Answer:
a joke and a cartoon together cost $80
c=$15 j=$65
Step-by-step explanation:
j=joke
c=cartoon
8j +6c = 610
6j+8c = 510
Multiply the first by 8
Multiply the second by -6
64j +48c = 4880
-36j -48c = -3060
ADD both (c will cancel)
28j = 1820
j= 65
PLUG j
8(65) + 6c = 610
520+6c = 610
6c= 90
c = 15
j + c = 65+15 = 80
A flashlight is projecting a triangle onto a wall
Answer:
24
Step-by-step explanation:
The the triangles are similar, the lengths of corresponding sides are in proportion.
15/20 = 18/n
3/4 = 18/n
1/4 = 6/n
n = 4 × 6
n = 24
Answer:
n = 24
Step-by-step explanation:
In similar triangles, corresponding sides are in same ratio.
[tex]\dfrac{n}{18}=\dfrac{20}{15}\\\\\\n=\dfrac{20}{15}*18\\\\\\n = 4*6\\\\n = 24[/tex]
Need help Please! Quick
Answer:
please see photo for details
Frankie is saving up to have spending money for her family vacation. If Frankie's current monthly net pay is $490.00 and her monthly expenses are $396.90 what percent of her net pay is left for savings?
19%
23%
67%
81%
The circumference of the base of a cone is 24 inches. The slant height of the cone is 20 inches.
What is the surface area of the cone? Express the answer in terms of .
240 square inches
384 square inches
480 square inches
624 square inches
The surface area of a cone with circumference base of 24π inches and slant height of 20 inches is 384π inches² in terms of π.
Surface area of a conesurface area = πr(r + l)
where
r = radiusl = slant heightTherefore,
l = 20 inches
24π = 2πr
r = 12
Therefore,
surface area = π(12)(12 + 20)
surface area = 12π(12 + 20)
surface area = 12π × 32
surface area = 384π inches²
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Answer:
B) 384 π square inches
Step-by-step explanation:
E2020
X + 2x + 8 = X = 10 + 6
Answer:
x = 8/3
Decimal form: 2.66666666667
Step-by-step explanation:
Given:
[tex]x+2x+8=10+6[/tex]
Solution:
[tex]\mathrm{Add\:similar\:terms:}\:x+2x=3[/tex]
[tex]3x+8=10+6[/tex]
[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]
[tex]3x+8-8=16-8[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]3x=8[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]
[tex]\frac{3x}{3}=\frac{8}{3}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=\frac{8}{3}[/tex]
[tex]x=2.66666666667[/tex]
~lenvy~
Answer/Step-by-step explanation:
Base on the given we are..
Solving for x:
Solve:
X + 2x + 8 = X = 10 + 6 {x+2x= 3x}
3x + 8 = 10 + 6 {10+6=16}
3x + 8-8=16-8 {16-8=8}
3x = 8 {divide both sides by same term}
3x/3 = 8/3
Therefore,
x = 8/3
Decimal form = 2.66666666667
[RevyBreeze]
Algebra: Right answer pls
Which statement about the graph of y = 4 (1.25)× is true?
The coordinates of the x-intercept are (4, 0)
The coordinates of the y- internet are (0, 4) (ʀɤɢʜʈ Åɴswɛɾ)
The equation of the asymptote is x = 4
The graph includes the point (0, 1.25)
Answer: B
Step-by-step explanation:
the sum of three consecutive natural numbers is 1146, find the numbers.
the three numbers in increasing order are ______ , _____, and ________
[tex]\text{Let the 3 consecutive numbers be}~ x,~x+1~ \text{and} ~x+2.\\\\\text{According to the condition,}\\\\x+x+1+x+2 = 1146\\\\\implies 3x +3 = 1146\\\\\implies 3(x+1) = 1146\\\\\implies x+1 = \dfrac{1146}3 = 382\\\\\implies x= 382-1 = 381\\\\\text{Now, the numbers are}~ 381,~382~\text{and}~383[/tex]
Solve for x. -14 - x = 14
Answer:
x= -28
Step-by-step explanation:
1. First you have to add 14 to both sides to get the x by itself. That's always the first thing you have to do. Get x by itself.
2. After that, you should have -x= 28. You can't leave it like that because it is still not simplified. It's basically saying 28 is the opposite of x. What's the opposite of positive? Negative.
3. Therefore, your final answer should be -28
Answer:
x = -28
Step-by-step explanation:
Hey! First, lets establish our equation :)
-14 -x = 14
Now, we are going to get our x alone on a single side, to do this, we are going to add 14 to both sides to be able to cut out -14 on the left side!
-14 -x = 14
+14 +14
-x = 28
The last thing we have to do is divide both sides by -1 to get x by itself without it being negative!
-x = 28
÷-1 ÷-1
x = -28
So, x, is equal to -28 (negative 28!) :)
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Bottles of water are packaged with
24 bottles per case. A store has
365 cases to sell. How many bottles
of water does the store have to sell?
Step-by-step explanation:
1 case = 24 bottles
365 cases = 365×24 = 8,760 bottles
I don't understand this problem
Answer:
Right angle (90°)
Step-by-step explanation:
Because, main Street and Oak Street are crossing each other at 90°.
Hope it helps you in your learning process.
Answer:
right angle
Step-by-step explanation:
because they're perpendicular lines
Peyton's family took a road trip to the Grand Canyon. Peyton fell asleep 77% of the way through the trip. If the total length of the trip was 1000 miles, how many miles had they travelled when Peyton fell asleep?
The miles Peyton's family had travelled when he fell asleep is 770 miles
How many miles had they travelled when Peyton fell asleep?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.
Miles when Peyton fell asleep = 77% x 1000 = 770 miles
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Help help help math math help
Answer:
x = - 4
Step-by-step explanation:
i hope its helped. thank you !
NO LINKS!!!
Part 3: Figure A is a dilated image of Figure B. Find the scale factor. #5 and 6
Answer:
Step-by-step explanation:
Scale:- 1box=1units
So
Take one side of each
B=6unitsA=10unitsScale factor(A to B)
[tex]\\ \rm\rightarrowtail \dfrac{6}{10}=\dfrac{3}{5}[/tex]
Scale factor (B to A) is 5/3#6
B=12A=6Scale factor (A to B)
[tex]\\ \rm\rightarrowtail \dfrac{12}{6}=2[/tex]
Scale factor (B to A)
[tex]\\ \rm\rightarrowtail \dfrac{6}{12}=0.5[/tex]
How could you demonstrate that the force of gravity acting on an object is proportional to the mass of the object?
Answer:
F = mg
Step-by-step explanation:
g is the constant of proportionality and force is the product of mass and the acceleration due to gravity
f is directly proportional to m, therefore, f = mg
Find the measure of the indicated arc
Step-by-step explanation:
we need the length of the arc ?
the length of the arc fully around the circle (360°) is the circumference of the circle : 2×pi×r
and the arc length for 123° is then
2×pi×r×123/360
but we would need r to calculate that. you did not provide that.
the only other thing that comes to mind is : the arc angle is indeed the angle at the center of the circle and is 123°.
i don't know how else to help you, as i cannot think of anything else you might need there.
It takes a boat 2 hours to go 16 miles downstream with the current and 4 hours to return against the current. Find the speed of the boat in still water and the speed of the current.
let's recall that d = rt, or namely distance = rate * time.
b = speed of the boat
c = speed of the current
now, we know that going downstream the boat went 16 miles total, that's going only one way, so the distance the boat travels downstream as well as upstream to return is 16 miles flat.
when going downstream, the boat is not really going at "b" speed, is really going at "b + c" speed, because the current is adding its speed to it, so is really going faster than "b".
when going upstream, the boat is not really going at "b" speed" either, is really going slower at "b - c" speed, because the current is against it and thus subtracting speed from "b".
let's take a look at those in a table
[tex]\begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Downstream&16&b+c&2\\ Upstream&16&b-c&4 \end{array}\qquad \qquad \begin{cases} 16=(b+c)(2)\\\\ 16=(b-c)(4) \end{cases} \\\\\\ \stackrel{16}{(b+c)(2)}~~ = ~~\stackrel{16}{(b-c)(4)}\implies 2b+2c~~ = ~~4b-4c\implies 2c=2b-4c[/tex]
[tex]6c=2b\implies \cfrac{6c}{2}=b\implies \boxed{3c=b} \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{16~~ = ~~(\stackrel{b}{3c}+c)(2)}\implies 16=4c(2)\implies 16=8c \\\\\\ \cfrac{16}{8}=c\implies \blacktriangleright \stackrel{mph}{2}=c \blacktriangleleft~\hspace{10em}3(2)=b\implies \blacktriangleright \stackrel{mph}{6}=b \blacktriangleleft[/tex]
You are debating about whether to buy a new computer for $800.00 or a refurbished computer with the same equipment for $640.00. If you are paid $10.00/hour and your deductions are FICA (7.65%), federal tax withholding (12%), and state tax withholding (8%), how many hours do you have to work to pay for the new computer?
111 hours
98 hours
87 hours
Total deduction
7.65+12+819.65+827.65%Now
Earnings after deduction
10-10(0.2765)10-2.7657.335$Total hours:-
640/7.33587.2587hoursYou will have to work 110.5 hours to buy the new computer.
What is tax?A tax is some specific financial amount or some other charged taxpayer by the government in order to fund government spending.
Given is that you have to buy a new computer for $800.00 or a refurbished computer with the same equipment for $640.00. If you are paid $10.00/hour and your deductions are -
FICA (7.65%),
Federal tax withholding (12%)
State tax withholding (8%).
Total money earned after all the deductions -
A{n} = 10 - {7.65% of 10 + 12% of 10 + 8% of 10}
A{n} = 10 - {7.65/100 x 10 + 12/100 x 10 + 8/100 x 10}
A{n} = 10 - {7.65/10 + 12/10 + 8/10}
A{n} = 10 - 2.765
An = 7.235
Cost of new computer = $800.
For 1 hour. you earned $7.235.
Then, you will earn $1 in (1/7.235) hours
So, you will earn $800 in (1/7.235 x 800) = 110.5
Therefore, you will have to work 110.5 hours to buy the new computer.
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Help..........................
Hello! I believe your answer is x= -4 so B
===
Hope this helps and feel free to give feedback
Answer:
x = -4
Step-by-step explanation:
what is 5b^-2/b^-3? I need to know
Answer:
5b
Step-by-step explanation:
Hope this helps <3
i) Find the first 4 terms in the expansion of
[tex](2 + x ^{2})^{6}[/tex]
in ascending powers of x.
ii) Find the term independent of x in the expansion of
[tex](2 + x ^{2})^{6}(1 - \frac{3}{x {}^{2} } ) {}^{2} [/tex]
Answer:
(i) [tex]64+192 x^2+240 x^4+160x^6[/tex]
(ii) 1072
Step-by-step explanation:
Part (i)
Using Binomial series formula:
[tex](2+x^2)^6=2^6+6C1 \cdot 2^{6-1}\cdot x^2+6C2 \cdot 2^{6-2}\cdot(x^2)^2+6C3 \cdot 2^{6-3}\cdot(x^2)^3[/tex]
[tex]=64+6 \cdot 32\cdot x^2+15 \cdot 16\cdot x^4+20 \cdot 8 \cdot x^6[/tex]
[tex]=64+192 x^2+240 x^4+160x^6[/tex]
Part (ii)
[tex](1-\frac{3}{x^2})^2=(1-\frac{3}{x^2})(1-\frac{3}{x^2})[/tex]
[tex]=1-\dfrac{6}{x^2}+\dfrac{9}{x^4}[/tex]
[tex](2+x^2)^6(1-\frac{3}{x^2})^2=(64+192 x^2+240 x^4+160x^6)\left(1-\dfrac{6}{x^2}+\dfrac{9}{x^4} \right)[/tex]
[tex]=64-\dfrac{384}{x^2}+\dfrac{576}{x^4}+192x^2-1152+\dfrac{1728}{x^2}+240x^4-1440x^2+2160+...[/tex]
There is no need to keep expanding since the remaining will include the variable.
Therefore, the term independent of x = 64 - 1152 + 2160 = 1072
find the total area of cardboard used in making a matchbox, complete with the sliding portion, 4cm long, 2.5cm wide, and 1.2cm deep (ignore the thickness of the cardboard)
Answer: 55.2 cm^2
Step-by-step explanation:
2(4x2.5 + 2.5x1.2 + 1.2x4) = 35.6 cm^2
(2x1.2x4 + 4x2.5) = 19.6 cm^2
(35.6 + 19.6) = 55.2 cm^2
the length of a rectagle is twice its width. if the perimeter of the rectangle is 36in, find its length and width
Answer:
Perimeter=36in
Length of one side=12
Length of the other side=12
Width of one side=6
Width of the other side=6
Step-by-step explanation:
6*2=12, so if the length is 12 half would be six. All of them added up is 36
Answer:
Length = 12inWidth = 6inStep-by-step explanation:
[tex]perimeter \: of \: a \: rectangle = 2(2x) + 2(x) \\ 36in = 4x + 2x = 6x \\ \frac{36in}{6} = \frac{6x}{6} \\ x = 6in \\ 2x = 2 \times 6in = 12in[/tex]
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find the zeros simplify all irrational and complex solutions
f(x)=x^4-11x^2-80
Answer:
Step-by-step explanation:
f(x)=x^4-11x^2-80=x^4-16x^2+5x^2-80
=x²(x²-16)+5(x²-16)
=(x²-16)(x²+5)
=(x-4)(x+4)[x²-(-5)]
=(x-4)(x+4)[x^2-(5i²)]
=(x-4)(x+4)(x-√5 i)(x+√5 i)
so zeros are 4,-4,√5 i,-√5 i
what is the relationship between the sine and cosine of the complementary angles in this diagram? drag and drop the answers into the boxes to correctly complete the statements.
Both sin(41) and cos(x) can be represented by the ratio ____. the angles measuring 41 and x are complementary angles. this means x+41=____. therefore x=____. since sin(41) = cos(x), this also shows that sin(41)=cos(_____).
Answer:
Step-by-step explanation:
Both sin(41) and cos(x) can be represented by the ratio b/c
What is complementary angles?If the sum of two angles is equal to 90 degrees, then such angles are called complementary angles. The total of the two angles' measurements determines their complement and supplement. The pair of angles is said to be complimentary if the product of the two angles equals the measurement of a right angle. Example:
40° is the complement of 50°.
50° is the complement of 40°.
sin (41) = b/c
cos (x) = b/c
∴both sin(41) and cos(x) can be represented by the ratio b/c
x + 41 = 90 (∵ complementary angles)
x = 90-41 = 49
∵ sin 41 = cos x
∴ sin 41 = cos (90-41)
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Find the value of x. Round your answer to the nearest tenth.
Answer:
Value of x is 34.9 (nearest tenth)[tex]~[/tex]
Step-by-step explanation:
In given right angled traingle:
AC (Hypotenuse) = 20∠ACB = 35° AB (Perpendicular) = x[tex]~[/tex]
In ∆ABC,
[tex]\: \: \: \: \dashrightarrow \: \: \: \sf \dfrac {AC}{AB} = \sin35° \\[/tex]
[tex]\: \: \: \: \dashrightarrow \: \: \: \sf \dfrac {20}{x} = 0.5736 \\[/tex]
[tex]\: \: \: \: \dashrightarrow \: \: \: \sf x = \dfrac {20}{0.5736} \\[/tex]
[tex]\: \: \: \:{ \pmb{ \pink{ \sf{ \dashrightarrow \: \: \: { x = 34.867 }}}}}[/tex]
Hence,
Value of x is 34.9 (nearest tenth)A cuple travels 420 miles to dr0p their dughter off at summer camp. The trip back has a short cut and is only 360 miles. And the gas mileage is 50% better
due to a lighter load. Write an expression for the total gas used and simplify.
The expression for the simplified total gas used is 1.43x.
How to write the expression of the total gaslet the gas used on the way to camp "x"
Then the gas used on the way back can be calculated as follows:
360 / 420 × 0.5 × x
To calculate the total fuel used, We need to add this to the 'x' used on the way.
Therefore,
total gas used = x + 360 / 420 × 0.5 × x = x + 0.43x = 1.43x
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Evaluate 14 - (2x - y), when x = 3 and y = 2 - -
.A) -7
.B) 10
.C) 13
.D) 18
20 POINTSS
10
solve:
14 - (2(x) - y)
given x : 3, y : 2, insert the following
14 - (2(3) - 2)14 - (6-2)14 - 410[tex]\\ \rm\rightarrowtail 14-(2x-y)[/tex]
[tex]\\ \rm\rightarrowtail 14-2x+y[/tex]
Put values[tex]\\ \rm\rightarrowtail 14-2(3)+2[/tex]
[tex]\\ \rm\rightarrowtail 14-6+2[/tex]
[tex]\\ \rm\rightarrowtail 10[/tex]
-3/5m + 8 = 20
what is the answer of m
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: - \frac{ 3}{5} m + 8 = 20[/tex]
[tex]\qquad \sf \dashrightarrow \: - \frac{ 3}{5} m = 20 - 8[/tex]
[tex]\qquad \sf \dashrightarrow \: - \frac{ 3}{5} m =12[/tex]
[tex]\qquad \sf \dashrightarrow \: - \frac{ }{} m =12 \times \frac{5}{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: - m = 4 \times 5[/tex]
[tex]\qquad \sf \dashrightarrow \:m = - 20[/tex]
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120 feet is to 150 feet as 8 feet is to ten feet write the proportion HELP PLEASE!!! AND PLEASE SHOW HOW TO DO IT
Answer:
Step-by-step explanation:
120/150 = 0.8
8/10 = 0.8
8x15=120
10x15=150
An arrow is shot vertically upward at a rate of 190 feet per second from ground level. Use the projectile formula
h
=
−
16
t
2
+
v
0
t
+
h
0
h
=
-
16
t
2
+
v
0
t
+
h
0
to determine when the height of the arrow will be 471 feet.
The height of the arrow will be 471 feet at 8.35s and 3.53s
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
h represent the height of the arrow after t seconds.
h(t) = -16t² + v₀t + h₀
v₀ is the initial velocity = 190 ft/s, h₀ is the initial height = 0m, hence:
h(t) = -16t² + 190t
At 471 feet:
471 = -16t² + 190t
0 = -16t² + 190t - 471
t = 8.35 or 3.53
The height of the arrow will be 471 feet at 8.35s and 3.53s
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