Answer:
[tex]x^{\frac{5}{12} }[/tex]
Step-by-step explanation:
In the question given we use the law of exponents;
[tex](a^{b})^{c} = a^{bc}[/tex]
If a base a is raised to a power b and the entire expression raised to a power c, the resulting expression is simply equal to the base a raised to the product of the two exponents b and c, that is bc.
In the case given,
a = x
b = 5/8
c = 2/3
To simplify the expression we simply multiply b and c;
bc = 5/8 * 2/3
= 5/12
The simplified expression is thus;
[tex]x^{\frac{5}{12} }[/tex]
Answer:
The correct answer is ((x⁵/⁸)²/³) = x⁵/¹²
Step-by-step explanation:
Points to remember:-
Identity
(xᵃ)ᵇ = xᵃᵇ
Here it is given that, ((x⁵/⁸)²/³)
To find the value of ((x⁵/⁸)²/³)
(5/8) * (2/3) = (5 * 2) /(8 * 3) = 10/24 = 5/12
By using identity (xᵃ)ᵇ = xᵃᵇ we can write,
((x⁵/⁸)²/³) = x⁽⁵/⁸⁾ˣ⁽²/³⁾
= x⁵/¹²
Therefore the correct answer is ((x⁵/⁸)²/³) = x⁵/¹²
consider the inequality-5(x+7)<-10 write an inequality representing the solution for x
Answer:
x > -5Step-by-step explanation:
-5(x + 7) < -10 use the distributive property a(b + c) = ab + ac
(-5)(x) + (-5)(7) < -10
-5x - 35 < -10 add 35 to both sides
-5x < 25 change the signs
5x > - 25 divide both sides by 5
x > -5
The beverage orders from school cafeteria are shown in the graph. If 760 students purchase a beveragehow many of the students chose water
according to the graph, 25% chose water, and
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 760}}{\left( \cfrac{25}{100} \right)760}\implies 190[/tex]
Find -2/3 divided by 4/6
-1
4/9
-9/4
1
Answer:
-1
Step-by-step explanation:
The given expression is:
[tex]-\frac{2}{3}\div \frac{4}{6}[/tex]
We multiply by the reciprocal to get:
[tex]-\frac{2}{3}\times \frac{6}{4}[/tex]
We factor so that we can cancel easily:
[tex]-\frac{2}{3}\times \frac{3\times 2}{2\times 2}[/tex]
Cancel the common factors to get:
[tex]-\frac{1}1}\times \frac{1\times 2}{1\times 2}[/tex]
This simplifies to:
[tex]-1[/tex]
Answer:The final answer is 1.
Step-by-step explanation:
Joan has a gym gift card worth $100. Each time she visits the gym. $12 is deducted from the amount remaining on the gift card. Which equation can be used to determine the amount of the money (m) , in dollars, remaining on the gift card after joan visits the gym d times
The equation to calculate the remaining money on Joan's gym gift card after d gym visits is m = 100 - 12d.
Explanation:To determine the amount of money (m), in dollars, remaining on Joan's gym gift card after she visits the gym d times, you can use a simple linear equation.
Since she starts with $100 on the card, and each gym visit costs $12, you subtract $12 for each visit from the initial amount. The equation that represents this situation is m = 100 - 12d.
Here, d is the number of times she visits the gym, and m is the money remaining on the card.
which statement is true about the value of the expression below (-2^3)^-2
1. it is between 0 and 1.
2. it is greater than one
3. it is less than -1
4. it is between -1 and 0
-2^3 will be -8 (we know it certainly)
(-8)^-2 =( 1/(-8) )^2 then we know , when we have power 2 for parentheses,can ignore the negativity : 1/64 and we know 0<1/64<1
So 1 is correct!!
Answer:it is between 0 and 1
Step-by-step explanation:
would 20, 40, 30 form a right angle
Yes because if you add forty and thirty that equals seventy plus twenty is 90 which is a right angle
Answer:
No
Step-by-step explanation:
It would not form a right triangle because if you square 20, 30, 40, and add 20^2 and 30^2 it would become 1,300, but 40^2 is 1,600 which does not make it a right triangle according to the Pythagorean Theorem.
a recipe that makes 18 cookies calls for 3/4 cups of sugar. How much sugar is needed to make 2 dozen cookies using this recipe?
