The polynomial can be reduced to -9x^4
Addition of Polynomial
To solve this, we can simply add the similar polynomials or polynomials with the same power. This will help us simplify the polynomial to the lowest possible value.
[tex]-7x^4 + 4x^4 -6x^4 = -9x^4[/tex]
The polynomial given is simplified to become -9x^4
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chegg a 12 ft ladder is leaning against a wall. if the top of the ladder slides down the wall at a rate of 4 ft/s, how fast (in ft/s) is the bottom moving along the ground when the bottom of the ladder is 6 ft from the wall?
The bottom is moving at a rate of [tex]4\sqrt{3}[/tex] ft/s along the ground when the botton of the ladder is at a distance of 6 ft from the wall.
Here we have been mentioned that a 12 feet ladder is leaning against the wall which is represened by AC in the below given triangle.
We have AB = y = distance of top of the ladder from the wall
BC = x = distance of bottom of the ladder from the wall
AC = z = height of the ladder = 12 ft (given)
The top of the ladder AB is sliding down at a rate of 4 [tex]ft/s[/tex]
∴ [tex]\frac{dy}{dt}[/tex] = - 4 ft/s (negative sign indicates that the top is sliding downwards)
Let the rate at which the bottom of the ladder is sliding be [tex]\frac{dx}{dt}[/tex]
Now in the right angled triangle [tex]ABC[/tex] by using Pythagoras theorem we have,
[tex]AB^{2} + BC^{2} =[/tex][tex]AC^{2}[/tex]
[tex]y^{2} +x^{2} = z^{2}[/tex] (equation 1)
When x = 6ft and z = 12 ft,
[tex]y^{2} +6^{2} = 12^{2}[/tex]
⇒ [tex]y^{2} = 144 - 36[/tex]
⇒ [tex]y^{2} = 108[/tex]
⇒ y = √108
⇒ y = 6 √3 ft
Differentiating equation 1 with respect to [tex]time[/tex] we get,
[tex]\frac{d}{dt} (y^{2} +x^{2} ) = \frac{d}{dt} (z^{2})[/tex]
⇒ 2y[tex]\frac{dy}{dt}[/tex] + 2x[tex]\frac{dx}{dt}[/tex] = 2z[tex]\frac{dz}{dt}[/tex]
Putting the values of dz/dt = 0 (as the height is constant) , dy/dt = - 4 ft/s , y = 6 √3 ft, x = 6ft and z = 12ft we have,
∴ 2(6√3) (-4) + 2(6)[tex]\frac{dx}{dt}[/tex] = 2(12)(0)
⇒ -48√3 + 12[tex]\frac{dx}{dt}[/tex] = 0
⇒ 12[tex]\frac{dx}{dt}[/tex] = 48√3
⇒ [tex]\frac{dx}{dt} = \frac{48\sqrt{3} }{12}[/tex]
⇒ [tex]\frac{dx}{dt} = 4\sqrt{3}[/tex] ft/s
Hence the rate at which the bottom of the ladder is sliding is [tex]\frac{dx}{dt} = 4\sqrt{3}[/tex] ft\s
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Carla wants to buy a set of dishes. The sale price is $72. What was the original price if it was %10 off
The original price of the dishes is $80
How to calculate the original price of the dishes ?
The sale price is $72
10% was off from the original price to get the sale price
The original price can be calculated as follows
100-10
= 90%
Let y represent the original price
72 ÷ 90/100
= 72 ÷ 0.9
= 80
Hence the original price of the dishes before 10% was taken off is $80
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(A) Reflected, then translated
(B) Rotated, then translated
(C) Rotated, then reflected
Answer:
I am 99% certain that the answer is c. because it has defiantly been reflected. and if you look at the points in order for them to be moved like that it would have had to have been rotated first.
answer is chope this helped!
Multiply or divide.write the productor quotient in simplest form. 1 4/9 (-2 4/7
Answer:
-3 [tex]\frac{5}{7}[/tex]
Step-by-step explanation:
Is this the problem?
1 4/9 (-2 4/7)
[tex]\frac{13}{9}[/tex][tex](\frac{-18}{7})[/tex] = [tex]\frac{-26}{7}[/tex]
-3 [tex]\frac{5}{7}[/tex]
or Josh made 7 pies. There were 7 slices in each strawberry pie and 9 slices in each blackberry pie. If Josh made 57 slices of pie in total, how many of each type of pie did he make?
