Answers
Okay, here we have this:
We need to simplify the following expression:
[tex]\begin{gathered} (5^{-4}(25)^4)^2 \\ =(5^{-4}(5^2)^4)^2 \\ =(5^{-4}\cdot5^8)^2 \\ =(5^{-4+8})^2 \\ =(5^4)^2 \\ =5^8 \end{gathered}[/tex]Finally we obtain that the correct answer is the option B.
Related Questions
how to solve 7.-4y=48
Answers
solve for y
[tex]\begin{gathered} 7-4y-7=48-7 \\ -4y=41 \\ -\frac{4y}{-4}=\frac{41}{-4} \\ y=-\frac{41}{4} \end{gathered}[/tex]Answer:
y = -41/4 or 10.25
Step-by-step explanation:
7 - 4y = 48
Move 7 across the equals sign to make y stand alone
-4y = 48 - 7
= 41
Divide both sides by the coefficient of y, which is -4
-4y/4 = 41/4
y = -41/4 or 10.25
A coordinate map of the local grocery store is shown below. ice cream is located at the point (-8,0) sprinkles. are located at the point (-8,6)
Answers
The points (-8,0) & (-8,6)
To find the distance between then
Apply the distance formulae for coordinates:
[tex]\text{ Distance=}\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]Substitute the coordinates:
[tex]\begin{gathered} \text{ Distance=}\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ \text{ Distance=}\sqrt[]{(6-0)^2+(-8-(-8))^2} \\ \text{ Distance=}\sqrt[]{6^2+0} \\ \text{Distance =6 units} \end{gathered}[/tex]So, Icecream is 6 units away from the sprinkles
Answer : 6 unit
use the diagrams to answer the following questions Number 7
Answers
To solve this we going to need the Tangent-Secant Interior Angle Theorem
Works in the following way
Using that formula we get
[tex]\begin{gathered} \beta=\frac{x}{2} \\ \\ 2\beta=x \\ \\ x=2*35\degree \\ x=70\degree \end{gathered}[/tex]Answer: x=70°
2. Calculate the distance MI for the length of the zipline cable. 3. Calculate the angle at which our zipliners will be descending toward the island . Safety regulations state that the angle at which a zipline cable meets the launching point cannot be smaller than 68 degrees . Please determine if we are in compliance with these regulations
Answers
right
[tex]\begin{gathered} AI)\text{ 400 ft} \\ MI)412.31\text{ f} \\ \text{angle = 76} \end{gathered}[/tex]Explanation
Step 1
AI?
we have a rigth triangle
then
let
[tex]\begin{gathered} AB=side1 \\ AI=side\text{ 2} \\ IB=\text{ hypotenuse} \end{gathered}[/tex]we can use the pythagorean Thoerem to find the missing vale
so
[tex]\begin{gathered} (AB)^2+(AI)^2=(BI)^2 \\ \text{replace} \\ 300^2+(AI)^2=500^2 \\ so \\ (AI)^2=500^2-300^2 \\ AI=\sqrt[]{500^2-300^2}=\sqrt[]{160000}=400 \\ AI=400 \end{gathered}[/tex]Step 2
MI?
let
[tex]\begin{gathered} \text{angle}=x \\ \text{opposite side=100 m} \\ \text{adjacent side=400 m} \end{gathered}[/tex]so, we need a function that relates those 3 values
[tex]\tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]replace
[tex]\begin{gathered} \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan x=\frac{400}{100} \\ \tan x=4 \\ \text{hence} \\ x=\tan ^{-1}(4) \\ x=75.96 \\ \text{rounded} \\ x=76\text{ \degree} \end{gathered}[/tex]As 76 is greater than 68, the zipline cable compliance with these regulations.
Also, the hypotenuse (zipline ) is
[tex]\begin{gathered} (MI)^2=(AI)^2+(AM)^2 \\ \text{replace} \\ (MI)^2=(400)^2+(100)^2 \\ (MI)^2=170000 \\ MI=\sqrt[]{17000} \\ MI=412.31\text{ ft} \end{gathered}[/tex]I hope this helps you
Suzy was reading Aniya's math notebook. Aniya wrote forty-six thousand three hundredfifteen > 46, 350. Suzy replied, "I think there is an errorExplain why Suzy said this using numbers, words, or another method to representyour thinking
Answers
it is an error because the number is
[tex]46,315[/tex]b. expanded form
[tex]\begin{gathered} 40,000+ \\ 6,000 \\ 300 \\ 50 \\ 0 \\ ------ \\ 46,350 \end{gathered}[/tex]c. 46,350 to the nearest thousand
[tex]46,350\longrightarrow46,000[/tex]Solve for r and s. 2r + 6s =6 and 6r +2s =2 what kid of line are they
Answers
r = 0, s = 1
The lines are neither parallel nor perpendicular
Explanation:The given equations are:
2r + 6s = 6........(1)
6r + 2s = 2........(2)
Multiply equation (1) by 3
6r + 18s = 18........(3)
Subtract equation (2) from equation (3)
16s = 16
s = 16/16
s = 1
Substitute s = 1 into equation (2)
6r + 2(1) = 2
6r + 2 = 2
6r = 2 - 2
6r = 0
r = 0/6
r = 0
Make r the subject of the formula in equation (1)
2r = -6s + 6
r = -3s + 6
The slope of the line represented by equation (1) = -3
Make r the subject of the formula in equation (2)
6r = -2s + 2
r = (-2/6)s + (2/6)
r = (-1/3)s + 1/3
The slope of the line represented by equation (2) = -1/3
As seen above, the slope are not equal and are not negative inverses of each other. therefore, the lines are neither parallel nor perpendicular
Cindy read a total of 8 books over 2 months. If Cindy has read 20 books so far, how many
months has she been with her book club? Solve using unit rates.
months
Submit
3
Answers
Student Beyonce You decide to buy a Super Size Hamburger Combo at the Burger Princess for 5.95. much change would you receive from 10.00. division Subtraction multiplication addition
Answers
Answer: 4.05
Just subtract 10.00 by 5.95 to get 4.05
hope this helps :)
The population of a village increases by 25% every year. The District Assemblygrants the village GH¢ 150.00 per head at the beginning of every year. If thepopulation of the village was 5.000 in the year 2005, calculate the Assembly'stotal grant from 2005 to 2010.
Answers
Explanation
We are given the following information:
• The population of a village increases by 25% every year.
,• The District Assembly grants the village GH¢ 150.00 per head at the beginning of every year.
,• The population of the village at the beginning of the year 2005 is 5,000.
We are required to determine the total grant from 2005 to 2010.
This is achieved th
Yurly and his brother Anduray are each mailing a birthday gift to a friend. Yuriy's package weighs one lesspound than three times the weight of Anduray's package. The combined weight of both packages is 7pounds.Part 3: Yuriy and Anduray each graph the system that represents this situation. Who is correct? Explain why.
Answers
Yuriy
Explanations:[tex]\begin{gathered} \text{Let the weight of Yuriy's package be w}_y \\ \text{Let the weight of Anduray's package be w}_a \end{gathered}[/tex]Yuriy's package weighs one less pound than three times the weight of Anduray's package.
[tex]w_y=3w_a-1[/tex]The combined weight of both packages is 7 pounds
[tex]w_y+\text{ }w_a=\text{ 7}[/tex]The graph representing the two equations is:
Compare the ratios in Table 1 and Table 2. Table 1 5 6 10 9 15 12 20 Table 2 7 10 20 21 30 28 40 Which statements about the ratios are true? Check all that apply. The ratio 3:5 is less than the ratio 7:10. Save and Exit Nexd Mark this and return
Answers
Table 1
3:5 , 6 : 10 , 9 :15 , 12 : 20
Table 2
7 : 10 , 14 : 20 , 21 : 30 , 28 : 40
Notice that all ratios in each table are equal. Additionally, since:
[tex]\frac{3}{5}=\frac{6}{10}[/tex]And 6<7, then the ratio 3:5 is less than the ratio 7:10.
Therefore, all ratios in table 1 are less than all ratios in table 2.
Some specific comparisons between ratios may apply as well. For example:
The ratio 14:20 (table 2) is greater than the ratio 9:15 (table 1).
3a) Find length between A(-3,8) and B(5,-4) in simplest radical form:
Answers
Find length between A(-3,8) and B(5,-4) in simplest radical form:
we know that
The distance between two points is equal to
[tex]d=\sqrt[]{(y2-y1)^2\text{ +(x2-x1)\textasciicircum{}2}}[/tex]we have
(x1,y1)=A(-3,8)
(x2,y2)=B(5,-4)
substitute in the formula
Find the center and the radius of the circle whose equation is x^2+y^2+8x-10y-23=0
Answers
Finding the equation of the standard form:
[tex]\begin{gathered} x^2+y^2+8x-10y-23=0 \\ x^2+y^2+8x-10y=23 \\ x^2+8x+16+y^2-10y+25=23+16+25 \\ \\ \\ (x+4)^2+(y-5)^2=64 \end{gathered}[/tex]
Based on the image, h = -4, k = 5 and r = 8, then...
Answer:
Center: ( -4, 5)
Radius: 8
Answer:the center would be (-4 -5)
Hope this helps
Suppose 225 trout are seeded into a lake. Absent constraint, their population will grow by 25% a year. If the lake can sustain a maximum of 3500 trout, use a logistic growth model to estimate the number of trout after 5 years. trout
Answers
It is known that the population growth model is given by:
[tex]P=P_0e^{kt}[/tex]Initial population is 225 so P0=225 so it follows:
[tex]P=225e^{kt}[/tex]Each year the population will increase by 25% so it follows:
[tex]\begin{gathered} P_0+0.25P_0=225e^k \\ e^k=\frac{5}{4} \\ k\ln e=\ln (\frac{5}{4}) \\ k\approx0.2231 \end{gathered}[/tex]So the population function is:
[tex]P=225e^{0.2231t}[/tex]The population in 5 years is given by:
[tex]P=225e^{0.2231\times5}\approx686.4960025[/tex]Hence the population of trout will be 686.4960025 after 5 years which can be rounded to 687.
A line has a slope of 2/3 and contains point A(-6,-4) and point B (a, 2) what is the value of a?
Answers
From the point-slope formula, we have:
[tex]y-y_0=m(x-x_0)[/tex]where m is the slope, (x_0,y_0) are known points.
In this case, we have the slope and two points, we can substitute in the formula to get:
[tex]\begin{gathered} \text{if:} \\ (x,y)=(-6,-4) \\ \text{and} \\ (x_0,y_0)=(a,2) \\ \Rightarrow-4-2=\frac{2}{3}(-6-a) \\ \Rightarrow-6=-\frac{2\cdot6}{3}-\frac{2}{3}a \\ \Rightarrow-6=-4-\frac{2}{3}a \\ \Rightarrow-6+4=-\frac{2}{3}a \\ \Rightarrow-2=-\frac{2}{3}a\Rightarrow a=-\frac{2}{-\frac{2}{3}}=\frac{3\cdot2}{2}=\frac{6}{2}=3 \\ a=3 \end{gathered}[/tex]therefore, a=3
Note: you can also find a if you use the slope formula.
A small town has two local high schools. High School A currently has 900 students and is projected to grow by 50 students each year. High School B currently has 500 students and is projected to grow by 100 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Graph each function and determine which high school is projected to have more students in 4 years.
Answers
ANSWER
Red line: function A(t)
Blue line: function B(t)
High school A is projected to have more students in 4 years.
EXPLANATION
We have,
• A: number of students in school A after t years
,• B: number of students in school B after t years
School A is projected to have 50 more students each year, while school B is projected to have 100 more students each year. Thus, both functions are linear.
High school A starts with 900 students and each year it will have 50 more,
[tex]A(t)=900+50t[/tex]On the other hand, high school B starts with 500 students and each year will have 100 more,
[tex]B(t)=500+100t[/tex]In 4 years each school will have,
[tex]A(4)=900+50\cdot4=900+200=1100[/tex][tex]B(4)=500+100\cdot4=500+400=900[/tex]The graphs of each function are lines. The graph of A is a line passing through points (0, 900) - which is the y-intercept, and (4, 1100).
The graph of B is a line passing through points (0, 500) and (4, 900).
From these calculations and from the graph, we can see that function A has a higher value than function B at t = 4. Hence High School A is projected to have more students in 4 years.
What is the measure in degrees of an angle that is
54/ 360
of a turn through a circle?
Answers
The measure of the angle through a circle will be 54°.
We are given that:
The measure in degrees of an angle = 54 / 360 of a turn through a circle.
This means that:
An arc should be proportional to the angle.
The circle have the angle as 360 degrees.
So, the angle will become:
54 / 360 × 360° = 54°
Therefore, we get that, the measure of the angle through a circle will be 54°.
Learn more about circle here:
https://brainly.com/question/24375372
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In the coordinate plane the vertices of angle RST are R(6,-1) S(1,-4) and T(-5,6). Prove that angle RST is a right triangle. State the coordinates of point P such that quadrilateral RSTP is a rectangle. Prove that your quadrilateral RSTP is a rectangle.
Answers
We are given coordinates of three points RST and are asked to prove that it forms a Right Triangle.
We kn
Jamie is cutting for a craft project.she has a ribbon that is 2 1/4 inches long. How many pieces of ribbon can she cut that are 3/8inches long
Answers
Total Lenght = 2 1/4
Lenght of each piece = 3/8
Divide the total lenght by the lenght of each piece:
Total lenght = 2 1/4 = (2*4+1)/4 = 9/4
Total lenght / lenght of each piece = (9/4 ) / (3/8)
To divide 2 fractions we can multiply by the inverse of the second fraction:
[tex]\frac{9}{4}\times\frac{8}{3}=\frac{72}{12}[/tex]Simplify by 12:
6
Answer: 6 pieces
A worker is getting a 3% raise. His current salary is $35,868. How much will his raise be?
Answers
Hello there. To solve this question, we'll simply have to multiply the percent and the salary to find how much will the raise of the worker.
Given his salary: $35,868 and knowing he'll get a 3% raise, we make:
3/100 * 35,868
107,604/100 = 1,07604
Rounding up the answer to the nearest tenth, we have that his raise will be $1,1.
801/4 is 5% of what number
Answers
5% could be express as 0.05
a number coul be express as x
then
[tex]x*0.05=\frac{801}{4}[/tex]solving for a number (x)
[tex]x=\frac{801}{4*0.05}=4005[/tex]4005
Which one of the following simplifications is incorrect?
Group of answer choices
sqrt(48x^4)*root(4)(16x^10)=8x^4root(4)(3x^2)
sqrt(4x)*sqrt(12x^8)=4x^4sqrt(3x)
sqrt(x^3)*sqrt(xy^4)= x^2y^2
root(3)(64)*sqrt(18)=12sqrt(2)
Answers
After simplification, the option 2, [tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex] is correct option.
In the given question,
We have to find which simplifications is incorrect.
Option 1: [tex]\sqrt{48x^4}\times\sqrt[4]{16x^{10}}=8x^4\sqrt[4]{3x^2}[/tex]
To check whether the given expression is true or not simplifying the left hand side expression.
We simplifying the left hand side by writing it as
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=\sqrt{16\times3\times (x^2)^2}\times\sqrt[4]{(2)^4\times x^{8}\times x^2}[/tex]
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=\sqrt{(4)^2\times3\times (x^2)^2}\times\sqrt[4]{(2)^4\times (x^{2})^4\times x^2}[/tex]
Now simplifying the roots
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=4\times x^2\times\sqrt{3}\times2\times x^2\times\sqrt[4]{ x^2}[/tex]
Now writing it in a simplified form
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=8\times x^{2+2}\times\sqrt{3}\sqrt[4]{ x^2}[/tex]
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=8x^{4}\sqrt{3}\sqrt[4]{ x^2}[/tex]
Hence, the simplified form of [tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}[/tex] is [tex]8x^{4}\sqrt{3}\sqrt[4]{ x^2}[/tex].
So the given statement is wrong.
Option 2. [tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex]
To check whether the given expression is true or not simplifying the left hand side expression.
We simplifying the left hand side by writing it as
[tex]\sqrt{4x}\times \sqrt{12x^8}=\sqrt{(2)^2\times x}\times \sqrt{3\times4\times (x^4)^2}[/tex]
[tex]\sqrt{4x}\times \sqrt{12x^8}=\sqrt{(2)^2\times x}\times \sqrt{3\times(2)^2\times ({x^4})^2}[/tex]
Now simplifying the roots
[tex]\sqrt{4x}\times \sqrt{12x^8}=2\sqrt{x}\times 2\times x^4\times\sqrt{3}[/tex]
[tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex]
Hence, the simplified form of [tex]\sqrt{4x}\times \sqrt{12x^8}[/tex] is [tex]4x^4\sqrt{3x}[/tex].
Hence, the option 2 is correct.
Since we get the write answer so we haven't solve the next option.
The next 2 options also can be solved in the way that we use in previous option to solve.
So the option 2 [tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex] is correct option.
To learn more about the simplification of expression link is here
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-2v + 9 = 25 what is it?
Answers
-2v + 9 = 25
-2v=25-9
-2v=16
v=16/-2
v=-8
Interior angle sum of a polygon: Find all the variables
Answers
We can see that angle d is the supplement of 97°. So d = 180°-97°= 83°
We can see that angle c and 97° are corresponding. So c=97°
If we see the triangle we can deduce that it is isosceles. So, the angles of the triangle would be (26°, 77°, 77°)( Since the sum of all angles must be equal to 180° and two angles must be equal)
The angle a is the supplement of angle 77°, so a= 180°- 77° = 103°.
The angle b is the supplement of angle 77°, so b= 180°- 77° = 103°.
Finally, we can find the angle e formulating the following equation:
540° - a - b - c- d = e (Since the sum of the angles of a pentagon must be equal to 540°)
540° - 103° - 103° - 97° - 83° = e (Replacing)
154° = e (Subtracting)
1 pointQuestion 5: Which one is NOT a correct description of these angles? *119BThey create a right angle.They are adjacent angles.UΟ Ο Ο ΟO They are complementary angles.O They are supplementary angles.
Answers
SOLUTION:
The one that is not a correct description of these anles is tption D. (They are supplementary angles)
EXPLANATION:
Two angles are said to be supplementary if they add up to be 180 and considering the sum of these angles which is 90 (right angle)
The points U, V, W and X all lie on the same line segment, in that order, such that the ratio of UV : VW:W X is equal to 1:3 : 4. If U X = 8, find VX.
Answers
The points U, V, W and X all lie on the same line segment, in that order, such that the ratio of UV : VW:W X is equal to 1:3 : 4. If U X = 8, find VX.
In this problem we have that
UV+VW+WX=UX -----> by addition segment postulate
we have
UX=8 units
so
UV+VW+WX=8 -------> equation A
UV/VW=1/3 ------> equation B
UV/WX=1/4 -----> equation C
Solve the system of equations
In equation B isolate the variable VW
so
3UV=VW
VW=3UV -------> equation D
In equation C isolate the variable WX
4UV=WX
WX=4UV ------> equation E
Substitute equation D and equation E in equation A
UV+(3UV)+(4UV)=8
solve for UV
8UV=8
UV=1
Find VW
VW=3UV
VW=3(1)=3 units
FInd WX
WX=4UV
WX=4(1)=4 units
Find out the value of VX
we have that
VX=VW+WX
substitute
VX=3+4=7 units
therefore
VX=7
how to solve this problem
Answers
Let
x -----> number of students that preferred vanilla cupcakes
y ----> number of students that preferred chocolate
we know that
x+y=750 -----> equation A
and
2/5=x/y
x=(2/5)y ------> equation B
substitute equation B in equation A
(2/5)y+y=750
solve for y
(7/5)y=750
y=750*5/7
y=536
find the value of x
x=(2/5)(736)
x=214
therefore
the answer is 214 students preferred vanilla cupcakesCan you please help me out with a question
Answers
We have the following diagram
We are told that the arc NOL has an angle measure of 300°. Recall that the angle measure of the whole circle is 360°. Since the whole circle is the sum of the measures of arcs LMN and NOL we have that the measure of the arc LMN is
[tex]\text{LMN+NOL=360}[/tex][tex]\text{LMN}+300=360[/tex]By subtracting 300 on both sides, we get
[tex]\text{LMN=360-300=60}[/tex]so arc LMN has a measure of 60°. However, note that measure of the arc LMN is the sum of the measures of arcs LM and MN. So
[tex]LM+MN=\text{LMN}=60[/tex]Now, note since lines MX and LM are perpendicular, we can do the following drawing
We can take a look at triangles LDX and NDX. Since the angles NDX and XDL are perpendicular, we can think of line MX as an axis of symmetry. That is, the left side of the circle with respect line MX is an exact copy of what is on the right. This means that the measure of the arc LM is the same as the measure of the arc MN. So we have that
[tex]LM\text{ + MN = MN+MN=2MN=60}[/tex]So, dividing both sides by 2, we get
[tex]MN\text{ =}\frac{60}{2}=30[/tex]So the measure of the arc MN is 30°.
write the number 9,700,000 in scientific notation
Answers
Explanation
[tex]9700000[/tex]All numbers in scientific notation or standard form are written in the form
[tex]a\cdot10^b^{}[/tex]where a is a number between 1 and 10, and b is a integer positive or negative
Step 1
Move the decimal 6 times to left in the number so that the resulting number, a= 9.7, is greater than or equal to 1 but less than 10
so
Help me question 20 please find the domain and range