Answer: 1.5
Step-by-step explanation:
Dozen means a lot. If 3/4 cups of sugar is needed, 3/ multiplied by 2 = 1.5
What is the answer to
20.25 x 6
Answer:
The answer is 121.50
Step-by-step explanation:
Multiple 6 by the 20 first so you get 120
Then multiply 6 by the .25 and you get 1.5
So just add 120 with 1.5 and you get 121.50
Answer:
121.5
Step-by-step explanation:
Bad at explaining look at picture.
If BCDE is congruent to OPQR, then BE is congruent to
Answer:
OR
Step-by-step explanation:
Answer:
Step-by-step explanation:
In simple language, two things are said to be congruent if they overlap each other i.e they have same size and shape. Angles are said to be congruent if they have same measure. Sides are congruent if they have same length .
We say that two triangles are said to be congruent if there is one to one correspondence between their angles and side.
Here, it's given that BCDE is congruent to OPQR i.e there is one to one correspondence between their sides and angles i.e
[tex]B\leftrightarrow O\,,\,C\leftrightarrow P\,,\,D\leftrightarrow Q\,,\,E \leftrightarrow R[/tex]
So, BE is congruent to OR .
Solve the system using substitution. Show all work.
y = x - 5
3x - y = 7
Solve the system using the Linear Combination Method. Show all work.
2x + 2y = 12
3x + y = 2
SHOW ALL WORK AND STEPS Please. The Teacher will not grade fully and give a failing grade without showing steps and all work.
And Don't be a freaking troll as I will report you for trolling with short improper answers.
Here is the answer I hope it helps
f(x)=2x and g(x)=2x+3,what is the value of f(g(-8))
Answer:
f(g(-8)) = -26
Step-by-step explanation:
Given:
f(x)=2x and g(x)=2x+3
Required:
f(g(-8))=?
Solution:
First we will find g(-8)
g(x) = 2x+3
g(-8)= 2(-8)+3
= -16 + 3
= -13.
so, g(-8) = -13
Now, for calculation f(g(-8)) we can put the value of g(-8) i.e, -13
so, f(x) = 2x
f(-13) = 2(-13)
= -26
so, f(-13) = -26
and f(g(-8)) = -26
triangle ABC was transformed to create triangle DEF.
Answer:
The answer is B.
Step-by-step explanation:
You can see that the triangles are identical, so find the side that matches with BA and there you have it. The corresponding side is ED. I hope this helps!
simplify without the absolute value
|x+3| ; if x=2
After substituting x=2 into the expression |x+3|, we get |2+3| which simplifies directly to 5, with the absolute value being unnecessary since the result is positive.
To simplify the expression |x+3| without the absolute value when x=2, we substitute the value of x into the expression. The absolute value of a number refers to the non-negative value of that number without considering its sign. Since 2 + 3 equals 5, which is positive, the absolute value is not necessary, and we can simply write the expression without it.
Therefore, |2 + 3| simplifies to 5.
A scientist is performing an experiment with a certain type of mold which is spreading every quarter of an hour. The function below represents the area covered by the mold after t hours.
The area covered by mold ___ by ___ % ___.
first blank: decreases, increases
second blank: 104, 4, 17, 8
third blank: every 15 minutes, every hour, every 4 minutes, every 30 minutes
fill in each blank with one of the options. Thank you!!
Answer:
"The area covered by mold increases by 4 % every 15 minutes."
Step-by-step explanation:
Since the mold is "spreading", the area is obviously, increasing.
By how much???
We can look at the function. The increasing factor is (1.04). The increasing factor is the part OVER 1, we have 4 units OVER 1, so it is increasing by 4%.
Since, the mold is spreading every QUARTER OF AN HOUR, this means 1/4th of an hour.