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 7(1.06)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 13.29 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 4 to d = 11, and what does it represent? (4 points)
From the given function, it is found that:
a. A reasonable domain for the function is of 0 ≤ d ≤ 11.
b. The y-intercept of the graph represents that the initial radius of the algae is of 7 mm.
c. The average rate of change between the 4th and the 11th day of the function means that the radius of the algae grew by an average of 0.64 mm a day.
What does the function represent?The function is modeled according to the following rule:
f(d) = 7(1.06)^d
In which:
d is the number of days.f is the radius of the algae.When the biologist concluded her study, the radius of the algae was approximately 13.29 mm, hence the upper bound of the domain is found as follows:
[tex]13.29 = 7(1.06)^d[/tex]
[tex](1.06)^d = \frac{13.29}{7}[/tex]
[tex]\log{(1.06)^d} = \log{\left(\frac{13.29}{7}\right)}[/tex]
[tex]d\log{1.06} = \log{\left(\frac{13.29}{7}\right)}[/tex]
[tex]d = \frac{\log{\left(\frac{13.29}{7}\right)}}{\log{1.06}}[/tex]
d = 11.
The smallest possible number of days is of 11, hence a reasonable domain for the function is:
0 ≤ d ≤ 11.
The y-intercept of the graph represents that the initial radius of the algae, as it is calculated when d = 0, hence it's value is given by:
[tex]f(0) = 7(1.06)^0 = 7[/tex]
The average rate of change of a function is given by the change in the output divided by change in the input, hence:
[tex]f(11) = 7(1.06)^{11} = 13.29[/tex][tex]f(4) = 7(1.06)^{4} = 8.84[/tex]r = (13.29 - 8.84)/(11 - 4) = 0.64 mm a day.
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*4) The image of the origin under a certain translation is (5,-6). The
image of point (-4,2) under the same translation is which?
(1) (1,-4)
(3) (-5,6)
4).
(2) (9,8)
(4) (-9,8)
[tex]2-\frac{x+1}{x-2} -\frac{x-4}{x+2}[/tex] can be written as a single fraction in the form [tex]\frac{ax+b}{x^{2} -4}[/tex] where a and b are integers.
work out the value of a, and the value of b
Answer:
a = 3 , b = - 18
Step-by-step explanation:
2 - [tex]\frac{x+1}{x-2}[/tex] - [tex]\frac{x-4}{x+2}[/tex]
express as a fraction with common denominator (x - 2)(x + 2)
= [tex]\frac{2(x-2)(x+2)-(x+1)(x+2)-(x-4)(x-2)}{(x-2)(x+2)}[/tex]
= [tex]\frac{2(x^2-4)-(x^2+3x+2)-(x^2-6x+8)}{x^2-4}[/tex]
= [tex]\frac{2x^2-8-x^2-3x-2-x^2+6x-8}{x^2-4}[/tex]
= [tex]\frac{3x-18}{x^2-4}[/tex]
compare to [tex]\frac{ax+b}{x^2-4}[/tex]
with a = 3 and b = - 18
(3x+15)° 2x° what measurement represents the measurements of the two angles?
A.60° and 120°
B. 66° and 114°
C. 33° and 147°
D. 56° and 124
ANSWER QUICK FOR BRAINIEST!
Solve the equation for x. −0.28x − 15.3 = 1.92 x = 61.5 x = −61.5 x = 47.8 x = −47.8
The value of x is −61.5 . option B
What is an algebraic expression?An algebraic expression is simply seen as one with terms, factors, variables, coefficients, constants.
These expressions may also consist of arithmetic operations, some of which includes;
AdditionDivisionSubtractionMultiplicationBracketParentheses, among others.Based on the information given, we have;
−0.28x − 15.3 = 1.92
To determine the value of the variable 'x' we need to take the following steps;
collect like terms from the equation
-0. 28x = 1. 92 + 15. 3
Add like terms
-0. 28x = 17.22
Divide both side by the coefficient of x
x = 17. 22/-0.28
x = - 61. 5
Hence, the value is - 61. 5
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Fill in the blanks below.Find the slope of the line passing through the points (-8, 4) and (-8. - 9).slope: ___
Solution:
The slope of a line that passes through two given points A and B, is expressed as
[tex]\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ where \\ (x_1,y_1)\text{ and \lparen x}_2,y_2)\text{ are the coordinates of the points through} \\ which\text{ the line passes.} \end{gathered}[/tex]Given that the line passes through the points (-8, 4) and (-8, -9), this implies that
[tex]\begin{gathered} x_1=-8 \\ y_1=4 \\ x_2=-8 \\ y_2=-9 \end{gathered}[/tex]By substituting these values into the slope formula, we have
[tex]\begin{gathered} slope\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-9-4}{-8-(-8)} \\ =\frac{-9-4}{-8+8} \\ =\frac{-13}{0} \\ \Rightarrow slope=\infty \end{gathered}[/tex]Hence, the slope of the line that passes through the points (-8, 4) and (-8. - 9) is evaluated to be
at infinity.
