[tex]~~~~~~(x-1)^{\tfrac 32} =27\\\\\implies \left[(x-1)^{\tfrac 12} \right]^3 = 3^3\\\\\implies (x-1)^{\tfrac 12} = 3~~~~~~~~~;[\text{Cube root on both sides}]\\\\\implies x -1 = 9~~~~~~~~~~~~;[\text{Square both sides}]\\\\\implies x = 10[/tex]
please show the steps
Answer:
x = -3, 0, or 7
Step-by-step explanation:
After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.
__
Step 1Write the equation in standard form.
4x³ -16x² -84x = 0
Step 2Factor out the common factor from all terms.
= 4x(x² -4x -21) = 0
Step 3Compare to the factored form of a quadratic:
(x +a)(x +b) = x² +(a+b)x +ab
This tells you the constants 'a' and 'b' in the factors can be found by considering ...
(a+b) = -4 . . . . the coefficient of the x term of the quadratic
ab = -21 . . . . . the constant term of the quadratic
It is often helpful to list factor pairs of the constant:
-21 = (-21)(1) = (-7)(3) . . . . integer pairs that have a negative sum
The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...
a = -7, b = 3
Step 4Put it all together.
4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation
Step 5Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:
4x = 0 ⇒ x = 0
x -7 = 0 ⇒ x = 7
x +3 = 0 ⇒ x = -3
Solutions to the equation are x ∈ {-3, 0, 7}.
_____
Additional comment
What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.
A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.
Which three-dimensional figure has nine edges?
rectangular prism
rectangular pyramid
triangular prism
triangular pyramid
Answer:
Triangular PrismStep-by-step explanation:
A geometrical shape that has 6 vertices and 9 edges is a triangular prism. A triangular prism is a three-dimensional object with two congruent...
Answer:
Triangular Prism
Step-by-step explanation:
Edge2022 :)
jenette ordered a large bucket of popcorn at the movies.the graph shows the amount of popcorn in her bucket over time
Answer:
A
Step-by-step explanation:
Solve 2(x + 1) = 2x + 2
Write a cosine function that has an amplitude of 4, a midline of 2 and a period of1
Answer:
see below
Step-by-step explanation:
start with cos (x)
amplitude 4
4 cos x
midline 2
4 cos (x ) + 2
period of 1 : 2 pi / 1 = 2 pi
multiply x by 2pi
4 cos ( 2 pi x) + 2
If xy + 1/(xy) = 2 , then what does (x^2)(y^2) + 1/((x^2)(y^2)) = ?
Show all work.
Show any graphical support.
Explain what happened with both the math work and the graph(s).
Think about what happened.
Would it happen with more terms or the next function in the sequence?
Why or why not? Explain.
The value of the expression will be [tex](xy)^2+\dfrac{1}{(xy)^2}=2[/tex]
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
The value of the expression is [tex]xy+\dfrac{1}{xy}=2[/tex]
So we need to find [tex](xy)^2+\dfrac{1}{(xy)^2}=?[/tex]
The value of the expression will be calculated as:-
[tex]xy+\dfrac{1}{xy}=2[/tex]
Squaring the above equation.
[tex](xy)^2+\dfrac{1}{(xy^2)}+2\times (xy)^2\times \dfrac{1}{(xy^2)}=4[/tex]
[tex](xy)^2+\dfrac{1}{(xy^2)}=2[/tex]
Again squaring the above expression.
[tex](xy)^4+\dfrac{1}{(xy^4)}+2\times (xy)^4\times \dfrac{1}{(xy^4)}=4[/tex]
[tex](xy)^4+\dfrac{1}{(xy^4)}=2[/tex]
Hence the value of the expression will be [tex](xy)^2+\dfrac{1}{(xy)^2}=2[/tex]
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Which of the following graphs is not a function ?
Answer:
I believe it should be the first one
Step-by-step explanation:
in the first one if you put a line straight it would cross it twice making it not function.
Answer:
The first one is not a function.
Step-by-step explanation:
When you perform the vertical line test on the graphs, the first graph is the only one that passes through a X value multiply times.
Please help me slove this i really need the answer
i need help with 7th grade math please 45 points need help ASAP + brainleist
Answer:
Area = 601.8760801 ft^2
Step-by-step explanation:
Area of Rectangle: Area = Length* Height
Area of a Semi-Circle = π*r^2 /2
Area of Rectangle: Area = 14 * 21 = 294 ft^2
Area of a Semi-Circle = π * 14^2 / 2 = π * 196/2 = π * 98 ft^2
Add the Two Area: 294 ft^2 + 98π ft^2 = 601.8760801 ft^2
Answer:
77.98 ft
Step-by-step explanation:
Perimeter :
2(21) + 14 + 3.14 x 742 + 14 + 21.9856 + 21.9877.98 ftPenelope has a bag that contains orange chews, apple chews, and lime chews. She performs an experiment. Penelope randomly removes a chew from the bag, records the result, and returns the chew to the bag. Penelope performs the experiment 33 times. The results are shown below:
A orange chew was selected 13 times.