An hour is 60 minutes, 1/4 of 60 = 15 minutes. Hence, it is increasing every 15 minutes.
To complete the statement:
The area covered by mold increases by 4 % every 15 minutes.
Answer:
i believe its every hour not 15 minutes
Step-by-step explanation:
Amber bought a condominium at a time when prices were at their highs. She paid $200,000. Since then, the market value has decrease by 5% per year. Write an exponential depreciation equation to model this situation. Approximately when will Amber's condominium be worth less than $140,000?
Answer:
$140,000(1 - .05)^t
Step-by-step explanation:
you have your total amount $140,000
it is decreased by 5% go behind the number and move two decimal points and you get .05
since is decreasing it would be 1 subtracted by ,05
$140,000(1 - .05)^t
"t" is the years it would be depreciated by
I do not see years but by knowledge i would say it is decreasing
Answer:
Since, the exponential decay function,
[tex]A=P(1-r)^t[/tex]
Where,
P = initial value,
r = rate per period,
t = number of periods,
Here, P = $ 200,000, r = 5% = 0.05,
Thus, the value of the condominium would be,
[tex]A=200000(1-0.05)^t=200000(0.95)^t[/tex]
Which is the required equation.
If A < 140,000
[tex]200000(0.95)^t < 140000[/tex]
By the graphing calculator.
[tex]t< 6.95364[/tex]
Hence, about after 7 years the condominium will be worth less than $140,000.
What’s the side of 200cm in a square
To find the length of a side of a square fins the square root of the area.
Area = 200 cm^2
Side = √200
Side = 10√2 (Exact length)
or 14.142 cm's ( round the decimal answer as needed.)
A circle has a sector with area 3/2pi and central angle of 60 what is the area of the circle?
Answer:
The area of the circle is [tex]9\pi \ units^{2}[/tex]
Step-by-step explanation:
we know that
A circle has a sector with area [tex]3\pi/2[/tex] and central angle of 60 degrees
The area of a complete circle subtends a central angle of [tex]360\°[/tex]
so
using proportion
Find the area of the circle
[tex]\frac{(3\pi/2)}{60} =\frac{x}{360}\\ \\x=(3\pi/2)*360/60\\ \\x=9\pi \ units^{2}[/tex]
Answer:
[tex]A = 9\pi[/tex]
Step-by-step explanation:
The total area of the circle is determine by simple rule of three:
[tex]A = \frac{360^{\textdegree}}{60^{\textdegree}} \cdot \left(\frac{3}{2}\pi\right)[/tex]
[tex]A = 9\pi[/tex]
Plz help me with this
Answer: A) 2.26
Step-by-step explanation:
[tex]log_3(12) = \dfrac{log(12)}{log(3)}=\dfrac{1.079}{0.477}=\large\boxed{2.26}[/tex]
Joe's mom gave him $40 for cutting their grass. He used the money to buy a $10.75 game and snacks that cost $3.25 each. Joe also bought a bouquet of flowers for his mom. If Joe came home with 1/4 of the money his mom gave him, how much did the flowers cost
Answer:
The flowers costed $26 but that is only if he bought 1 snack. It says snacks as in more than one but it didn't specify how many so it depends lol
Step-by-step explanation:
Help me asap!!!!!!! please!!!
Answer:
see attachment
Step-by-step explanation:
The applicable property of exponents is ...
[tex]\sqrt[n]{x^m}=x^{\frac{m}{n}}[/tex]
The 4th selection uses this property directly. The 3rd selection uses the property
[tex](a^b)^c=a^{bc}[/tex]
to show that the cubes of the two expressions are equivalent. Since all the numbers involved are real numbers, this is equivalent to showing the expressions equivalent.
Find the area of the triangle with a= 18.8, b= 11.6, c= 13.8. Round to the nearest tenth.
Answer:
B. 79.7 units^2
Step-by-step explanation:
got it right on edge :)
A flat screen television has a 50 inch diagonal and a height of 25 inches. How wide is the television rounded to the nearest tenth?
(Use the Pythagorean Theorem)
Answer
inches
Answer: 43.3 inches.
