Answer:
[tex]log_5 \ 125 = 3[/tex]
Step-by-step explanation:
[tex]log_5 \ 125 = log_2 \ 5^3 = 3 \times log_5 \ 5 = 3 \times 1 = 3[/tex]
The value of [tex]$\log _{5} 125$[/tex] can be estimated utilizing the logarithm rule. The value of [tex]$\log _{5} 125$[/tex] exists 3.
What is a logarithm?The logarithm stands for the inverse function of exponentiation. In logarithm base must be raised to yield a given number for an exponent.
Given:
[tex]$\log _{5} 125$[/tex]
Estimate the value of the given logarithm, we get
[tex]$\log _{5} 125=\log _{5}(5)^{3}$[/tex]
[tex]$\log _{5} 125=3 \log _{5} 5$[/tex]
From logarithm rule [tex]$\log m^{n}=n \log m$[/tex], we get
[tex]$\log _{5} 125=3 \times 1$[/tex]
[tex]$\log _{5} 125=3$[/tex]
Therefore, the value of [tex]$\log _{5} 125$[/tex] is 3.
To learn more about logarithm
https://brainly.com/question/26240264
#SPJ2
Joe drives for 3 hours and covers 201 miles. In miles per hour, how fast was he driving?
Answer:
67 mph
Step-by-step explanation:
201/3 = 67
What is the value of the expression 3m-4.2 If m equals 2.1
Answer:
2.1
Step-by-step explanation:
Given :
3m-4.2 where, m=2.1
Now,
3(2.1)-4.2
6.3-4.2
2.1
Answer is 2.1
Chung has 6 trucks and 5 cars in his toy box. Brian has 4 trucks and 5 cars in his toy box.
Which is the correct comparison of their ratios of trucks to cars?
StartFraction 6 Over 4 EndFraction less-than StartFraction 5 Over 5 EndFraction
StartFraction 6 Over 4 EndFraction greater-than StartFraction 5 Over 5 EndFraction
StartFraction 6 Over 5 EndFraction less-than StartFraction 4 Over 5 EndFraction
StartFraction 6 Over 5 EndFraction greater-than StartFraction 4 Over 5 EndFraction
Given:
Chung has 6 trucks and 5 cars in his toy box.
Brian has 4 trucks and 5 cars in his toy box.
To find:
The correct comparison of their ratios of trucks to cars.
Solution:
The ratio of trucks to cars is defined as:
[tex]\text{Ratio}=\dfrac{\text{Number of trucks}}{\text{Number of cars}}[/tex]
Chung has 6 trucks and 5 cars in his toy box. So, the ratio of trucks to cars is:
[tex]\text{Ratio}=\dfrac{6}{5}[/tex]
Brian has 4 trucks and 5 cars in his toy box.
[tex]\text{Ratio}=\dfrac{4}{5}[/tex]
We know that,
[tex]6>4[/tex]
[tex]\dfrac{6}{5}>\dfrac{4}{5}[/tex]
Therefore, the correct option is D.
Answer:
what the guy above me said
Step-by-step explanation:
so yeah he is right points
Can someone answer with steps and explanation? Thanks.
Answer:
[tex]x=-16\text{ or } x=7[/tex]
Step-by-step explanation:
Since ΔABC is mapped onto ΔDEF, we can write that:
[tex]\Delta ABC\cong \Delta DE F[/tex]
By CPCTC:
[tex]\angle A\cong \angle D[/tex]
And since ΔABC is isosceles with Vertex C:
[tex]\angle A \cong \angle B[/tex]
We are given that:
[tex]m\angle D=34[/tex]
Hence:
[tex]m\angle A=34=m\angle B[/tex]
We are also given that:
[tex]m\angle C=x^2+9x[/tex]
The interior angles of a triangle must sum to 180°. Thus:
[tex]m\angle A+m\angle B+m\angle C=180[/tex]
Substitute:
[tex](34)+(34)+(x^2+9x)=180[/tex]
Simplify:
[tex]68+x^2+9x=180[/tex]
Isolate the equation:
[tex]x^2+9x-112=0[/tex]
Factor:
[tex](x+16)(x-7)=0[/tex]
Zero Product Property:
[tex]x+16=0\text{ or } x-7=0[/tex]
Solve for each case:
[tex]x=-16\text{ or } x=7[/tex]
Testing the solutions, we can see that both yields C = 112°.
Hence, our solutions are:
[tex]x=-16\text{ or } x=7[/tex]
Find the area of the following shape:
Answer:
36cm^2
Step-by-step explanation:
total area: 6x(4+3)=42
total area excluding the space: 42-(2x3)=36
Answer:
36 cm squared
Step-by-step explanation:
To solve this problem, I first construct a line. (shown in yellow in the first photo)
I then find the area of the top rectangle. (6 cm * 4 cm = 24 cm squared.)
Next, I find the area of the lower rectangle. But...to do that I have to find the length of the line that I constructed. To do this, I do 6cm-2cm=4cm.
Then I can find the area of the lower rectangle. (4cm*3cm=12cm squared.)
add up the area of both of the rectangles and.........12+24=36 cm squared
Need help finding the factor of 2y^2-2y-4
Answer:
hope it helps you............
Answer:
2(y - 2)(y + 1)
Step-by-step explanation:
Given
2y² - 2y - 4 ← factor out 2 from each term
= 2(y² - y - 2) ← factor the quadratic
Consider the factors of the constant term (- 2) which sum to give the coefficient of the y- term (- 1)
The factors are - 2 and + 1, since
- 2 × 1 = - 2 and - 2 + 1 = - 1 , then
y² - y - 2 = (y - 2)(y + 1)
Then
2y² - 2y - 4 = 2(y - 2)(y + 1) ← in factored form
21(2-y)+12y=44 find y
Answer:
[tex]\textbf{HELLO!!}[/tex]
[tex]21\left(2-y\right)+12y=44[/tex]
[tex]42-21y+12y=44[/tex]
[tex]~add ~similar\:elements[/tex]
[tex]42-9y=44[/tex]
[tex]Subtract~42~from~both~sides[/tex]
[tex]42-9y-42=44-42[/tex]
[tex]-9y=2[/tex]
[tex]Divide\:both\:sides\:by\:}-9[/tex]
[tex]\frac{-9y}{-9}=\frac{2}{-9}[/tex]
[tex]y=-\frac{2}{9}[/tex]
----------------------
hope it helps...
have a great day!
A road has a scale of 1:50 000 The length of a road on the map is 8.5cm.Work out the length of the real road in kilometres
Answer:
ok so
8.5*150000
1275000 cm into kilometers is
12.75 kilometers
Hope This Helps!!!
Rectangle ABCD translates 4 units down and 2 units to the right to form rectangle A'B'C'D'. The vertices of rectangle ABCD are labeled in alphabetical order going clockwise around the figure. If AB = 3 units and AD = 5 units, what is the length of B'C'?
Answer:
The length of BC is 14 units.Step-by-step explanation:
[tex]hope \: \: it \: \: helps} \beta \alpha \infty [/tex]
The length of B'C' is 0 units.
What is translation?It is the movement of the shape in left, right, up, and down direction.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The length of AD = 5 units.
Since the rectangle translates down by 4 units,
The length of A'D' =5 units.
The width of the original rectangle is AB, which is 3 units.
Since the rectangle translates to the right by 2 units,
The width of the new rectangle = 3 units.
Now,
The length of B'C' is the same as the length of AD', which is 5 units.
Subtracting 5 units from 5 units gives us a length of 0 units.
Thus,
The length of B'C' is 0 units.
Learn more about translation here:
https://brainly.com/question/12463306
#SPJ7
If using the method of completing the square to solve the quadratic equation x^2+15x+21=0, which number would have to be added to "complete the square"?
Step-by-step explanation:
the answer is in the above image
Answer:
my answer is 225/5 sorry comments for wrong
A person walks 1/6 mile in 1/18 hour.
The person's speed is _ miles per hour.
This Is What I Got!
Hope This Helps! :)
Have A Good Day!!
And If You Can I Wouldn't Mind A Brainliest! :))
Answer:
Divide 1/6 miles to 1/12hour since u wanna find our miles per hour
So it’ll be : 1/6 / 1/12
= 1/6 x 12/1
= 2 miles
Solve the equation 2x^2 + 3 – 41 = –15 to the nearest tenth.
Hellllpppp
9514 1404 393
Answer:
x = {-4.4, +2.9}
Step-by-step explanation:
We assume you want to solve ...
2x^2 +3x -41 = -15
Adding 41 and factoring out the leading coefficient gives ...
2(x^2 +3/2x) = 26
Dividing by 2 makes it ...
x^2 +3/2x = 13
We can add the square of half the x-coefficient to "complete the square."
x^2 +3/2x +(3/4)^2 = 13 +(3/4)^2
(x +3/4)^2 = 13.5625 . . . . write the left side as a square
x +3/4 = ±√13.5625 . . . . . take the square root
x = -0.75 ±3.683 = {-4.433, +2.933} . . . . subtract 3/4 and evaluate
The solutions are approximately x = -4.4 and x = 2.9.
Find the distance between the pair of points: (0,1) and (1,0)
Answer:
sqrt(1^2 + 2^2)
[tex]\sqrt{2}[/tex]
Step-by-step explanation:
The storage container below is in the shape of a rectangular prism with a height of 6 feet and a length that is 2 feet more than its width.
Recall that the formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height.
Write the equation that represents the volume of the storage container in terms of its width.
A.
V = 6w2 + 12w
B.
V = 6w2 - 12
C.
V = 6w2 + 12
D.
V = 6w2 - 12w
Answer:
A
Step-by-step explanation:
Step 1, setting variables:
We already know the exact height of the prism: 6 feet. We can set the unknown width as variable x, and length as x+2 (length is two feet more than width).
Step 2, writing equations:
Great! We have everything now. Let us write the equation by substituting our variables in:
[tex]V=l*w*h\\V=6w(w+2)\\[/tex]
Ok! Let us expand the equation:
[tex]V=6w^2+12w[/tex]
[tex]\fbox{A}[/tex]
I hope this helps! Let me know if you have any questions :)
HELP ME PLEASE IF YOU DO YOU WILL GET BRAINLESS AND PLEASE EXPLAIN THE BEST YOU CAN
Answer:
<3=75°
Step-by-step explanation:
Angle 3 and angle 2x+95 are supplementary( supplementary angles add up to 180°)
So <3+2x+95=180
<3+2x=180-95
<3+2x=85( let's call this equation 1)
Next, angle 5 and angle 8x+71 are opposite angles (opposite angles are equal) therefore <5=8x+71
Now, <3 and <5 are co-interior angles(co-interior angles are supplementary)
So <3+8x+71=180
<3+8x=180-71=109
Thus, <3+8x=109(let's call this equation 2)
Now solving equation 1 and 2 simultaneously:
Make <3 the subject of equation 1
<3=85-2x
Put <3=85-2x into equation 2
85-2x+8x=109
6x=24
x=24/6=4
Now, remember that angle 2x+95 becomes
2(4)+95
8+95=103°
Therefore<3=180-105=75°
A fast-food chain claims one medium order of its onion rings weighs 114 grams. Patrice thinks she is getting less than what the restaurant advertises. She weighs the next 16 random orders of onion rings before she eats them and finds the sample mean is 112.4 grams and the standard deviation is 7.63 grams. What conclusion can be drawn α = 0.10?
Answer:
Patrice does not have sufficient evidence to reject the fast-food chain's claim.
Step-by-step explanation:
unless she already ate some fries, not enough evidence
 Marsha has a bag that contains 4 green marbles, 8 yellow marbles , and 20 red marbles . If she chooses one marble from the bag, what is the probability that the marble is not red?
PLEASE HELP IF YOURE GOOD AT GEOMETRY!!
Answer:
C. 3/8
HOPE THIS HELPS :)
Answer:
c. 3/8
Step-by-step explanation:
first you need the denomerator by adding all marbles together which equals 32. now for the munerator you need the sum of the green and yellow marbles. this equals 12. so your fraction is 12/32. next we simplify. we can divide both numbers by 4. getting us a fraction of 3/8.
i need to see the steps for simplifying 3(m-5)+m
Answer:
4m - 15
Step-by-step explanation:
a( x + y) = ax + ay
[tex]3( m - 5 ) + m\\\\3m - 15 + m \\\\4m - 15[/tex]
Answer:
4m-15
Step-by-step explanation:
Distrubite 3 through the parentheisis
3m-15+m
Collect like terms
4m-15
Hi, could someone help me solve this. so the question says to find the area of the shaded part (in black) , in terms of pie (π). the length of the square is 12 cm. the radius of the circle is 6cm. i came with the answer of (144-36π)/4. is this ok? below is the picture of the question.
Answer:
yes but can be simplified
Step-by-step explanation:
area of shaded part = ( area of square - area of circle ) / 4
= [tex]\frac{12^2-\pi (6)^2}{4}[/tex]
= [tex]\frac{144-36\pi }{4}[/tex]
= [tex]\frac{144}{4}[/tex] - [tex]\frac{36\pi }{4}[/tex]
= 36 - 9π
Joe told Mickey he got an hourly raise at work and his new rate will be $10.25 per hour. Mickey wants to know what Joe’s hourly rate was before his raise. If r represents the amount of the raise, which expression represents Joe’s hourly rate before his raise?
Answer:10.25-r= hourly rate
Step-by-step explanation:
ASAP there are three marbles in a bag. One is red and two are black. What is the probability of picking a black marble first, putting it back in the bag and then picking a black marble? Use the following probability to find the answer.
Answer:
[tex] \frac{4}{9} [/tex]
Step-by-step explanation:
[tex]p = \frac{favorable \: outcomes}{total \: outcomes} = \frac{4}{9} [/tex]
=============================================================
Explanation:
The probability you get a black marble on the first selection is 2/3 since we have 2 black marbles out of 2+1 = 3 total.
We put the marble back and then we have 2/3 as the probability of selecting another black marble on the second try. Nothing has changed because we put the marble back. That means the events are independent.
So we get (2/3)*(2/3) = 4/9 as the probability of selecting 2 black marbles in a row (with replacement).
to train for a race, you plan to run 1 mile the first week and double the number of miles each week for five weeks. How many miles will you run for the 5th week. math problem
Answer:
16 Miles
Step-by-step explanation:
For every week you simply multiply the number of miles from the previous week by 2, therefore
Week 1: 1
Week 2: 2
Week 3: 4
Week 4: 8
Week 5: 16
If Sarah turns 15 on august 27 and her graduation year is 2024 how old will she be when she graduates high school?
Answer:
She will be 17
Step-by-step explanation:
My sister is like that but she's graduating in 22'
It sort of depends where Sarah lives -.-
But if she starts high school when she's 15 (in 2021) and she graduates in 2024 it means high school is three years.
So 15 plus 3.
Sarah will be 18 when she graduates high school.
he speeds (in MPH) of automobiles traveling in a city are given below:
20, 35, 42, 52, 65, 49, 24, 37, 23, 41, 50, 58
The mean speed of the cars is
Answer:
Mean speed = 41.3 mph
Step-by-step explanation:
Given that,
The speeds of an automobiles are given below:
20, 35, 42, 52, 65, 49, 24, 37, 23, 41, 50, 58
We need to find the mean speed of the cars.
Mean = sum of observations/ no. of observation
[tex]M=\dfrac{20+35+42+52+65+49+24+37+23+41+50+58}{12}\\\\M=41.3[/tex]
So, the mean speed of the cars is equal to 41.3 mph.
The ice cream man just ended his shift for the day. Let 1/2x^2 6/11x + 8 represent the amount of chocolate ice cream bars he sold. Let 5/9x^2 + 2/3 represent the amount of vanilla ice cream bars he sold. Finally let 1/3x^2 + 4x + 4/3 represent the amount of strawberry ice cream bars he sold. Select all the statements that are true
a. The total amount of ice cream bars sold can be represented by the expression 25/18x^2+ 50/11x +10
b. The total amount of ice cream bars sold can be represented by the expression 25/18x^2 + 172/33x +28/3
c. He sold 1/6x^2 + 50/11x + 28/3 more chocolate than strawberry ice cream bars.
d. He sold 1/6x^2 - 38/11x + 20/3 more chocolate than strawberry ice cream bars.
Answer:
A and D
Step-by-step explanation:
Total ice cream bars sold = sum of chocolate sold , vanilla and strawberry ice-creams sold.
=(1/2)x2 + (6/11)x + 8 + (5/9)x2 + (2/3) +(1/3)x2 + 4x +(4/3) (Given in the question)
=(25/18)x2 + (50/11)x + 10 (Adding terms corresponding to x2,x ,constant respectively)
Difference in chocolate and strawberry bars =[ (1/2)x2 + (6/11)x + 8] - [(1/3)x2 + 4x +(4/3)]
= (1/6)x2 - (38/11)x +(20/3)
So, the correct options are A and D
Moving to another question will save this response.
1 points
Save Answer
Question 12
Mr Espent 65% of his salary on household expenses, and 15% of the remainder on travelling expenses and was finally left with R9 500. How much was his salary?
Answer:
rs.1680.67
Step-by-step explanation:
His salary = x
remaining % = 100 - 65 = 35%
= 100 - 15 = 85%
x × 35/100 × 85/100 = 500
x = 1680.67
Six consecutive numbers add up to a total of 69.what is the highest of these numbers?
Answer:
14
Step-by-step explanation:
9+10+11+12+13+14=69
The [tex]HIGHEST[/tex] of these numbers is [tex]14[/tex]
Let the [tex]CONSECUTIVE[/tex] numbers be : [tex]a, a+1, a +2,a+3,a+4,a+5[/tex]
Taking the sum :
[tex]a + a + 1 + a + 2 + a + 3 + a + 4 + a + 5 = 69\\6a + 15 = 69\\6a = 69 - 15\\6a = 54\\a = 54 / 6\\a = 9[/tex]
[tex]HIGHEST[/tex] value = [tex]a + 5 = 9 + 5 = 14[/tex]
Hence, [tex]HIGHEST[/tex] value = [tex]14[/tex]
Learn more : https://brainly.com/question/15974141
Can you solve this problem
Answer:
x = 18
Step-by-step explanation:
8 x 18 - 3 = 141
0.7(1.5 + y) = 3.5y - 1.47
Answer:
y = 0.9
Step-by-step explanation:
1.05 + 0.7y = 3.5y - 1.47
-3.5y + 0.7y = -1.47 - 1.05
-2.8y = -2.52
y = 9/10 = 0.9
Answer:
[tex]\textbf{HELLO!!}[/tex]
[tex]0.7\left(1.5+y\right)=3.5y-1.47[/tex]
[tex]1.05+0.7y=3.5y-1.47 \gets \textsl{Expand}[/tex]
[tex]1.05+0.7y-1.05=3.5y-1.47-1.05 \gets Subtract\; 1.05 \from\:both\:sides[/tex]
[tex]0.7y=3.5y-2.52[/tex]
[tex]0.7y-3.5y=3.5y-2.52-3.5y[/tex]
[tex]\mathrm{Subtract\:}3.5y\mathrm{\:from\:both\:sides} \nwarrow[/tex]
[tex]-2.8y=-2.52[/tex]
[tex]\frac{-2.8y}{-2.8}=\frac{-2.52}{-2.8} \hookleftarrow \mathrm{Divide\:both\:sides\:by\:}-2.8[/tex]
[tex]\boxed{\boxed{\underline{\textsf{\textbf{y=0.9}}}}}[/tex]
[tex]\bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet[/tex]
[tex]\textbf{HOPE IT HELPS}[/tex]
[tex]\textbf{HAVE A GREAT DAY!!}[/tex]
Alec bakes spherical rolls of bread. Each roll is about 8cm
wide. What is the approximate volume of each roll? Use
3.14 to approximate a.
Answer:
Step-by-step explanation:
2143.57