Answer:
29037.036 miles
Step-by-step explanation
There are two possible ways to solve this problem.
The first option starts with the $2800 dollars for the years. You first want to divide this by $2.70, because it will give you the amount of gallons of gas you can buy with that money.
2800/2.70 = 1037.037
This means you can buy 1037.037 gallons of gas in the year. Now you need to convert this to miles by multiplying by the amount of miles per gallon.
1037.037 x 28 = 29037.036 gallons
The second way to look at this is dimensional analysis. If you have learned this, then continue on reading this, but if you haven't I might only confuse you. I only suggest this because it can make it a little easier.
For the dimensional analysis, you need to start with what you are given and move to what you need to know, so you will start with the $2800 dollars and move to gallons. $2.70 per gallon and 28 miles per gallon are your conversion factors.
Set it up like this:
[tex]2800 dollars * \frac{1 gallon}{2.70 dollars} * \frac{28 miles}{1 gallon} = 29037.036 miles[/tex]
This allows the equation to be more organized, and you can check your work by canceling the units.
Hope this helps.
1. Which of the following is a true statement?
a. A perfect square is a number whose
square root is, an even number.
b. The inverse of squaring a number is to
divide the number by 2.
C. To square a number, multiply the number by
itself.
d. All of the above.
Thank you so much
Answer:
C. To square a number, multiply the number by itself.
Answer:
[C] To square a number, multiply the number by itself.
Step-by-step explanation:
To square a number you multiply it by itself.
Let's go through all answer:
[A] A perfect square is a number whose square root is, an even number.
Explain for [A]:
It incorrect because perfect squares can be odd or even
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[B] The inverse of squaring a number is to divide the number by 2.
Explain for [B]:
It incorrect because square roots are made by multiplying the number to itself.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[D] All of the above
Explain for [D]
Know that [A] and [B] is wrong you can know that [D] is 100% wrong.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Lenvy~
Help picture below problem 12
José plotted points on a coordinate plane to represent the vertices of a rectangle. The first
two points José plotted are shown below.
Jose's rectangle must have equal and parallel opposite sides
The coordinates of the other points could be C(7,5) and D(7,1)
How to determine the other points?The coordinates are given as;
A = (2,5).
B = (2,1).
To form a rectangle, each of the remaining points must have the same y-coordinates as points A and B.
So, we have:
C = (x,5)
D = (x,1)
Also, the remaining points must have the same x-coordinates.
i.e.
Cx = Dx
From the list of options, we have:
C(7,5) and D(7,1)
Hence, the coordinates of the other points could be C(7,5) and D(7,1)
Read more about rectangles at:
https://brainly.com/question/12500692
find the area of circle o if DCBO is a rectangle and DB measure 10 units
Answer:
[tex]100\pi[/tex]
Step-by-step explanation:
Step 1: Identity the radius.
Since O is the center of the circle, and C and E lie on the circumference, OC and OE are the radii of the circle and thus,
OC=OE.
Step 2: Consider the rectangle.
All diagonals in a rectangle are congruent so this means
DB= OC ( OC is also a diagonal).
Thus, OC= 10 units.
Step 3: Analyze
So this means OE is also 10 units as well.
Since we know the length of the radius, Use the area of circle,
[tex]\pi {r}^{2} [/tex]
[tex]\pi( {10}^{2} ) = 100\pi[/tex]
So the area of a circle is 100 pi.
Answer:
314.2 square units
Step-by-step explanation:
The diagonals of a rectangle are the same length, so segment OC is the same length as segment DB: 10 units. OC is a radius of the circle, which means the circle's radius is 10 units.
The area of a circle is given by ...
A = πr²
A = π(10 units)² = 100π units²
A ≈ 314.2 units²
The area of circle O is about 314.2 square units.
The sum of two numbers is 35. The smaller number is 11 less than the larger number. What are the numbers?
Answer:
12 & 23
Step-by-step explanation:
Let's make both of the statements into equations by making the numbers x & y.
"The sum of two numbers is 35" which means the two numbers added together is 35. So, x + y = 35.
"The smaller number is 11 less than the larger number." Let's make x the smaller number. So, x = y - 11.
So our equations are x + y = 35 and x = y -11. Using substitution, we can plug in (y-11) for x in the first equation.
y + y - 11 = 35. Combine the (y + y) to get 2y - 11 = 35. Add 11 to both sides of the equation, to get 2y = 46. Divide both sides by 2 to get y = 23.
Now, we can substitute 23 for y in either one of the equations, but I'm going to use the second one. x = y - 11 or x = 23 - 11 which equals 12.
Your 2 numbers are 12 and 23. Hope this helps! :)
Tim read 70% of his book containing 230 pages. How many pages does he have left?
Answer:
69
Step-by-step explanation:
To do this, you want to first find how many pages he has read
So, to get that you want to multiply 230 by 70% or 0.7 (70% = 0.7 because to get the percent, you multiply the number by 100)
230 * 0.7 = 161
BUT, since you want to find how many pages he has left, you subtract the amount of pages he has read by how many pagest here are in total like so:
230 - 161 = 69 pages left
If you have any questions feel free to ask in the comments, and if this helped it would be appreciated if you left a brainliest :)
How many patients had more than 5 cavities?
Answer:
2 patients had more than 5 cavities.
step-by-step explanation:
5 cavities = 26 cavities = 07 cavities = 2Here cavities > 5
so only 2 patients had more than 5 cavities also as had total 7 cavities.
Answer:
2 patients had more than 5 cavities
Step-by-step explanation:
Each dot represents a different patient.
"More than 5" means numbers greater than 5 (so from 6 onwards).
From inspection of the dot plot, there are 2 dots above all the numbers that are greater than 5.
Therefore, there are 2 patients who had more than 5 cavities.
**see annotated dot plot**
The area shaded with a pink rectangle is "more than 5 cavities"
Trigonometric Equations
Solve the equation over the interval [0°, 360°)
2sin^2theta-5sintheta+3=0
Step-by-step explanation:
The solutions are
S
=
{
30
º
,
150
º
,
270
º
}
Explanation:
The equation is
2
sin
2
θ
+
sin
θ
−
1
=
0
We can factorise the LHS
(
2
sin
θ
−
1
)
(
sin
θ
+
1
)
=
0
Therefore,
sin
θ
=
−
1
,
⇒
,
θ
=
270
º
sin
θ
=
1
2
,
⇒
,
θ
=
30
º
,
150
º
Ms. Bassie bikes a total of 11/12 mile to get to and from work each day. Write
an expression that can be used to find the total number of miles that Ms.
Bassie bikes to and from work over 5 days. Then evaluate the expression.
Answer:
Step-by-step explanation:
1 day, she travels 11/12 of a mile.
5 days, she travels 5 * 11/12 miles
5*11/12 = 55/12 = 4 7/12 miles.
Need some math help 50pts
Answer:
angle 1 and 3 are 127.3 degrees and angle 2 is 52.7 degrees
Step-by-step explanation:
so angle 2 is also 52.7 degrees because angle 2 and 4 are vertical oppostite angles
so we can look at it now that we have to find angle 1. since we know a line is 180 degrees we make angle 1 plus angle 2 equal to 180
let angle 1 be x
x + 52.7 = 180
x = 180 - 52.7
x = 127.3
Answer:
m∠1 = 127.3°
m∠2 = 52.7°
m∠3 = 127.3°
Step-by-step explanation:
Vertical Angle Theorem: When two straight lines intersect, the opposite vertical angles are always equal to each other.
⇒ m∠1 = m∠3 and m∠2 = m∠4
If m∠4 = 52.7° then m∠2 = 52.7°
Linear pair: Two adjacent angles which sum to 180°.
⇒ m∠1 + m∠2 = 180°
⇒ m∠3 + m∠4 = 180°
⇒ m∠3 + 52.7° = 180°
⇒ m∠3 = 180° - 52.7°
⇒ m∠3 = 127.3°
As m∠1 = m∠3 then m∠1 = 127.3° also.
PLEASE HELP PLEASE I WILL GIVE BRAINLIEST
Answer:
143
Step-by-step explanation:
I'm not sure if this is correct but this is what I came up with:
all angles combined must add to 360
125+55+37= 217
360-217=143
Pls help this my last question!
Answer:
Step-by-step explanati
- |10+8l=-2
how many terms of the geometric progression 6,12,24,......must be taken to get a sum of 49146
Answer:
13
Step-by-step explanation:
the sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a(r^{n}-1) }{r-1}[/tex]
where a is the first term and r the common ratio
here a = 6 , r = [tex]\frac{12}{6}[/tex] = 2 and [tex]S_{n}[/tex] = 49146 , then
[tex]\frac{6(2^{n}-1) }{2-1}[/tex] = 49146
6([tex]2^{n}[/tex] - 1) = 49146 ( divide both sides by 6 )
[tex]2^{n}[/tex] - 1 = 8191 ( add 1 to both sides )
[tex]2^{n}[/tex] = 8192 ( take log of both sides )
log [tex]2^{n}[/tex] = log 8192 , that is
n log 2 = log 8192 ( divide both sides by log 2 )
n = [tex]\frac{log8192}{log2}[/tex] = 13
[tex]\red{ \underline { \boxed{ \sf{Common \: Ratio,r = \frac{any\:observed\:term}{previous\:term}}}}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf Common \: Ratio,r = \frac{12}{6} [/tex]
[tex]\quad \boxed{\sf {Common \:Ratio,r = 2 }}[/tex]
Now,
[tex]\green{ \underline { \boxed{ \sf{Sum\: of \: G.P. \: to\: n\:term,S_n = \frac{a(r^n-1)}{r-1}}}}}[/tex]
where
a = first termr = common Ration= number of termsPutting Values -
[tex]\begin{gathered}\\\implies\quad \sf 49146 = \frac{6(2^n-1)}{2-1} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{\cancel{49146}}{\cancel{6}} = \frac{2^n-1}{1} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 8191= \frac{2^n-1}{1} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2^n-1 =8191 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2^n =8191+1 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2^n =8192 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2^n =2^{13}\quad(8192= 2^{13}) \\\end{gathered} [/tex]
Comparing powers on both sides-
[tex]\begin{gathered}\\\implies\quad \boxed{\sf{ n = 13}}\\\end{gathered} [/tex]
[tex]\longrightarrow[/tex]Therefore, to get a sum of 49146 , 13 terms of this G.P. should be taken.
A chemist has one solution that is 20% alcohol and another that is 60% alcohol.
How much of each solution must the chemist use to get 200 mL of a solution that is 52%
alcohol?
Answer:
solution 1= 40ml
solution 2= 160ml
Step-by-step explanation:
%alcohol= amount of alcohol/total solutionx100
0.52x200=104ml of alcohol present
0.2x L=0.2Lml of alcohol in solution one
0.6 x M=0.6Mml of alcohol in solution two
1st equation
0.2L+0.6M=104ml alcohol
times 10 to get whole
2L+6M=1040ml
2nd
same for this equation
10L+10M=2000ml
10L+10M=2000
2L+6M=1040
elimination method
=20L+20M=4000
-
=20L+60M=10400
-40M=-6400
M=160ml
2L+6 (160)=1040
2L=1040-960
2L=80
L=40ml
Write an equation for a perpendicular to y = - 2 x 2 and passing through the point (-4,-5)
Y=
[tex]======================================[/tex]
Perpendicular lines have slopes that are opposite reciprocals.
This means we take a number, flop it over, and change its sign.
So the slope of the given line is -2
Flop it over:
-1/2
Change its sign:
1/2
Now, let's write the equation in point-slope form:
y-y1=m(x-x1)
y-(-5)=1/2(x-(-4)
y+5=1/2(x+4)
y+5=1/2x+2
y=1/2x+2-5
[tex]\bold{y=\displaystyle\frac{1}{2} x-3}}[/tex]
[tex]==========================================[/tex]
Notes:-Hope everything's clear.Let me know if you have any questions!Enjoy your Day!Answered by:-~DnomaiD
;)
if <1 and <2 are vertical angles. If m<1=(5x +12) and m<2=(6x-11), find m<1
Answer:
its 23
Step-by-step explanation:
Jazmine is picking an outfit to wear to a party. She has 5 pairs of pants, 7 shirts, and 4 pairs of shoes to choose from. The number of possibilities Jazmine has to wear to the party is ———- than 120.
Please Help ASAP (show work if you want its not needed i just need the answer)
[tex] \cos(60) = \frac{12}{x} \\ [/tex]
[tex] \frac{1}{2} = \frac{12}{x} \\ [/tex]
[tex]x = 24[/tex]
_____________________________________________
[tex] \sin(60) = \frac{y}{x} \\ [/tex]
[tex] \frac{ \sqrt{3} }{2} = \frac{y}{24} \\ [/tex]
[tex]y = 12 \sqrt{3} [/tex]
Help help help please please
Answer:
The answer would be A.
Step-by-step explanation:
The answer would be A because the line is going down in question B, meaning that it would be a negative slope so that would not be correct. X=1x meaning that the line goes up one and goes right one block.Both of the slopes have the same y-interceptThe less than or equal sign (< with a line) is pointing away from y, meaning y is less than or equal to x+5. This doesn't matter in this graph in particular though because the inequality sign used for both graphs are the same here.Help me out please I don’t understand
[tex]\\ \sf\Rrightarrow y=-4(x+2)^2-1[/tex]
Compare to the vertex form of parabola
y=a(x-h)^2+kh=-2k=-1So vertex should be at (h,k)=(-2,-1)
Graph attached
The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number.
answer:
148ft²
explanation:
to solve this problem, we must set up a proportion.
[tex]\frac{side (L)}{area(L)} = \frac{side(S)}{area(S)} \\\frac{15}{185} = \frac{12}{x}[/tex]
15x=2220
x=148ft²
--
if this helped, please consider giving brainliest !
xzavier makes a conjecture that the sun of two odd integers is always an even integer which choice is the best proof of his conjecture
PLEASE I NEED THIS NOWWWWWWW
Answer:
2n+1
Step-by-step explanation:
i dont know but i tried to do it in paper and got this
Which verb form correctly completes this sentence?
No estoy convencido de que ellos ___________ lo que significa esta fiesta.
A.
comprenden
B.
comprendemos
C.
comprendan
D.
comprendes
Solve. 9 m 3 − 27 m 2 − 252 m = 0
Answer:
m = 0
m = 7
m = -4
Step-by-step explanation:
[tex]\sf 9m^3-27m^2-252m=0[/tex]
Divide by 9:
[tex]\sf \implies m^3-3m^2-28m=0[/tex]
Factor out common term m:
[tex]\sf \implies m(m^2-3m-28)=0[/tex]
Factor expression in parentheses:
[tex]\sf \implies m(m-7)(m+4)=0[/tex]
Therefore,
[tex]\sf \implies m=0[/tex]
[tex]\sf \implies m-7=0 \implies m=7[/tex]
[tex]\sf \implies m+4=0 \implies m=-4[/tex]
Help picture below problem 5
Answer:
option A is the correct answer!!
Step-by-step explanation:
mark me brainliest
A) angel OJP
Explanation(name by its vertex, by the three points of the angle (the middle point must be the vertex),
Choose the multiplication problem that correctly shows partial products.
A) A
B) B
C) C
Answer:
B) B
Step-by-step explanation:
2 times 4 is 8, so in this case the option is option b as none of the other options show this.
In total,
2 * 4 = 8
60 * 4 = 240
240 + 8 = 248
A culture started with 6000 becteria. after 4 hours it grew to 6600 becteria. Predict how many bacteria will be present after 10 hours. Round your answer to the nearest whole number. p=ae^kt
Answer:
7614
Step-by-step explanation:
The exponential growth of the bacteria culture can be modeled by the equation ...
p = a·b^(t/c)
where 'a' is the initial population, 'b' is the growth factor, and 'c' is the period over which that growth factor applies.
__
modelIn the given scenario, we have ...
a = 6000 bacteriab = 6600/6000 = 1.1 . . . . growth factorc = 4 hoursSo, our model is ...
p = 6000·1.1^(t/4)
__
applicationAfter 10 hours, the population is predicted to be ...
p = 6000·1.1^(10/4) ≈ 7614
We predict 7614 bacteria will be present after 10 hours.
__
Additional comment
If we compare the form we used to the one suggested in the proglem statement, we see
p = 6000·1.1^(t/4)p = 6000·e^(kt)For the bases of the exponential term to be the same, we must have ...
1.1^(t/4) = e^(kt)
(1.1^(1/4))^t = (e^k)^t . . . . . factor t from the exponent
1.1^(1/4) = e^k . . . . . . . match the bases
k = ln(1.1)/4 . . . . . take natural logs
k ≈ 0.0238275
and the equation becomes ...
p = 6000·e^(0.0238275t)
__
In terms of 'a', 'b', and 'c' used above, we find ...
k = ln(b)/c
27 is 0.5% of what number
Answer:
54
Step-by-step explanation:
27 is half of what number?
27 x 2 = 54
:)
Answer:
135
Step-by-step explanation:
27 x 0.5 = 135
Hope it helps!!!!!
need help please and I have more questions on the same topic like this .
Answer 1 1/4
Step-by-step explanation:
You can get this by finding 3/4 on the line plot and counting the x's. Then you must add the 3 x's which means 3 of 3/4 and sum is your answer. Be sure to change improper to proper fraction. 9/4 to 1 1/4.
Help me pls
Question 4 Part B (2 points): In part A you factored f(x) = 9m2 + 3m - 2. What are the x intercepts of this function? SELECT ALL THAT APPLY.
A.
m = -1/3
B.
m = 1/3
C.
m = -2/3
D.
m = 2/3
E.
m = 3
F.
m = -3
G.
m = 6
H.
m = -6
We need zeros
[tex]\\ \rm\Rrightarrow 9m^2+3m-2=0[/tex]
[tex]\\ \rm\Rrightarrow 9m^2-3m+6m-2=0[/tex]
[tex]\\ \rm\Rrightarrow 3m(3m-1)-2(3m-1)=0[/tex]
[tex]\\ \rm\Rrightarrow (3m-2)(3m-1)=0[/tex]
m=2/3mm=1/3