Answers
Let's solve the given logarithmic expression:
[tex]\text{ log}_4(64)\text{ = m}[/tex]We get,
[tex]\text{ log}_4(64)\text{ = m}[/tex][tex]\mathrm{Factor\: the\: number\colon\: }\: 64=4^3[/tex][tex]=\log _4\mleft(4^3\mright)[/tex][tex]\mathrm{Apply\: log\: rule}\colon\quad \log _a\mleft(a^x\mright)=x[/tex][tex]\log _4\mleft(4^3\mright)\text{ = 3 = m}[/tex]Therefore, m = 3.
Related Questions
What is the variable term in 2x+3?
Answers
In the expression
[tex]undefined[/tex]For / (x) = 4x+1 and g(x)=x2-5, find
Answers
We need to find g(x)/f(x) so we will put them over each other as a fraction
[tex]\frac{g(x)}{f(x)}=\frac{x^2-5}{4x+1}\text{ , x}\ne\frac{-1}{4}[/tex]In any algebraic fraction, denominators can not be zero, so we avoid any values make it equal to zero like -1/4 in our question
in a class of 20 students, 40% of them have a pet how many students have a pet
Answers
20 students represent 100% of the class, to find how many students are 40% of the class, we can use the next proportion:
[tex]\frac{20\text{ students}}{x\text{ students}}=\frac{100\text{ \%}}{40\text{ \%}}[/tex]Solving for x,
[tex]\begin{gathered} 20\cdot40=100\cdot x \\ \frac{800}{100}=x \\ 8=x \end{gathered}[/tex]8 students have a pet
write each ratio as a fraction in its simplest form12/10
Answers
The given ratio is,
[tex]\frac{12}{10}[/tex]Taking 2 as common from both 12 and 10 we have,
[tex]\frac{12}{10}=\frac{6\times2}{5\times2}=\frac{6}{5}[/tex]As there is no common factor between 6 and 5. it cannot be simplified further as fraction.
Thus, the answer is 6/5
A hot air balloon is sitting on the ground. Hot air was added causing the balloonto ascend at a rate of 4 feet per second for 60 seconds.A. Use integers to write an expression to determine the location of the airballoon relative to its starting location.
Answers
Since the rate in which the balloon ascends is constant this means that we can represent its altitude (the location relative to its starting point) as a linear function.
A linear funtion is given by:
[tex]y=mx+b[/tex]where m is the slope or rate of change and b is the y-intecept (the value of y when x=0).
In our case let x be the time it passes since the balloon started ascending and let y be its altitude. With this definition for the variables we conclude that in our case the rate of change is 4 and, since the ballon started on the ground, the valur of b is zero. Therefore the expression we need is:
[tex]y=4x[/tex]Note:
It is important to notice that this expression is only valid for:
[tex]0\leq x\leq60[/tex]This comes from the fact that that the balloon ascends at that rate for 60 seconds and the fact that the time can't be negative.
Answer: The answer to that would be y=4 x 60 or just write it as y= 240
But in expression form it would be 0<_x<_60
Hope this helps.
es? Explain your reasoning.
35. MP MODELING REAL LIFE A planet orbiting a star
at a distance such that its temperatures are right for
liquid water is said to be in the star's habitable zone. The
habitable zone of a particular star is at least 0.023 AU
and at most 0.054 AU from the star (1 AU is equal to the
distance between Earth and the Sun). Draw a graph tha
represents the habitable zone.
the distanco
Answers
♥it must orbit in a zone where liquid water is possible♥
How do I solve angle measurements and find the value of x on a polygon
Answers
ANSWER and EXPLANATION
We want to find out how to find the measurement of angles in a regular polygon.
To do this, first we have to know the total angle in the entire polygon.
To find this, we use the formula:
Total Angle = 180(n - 2)
where n = number of sides of the polygon
Now, after finding that total angle, we can find the individual angles in the polygon by dividing that total angle by the number of angles in the polygon.
For example, consider the diagram below:
Let us take that as a regular pentagon with 5 sides.
This means that n = 5.
Therefore, the total angle in the pentagon is:
Total Angle = 180(5 - 2)
Total Angle = 180 * 3 = 540 degrees.
Now, there are 5 angles in the polygon. Therefore, the value of x is:
[tex]x\text{ = }\frac{540}{5}=108^o[/tex]That is how to find the individual angles in a polygon.
what is 80% of 685?
Answers
To know the percentage of a quantity, we have to divide the percentage we want to know (in this case 80%), over 100%. Then, that part has to be multiplied by that result as it is the part that corresponds to 80%.
0. Dividing 80% over 100%
[tex]\frac{80}{100}=0.8[/tex]2. Multiplying by the quantity
[tex]0.8\times685=548[/tex]Answer: 548
Three years ago Maya was eleven times as old as her daughter Fiona. In four years time Maya will be four times as old as Fiona. How old are they now?
Answers
Let's call M the present age of Maya, and F the present age of Fiona.
Three years ago Maya was eleven times as old as Fiona. At that time, Maya's age was M-3, and Fiona's age was F-3. Thus, we have:
[tex]M-3=11(F-3)[/tex]Also, in four years Maya will be four times as old as Fiona. At that time, Maya's age will be M+4, and Fiona's age will be F+4. Thus, we have:
[tex]M+4=4(F+4)[/tex]Now, we need to solve the system of those two equations to find M and F. Subtracting the second equation from the first, we obtain:
[tex]\begin{gathered} M-3-(M+4)=11F-33-(4F+16) \\ \\ M-3-M-4=(11-4)F-33-16 \\ \\ -7=7F-49 \\ \\ -7+49=7F-49+49 \\ \\ 42=7F \\ \\ \frac{42}{7}=\frac{7F}{7} \\ \\ 6=F \\ \\ F=6 \end{gathered}[/tex]Now, we can use the above result to find M:
[tex]\begin{gathered} M+4=4(6+4) \\ \\ M+4=40 \\ \\ M+4-4=40-4 \\ \\ M=36 \end{gathered}[/tex]Therefore, now Maya is 40 years old and Fiona is 6 years old.
So my teacher teach us about this leason but I did not understand it at all can someone please teach me.
Answers
x + 2= 2(2x - 14 )
We will first find x
x + 2 = 4x - 28
collect like term
4x - x = 28 + 2
3x = 30
Divide both-side of the equation by 3
x = 10
But TU = 2x - 14
substitute x = 10 in the above and evaluate
TU = 2(10) - 14 = 20 - 14 = 6
Hence the length of TU is 6
to which set or sets of numbers does the number 5 belong?A. rational numbers only b. integers c. integers and rational numbers or D. integers,whole numbers, and rational numbers
Answers
5 belongs to the set of integers, whole numbers and rational numbers, so the answer is D.
function notations For the function below for which values of x does f (x)=3 ?
Answers
Answer:
x = 2
Explanation:
Each ordered pair in the function has the form (x, f(x)). So, the first coordinate is x and the second coordinate of each pair is f(x).
Then, the ordered pair that has a second coordinate equal to 3 or f(x) = 3 is the pair (2, 3). Therefore, the value of x that does f(x) = 3 is x = 2
So, the answer is x = 2
Find all the roots of the following equations2x^3+x^2-7x-2=0
Answers
Let's begin by listing out the information given to us:
2x³ + x² - 7x- 2 = 0
We will proceed to factorise, we have:
(x + 2)(2x² − 3x - 1) = 0
We will proceed to equate the factors to zero, we have:
x + 2 = 0⇒ x = -2
⇒ x = -2
2x² − 3x - 1 = 0
We will use the quadratic formula, we have:
[tex]\begin{gathered} 2x^{2}-3x-1=0 \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ a=2,b=-3,c=-1 \\ x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(2)(-1)}}{2(2)} \\ x=\frac{3\pm\sqrt[]{9+8}}{4}=\frac{3\pm\sqrt[]{17}}{4} \\ x=\frac{3\pm\sqrt[]{17}}{4}\Rightarrow x=\frac{3+\sqrt[]{17}}{4},\frac{3-\sqrt[]{17}}{4} \\ x=\frac{3+\sqrt[]{17}}{4},\frac{3-\sqrt[]{17}}{4} \end{gathered}[/tex]
The formula for finding the distance traveled, base on the speed and time, is D= RT, whereD is distanceR is rateT is timeUnits must be consistent. If the unit for D is miles and the unit for T is minutes, what must the units for R be?_______Solve this formula for R.R=______If a bicyclist rides for 140 minutes at an average speed of 14 miles per hour, how far was the ride, to 1 decimal place?_______ miles.At what speed must a bicyclist ride to cover 60 miles in 1.5 hours, to 1 decimal place?______ miles/hour
Answers
Given:
a)
The formula for finding the distance traveled, based on the speed and time, is D= RT, where D is distance, R is rate and T is time.
The unit for D is miles and the unit for T is minutes.
b)
A bicyclist rides for 140 minutes at an average speed of 14 miles per hour.
c)
A bicyclist ride to cover 60 miles in 1.5 hours.
Required:
a)
We need to find the units fir R.
b)
We need to find the distance.
c)
We need to speed.
Explanation:
a)
The given formula is
[tex]D=RT[/tex]Divide both sides of the equation by T.
[tex]\frac{D}{T}=\frac{RT}{T}[/tex][tex]\frac{D}{T}=R[/tex]Substitute D =miles and T= minutes in the formula.
[tex]miles=R\times minutes[/tex][tex]\frac{miles}{minutes}=R[/tex]We can rewrite miles by the hour. since 60 minutes = one hour
[tex]60\text{ }\frac{miles}{hour}=R[/tex]The most common unit of speed is miles/ hour.
Answer:
The unit of R is miles/hour.
b)
T =140 minutes and R =14 miles per hour.
Convert the minutes onto hours.
Divide 140 by 60 to convert units.
[tex]T=\frac{140}{60}hours[/tex][tex]T=\frac{7}{3}hours[/tex]Consider the formula.
[tex]D=RT[/tex]Substitute R =14 and T=7/3 in the formula.
[tex]D=14\times\frac{7}{3}[/tex][tex]D=32.7miles[/tex]Answer:
The bicycle was ridden 32.7 miles.
c)
D =60 and T =1.5
Consider the formula.
[tex]D=RT[/tex]Substitute D =60 and T =1.5 in the formula.
[tex]60=R\times1.5[/tex]Divide both sides by 1.5.
[tex]\frac{60}{1.5}=R\times\frac{1.5}{1.5}[/tex][tex]40=R[/tex]Answer:
The speed of the bicycle is 40 miles/hour.
Final answer:
The same set of data has been fit using two different functions. The following images show the residual plots of each function. A residual plot where the points are scattered around the x-axis with no pattern.© 2018 StrongMind. Created using GeoGebra. A residual plot where the points are scattered in a u-shape.© 2018 StrongMind. Created using GeoGebra. Which function is a better fit for the data, and why?Select the option that correctly answers both questions.
Answers
Answer:
Function B, because the points have more variation around the x-axis.
Step-by-step explanation:
Remember that if the points in a residual plot are randomly dispersed around the horizontal axis, a regression model is appropriate for the data. Therefore, the function that is the best fit for the data is function B, because the points have more variation around the x-axis.
Find fractional notation. 12.3% = (Simplify your answer. Type an integer or a fraction.)
Answers
The repeating decimal is 12.3.
To transform the repeating decimal into a fraction, first, we subtract all the digits 123 with the whole number 12
[tex]123-12=111[/tex]Then, we divide 111 by 9 because the repeating decimal has one digit only.
[tex]\frac{111}{9}[/tex]Hence, the fractional notation is 111/9 %.Jeremy needs to mail five Christmas packages to his family. The first two weigh 3 pounds each and theother three weigh 2 pounds each. If two-day shipping costs $0.37 per ounce and ground shippingcosts $0.30 per ounce, how much will he save by shipping all of his packages by ground rather thantwo-day?
Answers
We know that
• The first two weigh 3 pounds.
,• The other three weigh 2 pounds,.
,• Two-day shipping costs $0.37 per ounce.
,• Ground shipping costs $0.30 per ounce.
We also know that 1 pound is equal to 16 ounces.
So, the weights are
[tex]3\cdot16=48[/tex][tex]2\cdot16=32[/tex]So, the cost of each package of 48 ounces is
[tex]48\cdot0.37=17.76[/tex]Therefore, each 3 pounds package costs $17.76 with two-day shipping.
We repeat the process for the other packages.
[tex]32\cdot0.37=11.84[/tex]Therefore, each 2 pounds package costs $11.84 with two-day shipping. So, the total is
[tex]2(17.76)+3(11.84)=35.52+35.52=71.04[/tex]Sending all packages with two-day shipping costs $71.04.
We repeat all the process for ground shipping.
[tex]2\cdot48\cdot0.30=28.8[/tex][tex]3\cdot32\cdot0.30=28.8[/tex]Both services cost $28.8 each, so the total is $57.6.
IF we compare both services, we have
[tex]71.04-57.6=13.44[/tex]Therefore, he will save $13.44.Find the slope of the tangent line to f(x) when x= -3. Two points on the line tangent to f(x) at x = -3 are: (-4,-7) and (1,3).
Answers
When x = -3, the line that's tangent to f(x) is shown in the given image. So, in order to find the slope of f(x) at x = -3, we need to find the slope of that line.
The slope of a line is given by the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]Now, notice that the points (-4,-7) and (1,3) belong to the tangent line. Therefore, we can use them to find the slope:
y₂ = 3
y₁ = -7
x₂ = 1
x₁ = -4
So, we have:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-7)}{1-(-4)}=\frac{3+7}{1+4}=\frac{10}{5}=2[/tex]Therefore, the slope is 2.
Describe the association represented in the graph.no associationstrong, negativestrong positive D weak, negative.
Answers
Given:
the scatter plot is shown in the graph
We will Describe the association represented in the graph.
As shown, when drawing a line of best fit of the points, the line will be with a negative slope that will be a strong negative
So, the answer will be: strong, negative
POS The radius of a cylindrical box of oatmeal is 5 centimeters. The height of the box is 18 centimeters. 5 cm 18 cm QATMEAL Which measurement is closest to the total surface area of the oatmeal box in square centimeters? A 597 cm2 B 361 cm? C 314 cm? D 723 cm?
Answers
Explanation
Step 1
to find the area, imagine the unfolded cylindrical box
Let
length=18 cm
width=2*pi*radius
radius= 5 cm
[tex]\begin{gathered} \text{width}=2\cdot\pi\cdot5\text{ cm} \\ \text{width}=10\cdot\pi\cdot\text{cm} \\ \text{width}=31.4\text{ cm} \end{gathered}[/tex]Step 2
now, the total area would be
[tex]\begin{gathered} \text{total area= area of the rectangle+twice area of the circle} \\ \text{replacing} \\ \text{total area=(length}\cdot widht9+2(\pi\cdot radius^2) \\ \text{total area=(18 cm}\cdot31.4\text{ cm)+2(3.14}\cdot25cm^2) \\ \text{total area=565.2 cm}^2+157.07cm^2 \\ \text{total area=722.27 cm}^2 \\ \text{rounded} \\ 723cm^2 \end{gathered}[/tex]I hope this helps you
PERCENT PROBLEMS The local toy store manager found all the wrong percents marked on the following toys. The ball is 35% off, the game system is 45% off, the doll and airplane are both 65% off. Find the sale prices if the dump truck's sale price was the original price of the doll and the ball. The original price of the game system was $280 more than the sale price of the dump truck and $10 less than the original price of the airplane. to spe PLATTEGRONY
Answers
The sale prices of the toys obtained from their original prices and the percentage discounts are;
Toy [tex]{}[/tex] The selling price of the
Truck [tex]{}[/tex] $16.99
Ball [tex]{}[/tex] $11.04
Doll [tex]{}[/tex] $5.95
Game system [tex]{}[/tex] $192.97
Airplane [tex]{}[/tex] $107.41
What is a percentage?A percentage is the expression of a ratio or fraction between two quantities in which the denominator of the fraction is 100.
From the a similar question online, we have;
The price of the truck = $16.99
The original price of the doll = $16.99
Original price of the ball = $16.99
Original price of the game system = $280 + $16.88 = $296.88
Original price of the airplane = $296.88 + $10 = $306.88
The sale prices are therefore;
Sale price of the ball = $16.99 - 35% × $16.99 ≈ $11.04
Sale price of the doll = $16.99 - 65% × $16.99 ≈ $5.95
Sale price of the game system = $296.88 - 35% × $296.88 ≈ $192.97
Sale price of the airplane = $306.88 - 65% × $306.88 = $107.41
Learn more about percentages here:
https://brainly.com/question/24339661
#SPJ1
Parallelogram ABCD has vertices A(8,2), B(6,-4), and C(-5,-4). Find the coordinates of D.
Answers
Given:
ABCD is the parallelogram.
vertices are A(8,2), B(6,-4), and C(-5,-4)
We know the diagonals of the parallelogram bisect each other.
Find the midpoint of AC.
[tex]\begin{gathered} m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ (x_1,y_1)=(8,2) \\ (x_2,y_2)=(-5,-4) \\ m=(\frac{8-5}{2},\frac{2-4}{2}) \\ m=(\frac{3}{2},-\frac{2}{2}) \\ m=(\frac{3}{2},-1) \end{gathered}[/tex]Now, the midpoint of BD is given as,
[tex]\begin{gathered} m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ m=(\frac{3}{2},-1) \\ B\mleft(6,-4\mright),D(x,y) \\ (\frac{3}{2},-1)=(\frac{6+x}{2},\frac{-4+y}{2}) \\ \frac{6+x}{2}=\frac{3}{2},\frac{-4+y}{2}=-1 \\ 6+x=3,-4+y=-2 \\ x=-3,y=2 \end{gathered}[/tex]The coordinate of D is (-3,2).
What is the length of the dotted line in the diagram below? Round to the nearesttenth.
Answers
From the given figure
The rectangle has a width of 3 and its length is the hypotenuse of a right triangle with legs 5 and 7
Then we will find at first the hypotenuse of the triangle using the Pythagoras Theorem
[tex]\begin{gathered} L=\sqrt[]{7^2+5^2} \\ L=\sqrt[]{49+25} \\ L=\sqrt[]{74} \end{gathered}[/tex]Now, to find the dotted line we will do the same with the length and the width of the rectangle
[tex]\begin{gathered} D=\sqrt[]{L^2+W^2} \\ L=\sqrt[]{74},W=3 \\ D=\sqrt[]{(\sqrt[]{74})^2+(3)^2} \\ D=\sqrt[]{74+9} \\ D=\sqrt[]{83} \\ D=9.110433579 \end{gathered}[/tex]Round it to the nearest tenth
The length of the dotted line is 9.1
a recipe for cookies calls for 1/4 cup of brown sugar for one batch how many batches can be made with 3/8 cups of brown sugar
Answers
1) Gathering the data
1/4 cup of brown sugar ------ 1 batch
3/8 ---------------------------------- x
2) Let's solve this problem by setting a proportion to solve this:
1/4 cup of brown sugar ------ 1 batch
3/8 ---------------------------------- x
Since it is a proportion then we can cross multiply those fractions:
[tex]\begin{gathered} \frac{1}{4}x=\frac{3}{8} \\ 8x=12 \\ \text{Divide both sides by 8} \\ x=\frac{12}{8}\text{ =}\frac{3}{2} \end{gathered}[/tex]3) So with 3/8 cups of sugar, we can make 3/2 batches or 1.5 batches
The population of a small town in central Florida has shown a linear decline in the years 1985-1997. In 1985 the population was 46000 people. In 1997 it was 38080 people.
Answers
Given:
(1985,46000)
(1997,38080)
(a)
General linear equation is:
[tex]y=mx+c[/tex]here y represent the population and x represent time so equation is:
[tex]p=mt+c[/tex][tex]\begin{gathered} \text{slope}=m \\ m=\frac{p_2-p_1_{}}{t_2-t_1} \end{gathered}[/tex][tex]\begin{gathered} (p_1,t_1)=(1985,46000) \\ (p_2,t_2)=(1997,38080) \end{gathered}[/tex]
slope is:
[tex]\begin{gathered} m=\frac{p_2-p_1}{t_2-t_1} \\ m=\frac{38080-46000}{1997-1985} \\ m=\frac{-7920}{12} \\ m=-660 \end{gathered}[/tex]So equation is:
[tex]\begin{gathered} p=mt+c \\ p=-660t+c \end{gathered}[/tex]Point (1985,46000)
[tex]\begin{gathered} p=-660t+c \\ p=46000 \\ t=1985 \\ p=-660t+c \\ 46000=-660(1985)+c \\ c=46000+1310100 \\ c=1356100 \end{gathered}[/tex]So equation is:
[tex]\begin{gathered} p=mt+c \\ p=-660t+1356100 \end{gathered}[/tex](b)
population in 2000.
[tex]t=2000[/tex][tex]\begin{gathered} p=mt+c \\ p=-660t+1356100 \\ t=2000 \\ p=-660(2000)+1356100 \\ p=36100 \end{gathered}[/tex]so population in 2000 is 36100.
a. Use symbols and proper notation to name the angle shown on thegraph. Write all three correct names.
Answers
The correct names are:
∠RST (the three points involved with the vertex at the middle)
∠TSR (same as the previous name, but with other order)
∠S (the letter of the vertex)
I need to know if it’s A b c or D
Answers
The value of x is 1.
Step - by - Step Explanation
What to find? The value of x.
Given:
From the diagram,
• Inscribed angle = 70°
,• arc length = 141x - 1
The formula we can use to solve the given problem is;
[tex]\text{Inscribed angle =}\frac{1}{2}(\text{ length of arc)}[/tex]Substitute the values into the formula.
[tex]70=\frac{1}{2}(141x\text{ - 1)}[/tex]Simplify the above.
To simplify, first multiply both-side of the equation by 2.
[tex]70\times2=\cancel{2}\times\frac{1}{\cancel{2}}(141x-1)[/tex]140 = 141x - 1
Add 1 to both-side of the equation.
140 + 1 = 141x -1 + 1
141 = 141x
Divide both-side of the equation by 141.
[tex]\frac{\cancel{141}x}{\cancel{141}}=\frac{141}{141}[/tex]x = 1
5.1234 to the thousandths 6.6666 to the thousandths
Answers
Answer:
[tex]\begin{gathered} 5.1234\approx5.123 \\ 6.6666\approx6.667 \end{gathered}[/tex]Explanation:
We want to round up the given number to the nearest thousandths.
[tex]5.1234[/tex]To the nearest thousandth which is also to 3 decimal place, we have;
[tex]\approx5.123[/tex]Also;
[tex]6.6666[/tex]To the nearest thousandth, we have;
[tex]6.667[/tex]Note that numbers from 5 above will be rounded up, while numbers below 5 will be rounded down.
For any number a, |a|=A-1B. sqrt a^2C. 1D. a^2
Answers
EXPLANATION
The module of any number, as in this case |a|, is the same number with positive sign, in this case the appropiate option is sqrt(a^2) ---> OPTION B.
which one of the following options is true when considering the expansion of the binomial expression (x+y)^4?A) The sum of the exponents of each term of the expansion of (x+y)^4 is 5.B) The expansion of (x+y)^4 will yield 4 termsC) The last term of the expansion of (x+y)^4 is y^4D) The coefficients of the expansion of (x+y)^4 are: 1,4,4,1.
Answers
Given:
[tex](x+y)^4[/tex]To Determine: The binomial expansion of the given
Solution
Using binomial expansion formula below
[tex](x+y)^n=\sum_{k\mathop{=}0}^n(^n_k)x^{n-k}y^k[/tex]