Answer:
2300
Step-by-step explanation:
53%=1219
100=X
X=[(1219)(100)]/53=2300
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
53% = 1219
100% = 2300
The total number of seats in the theater is 2300
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of seats filled by all the students = 1219
1219 is 53% of the total seats in the theater.
This means,
53% = 1219
Now,
Total number of seats in the theater = 100%
53% = 1219
Multiply 100/53 on both sides.
100/53 x 53% = 100/53 x 1219
100% = 2300
Thus,
The total number of seats in the theater is 2300
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URGENT PLEASE ANSWER THESE
Answer:
1A) 2 gallons of 20% solution and 3 gallons 15% solution needed
1B) 4 gallons of 20% solution and 1 gallons 15% solution needed
Step-by-step explanation:
1A) adding 20% salt and 15% water making 5 gallons of 17%
20% salt + 15% salt = 5 gallons of 17% salt
0.20x + 0.15(5 - x) = 0.17(5)
0.20x + 0.75 - 0.15x = 0.85
0.20x + 0.75 - 0.75 - 0.15x = 0.85 - 0.75
0.20x - 0.15x = 0.10
0.05x = 0.10
0.05x/ 0.05 = 0.10/0.05
x = 2 gallons (amount of 20% solution needed)
5 - x = 5 - 2 = 3 gallons (amount of 15% solution needed)
1B)
0.20x + 0.15(5 - x) = 0.19(5)
0.20x + 0.75 - 0.15x = 0.95
0.20x + 0.75 - 0.75 - 0.15x = 0.95 - 0.75
0.20x - 0.15x = 0.20
0.05x = 0.20
0.05x / 0.05 = 0.20/0.05
x = 4 gallons (amount of 20% solution needed)
5 - x = 5 - 4 = 1 gallons (amount of 15% solution needed)
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what is the decimal of 1/2
Answer:
0.5
one divide by two is zero point five
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above2[/tex]
We need to find the decimal form of [tex]\boldsymbol{\sf{\displaystyle\frac{1}{2}}}[/tex].
But first we need to convert it into a fraction whose
denominator is 10, or 100, or 1,000, etc.
The closest number that's divisible by 2 is 10.
So that's the new denominator of the fraction.
Now we should also multiply the top times the number
that we multiplied the bottom by. See how this works?
[tex]\boldsymbol{\sf{\displaystyle\frac{1\times5}{2\times5}}}[/tex]. This yields
[tex]\boldsymbol{\sf{\displaystyle\frac{5}{10}}}[/tex]. And 5/10 in decimal-form yields
[tex]\boldsymbol{\sf{0.5}}[/tex].
[tex]\orange\hspace{300pt}\above3[/tex]
[tex]\LARGE\boldsymbol{\sf{calligraphy}}[/tex]
Simplify the expression to a polynomial in
standard form:
(3x-1)(3x^2+3x+8)
Answer:
9x^3+6x^2+21x-8
Step-by-step explanation:
(3x-1) (3x ^ 2 + 3x + 8) =3x(3x ^ 2 + 3x + 8) +(-1)(3x ^ 2 + 3x + 8) =9x^3+9x^2+24x-3x^2-3x-8 = 9x^3+6x^2+21x-8
Answer:
[tex]\huge\boxed{\sf 9x^3+6x^2+21x-8}[/tex]
Step-by-step explanation:
Given expression:= [tex](3x-1)(3x^2+3x+8)[/tex]
[tex]Expand[/tex]
[tex]= 3x(3x^2+3x+8)-1(3x^2+3x+8)\\\\Multiply\\\\=9x^3+9x^2+24x-3x^2-3x-8\\\\Combine \ like \ terms\\\\= 9x^3+9x^2-3x^2+24x-3x-8\\\\= 9x^3+6x^2+21x-8\\\\\rule[225]{225}{2}[/tex]
Independent Practice
An image on a slide is similar to its projected image. A slide is 35 mm wide and 21 mm high. Its projected image is 85 cm wide. To the nearest centimeter, how high
is the image?
A. 51 cm
B. 5.1 cm
C.
D.
142 cm
9 cm
Answer:
Projected height = (85 *21) / 35 = 51 cm
Step-by-step explanation:
Since the images are similar, we can set up the proportional equation like this:
Slide width / Slide height = Projected width / Projected height
35 mm / 21 mm = 85 cm / Projected height (in cm)
Projected height = (85 *21) / 35 = 51 cm
Which exponential equation is equivalent to this logarithmic equation? log x = 4
Answer:
[tex]x=10^{4}[/tex]
Step-by-step explanation:
Switching from Logarithmic to Exponential form:An exponential base is the inverse of a logarithm with the same base. Given the equation log x = 4, note that the base of the logarithm isn't written in (it has no subscript). By default, the base of the logarithm function is base-10. So, to rewrite the equation using an exponential, we need to undo the logarithm with an exponential of the same base.
[tex]\log(x)=4[/tex]
[tex]10^{\log{(x)}}=10^{4}[/tex]
[tex]x=10^{4}[/tex]
Analogies with Addition/SubtractionThink about the equation x + 7 = 10.
I could tell you this is the equation in "addition form". What if I asked you to write an equation in "subtraction form"? While neither "addition form" nor "subtraction form" have been defined explicitly, one could undo the addition, and get an equation with subtraction in it, which one could argue is a "subtraction form" of the equation.
[tex]x+7=10[/tex]
Subtracting 7 from both sides to undo the addition...
[tex](x+7)-7=(10)-7[/tex]
Simplifying the left side since the "+7" and "-7" cancel...
[tex]x=10-7[/tex]
This is arguably in a "subtraction form" (there's a subtraction in it), whereas the original equation had addition in it.
While we could simplify this particular equation's right-hand side, we might not always be able to (what if the 10 had been a "y"... then the "y" and the "7" aren't like terms, and they would have to remain separate)
Similarly, in the logarithm problem, one could simplify 10^4 (it's 10,000), but one doesn't have to, and one won't always be able to.
For the logarithm problem, x=10^4 is the exponential form, as requested.
help asap 20 points
Select the correct answer from each drop-down menu.
Answer: (99/13, 150/13)
Step-by-step explanation:
I'm too lazy to explain so here's a screen shot from desmos.
how to solve part ii and iii
(i) Given that
[tex]\tan^{-1}(x) + \tan^{-1}(y) + \tan^{-1}(xy) = \dfrac{7\pi}{12}[/tex]
when [tex]x=1[/tex] this reduces to
[tex]\tan^{-1}(1) + 2 \tan^{-1}(y) = \dfrac{7\pi}{12}[/tex]
[tex]\dfrac\pi4 + 2 \tan^{-1}(y) = \dfrac{7\pi}{12}[/tex]
[tex]2 \tan^{-1}(y) = \dfrac\pi3[/tex]
[tex]\tan^{-1}(y) = \dfrac\pi6[/tex]
[tex]\tan\left(\tan^{-1}(y)\right) = \tan\left(\dfrac\pi6\right)[/tex]
[tex]\implies \boxed{y = \dfrac1{\sqrt3}}[/tex]
(ii) Differentiate [tex]\tan^{-1}(xy)[/tex] implicitly with respect to [tex]x[/tex]. By the chain and product rules,
[tex]\dfrac d{dx} \tan^{-1}(xy) = \dfrac1{1+(xy)^2} \times \dfrac d{dx}xy = \boxed{\dfrac{y + x\frac{dy}{dx}}{1 + x^2y^2}}[/tex]
(iii) Differentiating both sides of the given equation leads to
[tex]\dfrac1{1+x^2} + \dfrac1{1+y^2} \dfrac{dy}{dx} + \dfrac{y + x\frac{dy}{dx}}{1+x^2y^2} = 0[/tex]
where we use the result from (ii) for the derivative of [tex]\tan^{-1}(xy)[/tex].
Solve for [tex]\frac{dy}{dx}[/tex] :
[tex]\dfrac1{1+x^2} + \left(\dfrac1{1+y^2} + \dfrac x{1+x^2y^2}\right) \dfrac{dy}{dx} + \dfrac y{1+x^2y^2} = 0[/tex]
[tex]\left(\dfrac1{1+y^2} + \dfrac x{1+x^2y^2}\right) \dfrac{dy}{dx} = -\left(\dfrac1{1+x^2} + \dfrac y{1+x^2y^2}\right)[/tex]
[tex]\dfrac{1+x^2y^2 + x(1+y^2)}{(1+y^2)(1+x^2y^2)} \dfrac{dy}{dx} = - \dfrac{1+x^2y^2 + y(1+x^2)}{(1+x^2)(1+x^2y^2)}[/tex]
[tex]\implies \dfrac{dy}{dx} = - \dfrac{(1 + x^2y^2 + y + x^2y) (1 + y^2) (1 + x^2y^2)}{(1 + x^2y^2 + x + xy^2) (1+x^2) (1+x^2y^2)}[/tex]
[tex]\implies \dfrac{dy}{dx} = -\dfrac{(1 + x^2y^2 + y + x^2y) (1 + y^2)}{(1 + x^2y^2 + x + xy^2) (1+x^2)}[/tex]
From part (i), we have [tex]x=1[/tex] and [tex]y=\frac1{\sqrt3}[/tex], and substituting these leads to
[tex]\dfrac{dy}{dx} = -\dfrac{\left(1 + \frac13 + \frac1{\sqrt3} + \frac1{\sqrt3}\right) \left(1 + \frac13\right)}{\left(1 + \frac13 + 1 + \frac13\right) \left(1 + 1\right)}[/tex]
[tex]\dfrac{dy}{dx} = -\dfrac{\left(\frac43 + \frac2{\sqrt3}\right) \times \frac43}{\frac83 \times 2}[/tex]
[tex]\dfrac{dy}{dx} = -\dfrac13 - \dfrac1{2\sqrt3}[/tex]
as required.
The equation y = ax describes the graph of a line. If the value of a is negative,
the line:
Answer:
The line has a downward slope
Step-by-step explanation:
If y = ax, it means that a represents the slope of the line. So, if A is negative, the line has a downward slope. In other words, for every increase in the value of x, there is a decrease in the value of y (increase in the negative direction). You can imagine the line y = -x, where the value of a is -1. When x is 1, y is -1; when x is 2, y is -2; when x is 5, y is -5. You can imagine that the graph looks like a diagonal line, much like y = x, except the function values are positive in the second quadrant and negative in the fourth (it slants downward to the right side). I hope that answers your question.
Which of the following represents a function?
(5, 1), (5, 2), (5, 3), (5, 4)
(-5, 6), (-5, 6), (-5, -6), (-5, -6)
(8, 3), (8, 3), (-8, -3), (-8, -3)
(3, 9), (-7, 1), (6, 12), (3, -9)
Answer:
(8,3),(8,3),(-8,-3),(-8,-3)
Step-by-step explanation:
A function is defined as a relation in which each domain element (x-value) is paired with exactly one range element (y-value).
This means that each value we input for x must have only one possible output. If the same x-value yields more than one y-value, it is not a function.
The correct answer, as shown above, meets the criteria of a function, as each x-value is shown to produce exactly one y-value. In this set of ordered pairs, if x=8, then y=3, and if x=-8, then x=-3.
In the other sets of ordered pairs, however, one x-value has more than one possible y-value. Let's use the first set as an example:
(5,1),(5,2),(5,3),(5,4)
Inputting 5 as x produces four different y values; there is no one y value for the x-value. y could equal 1, 2, 3, or 4.
Kirsten is knitting and hates to donate to a local charity. Each hat takes 3 hours to make. If Kirsten knitted 3 hats and a third of another hat. how many hours did she spend knitting?
A courier travels due North at an average speed of 40km/h for 6 minutes to collect a parcel, before travelling 10km due East to deliver it. He then travels due South at an average speed of 30km/h for 12 minutes to collect another parcel. Find the shortest distance between the courier and his starting point.
Answer:
Step-by-step explanation:
Answer:10.2km
He took the route eastwards then southwards
Explain weather this equation is a linear equation
4. y = 1 - x
Answer:
Yes, it is a linear equation.
Step-by-step explanation:
Linear equation:An equation of the form ax + by +c = 0, where x and y are two variables and a, b,c are the non-zero real numbers is called a linear equation and the degree of the equation is 1.
y = 1 - x
x + y - 1 = 0
Where a = 1 ; b=1 and c = -1
So, y = 1 -x is a linear equation.
You design a logo for your soccer team. The logo is 3 inches by 5 inches. You decide to dilate the logo to 1.5 inches by 2.5 inches. What is the scale factor of this dilation?
Answer:
1/2
Step-by-step explanation:
The dimensions are cut in half ....scale factor 1/2
write 8n^2-13n+5 in factor form
Answer:
[tex](8n - 5)(n-1)[/tex]
Step-by-step explanation:
Hello!
We can factor this by grouping. We have to find two numbers that add up to -13 but multiply to 8 * 5 .
The two numbers that work are -8 and -5. Expand -13n to -8n and -5n.
Factor by Grouping[tex]8n^2 - 13n + 5[/tex][tex]8n^2 - 8n - 5n + 5[/tex][tex]8n(n -1) -5(n - 1)[/tex][tex](8n - 5)(n-1)[/tex]The factored expression is [tex](8n - 5)(n-1)[/tex].
Line I has a slope of 13/7. The line through which of the following pair
of points is perpendicular to l?
Answer:
Step-by-step explanation:
You need to find the set of points that will yield a slope that is the negative reciprocal of the slope of Line L because perpendicular lines have negative reciprocal slopes. The negative reciprocal of 13/7 is -7/13. Which set of points will produce this result? The formula for finding the slope is:
m = (y2 - y1)/(x2 - x1)
Consider the second set of coordinates.
(2 - (-5))/(-7 - 6) = (2 + 5)/(-13) = -7/13
The second set of coordinates satisfy the condition.
The formula s = startroot startfraction s a over 6 endfraction endroot gives the length of the side, s, of a cube with a surface area, sa. how much longer is the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters? startroot 30 endroot minus 4 startroot 5 endroot meters m startroot 30 endroot minus 2 startroot 5 endroot meters m startroot 10 endroot meters m 2 startroot 15 endroot meters m
Step-by-step explanation:
so, let me get this straight :
s = sqrt(sa/6)
this is because the surface area of a cube consists of 6 squares (as everybody knows that dice have 6 equal sides).
and the area of a single square is side².
for a cube with sa = 180 m² we have
s = sqrt(180/6) = sqrt(30)
for a cube with sa = 120 m² we have
s = sqrt(120/6) = sqrt(20) = sqrt(4×5) = 2×sqrt(5)
so, the side length of the larger cube is
sqrt(30) - 2×sqrt(5) meters
longer than the side length of the smaller cube.
in other words, the difference between both side lengths.
Answer:
answer above is correct, its B
Step-by-step explanation:
A group of summer campers went on a trip.
22 campers rode in cars with their parents
while the rest filled four buses. How many
campers were on each bus if a total of 150
campers went on the trip?
Answer:
Answer is 32
Step-by-step explanation:
150-22=128
128÷4=32
Suzanne walks four miles every third day. What is the fewest number of miles she can walk in February
36 miles is the fewest number of miles she can walk in February
There are 28 days in February.
Every third day is 28/3 = 9.333 = 9 days of walking.
since she walks four miles,
9*4 = 36
Hence, 36 miles is the fewest number of miles she can walk in February
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from two points one on each leg of an isosceles triangle perpendicular are drawn to the base prove that the triangles formed are similar
The description below proves that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.
How to prove an Isosceles Triangle?Let ABC be an isosceles triangle such that AB = AC.
Let AD be the bisector of ∠A.
We want to prove that BD=DC
In △ABD & △ACD
AB = AC(Thus, △ABC is an isosceles triangle)
∠BAD =∠CAD(Because AD is the bisector of ∠A)
AD = AD(Common sides)
By SAS Congruency, we have;
△ABD ≅ △ACD
By corresponding parts of congruent triangles, we can say that; BD=DC
Thus, this proves that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.
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Solve the questions by factoring! Please help asap!
Answer:
Step-by-step explanation:
A boat is 400 feet away from one dock and 500 feet away from the another dock. the angle between the paths is 45°. what is the approximate distance between the docks?
Answer:
The approximate distance between the docks is 357 feet
Step-by-step explanation:
Let the distance between docks be d.
This is the opposite side to 45° angle of triangle with other sides 400 ft and 500 ft.
Use the law of cosines to find the value of d:
[tex]d = \sqrt{400^2+500^2-2*400*500*cos45} =357[/tex] (rounded)The formula for the perimeter of a rectangle is P=2(l+w). Part A. Rewrite the formula for the perimeter of a rectangle in terms of the width, w. In your final answer, include all of your work. Part B. In two or more complete sentences, describe the process you followed while isolating the variable w in the equation P=2(l+w).
The expression that represents the width is w = (P-2l)/2
Subject of formulaGiven the formula for calculating the perimeter of a triangle expressed as:
P = 2(l + w)
where
l is the length
w is the width
Make w the subject of the formula
Given
P = 2(l + w)
Expand
P = 2l + 2w
Subtract 2l from both sides
P - 2l = 2w
Divide both sides by2
2w/2 = (P-2l)/2
w = (P-2l)/2
Hence the expression that represents the width is w = (P-2l)/2
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Y is inversely proportional to the square root of x if y=3 when x=25 find y when x is 9
Answer:
[tex]y=5[/tex]
Step-by-step explanation:
[tex]\textsf{If }y \textsf{ is \underline{inversely proportional} to the square root of }x, \textsf{ then}:[/tex]
[tex]y \propto\dfrac{1}{\sqrt{x}} \implies y=\dfrac{k}{\sqrt{x}}\quad \textsf{(where k is some constant)}[/tex]
[tex]\textsf{When }x=25, y = 3:[/tex]
[tex]\implies 3=\dfrac{k}{\sqrt{25}}[/tex]
[tex]\implies 3=\dfrac{k}{5}[/tex]
[tex]\implies k=15[/tex]
Inputting the found value of k into the equation:
[tex]\implies y=\dfrac{15}{\sqrt{x}}[/tex]
To find the value of y when x is 9, substitute x = 9 into the found equation:
[tex]\implies y=\dfrac{15}{\sqrt{9}}[/tex]
[tex]\implies y=\dfrac{15}{3}[/tex]
[tex]\implies y=5[/tex]
A coupon gives a total 20% off a total of 5 cans of green beans at the grocery store. If the green beans cost $0.75 per can, how much money is saved with the coupon?
$0.75
$0.15
$3.75
$1.88
Area=
Help me please thanks
The area of the shaded region shown in the figure is 80π unit²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Area of the shaded region = area of semicircle IL - area of semicircle JK + area of semicircle IJ + area of semicircle KL
Area of the shaded region = area of semicircle IL + area of semicircle IJ = (0.5 * π * 12²) + (0.5 * π * (12/3)²) = 80π
The area of the shaded region shown in the figure is 80π unit²
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True or False? If ab<0, then a<0, b>0 or a>0, b<0
Answer:
True
Step-by-step explanation:
If ab < 0, then ab = negative #.
In order for ab to be a negative #, one of them has to be negative while the other one needs to be positive.
Example:
a = -2, b = 1
ab < 0
(-2)(1) < 0
-2 < 0, TRUE
a < 0
-2 < 0, TRUE
b > 0
1 > 0, TRUE
If I switch a = -2 to 1 and b = 1 to -2, a > 0 and b < 0 is true too.
The polynomial 2x3 − 5x2 + 4x − 10 is split into two groups, 2x3 + 4x and −5x2 − 10. The GCFs of each group is then factored out.
Answer:
(x² + 2)(2x - 5)
Step-by-step explanation:
assuming the expression has to be factorised
2x³ - 5x² + 4x - 10 ← rearranging terms as indicated
= 2x³ + 4x - 5x² - 10 ( factor the first/second and third/fourth terms )
= 2x(x² + 2) - 5(x² + 2) ← factor out (x² + 2) from each term
= (x² + 2)(2x - 5) ← in factored form
change the unit of length 6ft 2in= ___ft?
Answer:
Step-by-step explanation:
Comment
You don't have to do anything to the 6 feet. It already is in feet. It's the 2 inches you have to worry about.
2 inches = 2/12 of a foot.
2/12 = 1/6 = 0.167 feet
Answer
6 feet 2 inches = 6.167 feet
Step-by-step explanation:
Point Z is equidistant from the vertices of ΔTUV.
Point Z is equidistant from the vertices of triangle T U V. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C.
Which must be true?
Line segment T A is-congruent-to line segment T B
Line segment A Z is-congruent-to line segment B Z
AngleBTZ Is-congruent-to AngleBUZ
AngleTZA Is-congruent-to AngleTZB
An isosceles triangle is one with two equal-length sides. The correct option is C.
What is an isosceles triangle?An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.
The diagram as per the given conditions is drawn below.
In ΔUTZ, since the sides UZ and TZ are equal because the point z is equidistance from T and U, therefore, the triangle is an isosceles triangle. Thus, ∠BTZ≅TZB.
Hence, the correct option is C.
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If B=3n-10B=3n−10 and C=n^{2}-6n-6,C=n
2
−6n−6, find an expression that equals 2B-3C2B−3C in standard form.
The expression of 2B - 3C in standard form is -3n^2 + 24n - 2
Functions and valuesGiven the following expressions
B = 3n - 10
C = n^2-6n-6
Required
2B - 3C
Substitute
2B - 3C = 2(3n -10) - 3(n^2-6n-6)
2B - 3C = 6n - 20 -3n^2+18n+18
2B - 3C = -3n^2 + 24n - 2
Hence expression of 2B - 3C in standard form is -3n^2 + 24n - 2
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