Step-by-step explanation:
According to the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse, and "b" and "c" are the legs of the right triangle.
Let be "c" the width of the television.
We can indentify in the figure that:
[tex]a=50in\\b=25in[/tex]
Then, we can substitute values and solve for "c":
[tex](50in)^2=(25in)^2+c^2\\\\c=\sqrt{(50in)^2-(25in)^2}\\\\c=43.30in[/tex]
Rounded to the nearest tenth:
[tex]c=43.3in[/tex]
Final answer:
The width of a flat screen television with a 50 inch diagonal and a 25 inch height is found to be approximately 43.3 inches when calculated using the Pythagorean Theorem.
Explanation:
To find the width of a flat screen television with a 50 inch diagonal and a height of 25 inches, we will apply the Pythagorean Theorem. The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the diagonal is the hypotenuse (c), the height is one leg (a), and the width is the other leg (b).
The Pythagorean Theorem is written as:
a2 + b2 = c2
Using the given measurements:
252 + b2 = 502
Solving for b, we have:
b2 = 502 - 252
b2 = 2500 - 625
b2 = 1875
b = √1875
b ≈ 43.3 inches (rounded to the nearest tenth)
Therefore, the width of the television is approximately 43.3 inches.
Given the function f(x)=6|x-2|+3, for what values of x is f(x)=39?
Answer:
The values of x are -4 and 8
Step-by-step explanation:
39=6|x-2|+3 move the 39 and 6 to the opposite sides and simplify
-6|x-2|=-36 divide both side by -6
|x-2|=6 separate it into the possible equations
x-2=6 so, x=8
or
x-2=-6 so, x=-4
Need help on how to do number 20
Answer:
J is correct
Step-by-step explanation:
You need to simplify top as
[tex](27m^{12}n^3 )(2m^2n^5p)=54m^14n^8p[/tex]
Then can easily see the correct answer is J.
Answer:
Step-by-step explanation:
please help me...
Problem:
The standard form of a circle is (x-h)2+(y-k)2=r2 and vertex form for the parabola, y-k=a(x-h)2. The (h,k) pair is the center of the circle and the vertex of the parabola. The radius of the circle is ‘r’ and the focal length of the parabola is f=1/(4a). For the following General Conic Equation: x2+y2-2x-4y-4=0 complete the following problems showing all your work:
A. Complete the square showing all your work to convert to Standard Form:
B. If this is a circle, state the coordinates of the center and give the radius. If this is a parabola, then state the coordinates of the vertex and give the focal length. Show all your work.
C. Sketch (or plot, or graph) the Conic. Label the point and values you found in part B. Also label the top-most, bottom-most, right-most, and left-most points on the circle or the focus and directrix on the parabola.
Answer:
Part A) [tex](x-1)^{2}+(y-2)^{2}=3^{2}[/tex]
Part B) The coordinates of the center are [tex](h,k)=(1,2)[/tex] and the radius is equal to [tex]r=3\ units[/tex]
Part C) The graph in the attached figure
Step-by-step explanation:
we have
[tex]x^{2} +y^{2}-2x-4y-4=0[/tex]
Part A) Convert to standard form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}-2x) +(y^{2}-4y)=4[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side
[tex](x^{2}-2x+1) +(y^{2}-4y+4)=4+1+4[/tex]
[tex](x^{2}-2x+1) +(y^{2}-4y+4)=9[/tex]
Rewrite as perfect squares
[tex](x-1)^{2}+(y-2)^{2}=3^{2}[/tex] ------> Is a circle
Part B) If this is a circle, state the coordinates of the center and give the radius.
we know that
The equation of the circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center
r is the radius
In this problem we have
[tex](x-1)^{2}+(y-2)^{2}=3^{2}[/tex]
therefore
The coordinates of the center are [tex](h,k)=(1,2)[/tex]
The radius is equal to [tex]r=3\ units[/tex]
Part C) Plot the circle
using a graphing tool
see the attached figure
The median of the set of data below is 9.