A apple chew was selected 9 times.
A lime chew was selected 11 times.
Based on these results, express the probability that the next chew Penelope removes from the bag will be apple or lime as a percent to the nearest whole number.
The probability that the next chew Penelope removes from the bag will be apple or lime as a percent is 60.6%.
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Here, Number of apple and lime is 9 + 11 =20
Total bag contains = 13 + 9 + 11 = 33
Probability = Number of apple or line / Total
= 20 / 33
= 60.6 %
Thus, The probability that the next chew Penelope removes from the bag will be apple or lime as a percent is 60.6%.
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Please solve (15 points)
three bells rings at intervals of 30min, 40min and 48min. The bells rang at 1230h.What time, in a. m/p.m, will they ring together next?
pls help with this problem
Answer:
D
Step-by-step explanation:
The median is 8, so it is less than 9.
Answer:
Option D is not true
Step-by-step explanation:
The mode is the highest occuring number.From the data.
The mode is 9 and is greater than 7.This mean option A is correct.
The range is the difference between the highest number and the lowest which is 15-4 =11.Hence option C is correct because the range is more than 10.
The median when the data is arranged in either ascending or descending order i.e (15,12,11,9,9,7,5,4).Hence,the middle numbers are 9 and 9.To get the median,we get the average of the numbers which will be 9+9=18 ÷2= 9. The median is 9 which means option D is not correct.
The mean will be the addition of the numbers divided by the number of items
[tex] \frac{9 + 15 + 5 + 7 + 9 + 12 + 11 + 4}{8} [/tex]
[tex] = \frac{72}{8} [/tex]
[tex] = 9[/tex]
The mean is equal to 9 which means Option B is correct.
This implies that the only option which is incorrect is option D
which is greater, 2,670 meters or 2 kilometers? explain.
Answer: 2,670 meters
Step-by-step explanation:
2 kilometers = 2000 meters
2,670 > 2000
The greater value between 2,670 meters or 2 kilometers is 2,670 meters.
What is unit conversion?
It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
We are given that;
Two measurements 2,670 meters or 2 kilometers
Now,
To compare 2,670 meters and 2 kilometers, we need to convert them to the same unit of measurement.
There are 1,000 meters in a kilometer. So 2 kilometers is equal to:
2 km * 1,000 m/km = 2,000 meters
Now we can compare 2,670 meters and 2,000 meters. We can see that 2,670 meters is greater than 2,000 meters, because 2,670 is a larger number than 2,000.
Therefore, by conversion the answer will be 2,670 meters is greater than 2 kilometers.
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PLEASE HELP WILL MARK BRAINLIEST
First try was incorrect
Ivy is making fasnacht (deep-fried German doughnuts) to sell the
Tuesday before Ash Wednesday, her bakery's biggest fasnacht day of
the calendar year. She has 6 pounds of butter and her recipe calls for
1
2
cup of butter per 1.5 dozen fasnacht. If 1 pound of butter is 2 cups,
then how many cups of butter will Ivy have left over after making 30
Answer:
3 cups of butter ivy will have left over
Calculate the diameter of the
circle.
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[tex]\diamond\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
[refer to attachment for question]
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
Remember, the radius is exactly one-half of the diameter, so if we need to find the diameter, we multiply the radius times 2:-
r=6.5m
d=13m
r=9.1 ft
d=18.2 ft
Good luck with your studies.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - -
Given: 1 = 2
If AB = 10, AC = 6, and BC = 6, find AD:
The length of AD in triangle ABC in which ∠1 = ∠2 is 3.75.
What is Angle Bisector?The (interior) bisector of an angle, also called the internal angle bisector, is the line or line segment that divides the angle into two equal parts.
Here, Let the lenght of AD be x
AB = 10 , AC = 6 and BC = 6
by Angle-Bisector theorem which states that
if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides.
So, CD/BD =AC/AB
CD/(BC-CD) = 6/10
10. CD = 6.BC - 6.CD
16 CD = 6 X 6
16 CD = 36
CD = 36/16
CD = 2.25
Now, AD = AC - CD
AD = 6 - 2.25
AD = 3.75
Thus, the length of AD in triangle ABC in which ∠1 = ∠2 is 3.75.
