Answer:
Yes, Juanita is correct.
Step-by-step explanation:
Given:
The function given is:
[tex]f(x)=x^2+64[/tex]
The roots of a function means the values of 'x' for which the function intersects or touches the x-axis. Therefore, the roots are nothing but the x-intercepts of the function.
In order to find the roots of the above function, we should equate it to 0.
So, [tex]f(x)=0[/tex]
[tex]x^2+64=0\\\\x^2=-64[/tex]
We know that, square of any number is always a positive quantity. But here, the square of 'x' is -64 which is a negative number. This is not possible.
So, there is no real solution to the given function. In other words, we can say that the function doesn't intersect the x-axis.
Therefore, Juanita is correct in her argument.
What is x if 3x − 1 divided 4 = −5?
Answer:
x=-19/3
Step-by-step explanation:
(3x-1)/4=-5
3x-1=-5*4
3x-1=-20
3x=-20+1
3x=-19
x=-19/3
Answer:
Step-by-step explanation:
3x-1/4=-5
3x-0.25=-5
3x=-5.25
x=-1.75
Find 2x^2y if x=-1 and y=3
Answer:
6
Step-by-step explanation:
(-1)^2=(-1)(-1)=1
2(1)(3)=2*3=6
2x*2y
Replace x with -1 and y with 3
2(-1) * 2(3)
2*-1 = -2
2*3=6
Now multiply -2 with 6 and it should be -12.
Can someone solve this quick plz
Answer:
length = x + 5
Step-by-step explanation:
Given
area = x² + 8x + 15 and area = length × width
We require to factorise x² + 8x + 15
Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)
The factors are + 5 and + 3, since
5 × 3 = 15 and 5 + 3 = 8, thus
x² + 8x + 15 = (x + 5)(x + 3)
x + 3 is the width, thus x + 5 is the length
What is the slope, m, and the y-intercept of the line that is graphed below?
NO
-5
4-3-2-1, 1
1
2
3
4
5
x
This looks confusing. Can you try reposting this to make it look clear?
please help me!! what's the expression in simplest form?
Answer:
2a² - 2b - 1
Step-by-step explanation:
Given
- 5 + b + 2a² - 3b + 4 ← collect like terms
= 2a² + (b - 3b) + (- 5 + 4)
= 2a² + (- 2b) + (- 1)
= 2a² - 2b - 1
Please help! Thanks in advance!
Answer:
The are certain things that need to be carefully observed when you add or combine the polynomials. Here is the list of certain rules for adding/combining polynomials.
Step-by-step explanation:
The are certain things that need to be carefully observed when you add or combine the polynomials - especially the polynomials with more than one variable.
Here are some of the rules for adding polynomials:
First we must identify like terms in the given polynomials, and then combine them based on the correct integer operations.When there is a plus sign, we add polynomials. It must be noted that, within polynomials, we need to add or subtract like terms. For example, when we combine like terms, such as 4x and 5x, we tend to add their coefficients i.e. 4x + 5x = 9xPlease remember we can not add polynomials if they have different exponents. For example, x²+ x can not be added.Lets add and simplify the following polynomials.
(4x + 7y) + (5x – 3y)
First clear the parenthesis.4x + 7y + 5x – 3y
Then make sue to group the like terms in accordance to their variables - try to keep them in alphabetically order, and ultimately just simplify.4x + 5x + 7y - 3y
9x + 4y
So, 9x + 4y is the answer.
Note: I can not further combine or add 9x + 4y as they are un-like. The reason is simple; un-like polynomials have different variables.
The polynomials can be add vertically too.
Just put each variable in its own columnFirst column can be termed as x-column and second column can be termed as y-columnChoosing the horizontal or vertical method is just a matter of taste.Here is the vertical method of adding (4x + 7y) and (5x – 3y) .
4x +7y
5x -3y
________
9x + 4y
________
Keywords: add, combine, polynomials
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Determine weather the rule represents an exponential function. EASY 40 POINTS
Exponential functions are something like y = 2^x where the variable is in the exponent (ie the exponent isnt a fixed number). What is given here, y = 3x^3, is a cubic function. You can also call this a power function. Power functions are of the form a*x^b, where a & b are constants.
How many solutions are there to the system of equations?
StartLayout enlarged left-brace 1st row 4 x minus 5 y = 5 2nd row negative 0.08 x + 0.10 y = 0.10 EndLayout
no solutions
one solution
two solutions
an infinite number of solutions
Answer:
The system has no solutions
Step-by-step explanation:
we have
[tex]4x-5y=5[/tex] -----> equation A
[tex]-0.08x+0.10y=0.10[/tex] ----> equation B
Isolate the variable y in the equation A
[tex]5y=4x-5[/tex]
[tex]y=\frac{4}{5}x-1[/tex]
[tex]y=0.8x-1[/tex] -----> equation A'
Isolate the variable y in equation B
[tex]0.10y=0.08x+0.10[/tex]
[tex]y=\frac{0.08}{0.10}x+1[/tex]
[tex]y=0.8x+1[/tex] ------> equation B'
Compare the equations A' and B'
The lines have the same slope but different y-intercept
Are parallel lines
therefore
The system has no solutions
Answer:
A. no solutions
Step-by-step explanation:
100% on edge
According to the theorem, which statement, about Parallelogram ABCD is true?
bisect = to cut into two equal halves.
so from that theorem Juan used we can derive that once both diagonals bisect each other, the halves of AO = OC and DO = OB.
2x + 7 = 4 + x solve equation using tables
Answer:
x=-3
Step-by-step explanation:
2x+7=4+x
2x-x+7=4
x+7=4
x=4-7
x=-3
Find ∫sin²x cos3x dx
Answer:
[tex]-\frac{1}{4} sin(x)+\frac{1}{6} sin(3x)-\frac{1}{20} sin(5x)+C[/tex]
Step-by-step explanation:
We begin with the integral [tex]\int{sin^2(x)cos(3x)} \, dx[/tex]
First, we can apply the power reducing formula to [tex]sin^2(x)[/tex]
This formula states: [tex]sin^2(x)=\frac{1}{2} -\frac{1}{2} cos(2x)[/tex]
This gives us
[tex]\int{(\frac{1}{2} -\frac{1}{2} cos(2x))(cos(3x)} \, dx \\\\\int{(\frac{1}{2}cos(3x) -(\frac{1}{2} cos(2x)cos(3x)} \, dx \\\\\frac{1}{2} \int{cos(3x)} \, dx -\frac{1}{2} \int{cos(2x)cos(3x)} \, dx[/tex]
Now, we can use integrate the first integral
[tex]\frac{1}{2} \int{cos(3x)} \, dx\\u=3x\\du=3dx\\\\\frac{1}{6} \int{3cos(u)} \, du\\\\\frac{1}{6} sin(u)+C\\\\\frac{1}{6} sin(3x)+C[/tex]
And now we can begin to integrate the second
[tex]-\frac{1}{2} \int{cos(2x)cos(3x)} \, dx[/tex]
To integrate this, we need to use the Product-to-sum formula, which states
[tex]cos(\alpha )cos(\beta )=\frac{1}{2} [cos(\alpha +\beta )+cos(\alpha -\beta )[/tex] . For this formula, we will use [tex]\alpha =3x\\\beta =2x[/tex]
This gives us
[tex]-\frac{1}{2} \int{\frac{1}{2}[cos(5x)+cos(x)] } \, dx \\\\-\frac{1}{4} \int{[cos(5x)+cos(x)] } \, dx\\\\-\frac{1}{4}\int{cos(5x)} \, dx -\frac{1}{4}\int{cos(x)} \, dx[/tex]
We can then use the same process of u-substitution as the previous to get the answer of [tex]-\frac{1}{20} sin(5x)-\frac{1}{4} sin(x)+C[/tex]
Lastly, we can add the values of the two integrals together to give us the final solution of
[tex]-\frac{1}{4} sin(x)+\frac{1}{6} sin(3x)-\frac{1}{20} sin(5x)+C[/tex]
F(x)= x^3-9x
What is the average rate of change of f over the interval [1,6]?
Answer: 34
Step-by-step explanation:
The average rate of change of f(x)= x³-9x in interval [1,6] is 34.
Average rate of changeIf f(x) is a function the [a,b] is interval then the average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]
How to find the average rate of change of f?Given the function is f(x)= x³-9x and the interval is [1,6].
then first we have to find the value of f(1) and f(6).
So
f(1) = (1)³-9(1)
= 1-9
= -8
and
f(6) = (6)³-9(6)
= 216- 54
= 162
therefore average rate of change of f is
[tex]\frac{f(6)-f(1)}{6-1}= \frac{162+8}{6-1}[/tex]
= 170/5
= 34
Hence the average rate of change of f is 34.
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what does a midpoint of a line segment create? Choose All The Apply.
(in pic below)
Answer: Two lines of equal length
A point equidistant from two end points
Step-by-step explanation:
The mid - point of a line segment is the point on the segment that is equidistant from the endpoints.
It is not equidistant to all point on the segment , it is only equidistant from the endpoints.
With this , the first option is out.
The midpoint of a line divides the line into two equal part , so the second option holds and the third option holds too.
100 POINTS! PLEASE HELP!
What is the equation for the line?
Enter your answer in the box.
Answer:
[tex]y=-4x+5[/tex]
Step-by-step explanation:
Step 1: Find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{13-5}{-2-0}[/tex]
[tex]m=-\frac{8}{2}[/tex]
[tex]m=-4[/tex]
Step 2: Use point slope form
[tex](y-5) = -4(x-0)[/tex]
[tex]y-5 + 5=-4x + 5[/tex]
[tex]y=-4x+5[/tex]
Answer: [tex]y=-4x+5[/tex]
y=-4x+5
Step-by-step explanation:
Step 1: Find the slope
m=\frac{y_2-y_1}{x_2-x_1}
m=\frac{13-5}{-2-0}
m=-\frac{8}{2}
m=-4
Step 2: Use point slope form
(y-5) = -4(x-0)
y-5 + 5=-4x + 5
y=-4x+5
How do I solve 42÷227
Answer:
42÷227=42/227
Step-by-step explanation:
Answer:
0.185
Step-by-step explanation:
Do the long division.
answer and explanation please!
The value of x is 58°
Step-by-step explanation:
we can see in the figure that the triangle formed is a right-angled triangle
In a right-angled triangle, one angle is always 90 degrees and the other two angles are complementary i.e. their sum is 90 degrees
So,
Using the axiom
[tex]32 + x = 90\\x = 90-32\\x = 58[/tex]
Hence,
The value of x is 58°
Keywords: Triangles, angles
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Nadia spent 1/4 of her money on a shirt and 2/5 of her money on new shoes. What fraction of Nadias money was spent?
Answer:
13/20 of her money was spent.
Step-by-step explanation:
To find the answer you have to add these two fractions together, and to do that you must find a common denominator.
For this problem I chose to use 20 for the denominator since it is the smallest number that both 4 and 5 have in common.
Keep in mind that, whatever you do to the denominator, you must also do to the numerator, so if you multiply 5 by 4, you must also multiply 2 by 4.
5/20 + 8/20 = 13/20
in six years rose will be two times as old as anne. Four years ago, anne was one third the age of rose. how old are they now
Answer:
Rose is 34.
Anne is 14.
Step-by-step explanation:
Let rose be x years age now and anne be y years old now. Then:
x + 6 = 2 (y + 6)
x - 4 = 3(y - 4)
Subtracting:
6 - -4 = 2y + 12 - (3y - 12)
10 = - y + 24
-y = -14
y = 14
Substituting for y:
x + 6 = 2(14+6)
x = 40 - 6 = 34.
10 POINTS!!!!
2.Point p is chosen at random on CF. Find the probability that p is on DE .
Answer:
[tex]\frac{8}{17}[/tex]
Step-by-step explanation:
The total length of CF is 17 units and the length of DE is 8 units, so the probability of p being on DE is [tex]\frac{8}{17}[/tex]
Answer:
8/17 is correct.
Step-by-step explanation:
Given an arithmetic sequence with a3=5 and a5=19, find the 24th term.
The 24th term is 152
Step-by-step explanation:
The formula of the nth term of an arithmetic sequence is:
[tex]a_n=a+(n-1)d[/tex] , where
a is the first termd is the common difference between consecutive termsThe third term means n = 3
∵ [tex]a_3=a+(3-1)d[/tex]
∴ [tex]a_3=a+2d[/tex]
∵ [tex]a_3[/tex] = 5
- Equate the right hand sides of the third term
∴ a + 2d = 5 ⇒ (1)
The fifth term means n = 5
∵ [tex]a_5=a+(5-1)d[/tex]
∴ [tex]a_5=a+4d[/tex]
∵ [tex]a_5[/tex] = 19
- Equate the right hand sides of the fifth term
∴ a + 4d = 19 ⇒ (2)
Now we have a system of equations to solve it
Subtract equation (1) from equation (2) to eliminate a
∴ 2d = 14
- Divide both sides by 2
∴ d = 7
- Substitute the value of d in equation (1) to find a
∵ a + 2(7) = 5
∴ a + 14 = 5
- Subtract 14 from both sides
∴ a = -9
The twenty fourth term means n = 24
∵ a = -9 and d = 7
- Substitute the values of a and d in the formula of the nth term
∴ [tex]a_24=-9+(24-1)(7)[/tex]
∴ [tex]a_24=-9+(23)(7)[/tex]
∴ [tex]a_24=-9+161[/tex]
∴ [tex]a_24=152[/tex]
The 24th term is 152
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What is 3/4 divided by 1/2
Answer:
3/2
Step-by-step explanation:
(3/4)/(1/2)=(3/4)(2/1)=6/4=3/2
Answer: in decimal form it is 0.375
Step-by-step explanation:
Length: 32 in
Width: 9 in
Height: 9 in
Which is the best estimate of the lateral area of a cube with edges that are 2.1 inches long?
Answer:
The lateral Area of a cube [tex]= 17.64in^{2}[/tex]
Step-by-step explanation:
In Mathematics Geometry, the lateral surface of a solid object like cube would be the face of the sold on its side, excluding base. Meaning, any surface, apart from base, would be included to determine the lateral surface of the solid.
A cube has six sides - also called faces.
A cube has a base i.e. the bottom side of the cube, and an ant-bottom base i.e. the top side of the cube.
So, lateral area of a cube would exclude both bottom side base and anti-bottom side base. In other words, it is the area of all the sides of the object, excluding the area of its base and top.
Hence, lateral area of a cube is the square of all the remaining four sides of the object, excluding the area of its base and top.
Hence, the lateral area of a cube can be calculated by the formula:
Lateral Area of a cube [tex]= 4s^{2}[/tex], where s is the length of one edge.
So,
As the given length of edge = s = 2.1
So,
lateral Area of a cube [tex]= 4s^{2}[/tex]
[tex]= 4(2.1)^{2}[/tex]
[tex]= 17.64in^{2}[/tex]
Keywords: cube, lateral area
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the zeros of f(x) algebraically
Answer:
The zeros are 4, -6, and 1.
Step-by-step explanation:
Given f(x) = x³ + x² - 26x + 24
(x - 4) is a factor of f(x). That means it is a zero of f(x).
To find the remaining factors algebraically, we take out the factor (x - 4) from f(x).
That is, [tex]$ f(x) = x^3 + x^2 - 26x + 24 $[/tex]
[tex]$ \implies x^3 - 4x^2 + 5x^2 - 20x - 6x + 24 $[/tex]
Taking [tex]$ x^2 $[/tex] out, we have:
[tex]$ = x^2(x^2 - 4) + 5x(x - 4) - 6(x - 4) $[/tex]
Taking (x - 4) common out, we have:
[tex]$ = (x - 4) \{x^2 + 5x - 6\} $[/tex]
[tex]$ = (x - 4)(x^2 + 6x - x - 6) $[/tex]
[tex]$ = (x - 4)\{x(x + 6) -1(x + 6)\} $[/tex]
[tex]$ = (x - 4)(x + 6)(x - 1) $[/tex]
This means the zeros are 4, -6, & 1.
can someone help me with this problem
[tex]4b + 3 = - 9[/tex]
we have to find what b is
Answer: b= -3
Step-by-step explanation:
In a figure, OB is the radius of a big semicircle and XB is the radius of the small semicircle. Given that OX = 14 cm, Calculate the area and the perimeter of the shaded region in the figure.
(Take π = 22/7).
Answer:
perimeter of the shaded region = 88 +44+28 =160 cm
Step-by-step explanation:
perimeter of shaded region = length AO + arc OB + arc AB
length AO = radius of bigger circle
radius of bigger circle = OX + OB = 2×radius of smaller circle = 2×14 cm = 28 cm
therefore AO = 28 cm
length of arc oB= half of circumference of smaller circle = [tex]\pi[/tex]×14 = 44 cm
length of arc ab = half of circumference of bigger circle = [tex]\pi[/tex]×28 =[tex]\frac{22}{7}[/tex]×28= 88
therefore perimeter of the shaded region = 88 +44+28 =160 cm
area of the shaded region = half of area of bigger circle - half of area of smaller circle
=[tex]\frac{1}{2} \pi 28^{2} -\frac{1}{2} \pi 14^{2}[/tex]
=[tex]\frac{\pi }{2} (28^{2} -14^{2} )[/tex]
solving we gen area of shaded region = 924
What is the equation of the line that has a slope of -1/3 and a y intercept of 5/2
Answer:
y=-1/3x+5/2
Step-by-step explanation:
Slope intercept form makes this a breeze. Essentially, just plug these values into the following formula:
y = [SLOPE]x + [Y-INTERCEPT]
Answer:
y=-1/3x+5/2
Hope this helps
100 points and brainiest
Which of the following is true?
|−6| < 5
|−6| < |5|
|−5| < |−6|
|−5| < −6
Answer:
l-5l < l-6l
Step-by-step explanation:
the absolute will remove the negative of both numbers
Answer: |−5| < |−6|
Step-by-step explanation:
The function of the absolute symbol is to cancel out negative , considering the values one after the other.
/ - 6/ < 5 is the same as 6 < 5 ....... this is not true
(ii) /-6/ < /5/ is the same as 6 < 5 ..... this is not true
(iii) /-5/ < / -6/ is the same as 5 < 6 ...... this is true
(iv) /-5/ < -6 is the same as 5 < -6 ..... this is not true
2 cars raced at a track. the faster car traveled 20mph faster than the slower car. in the time that the slower car traveled 165 miles, the faster car traveled 225 miles. if the speeds of the cars remained constant, how fast did the slower car travel during the race.
Answer:
The speed of slower car is 55 miles per hour.
Step-by-step explanation:
Given as :
The speed of slower car = [tex]s_2[/tex] = s mph
The speed of faster car = [tex]s_1[/tex] = ( s + 20 ) mph
The distance cover by slower car = [tex]d_2[/tex] = 165 miles
The distance cover by faster car = [tex]d_1[/tex] = 225 miles
The time taken by both cars for travelling = t hours
The speed of the cars remains constant
Now, According to question
∵ Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]
So, For slower car
t = [tex]\dfrac{d_2}{s_2}[/tex]
Or, t = [tex]\dfrac{165}{s}[/tex] ............1
So, For faster car
t = [tex]\dfrac{d_1}{s_1}[/tex]
Or, t = [tex]\dfrac{225}{s+20}[/tex] ............2
Now, equating both the equations
I.e [tex]\dfrac{225}{s+20}[/tex] = [tex]\dfrac{165}{s}[/tex]
By cross multiplying
Or, 225 × s = 165 × (s + 20)
Or, 225 s = 165 s + 3300
Or, 225 s - 165 s = 3300
Or, 60 s = 3300
∴ s = [tex]\dfrac{3300}{60}[/tex]
I.e s = 55 miles per hour
So , The speed of slower car = [tex]s_2[/tex] = s = 55 miles per hour
Hence , The speed of slower car is 55 miles per hour. Answer
the ratio of the corresponding linear measures of two similar cans of cat food is 4:3. the larger can has a SA of 100 inches. find the surface area of the smaller can. round to the nearest tenth.
Answer:
56.3 in²
Step-by-step explanation:
Given 2 similar figures with linear ratio = a : b, then
area ratio = a² : b²
Here linear ratio = 4 : 3, thus
area ratio = 4² : 3² = 16 : 9
Let x be the surface area of the smaller can then by proportion
[tex]\frac{16}{100}[/tex] = [tex]\frac{9}{x}[/tex] ( cross- multiply )
16x = 900 ( divide both sides by 16 )
x ≈ 56.3 in² ( to the nearest tenth )
The surface area of the smaller can is approximately 56.3 square inches.
The student's question involves finding the surface area of a smaller can based on its similarity ratio to a larger can. Given that the ratio of the corresponding linear measures of two similar cans is 4:3 and the larger can has a surface area of 100 square inches, we can determine the surface area of the smaller can by using the square of the ratio between their sizes. Since the ratio of their surface areas is the square of their linear dimensions ratio, we can set up the calculation as follows:
[tex](3/4)^2 = x/100,[/tex]
where x represents the surface area of the smaller can. Solving for x:
[tex](3/4)^2 = (9/16) = x/100,[/tex]
x = (9/16) * 100,
x = 56.25.
Therefore, the surface area of the smaller can is approximately 56.3 square inches when rounded to the nearest tenth.
Type the correct answer in the box
A component in a music system has a life expectancy of 2400 hours with a standard deviation of 300 hours. If an average person listens to
music for 1,000 hours in a year, the probability that the component lasts for more than 3 years is
Reset
Ned
2019 Ementum
seserved
If an average person listens to music for 1,000 hours in a year, the probability that the component lasts for more than 3 years is 2.3%.
In Mathematics and Statistics, the z-score of a given sample size or data set can be calculated by using the following formula:
Z-score, z = (x - μ)/σ
Where:
σ represents the standard deviation.
x represents the sample score.
μ represents the mean score.
Since an average person listens to music for 1,000 hours in a year, the total life span of the component for 3 years can be calculated as follows;
Total life span = 3 × 1000
Total life span = 3000 years.
By substituting the parameters into the z-score formula, we have the following:
Z-score, z = (3000 - 2400)/300
Z-score, z = 2.0
Based on the standardized normal distribution table, the required probability is given by:
P(X > 3000) = P(x > Z)
P(X > 3000) = 1 - P(Z < 2)
P(X > 3000) = 1 - 0.9773
Probability = 0.0227 × 100.
Probability = 2.27 ≈ 2.3%.