Graph the dilated image of triangle XYZ using a scale factor of 1.5 and (0,0) as the center of dilation
Please find attached the dilated image of triangle ΔXYZ obtained by using a scale factor of 1.5, with the center of dilation at (0, 0), giving the coordinates of the vertices at the points X'(-6, 3), Y'(9, 0) and Z'(-3, -6).
What is a dilation transformation?A dilation transformation is one in which the lengths of a figure are scaled up or down.
From a similar question online, we have:
The vertices of the triangle ΔXYZ are: X(-4, 2), Y(6, 0), and Z(-2, -4)
The given center of dilation is (0, 0)
The scale factor of the dilation is 1.5
The coordinates of the points on the image following a dilation of the point (x, y) by a scale factor of k about the origin is given by the formula:
(x, y) [tex]\underrightarrow{R_k}[/tex] (k·x, k·y)
Therefore, the coordinates of the vertices of the image of the triangle ΔXYZ following a dilation by a scale factor of 1.5 are:
X(-4, 2) [tex]\underrightarrow{R_k}[/tex] X'(1.5×(-4), 1.5×2) = X'(-6, 3)
Y(6, 0) [tex]\underrightarrow{R_k}[/tex] Y'(1.5×6, 1.5×0) = Y'(9, 0)
Z(-2, -4) [tex]\underrightarrow{R_k}[/tex] (1.5×(-2), 1.5×(-4)) = (-3, -6)
The vertices of the dilated image of ΔXYZ, which is ΔX'Y'Z' are; X'(-6, 3), Y'(9, 0), Z'(-3, -6)
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Merlyn’s weight went down from 125 pounds to 110 pounds after dieting. What was her percent weight loss?
i do NOT understand at all desperate need of help !!
Lets first look at the cost per round with the 25 round pass
Take the total cost and divide by the number of rounds
$84 / 25 rounds
$ 3.36 per round
OR
They can pay 3.25 per round with the single pay
$3.25 is less than 3.36 so it is cheaper ( less per round) to pay the single round price
Option 2 $3.25 is cheaper
The following is a list of 4 measurements.10, 11, 15, 6Send data to calculatorSuppose that these 4 measurements are respectively labeled X1, X2, ..., *4. Compute the following.4Σi=1
Given the measurements:
x1 = 10
x2 = 11
x3 = 15
x4 = 6
We're asked to find:
[tex]\sum ^4_{i=1}(x_i)^2=x^2_{1^{}}+x^2_2+x^2_3+x^2_4[/tex]Which is
100+121+225+36
=482
x = 6 % 2
if x == 1:
print("ONE")
else:
print("TWO")
Answer:ok
Step-by-step explanation: good job
The output of the program code block given will be two.
What is Python Programming language?Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation.
Given is the following code structure -
x = 6 % 2
if x == 1:
print("ONE")
else:
print("TWO")
If we dry run the program, we can write -
x = 6 % 2
x = 0
Now, x is not equal to 1, therefore, it will print two.
Therefore, the output of the program code block given above will be two.
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2x + 8 = -4 I NEED ALL PLS
Answer:
Answer down below!
Step-by-step explanation:
Let's write out the equation!
2x + 8 = -4
To solve this, you have to subtract the 8 and bring it over to -4
That would look something like:
2x -(+8) = -4 -8
That leaves you with 2x = -12
Now you divide 2 and -12 which will give you
-6
Answer:X= - 6
Step-by-step explanation:
MOVE +8 to the right which would make it negative so -8-4.You would add both numbers which would be -12 and then u divide -12 with 2 so
-12/2 is -6
Draw the graph of y=2x+1
Answer: Here you go
Step-by-step explanation:
100!/12^50
Solve! Thanks.
After solving : 100!/12^50, we get 1.025513e+104
Here, 100 factorial or 100!
Describe Factorial.The result of multiplying an integer by each natural number below it is the factorial of that number.
A factorial can be symbolically denoted by the sign "!"
The first n natural integers are added together to form "n factorial," which is represented by the number n.