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x 10xy) + 16x
19 +11z +2 (-2-z)
Answer:
Don't understand retype your question
Translate shapes
Draw the image of AABC under a translation by 2 units down.
y
6
5+
3
2
A
A
-7 -6 4 -3 -2
2
1 2 3 4 5 6 7
-24
-3
Answer:
Just think about it.............. 77 + 33 = 100
Step-by-step explanation:
You add
Please help please .,.,
Answer:
219.8 square cm
Step-by-step explanation:
[tex]s = 2\pi r^{2} +2\pi rh\\s=2(3.14)5^{2} +2(3.14)(5)(2)\\s = 6.28(25)+6.28(10)\\s = 157+62.8\\s=219.8 cm^{2}[/tex]
6) The combined area of town A and town B is 104,000 square miles. The area of town A is 10,000 square miles more than that of town B. Find the area land of each town.
Step-by-step explanation:
Town B = 47000 square miles
Town A = 57000 square miles
Kenosha is having a lunch with 4 of her friends at a fancy restaurant. The bill total is $175.50 if a 20% tip is added onto the total how much each person need to contribute
Answer:
$8.78
Step-by-step explanation:
first you need to find 20% of $175.50
which is 35.10
then you divide 35.10 by 4 leaving you with 8.78
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What is the discriminant of the polynomial below?
4x² + 4x+1
Discriminant means that delta=b^2-4ac
(4)^2-4(4)(1)=0
If the discriminant is equal to 0, the quadratic equation has 1 real solution.
200(x-0.3)=600
-10(x-1.7)=-3
Answer:
x = 33.
x = 2.
Step-by-step explanation:
200(x-0.3)=600
200x - 60 = 600
200x - 60 + 60 = 600 + 60
200x = 660
x = 660/200
x = 3.3.
-10(x-1.7)=-3
-10x + 17 = -3
-10x + 17 - 17 = -3 - 17
-10x = -17 - 3 = -20
x = 2.
A healthy school lunch that is $0.75 more than the current lunch has a higher economic
The fact that the healthy school lunch has a higher price than the current lunch means that it has a higher economic cost.
What is an economic cost?An economic cost in this scenario, is the increased cost that comes with a commodity having greater perceived value.
A healthy school lunch will help a person stay healthy which is why it has more value than the current lunch. This is the reason for its higher price.
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Answer: cost
Step-by-step explanation:
Whats the difference between 16x + 5 and 4x + 5
The number of students who signed a petition for more after-school sports is 195, or 30% of the students at school. Terry's calculations show that there are 58.5 students, but he knows that number is incorrect. What is the correct enrollment? What was Terry's error?
Question content area bottom
Part 1
The correct enrollment is
enter your response here student(s). Terry found
▼
the percent of 195 that 30 is
30% of 195
what 195 is 30% of
instead of finding
▼
Answer:
650
Step-by-step explanation:
195
_. of 30
100
and these 30 zero cut and 100 zero also cut and 3 * 195= 65 and 65 x 10 =650
Which of the following best describes the graph shown below ?
B. This is the graph of a function, but it is not one-to-one
Step-by-step explanation:A function is a type of graph that has a specific relationship between the x and y values.
Vocabulary
First, let's define the words that were used in the answer choices.
Function - A function is a type of relationship where the x-values do not repeat. This means that each x-value has only one specific y-value.One-To-One - A one-to-one function still has no repeating x-values; however, y-values also do not repeat. This means that each y-value has only one x-value and vice versa.Finding a Function
There are different ways to find if a relationship is a function, but with a graph, the easiest way is the vertical line test. The vertical line test is when you draw vertical lines over your graph. If you are able to draw a vertical line everywhere without that line crossing the graph more than once, then the graph is a function.
In this graph, there is no spot in which a vertical line would intersect with the graph more than once. Since it passed the vertical line test, this must mean that x-values never repeat. Thus, this is a function.
Finding a One-To-One Function
Now that we know this is a function, we need to find if this is a one-to-one function. Once again, this can be done multiple ways, but one way is the horizontal line test. This test is similar to the method above; however, horizontal lines are used. In this test, you draw horizontal lines are drawn on the graph. If you can draw a horizontal line at every value without the line intersecting more than once, then it is a one-to-one function.
On this graph, if you were to draw a horizontal line at any of the y-values between 0 and 6, then the line would intersect multiple times. This means that y-values do repeat. Thus, this is not a one-to-one function.
In Detroit the high temperatures in degrees Fahrenheit for
five days in January were -12°, -8°, -3°, 6°, -15°. What was the
average temperature for these five days?
Answer:
-6.4 degrees.
Step-by-step explanation:
The average temperature
= (-12 -8 -3 + 6 - 15) / 5
= -32/5
= -6.4 degrees.