and ordered pairs. What is the range of a function?
ANSEWERS:
The range is the input.
The range is all numbers.
The range is any x-value.
The range is the output.
(D) The range is the output.
The domain of a function is the set of values that we are allowed to enter into our function. The x values for a function like f make up this set (x).
The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. They are the y values.
The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. The domain and range of a function are the components of a function.
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Jane scored 27 out of 42 on her Maths test and 39 out of 61 in a Science test.
What were her percentages in both subjects to 1 decimal place?
Jane scored 27 out of 42 on her Maths test and 39 out of 61 in a Science test, the percentage in Maths and Science is 64.2% and 63.9% respectively.
What is Percentage?Percent derived from the Latin word, per centum which means “by the hundred.”
Percentage is the number or ratio which is expressed in the fraction of 100 it indicate the hundredth part of any quantity. It is denoted as "%". It is used to compare the first quantity against the second. It can be calculated by dividing the value with the total value and multiplied by 100.
The formula used to calculate percentage is= (value/total value)×100%.
For given information,
Percentage for Maths test = (27/42)*100 = 64.2%
Percentage for Science test= (39/61)*100 = 63.9%
Thus, Jane scored 27 out of 42 on her Maths test and 39 out of 61 in a Science test, the percentage in Maths and Science is 64.2% and 63.9% respectively.
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1. What is the value of x?
X-2
4
Answer:
.......
.......
Step-by-step explanation:
.....
.....
.....
....
....
The following augmented matrix which represents a linear system. Solve the linear system for x, y, and z.
If there is an infinite number of solutions, express the solutions in terms of z. If there is no solution, put DNE
in each answer.
1 -2 -1
-1 3 3
-1 45
x =
y =
2
-1
Z= Z
2
--1
Question Help: Video
Answer: [tex]x=-3z+4, y=-2z+1, z=z[/tex]
Step-by-step explanation:
We have the system:
[tex]x-2y-z=2\\\\-x+3y+3z=-1\\\\-x+4y+5z=0[/tex]
Adding the first and second equations yields [tex]y+2z=1[/tex].
Adding the first and third equations yields [tex]2y+4z=2[/tex].
We know that there are infinitely many solutions, so [tex]y=1-2z[/tex].
Substituting this result back into the first equation,
[tex]x-2(1-2z)-z=2\\\\x-2+4z-z=2\\\\x+3z-2=2\\\\x=-3z+4[/tex]
The solution in term of z variable is; x = 4 - 3z
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We have the linear system:
x - 2y - z = 2
-x + 3y + 3z = -1
-x + 4y + 5z = 0
Adding the first and second equations;
y + 2z = 1
Now Adding the first and third equations yield;
2y + 4z = 2
We know that there are infinitely many solutions, so;.
y = 1-2z
Then Substituting this result back into the first equation;
x - 2y - z = 2
x - 2( 1-2z) - z = 2
x - 2 + 4z - z = 2
x -4 + 3z = 0
x = 4 - 3z
The solution in term of z variable is; x = 4 - 3z
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Please answer need to turn in
Answer:
c
Step-by-step explanation:
i did the question
Answer:
I'm pretty sure it's C... rational number because 0.3% can be written like a fraction!
Step-by-step explanation:
I'm sure that's the answer hope it helps!
Good luck!!!
What is the y-intercept?
10. Write the equation of the trend line.
11. What is the exact y-value when x=12?
12. What is the exact x-value when y = 4?
13. What is the exact y- value when x=-6
Considering the linear function, the features are given as follows:
9. y-intercept: (0,2).
10. Equation: y = 5x/6 + 2.
11. y when x = 12: y = 12.
12. x when y = 4: x = 2.4.
13. y when x = -6: y = -3.
What is a linear function?The slope-intercept representation of a linear function is given by the rule shown as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the value of y when the function crosses the y-axis.In this problem, the function crosses the y-axis at y = 2, hence the intercept is:
b = 2.
When x increases by six, y increases by five, hence the slope is:
m = 5/6.
Thus the equation is:
y = 5x/6 + 2.
The numeric values for the function are given as follows:
x = 12: y = 5(12)/6 + 2 = 10 + 2 = 12.x = -6: y = 5(-6)/6 + 2 = -5 + 2 = -3.The solution when y = 4 is given as follows:
4 = 5x/6 + 2.
5x/6 = 2
5x = 12
x = 12/5
x = 2.4.
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Pyramid A is a right square pyramid with a height of 72 m and a square
base with a perimeter of 396 m. Pyramid B has a square base with a
perimeter of 496 m and a height of 239 m. Which pyramid has the
greater volume and by how many times as great?
Answer:
B by a factor of about 5.208
Step-by-step explanation:
Given two right square pyramids (A and B) with perimeters 396 m and 496 m, and corresponding heights of 72 m and 239 m, you want to which has the greater volume and by what factor.
VolumeThe volume of a right square pyramid is proportional to its height and to the square of its perimeter.
Pyramid B has both a longer perimeter and a greater height, so Pyramid B has the greater volume.
RatioThe constant of proportionality between the dimensions and the volume is the same for both pyramids, so the ratio of their volumes is ...
Vb/Va = ((Pb)²Hb)/((Pa)²Ha) = (496²·239)/(396²·72) ≈ 5.208
Pyramid B has about 5.2 times the volume of Pyramid A.
__
Additional comment
The volume of a right square pyramid is given by ...
V = 1/3s²h . . . . . where s is the side length and h is the height
V = 1/3(P/4)²h = (1/48)P²h . . . . where P is the perimeter of the base
Given S(2,-9), 7(6, -6), U(9,-7), and V (6, y). Find y such that ST perpendicular UV.
For the given points S(2,-9), 7(6, -6), U(9,-7), and V (6, y), the value of y such that ST is perpendicular to UV is -3.
What is the slope of a line?
A line's slope, also known as its gradient, is defined as the value of a line's steepness or direction in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.
If P(a, b) and Q(c, d) are two given points on a coordinate plane, then the slope of line PQ can be computed using the formula
[tex]Slope(m) = \frac{d-b}{c-a}[/tex]
The slope of two perpendicular lines:
If two perpendicular lines are given then the product of their slopes will be equal to -1.
The given points are S(2,-9), 7(6, -6), U(9,-7), and V (6, y).
The slope of line ST [tex]=\frac{-6-(-9)}{6-2}[/tex]
[tex]= \frac{-6+9}{4}\\ = \frac{3}{4}[/tex]----------------(I)
Now, finding the slope of line UV,
The slope of line UV [tex]=\frac{y-(-7)}{6-9}[/tex]
[tex]=\frac{y+7}{-3}[/tex] ---------------(II)
Now, by using the property of slopes of two perpendicular lines, we can write
Slope of line ST × Slope of line UV = -1
[tex]\frac{3}{4} *\frac{y+7}{-3}=-1 \\y+7=4\\y=4-7\\y=-3[/tex]
Hence, For the given points S(2,-9), 7(6, -6), U(9,-7), and V (6, y), the value of y such that ST is perpendicular to UV is -3.
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IXL Help Fast Please !
Answer:
y=-10-7
Step-by-step explanation:
3=-10(-1)+5/4
3=10+5/4
3=11 1/4
11 1/4-3=8 1/4
5/4-33/4=-28/4=-7
3=-10(-1)-7
3=10-7
3=3
Answer:
y=-10x-7
Step-by-step explanation:
3=-10(-1)+5/4
3=10+5/4
3=11 1/4
11 1/4-3=8 1/4
5/4-33/4=-28/4=-7
3=-10(-1)-7
3=10-7
3=3
please help me (20pts)
Answer: Table A
Step-by-step explanation:
The table must have a constant rate of change on both sides. Table B goes up by 2, then 2, then 3, which breaks the pattern (this is in the y-axis).
Table C goes up by 3, then 4, then 4, which is ALSO an inconsistent pattern (in the x-axis). Table D goes up by 2, then 1, then 2, which is also inconsistent (y-axis).
This leaves Table A, which has a consistent pattern on both sides.
Franklin Templeton has just invested $10,760 for his son (age one). This money will be used for his son’s education 17 years from now. He calculates that he will need $54,343 by the time the boy goes to school. What rate of return will Mr. Templeton need in order to achieve this goal?
Answer:
9.995%
Step-by-step explanation:
principal-10760
n(time)-17
rate-?
amount-54343
formula of compound interest[tex]a = p(1 + \frac{r}{100} ) {}^{n} [/tex]
54343=10760(1+(r/100))^17
divide both sides by 107605.05=(1+(r/100))^17
multiply both sides by ^1/171.09995=1+(r/100)
like terms together i.e the whole numbers0.09995=r/100
multiply both sides by 100r=9.995%
Hello! Can someone please help me out I would appreciate it a lot thank you :) look in the photo. I’ll give brainly
The radius is the distance from the center to a point on a circle.
The diameter is twice the radius.
1. 3 yd, 6 yd
2. 46 in, 92 in
3. 23 ft, 46 ft
A trainer devised a 40 minute workout plan for client. The table shows the number of minutes spent on each type of exercise.
TABLE:
Endurance:8
Strength:16
Balance:4
Flexibility:12
The grid has 100 squares and each exercise will be represented by the following percentages:
Endurance = 20% (20 squares)Strength = 40% (40 squares)Balance = 10% (10 squares)Flexibility = 30% (30 squares).What are percentages?Percentages refer to the ratio or proportion of a value when compared to the whole.
Percentages are fractional values, computed as a quotient of the part with respect to the whole, and usually expressed over 100.
The percentage sign (%) is used to depict values in percentages.
TABLEExercise Minutes Percentage
Endurance: 8 20% (8/40 x 100)
Strength: 16 40% (16/40 x 100)
Balance: 4 10% (4/40 x 100)
Flexibility: 12 20% (12/40 x 100)
Total 40 100% (40/40 x 100)
Thus, the percentage representation of the exercises on the grid shows that Endurance occupies 20%, Strength 40%, Balance 10%, and Flexibility 30%.
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Question Completion:In the grid below, represent the percentage of each exercise.
Mrs.Gomez is buying a triangular table for the corner of her classroom.The side lengths of the table are 5 feet.3 feet,and 4 feet.Is this triangular table a right triangle?
Answer:
Yes, this triangular table is a right triangle. It is a 3, 4, 5 Pythagorean triple.
What is a right triangle?
A right triangle is a triangle in which one of the angles is 90 degrees, making the other two angles acute angles.
What is a Pythagorean triple?
A Pythagorean triple is a set of three whole numbers, a < b < c, for which,
a^2 + b^2 = c^2
Answer:
yes it is a right triangle
Step-by-step explanation:
to find out we can use the Pythagorean theorem
a^2+b^2=c^2
We can use the shorter angles for a and b and see if this equals 5
3^2+4^2=c^2
9+16=c^2
25=c^2
Square root both sides
5=c
This triangle is a right triangle
Hopes this helps please mark brainliest
Carlos is a software salesman. Let y represent his total pay (in dollars). Let x represent the number of copies of History is Fun he sells. Suppose that x and y are related by the equation 2500+110x=y. Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the change in Carlos's total pay for each copy of History is Fun he sells?
What is Carlos's total pay if he doesn't sell any copies of History is Fun?
The total pay change for each issue of Math is Fun sold by Carlos is $110. If he doesn't sell copies of Math is Fun, Carlos's gross wages are $2500 for him.
Given that:
x represents the number of copies of Math is Fun he sells. Suppose that x and y are related by the equation 2500 + 110x = y.
Equation: The equation is the values of two expressions that are equal.
Here,
For equation,
y = 2500 + 110x
The change in Carlos's total pay for each copy of Math is Fun he sells,
Differentiate the equation,
dy/dx = 110
The total pay for each copy of Math is Fun he sells is $110.
Carlos's total pay if he doesn't sell any copies of Math is Fun,
x = 0
y = 2500
Carlos's total pay if he doesn't sell any copies of Math is Fun is $2500.
Thus, the change in Carlos's total pay for each copy of Math is Fun he sells is $110. Carlos's total pay if he doesn't sell any copies of Math is Fun is $2500.
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Set up and solve a proportion for the following problem The ratio of the length of an airplane wing to its width is to 1. If the length of a wing is 24.5 meters, how wide must it be?
Let W=width of wing
The ratio (Length/Width) is given and is constant, so you can set ratios equal (this is a proportion):
Length / Width = 8/1 = 32.3/W
(1) cross-multiply, (2) invert both sides, multiply both sides by one of the denominators ... any legal operation of algebra in order to isolate W.
multiply both sides by (W/8):
W = 32.3/8 = 4.04
Kevin needs to read 3 novels each month.
Let N be the number of novels Kevin needs to read in M months.
Write an equation relating N to M. Then use this equation to find the number of novels Kevin needs to read in 19 months.
Kevin needs to read 57 novels in 19 months.
Given,
The number of novels Kevin needs to read in a month = 3
N = Number of novels Kevin needs to read in M months.
Write an equation with M and N.
That is,
Kevin needs to read 3 novels in one month.
So, number of novels, N Kevin reads in M months, 3M = N
The equation is;
3M = N
Now,
The number of months Kevin needs to read the novels = 19
Then,
The number of novels Kevin reads in 19 months;
3M = N
3 × 19 = 57
That is,
Kevin needs to read 57 novels in 19 months.
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A shed for holding sports equipment is 180 inches
long. There are 12 inches in 1 foot. How many feet
long is the shed?
Answer: 15 feet
Step-by-step explanation:
180 inch = 15 feet
Question 4 of 10
Which two correctly relate the attraction between the particles of a liquid and
the temperature at which the liquid changes state?
A. Strong attractions mean the liquid melts at a lower temperature.
B. Strong attractions mean the liquid boils at a lower temperature.
C. Strong attractions mean the liquid boils at a higher temperature.
D. Strong attractions mean the liquid melts at a higher temperature.
SUBMIT
Answer: a,c
Step-by-step explanation:
The Gallup Poll reported that 48% of Americans spend more than an hour a day using the Internet. If 6 people are selected at random, find the probability that they all spend more than an hour a day using the Internet. Please round the final answer to 2 or 3 decimal places.
Answer:
the answer is that there is 8 percent that they all will spend an hour on the internet.
Step-by-step explanation:
Harry asked a sample of 444 people how many siblings they had. Here are their responses: 0, 0, 1, 30,0,1,30, comma, 0, comma, 1, comma, 3 The mean is \bar x =1 x ˉ =1x, with, \bar, on top, equals, 1 sibling. Which of these formulas gives the standard deviation? Choose 1 answer:
The formulas give the standard deviation will be sₓ=√(0-1)²+(0-1)²+(1-1)²+(3-1)²/4.Option C is correct.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
It is given that, Harry asked a sample of 4 people how many siblings they had. Here are their responses:0,0,1,3 The mean is 1 sibling.
[tex]\bar x =1 \\\\ n =4[/tex]
The formulas give the standard deviation as,
[tex]\rm s_x = \sqrt{\frac{(x_1-\bar x)^2+(x_2-\bar x)^2 +(x_3- \bar x)^2 }{n-1} } \\\\ s_x = \sqrt{\frac{(0- 1)^2+(0-1)^2 +(1- 1)^2 + (3-1)^2}{3} }[/tex]
Thus, the formulas give the standard deviation will be sₓ=√(0-1)²+(0-1)²+(1-1)²+(3-1)²/4.Option C is correct.
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Base Number is unknown: a/?= x/100?
Answer:
A. x= .100
Step-by-step explanation:
What are the names of a circle with H
If the length of HJ is 7 unit then the length of EI is 14 unit.
What is a circle?A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.
We are given a circle with center H.
Therefore, the radius of the circle is found as; HJ
Then the Diameter is the line from one point in the circle to the other point through the center of the circle.
Diameter of the circle = EI
Since we know that One of the theorems of a circle states that the angles in the same segments or on the same chord are equal.
Then the name of the chord is FG.
If the length of HJ is 7 unit then the length of EI is;
EI = 2 HJ
EI = 14 unit.
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How many rows are left?
7/15 rows are left after crows ate some rows.
Total no. of rows he planted = 1 2/3
= 1 + 2/3
= (3 + 2)/3
= 5/3
No. of rows crows ate = 1 1/5
= 1 + 1/5
= (5 + 1)/5
= 6/5
No. of rows left = 5/3 - 6/5
= (25 - 18)/15
= 7/15
Hence, no. of rows left is 7/15.
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Round 1.2345678 to 5 decimals places
Answer:
1.23457
Step-by-step explanation:
You count 5 places from the decimal point. Then since 6 is greater than 5 you round up
An expression is given. 8x What is the value of the expression when .x = 3?
Answer:
when x = 3
8(3)
8*3=24
all you have to do is to substitute x into the expression
SCHOOL Antonio earned these scores on the first three tests in history this term: 89, 92, and 81. What is the lowest score that Antonio can earn on the fourth and final test of the term if he wants to have an average of at least 87?
Answer:
86
Step-by-step explanation: 89+92+81+x=total score=262+x
avg score = 87= (262+x)/4
262+x=348
.
x=86
.
Check,,,(89,92,81,86)/4 = 87
Answer: 86
Step-by-step explanation:
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
The solution is
1) Angles 7 and 6 are Vertical angles
2) Angles 1 and 8 are Alternate exterior angles
3) Angles 4 and 5 are Alternate interior angles
4) Angles 2 and 6 are Corresponding angles
5) Angles 6 and 8 are Complementary angles
What are angles in parallel lines?
Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.
We can conclude three factors determining parallel lines ,
Alternate angles are equalCorresponding angles are equalCo-interior angles add up to 180°Given data ,
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.
Each pair of alternate angles around the transversal are equal to each other.
The pairs of angles formed on the same side of the transversal that are either both obtuse or both acute and are called corresponding angles and are equal in size.
Each pair of corresponding angles on the same side of the intersecting transversal are equal to each other.
Co-interior angles on the same side of an intersecting transversal add to 180°
Hence , the angles are
1) Angles 7 and 6 are Vertical angles
2) Angles 1 and 8 are Alternate exterior angles
3) Angles 4 and 5 are Alternate interior angles
4) Angles 2 and 6 are Corresponding angles
5) Angles 6 and 8 are Complementary angles
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