100! = 100 × 99 × 98 × .... × 3 × 2 × 1 = 9.332621544 E+157.
This product is too big to calculate manually and hence a calculator is used.
Now, 9.332621544 E+157 / 12 ^ 50 = 1.025513e+104
Hence, after solving 100!/12^50, we get 1.025513e+104
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y= 24 will this be a vertical or horizontal line?
It will be a horizontal line
A uniform continuous distribution has a maximum of 14 and a minimum of 2. Samples of size 36 are drawn from the distribution. What is the variance of the sample means?.
The variance of the sample mean is 12/35 = 0.3429.. This is a result of uniform distribution.
The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive.
According to the question, we have
Sample size (n) = 36; uniform continuous distribution has a maximum of 14 and a minimum of 2.
The notation for the uniform distribution is
X U(a,b), where a= the lowest value of x and b= the highest value of x. The probability density function is f(x) = 1/(ba ) fo axb .
b = 14 and a = 2.
Variance in uniform distribution = (b-a)² / 12.
Put the value of a and b,
Variance = ( 14-2)²/12 = 12
Sample variance is used to calculate the variability of sample sets.
The variance of the sample means = variance / (sample size- 1) 9= (b-a)²/ (n-1)
= 12/35= 0.342
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a florist shop gets an average of 18 phone orders in a 2 hour time period. in order to find the probability that the florist shop will get at most 4 phone orders in a 30 minute period using the poisson distribution, what is the average number of phone orders per 30 minutes?
If the probability that the florist shop will get at most 4 phone orders in a 30 minute period using the Poisson distribution, the average number of phone orders per 30 minutes is 5.
How to find the average number of phone order?Given data:
Average 18 phone order in 2 hour
4 phone orders in a 30 minute
Let x represent the average number of phone orders in 30 minutes.
Hence
then x30=18/120
Solving for x
x =18(30)/120
x = 540 / 120
x = 4.5
x = 5 (Approximately)
Therefore we can conclude that 5 is the average number of phone that was order.
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when Mrs. Smith makes chocolate-chip cookies, she uses 3/8 cup of chocolate chips for every 2 cups of flour. How many cups of chocolate chips would she use for 12 cups of flour?
In 12 cups of flour,we are going to have 2 cups of flour in six(6) places.
Thus, for 12 cups of flour, Mrs Smith will use:
[tex]\begin{gathered} \frac{3}{8}\times6\text{ cup of chocolate chips} \\ \Rightarrow\frac{18}{8}=\frac{9}{4\text{ }}cup\text{ of chocolate chips} \end{gathered}[/tex]Could i have help with this question please?
Int the place of F(x) PLUG IN 4X+6 AND THEN SIMPLIFY THE EXPRESSION.BELOW IS THE RESPONSE:
[tex]g(x) = \frac{1}{2} \times (4x + 6) \\ g(x) = \frac{1}{2} \times 2(2x + 3) \\ g(x) = 2x + 3[/tex]
g(x)=2x+3
IT MEANS IN THE BLANKS YOU WILL INSERT 2 IN THE FIRST BLANK AND IN THE SECOND BLANK INSERT 3
HOPE THIS HELPS
rewrite 1/4 book 1/3hour as a unit rate
Based on the mathematical statement, the unit rate is 3/4 books per hour
How to rewrite the expression as a unit rate?The mathematical statement is given as
"rewrite 1/4 book 1/3hour as a unit rate"
The above means that
Book = 1/4
Time = 1/3 hour
The unit rate is then calculated as
Unit rate = Book/Time
Substitute the known values in the above equation
So, we have the following equation
Unit rate = (1/4)/(1/3)
Evaluate
Unit rate = 3/4
Hence, the solution is 3/4 books per hour
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Given: f(x) = 2×+ 4, g(×) = ײ +4×+4 and h(×)= ײ-4
Find:
1. (fg) (×)
2. (hg) (×)
3. (fh) (2)
4. (gf) (×)
5. (gh) (×)
6. (fh) (×)
7. (hg) (1)
The results of the operation of multiplication between two functions are, respectively:
2 · x³ + 12 · x² + 24 · x + 16 x⁴ + 4 · x³ - 16 · x - 16 - 32 2 · x³ + 12 · x² + 24 · x + 16 x⁴ + 4 · x³ - 16 · x - 16 2 · x³ - 4 · x² - 8 · x - 16 - 27How to find the product of two functions
According to function theory, there are five operations between two functions to create resulting functions:
Addition - f(x) + g(x) = (f + g) (x).Subtraction - f(x) - g(x) = (f - g) (x).Multiplication - f(x) · g(x) = (f · g) (x).Division - f(x) / g(x) = (f / g) (x).In this problem we must use the operation of multiplication between two functions.
Case 1
(f · g)(x) = (2 · x + 4) · (x² + 4 · x + 4)
(f · g)(x) = (2 · x + 4) · x² + 4 · (2 · x + 4) · x + 4 · (2 · x + 4)
(f · g)(x) = 2 · x³ + 4 · x² + 8 · x² + 16 · x + 8 · x + 16
(f · g)(x) = 2 · x³ + 12 · x² + 24 · x + 16
Case 2
(h · g)(x) = (x² - 4) · (x² + 4 · x + 4)
(h · g)(x) = (x² - 4) · x² + (x² - 4) · (4 · x) + (x² - 4) · 4
(h · g)(x) = x⁴ - 4 · x² + 4 · x³ - 16 · x + 4 · x² - 16
(h · g)(x) = x⁴ + 4 · x³ - 16 · x - 16
Case 3
(f · h)(x) = (2 · x + 4) · (x² - 4)
(f · h)(x) = 2 · x³ - 8 · x + 4 · x² - 16
(f · h)(x) = 2 · x³ - 4 · x² - 8 · x - 16
(f · h)(2) = 2 · 2³ - 4 · 2² - 8 · 2 - 16
(f · h)(2) = - 32
Case 4
(g · f)(x) = (x² + 4 · x + 4) · (2 · x + 4)
(g · f)(x) = 2 · x³ + 12 · x² + 24 · x + 16
Case 5
(g · h)(x) = (x² + 4 · x + 4) · (x² - 4)
(g · h)(x) = x⁴ + 4 · x³ - 16 · x - 16
Case 6
(f · h)(x) = (2 · x + 4) · (x² - 4)
(f · h)(x) = 2 · x³ - 4 · x² - 8 · x - 16
Case 7
(h · g)(x) = (x² - 4) · (x² + 4 · x + 4)
(h · g)(x) = x⁴ + 4 · x³ - 16 · x - 16
(h · g)(1) = 1⁴ + 4 · 1³ - 16 · 1 - 16
(h · g)(1) = - 27
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Dividing decimals by whole numbers !pls helpp divide 4./280.8
When dividing 4 by 280.8, the answer gotten is 0.014245.
What are decimals?It should be noted that decimal numbers are numbers that have whole numbers as well as fractional parts. One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5. Examples are 2.4 and 9.34.
To divide a decimal by a whole number, follow these steps.
Directly above the decimal point in the dividend, place the decimal point in the quotient.Divide using full numbers in the same way as you would.Divide until there is no remainder or until a pattern emerges in the quotient. Whenever necessary, annex zeros.In this case, Dividing 4 by 280.8 will give a value of 0.014245.
Therefore the value is 0.014245.
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Dividing 4 by 280.8 gives
How to divide 4 by 280.8given data
4 ÷ 280.8
4 ÷ 280.8 = 4 / 280.8
= 4 / 280.8
= [tex]\frac{4}{\frac{2808}{10} }[/tex]
= 4/1 * 10 /2808
= 40 / 2808
= 20 / 1404
= 10 / 702
= 5 / 351
5//351 is the lowest form of the fraction and in decimal it is solved as
= 5 / 351
= 0.01424501425
= 0.0142 ( to 4 decimal place )
What are decimals?Decimals refers to number types which are displayed using points. The points used here is called decimal points.
Numbers appearing after the decimal point is not a whole number. If the set of number bearing decimal point has zero as the first and only number, then the whole number is not up to a whole number.
This is synonymous to the case of the solved problem. The number 0.0142 does not have a whole number part. Hence the number is less than 1
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help please i need it
Answer: 116 degrees
Step-by-step explanation: add JKM and MKL together to get JKL
From a temperature of -29.03° F, a solution heats up 26.5° F.
What is the resulting temperature of the solution?
Think about the situation. What operation does the situation require?
Drag a word to the box to correctly complete the statement.
Answer:
Remember, a positive and a negative while being added is always a negative outcome, so when you add -29.03 + 26.5, you get -2.53
find two consecutive integers such that 3 times the larger exceeds twice the smallest by 34
Answer:
31 & 32
Step-by-step explanation:
3 x 32 = 96
2 x 31 = 62
62 + 34 = 96