4,9.9.9, 8, 7, 6, 1, 2
True
False
Answer:
False
Step-by-step explanation:
Set the data in order.
1, 2, 4, 6, 7, 8, 9, 9, 9
Now try finding the middle of the data set by taking out the sides equally one by one.
1, 2, 4, 6, 7, 8, 9, 9, 9
2, 4, 6, 7, 8, 9, 9
4, 6, 7, 8, 9
6, 7, 8
7
7 is the median
The median of the data set [1, 2, 6, 7, 8, 9.4, 9.9, 9.9] is not 9.4, but instead is 7.5, which is calculated by getting the average of the two middle values, in this case, 7 and 8.
Explanation:The given set of data is: [9.4, 9.9, 9.9, 8, 7, 6, 1, 2]. The first step is to put the data in numerical order, so we have [1, 2, 6, 7, 8, 9.4, 9.9, 9.9]. The median is the middle value in an ordered data set. Since this set has an even number of data values (8), the median is calculated as the average of the two middle values. Here, the middle values are 7 and 8. Therefore, to find the median, we add these two values together and divide by 2. Hence, 7 + 8 = 15, and 15 divided by 2 equals 7.5. Therefore, the median of this data set is 7.5, not 9.4.
Learn more about Median Calculation here:https://brainly.com/question/30090626
#SPJ3
Use addition to solve the linear system of equations. Include all of your work in your final answer. 3x-y=6 and y=x-4
Answer:
x = 1, y = -3
Step-by-step explanation:
So, we have two equations to start with: 3x-y=6 and y = x-4, we want to resolve the equations by addition.
We sum up the left sides of the equations together and the right sides together, and simplify, we have:
3x - y + y = 6 + x - 4
3x = 2 + x ==> 2x = 2 ==> x = 1
To find y, we place the value of x in any of the two equations:
y = x - 4 = 1 - 4 = -3
You verify that the solution is valid by entering the values of x and y in the other equation:
3x - y = 6 becomes
3 (1) - (-3) = 6
3 + 3 = 6
Answer:
x = 1 and y = -3
Step-by-step explanation:
The given linear equations are,
3x - y = 6 and y = x - 4
To solve the system of equations
Let 3x - y = 6 -----(1)
y = x - 4
x - y = 4 ----(2)
(2) * -3 ⇒ -3x + 3y = -4 ----(3)
(2) + (3) ⇒
3x - y = 6
-3x + 3y = -12
0 +2y = -6
y = -6/2 = -3
x - y = 4
x = 4 + y = 4 + -3 = 1
x = 1 and y = -3
Rena pushes the elevator button but the elevator does not move the mass limit for the elevator is 450 kg But Reena and her load of identical Packages mass A total of 620 KG each package has a mass of 37.4 KG
Answer:
1) 620- 37.4p≤450
2) 5
Step-by-step explanation:
Total weight of rena and packages = 620 kg
lift limitation= 450 kg
mass of each load= 37.4 kgs
As the mass limit for the elevator is 450 kg therefore the from the Total weight of rena and packages (620 kgs) rena needs to subtract weight of some number of packages (p x 37.4)
hence
620- 37.4p≤450
2)
Solving for minimum whole number of packages p, rena needs to remove to meet the elevator limitation:
620- 37.4p≤450
37.4p≤-450+620
37.4p≥170
p≥4.5
rounding off to whole number
p≥5 !
Maria, Kara, and Tommy order 1 pizza to share. Maria eats 1/4 of the pizza, Kara eats 1/8 of the pizza, and Tommy eats 3/8 of the pizza. How much of the pizza is left?
Answer:
3/4
Step-by-step explanation:
So you give them all a common denominator of 8. This means Maria eats 2/8 of the pizza, Kara eats 1/8 of the pizza, and Tommy eats 3/8 of the pizza. When you add them you get 6/8 which simplified to 3/4.
How many times greater is the value of the 2 in 270,413 than the value of the 2 in 419,427?
It is 4 down the value so just do tens hundreds,thousands
Answer: 10,000
Step-by-step explanation: