Answer:
Our y-intercept is (0, -36).
Our real zeros are: (-2√3, 0) and (2√3, 0)
And our imaginary zeros are: (i√3, 0) and (-i√3, 0)
Step-by-step explanation:
We have the function:
[tex]y=x^4-9x^2-36[/tex]
Let's identify the y- and x-intercepts.
Y-Intercept:
To determine the y-intercept, we will substitute 0 for x and solve for y. So:
[tex]y=(0)^4-9(0)^2-36[/tex]
Evaluate:
[tex]y=-36[/tex]
Therefore, our y-intercept is at (0, -36).
X-Intercepts:
To determine our x-intercepts, we need to substitute 0 for y and solve for x. So:
[tex]0=x^4-9x^2-36[/tex]
Now, we can factor. Before doing so, we can make the factored easier to see by converting this into quadratic form. Let's let u=x². Then:
[tex]0=(u^2)^2-9(x^2)-36[/tex]
Substitute:
[tex]0=u^2-9u-36[/tex]
Now, let's factor. We can use -12 and 3. So:
[tex]0=u^2+3u-12u-36 \\ 0=(u(u+3)-12(u+3)) \\ 0=(u-12)(u+3)[/tex]
Now, we can substitute back u:
[tex]0=(x^2-12)(x^2+3)[/tex]
Zero Product Property:
[tex]x^2-12=0\text{ or } x^2+3=0[/tex]
Solve for x in each case:
[tex]x^2=12 \text{ or } x^2=-3[/tex]
Take the square root of both sides. Since we're taking an even root, we will need plus/minus. Therefore:
[tex]x=\pm\sqrt{12}=\pm2\sqrt{3}\text{ or } x=\pm\sqrt{-3}=\pm i\sqrt{3}[/tex]
Therefore, our zeros (both real and imaginary) are: (2√3, 0), (-2√3, 0), (i√3, 0), and (-i√3, 0)
cions: 5
3. Raymond is reproducing his favorite painting. The original painting is 48 inches
long and 36 inches wide. If Raymond's canvas is 36 inches long, how wide will it
need to be for the reproduction to be proportional to the original?
18 inches
48 inches
24 inches
27 inches
Determine the number of real solutions of the following system of equations.
y = x^2 + 1
y=1
O 3
O 0
O 2
O 1
How much time will it take for a bug to travel 5 meters across the floor if it is traveling a 1m/s
Answer:
5 sec
Step-by-step explanation:
1m=1 sec
5m=5 x 1
=5
Answer:
5 sec
Step-by-step explanation:
speed= distance/ time
1 m/s = 5 m/ time
time= 5 sec
consider the function f(x) for which f(e)=7 and f'(e)=6 find h'(e) for the function h(x)=f(x)^x
h'(e)=
Answer:
[tex]h'(e) = 7^{e-1}\cdot [7\cdot \ln 7+6\cdot e][/tex]
Step-by-step explanation:
Let [tex]h(x) = f(x)^{x}[/tex], the first derivative of the function is found by applying the concept of implicit differentiation:
[tex]h(x) = f(x)^{x}[/tex] (1)
[tex]\ln h(x) = x\cdot \ln f(x)[/tex]
[tex]\frac{h'(x)}{h(x)}=\ln f(x) +\frac{x\cdot f'(x)}{f(x)}[/tex]
[tex]h'(x) = h(x) \cdot \left[\ln f(x)+\frac{x\cdot f'(x)}{f(x)} \right][/tex]
[tex]h'(x) = f(x)^{x}\cdot \left[\ln f(x)+\frac{x\cdot f'(x)}{f(x)} \right][/tex]
[tex]h'(x) = f(x)^{x-1}\cdot [f(x)\cdot \ln f(x)+x\cdot f'(x)][/tex] (2)
If we know that [tex]x = e[/tex], [tex]f(e) = 7[/tex] and [tex]f'(e) = 6[/tex], then [tex]h'(e)[/tex] is:
[tex]h'(e) = 7^{e-1}\cdot [7\cdot \ln 7+6\cdot e][/tex]
What 90
4 l is
3
?
You have 41 students three are absent what percentage of students are absent?
Answer:
Step-by-step explanation:
If 41 students is in the roll (total), then
[tex]\frac{3}{41}[/tex] = [tex]\frac{x}{100}[/tex] ⇒ x = [tex]\frac{3*100}{41}[/tex] ≈ 7.3 %
If the variables cancel on each side, and the given equation is TRUE, for example 3=3, then the equation has NO SOLUTION. TRUE OR FALSE
A goat is tired to a pole at the center of a square of length of side 20m. If the rope is 10m long. Calculate the (I) area of the square that can't be grazed by the goat (ii) fraction of grazed portion to the whole area
Answer:
percentage = 78.54%
Step-by-step explanation:
The area of a square of side length x is:
[tex]A_s=x^2[/tex]
The area of a circle of radius r is:
[tex]A_c=\pi r^2[/tex]
The goat is tied to a pole at the center of a square of a side length of x=20 cm.
The area of the square is:
[tex]A_s=20^2[/tex]
[tex]A_s=400~m^2[/tex]
The rope is 10 m long. The goat is able to graze an area of:
[tex]A_c=\pi 10^2[/tex]
[tex]A_c=100\pi~m^2[/tex]
(i)
Since the diameter of the circle (20 m) is equal to the length of the square, the area of the circle is contained in the square and the area of the square not grazed by the goat is:
[tex]A = A_s-A_c=400~m^2-100\pi~m^2[/tex]
[tex]A=100(4-\pi)~m^2[/tex]
Calculating:
[tex]A = 85.84~m^2[/tex]
(ii)
The percentage can be calculated as:
[tex]\displaystyle \frac{A_c}{A_s}*100=\frac{100\pi}{400}*100=25\pi[/tex]
Calculating:
percentage = 78.54%
Write each of the following numbers as a power with an exponent to the base 2:16
Given:
The number is 16.
To find:
The given number as a power with an exponent to the base 2.
Solution:
First write the given number as the product of the prime factors.
The factor form of 16 is
[tex]16=2\times 2\times 2\times 2[/tex]
[tex]16=2^4[/tex]
Therefore, the given number 16 as a power with an exponent to the base 2 is [tex]2^4[/tex].
Answer:
2^4
Step-by-step explanation:
a shoe store was sells 2 pairs of shoe for $25.10.how much it would cost to buy 7 pairs of shoes?
Answer: 87.85 dollars to buy 7 pairs
Rachel worked 2.5 hours on Monday, 3.5 hours on Tuesday, 2 hours on Thursday, and 5 hours on Saturday. She is paid $10.66 per hour. How much money did Rachel earn that week?
Answer:
$138.58
Step-by-step explanation:
You would first set up an equation. You want to know how much money Rachel earned that week, so let's refer to that by using variable t for total money earned this week.
Next, we also know that Rachel is paid 10.66 per hour, so we'll be multiplying it by the number of hours she worked this week. This allows us to set our equation up as follows:
10.66(2.5+3.5+2+5) = t
You would now add like terms.
10.66(13) = t
You would now multiply 10.66 and 13(total number of hours worked this week).
This would get us 138.58, or the total numnber of money Rachel earned this week.
please help me I asked like 2 times and no one has helped :/
Answer:
A and B are parallel.
Ali has a collection of 177 snap-together building blocks. Ali has one fourth as many red blocks as blue blocks, half as many white blocks as black blocks, an equal number of black and blue blocks, and 34 miscellaneous blocks of other colors. How many red blocks does Ali have?
Help me plz!
Answer:
The number of red blocks Ali has is 13 red balls
Step-by-step explanation:
The given parameters are;
The number of snap-together building blocks Ali has = 177
The number of red blocks Ali has = 1/4 × The number of blue blocks Ali has
The number of white blocks Ali has = 1/2 × The number of black blocks Ali has
The number of black blocks Ali has = The number of blue blocks he has
The number of miscellaneous blocks Ali has = 34
Let x represent the number of blue blocks Ali has, therefore, we have;
The number of red blocks Ali has = 1/4 × x
The number of black blocks Ali has = The number of blue blocks = x
x = 1/2 × The number of white blocks Ali has
∴ The number of white blocks Ali has = 2·x
The number of known colored blocks Ali has = 177 - 34 = 143
Therefore, we have;
x + 1/4·x + x + 1/2·x = 143
11/4·x = 143
x = 143 × 4/11 = 52
Therefore, the number of blue blocks Ali has = x = 52 blue balls
The number of red blocks Ali has = 1/4 × The number of blue blocks Ali has = 1/4 × 52 = 13
The number of red blocks Ali has = 13 red balls.
A hot air balloon is descending at a rate of 6.75 feet per second.
What is the change in the balloon's height after 3 1/3 seconds?
The hot air balloon descends 22.498 feet after 3.333 seconds.
How much does a hot air balloon's height decreases?
The situation indicates that the height decrease is directly proportional to time. The distance is equal to the product of speed (v), in feet per second, and time (t), in seconds.
s ∝ t
s = v · t (1)
If we know that v= 6.75 ft / s and t = 3.333 ft, then the change in the height of the hot air balloon is:
s = (6.75 ft / s) · (3.333 s)
s = 22.498 ft
The hot air balloon descends 22.498 feet after 3.333 seconds.
To learn more on direct variation: https://brainly.com/question/14254277
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In the rectangle below,
Answer:
Step-by-step explanation:
In a rectangle, diagonals are equal and bisect each other
BE = AE
6x - 5 = 2x + 7
6x - 2x - 5 = 7
4x - 5 = 7
4x = 7 + 5
4x = 12
x = 12/4
x = 3
AE = 2x + 7
= 2*3 + 7
= 6 + 7
AE = 13
AC = 13 + 13
AC = 26
m∠EBC = 50
In rectangle, each angle is 90
m∠ABE + m∠EBC = 90
m∠ABE + 50 = 90
m∠ABE = 90 - 50
m∠ABE = 40
In rectangle, AB // DC and DB transversal
m∠ECD = m∠ABE { alternate interior angles}
m∠ECD = 40
Which of the following terms is described as “the ratio of two polynomial
expressions”?
a. Linear Algebraic Expression c. Rational Algebraic Expression
b. Linear Algebraic Equation d. Rational Algebraic Equation
Answer:
rational algebraic expression
Answer:
C
Step-by-step explanation:
from 12 teachers to 48 teachers rounded to the nearest percent
Answer:
20%
Step-by-step explanation:
i don't know if this it what you want bc there isn't enough info. 12+48=60
12/60=1/5
1/5=.2
.2=20%
Hhhhhheelllp ASAPpppppp
Answer:
c
Step-by-step explanation:
Which of the following results in the expression 0.22 x 86? (1 point)
Answer:
18.22
Step-by-step explanation:
Jordan and $35 for taking care of his neighbors lawn suppose the neighbor gave him a $15 tip which would be the total amount Jordan earned
Jordan made a total of $50 for maintaining his neighbor's yard.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
given, Jordan earned $35 for taking care of his neighbors lawn suppose the neighbor gave him a $15 tip.
Thus,
Total money Jordan earned = Salary + tip
Total money Jordan earned = 35 + 15
Total money Jordan earned = 50
therefore, the total amount Jordan earned is $50 for taking care of his neighbor's lawn.
Learn more about Mathematical operations here:
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Find the slope of the line (4,2) (-3,-2)
Answer:
m=4/7
Step-by-step explanation:
slope: y2-y1/x2-x1
What is the slope of the line in this graph?
y 10
9
18
17
6
4
3
12
1
X
4
5
6
7
8
9
10
Answer : 5/7 for sure is the answer
Which value is equivalent to (7•3•2/7•5) ^2 × (7^0/5^-3)^3 × 5^-9
(please help I'm confused picture makes more sense)
Answer:
36/25
Step-by-step explanation:
If you need help and nobody is answering you or they don't know how to do it. Look at picture below
trapezoid has parallel sides with length 10 cm. and 15 cm. Give the area of the trapezoid.
Answer:
150
Step-by-step explanation:
Length times width you learned about that in elementary school every one has.
Answer:
150
Step-by-step explanation:
Help please by slope and y- intercept
Answer:
Slope = -3/4Y - intercept = -3Step-by-step explanation:
y = mx + b
mx = slope
b = intercept
1. Simplify the equation
4y = -3x - 12
2. Divide both sides by 4
y = -3/4 x - 3
3. Make a graph
First start at the y-intercept, (0, -3)*
Then, use the pattern -3/4
It is called rise over run.
But, when the slope is negative you have to go down instead of up. So you have to go down 3 and 4 to the right.
Continue that pattern until you get your result.
But when you have to go to the upper part of the graph go up 3 and over 4 to the left.
Continue this pattern.
This also applies to other graphs.
* = remember a y-intercept always has a 0 as the x - coordinate.
Hope this helped,
Kavitha
Taylor had 100 pieces of Lego in her collection, but she lost 15 pieces. What
percent did she lose?
Answer:
15%
Step-by-step explanation:
Percent is (usually) out of 100. So since the unit is already 100 you can just look at how much she did lose. (^-^)
Please help me, I'm really confused. Given that a ∥ b and m∠6 is 1/8 of m∠4, find m∠4 and m∠6.
9514 1404 393
Explanation:
Finish the Given statement, make use of the relationships of angles and parallel lines, then finish the algebra.
__
2. m∠6 = (1/8)m∠4 . . . . Given
3. m∠6 + m∠4 = 180° . . . . 3. same-side interior angles are supplementary
4. m∠6 + 8·m∠6 = 180° . . . . 4. Substitution (from 2, above: 8·m∠6 = m∠4)
Here is the "algebra" that gets you to line 5:
4a. 9m∠6 = 180° . . . collect terms
4b. m∠6 = 20° . . . . . divide by 9
4c. m∠4 = 8·20° = 160° . . . use the same relation as in step 4
5. m∠6 = 20°, m∠4 = 160° . . . . Algebra
m∠6=1/8m∠4
m∠6+m∠4=180° S.S int. of parallel lines
m∠6+8·m∠4=180°
m∠6=20° m∠4=160°
Please help!
Part A: Which quantity is the independent variable?
Part B: Which quantity is the dependent variable?
Part C: Which graph is scaled appropriately for this situation?
Answer:
oooooooooooo
Step-by-step explanation:
mark me as a brainlist
BRAINLIEST TO THE CORRECT ANSWER PLEASE HELP ME I BEG U
Chelsea's catering company charges a fixed rate for each hour of an event they work plus a set-up fee. The total cost (C) of the company's last 4 events according to the total hours (h) they worked is found
in the table above.
Which statement is the best representation of the total cost to hire Chelsea's catering company?
A.C= 100* + 25
B. C = 75h + 325
C.C= (100 + 75)"
D. C- 100 + 75h
PLS HELP
Answer:
I believe is D. C= 100$+75h
Step-by-step explanation:
Looks like for each day they paid 100$ fee + 75$ per each hour.
helppppp please I will give brainliest
Answer:
y = -1/2x
Step-by-step explanation:
The slope is negative and 1/2, and y-intercept is 0
Given f(x) = 2x2 + 4x - 3 and g(x) = 5x – 2, find f(x) · g(x).
Must show all work to receive credit! Show your work in the box below.
Answer:
i don't have and idea
Step-by-step explanation: