ANSWER
271 pre-sale tickets were sold.
EXPLANATION
Let p represent the number of pre-sale tickets and t represent the number of tickets sold.
According to the question,a total of 800 pre-sale tickets and tickets were sold .
This implies that,
[tex]p + t = 800[/tex]
Also the number of tickets sold is 13 less than twice the number of pre-sale tickets.
This gives another equation:
[tex]t = 2p - 13[/tex]
We substitute, the second equation into the first equation to obtain:
[tex]p + 2p - 13 = 800[/tex]
This implies that;
[tex]3p = 813[/tex]
Divide both sides by 3
[tex]p = \frac{813}{3} = 271[/tex]
Hence 271 pre-sale tickets were sold.
By setting up an algebraic equation and denoting pre-sale tickets as x, we discover that 271 pre-sale tickets were sold for the football city championship game.
To solve the problem of how many pre-sale tickets were sold for the football city championship game, we can set up an algebraic equation. Let's denote the number of pre-sale tickets as x. According to the question, the number of tickets sold at the gate is thirteen less than twice the number of pre-sale tickets, which we can express as 2x - 13. We are given that the total number of tickets sold is 800.
So, we set up the equation:
x + (2x - 13) = 800
Combining like terms, we get:
3x - 13 = 800
Adding 13 to both sides:
3x = 813
Then we divide both sides by 3 to find the value of x:
x = 813 / 3
x = 271
Therefore, 271 pre-sale tickets were sold.
What is f(g(x)) for x > 5?
Answer:
[tex]\large\boxed{B.\ 4x^2-41x+105}[/tex]
Step-by-step explanation:
[tex]f(x)=4x-\sqrt{x}\\\\g(x)=(x-5)^2\\\\f(g(x))\to\text{put}\ x=(x-5)^2\ \text{to}\ f(x):\\\\f(g(x))=f\bigg((x-5)^2\bigg)=4(x-5)^2-\sqrt{(x-5)^2}\\\\\text{use}\\(a-b)^2=a^2-2ab+b^2\\\sqrt{x^2}=|x|\\\\f(g(x)=4(x^2-2(x)(5)+5^2)-|x-5|\\\\x>5,\ \text{therefore}\ x-5>0\to|x-5|=x-5\\\\f(g(x))=4(x^2-10x+25)-(x-5)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\f(g(x))=(4)(x^2)+(4)(-10x)+(4)(25)-x-(-5)\\\\f(g(x))=4x^2-40x+100-x+5\\\\\text{combine like terms}\\\\f(g(x))=4x^2+(-40x-x)+(100+5)\\\\f(g(x))=4x^2-41x+105[/tex]
Answer: Option B
[tex]f(g(x)) = 4x^2 -41x + 105[/tex]
Step-by-step explanation:
We have 2 functions
[tex]f(x) = 4x -\sqrt{x}[/tex]
[tex]g(x) = (x-5)^2[/tex]
We must find [tex]f(g(x))[/tex]
To find this composite function enter the function g(x) within the function f(x) as follows
[tex]f(g(x)) = 4(g(x)) -\sqrt{(g(x))}[/tex]
[tex]f(g(x)) = 4(x-5)^2 -\sqrt{(x-5)^2}[/tex]
By definition [tex]\sqrt{a^2} = |a|[/tex]
So
[tex]f(g(x)) = 4(x-5)^2 -|x-5|[/tex]
Since x is greater than 5 then the expression [tex](x-5)> 0[/tex].
Therefore we can eliminate the absolute value bars
[tex]f(g(x)) = 4(x-5)^2 -(x-5)[/tex]
[tex]f(g(x)) = 4(x^2 -10x + 25) -(x-5)[/tex]
[tex]f(g(x)) = 4x^2 -40x + 100 -x+5[/tex]
[tex]f(g(x)) = 4x^2 -41x + 105[/tex]
Which type of sequence is represented by the given table?
x
1
2
3
4
y
4
-9.6
23.04
-55.296
A.
The table represents a geometric sequence because the successive y-values have a common ratio of -2.4.
B.
The table represents an arithmetic sequence because the successive y-values have a common difference of -17.
C.
The table represents a geometric sequence because the successive y-values have a common ratio of 0.4.
D.
The table represents an arithmetic sequence because the successive y-values have a common difference of 4.2.
Answer:
A.
The table represents a geometric sequence because the successive y-values have a common ratio of -2.4.
Step-by-step explanation:
A geometric sequence, with a first term a and common ratio r, is generally represented as;
[tex]a,ar,ar^{2},ar^{3},ar^{4},............ar^{n}[/tex]
The first term refers to the first number that appears in the sequence. The common ratio is the constant that multiplies a preceding value to obtain the successive one. That is, to obtain [tex]ar^{2}[/tex] from [tex]ar[/tex] we multiply [tex]ar[/tex] by the common ratio r.
In the table given the y-values are as follows;
4, -9.6, 23.04, -55.296
To obtain the common ratio we simply divide each value by the preceding one;
(-9.6)/4 = -2.4
23.04/(-9.6) = -2.4
(-55.296)/23.04 = -2.4
Since the sequence of numbers has a common ratio then it qualifies to be a geometric sequence. Thus, the table represents a geometric sequence because the successive y-values have a common ratio of -2.4.
Answer:
The table represents a geometric sequence because the successive y-values have a common ratio of -2.4
1. To calculate the height of a tree,
Marie measures the angle of elevation
from a point A to be 34º. She then
walks 10 feet directly toward the tree,
and finds the angle of elevation from
the new point B to be 41°. What is the
height of the tree?
Answer:
h ≈ 30.10 ft
Step-by-step explanation:
Marie measures the angle of elevation from a point A to a tree as 34° . She works 10 ft directly towards the tree and discovered the new angle of elevation is 41°. The height of the tree can be computed below.
let
a = distance from point B to the tree
h = height of the tree
The right angle triangle formed from point B, we can use tan to find the height of the tree.
tan 41° = opposite /adjacent
tan 41° = h/a
cross multiply
h = a tan 41°
The right angle formed from point A
tan 34° = opposite/adjacent
tan 34° = h/(a + 10)
(a + 10)tan 34° = h
Therefore,
a tan 41° = (a + 10)tan 34°
0.8692867378
a = 0.6745085168(a + 10)
0.8692867378a = 0.6745085168a + 6.7450851684
collect like terms
0.8692867378a - 0.6745085168a = 6.7450851684
0.194778221a = 6.7450851684
a = 6.7450851684/0.194778221
a = 34. 629565532 ft
height of the tree can be find with
h = a tan 41°
h = 34. 629565532 × 0.8692867378
h = 30.103022053 ft
h = 30.10 ft
I need help please?!!!!
The answer is -2. X is -2.
Find the area of each circle, both in terms of pi and to the nearest tenth. use 3.14 for pi
Circle with radius 9 in.
Answer: 254.47
Step-by-step explanation: A=3.14*r to the power of two=3.14*9 squared=254.47
3.14*9^2=254.34 this would be the answer
Ignore the top just answer both of the questions at the bottom plz
Answer:
y = 5x+2 , y=x-6
Step-by-step explanation:
just by looking at the table you can see for the first one 5x + 2 satisfies the table, and x-6 satisfies the right table.
for the first table the equation is:
[tex]x(5) + 2 = y[/tex]
and for the second it's:
[tex]x - 6 = y[/tex]
The basketball team sold t-shirts and hats as a fundraiser they sold a total of 23 items and made a profit of $246 they made a profit of $10 for every t shirt they sold and $12 for every hat they sold dertermine the number of t shirts and the number of hats the basketball team sold
The basketball team sold a total of 23 items (t-shirts and hats) and made $246. By setting up and solving a system of equations, it was determined that they sold 15 t-shirts and 8 hats.
To determine the number of t-shirts and hats sold by a basketball team for a fundraiser, given that they sold a total of 23 items and made a profit of $246, with a profit of $10 per t-shirt and $12 per hat sold. To solve this problem, we can set up a system of linear equations and solve for the two variables representing the number of t-shirts (T) and the number of hats (H).
Let T represent the number of t-shirts and H represent the number of hats.
We know that T + H = 23 (since 23 items were sold in total).
We also know that the profit from t-shirts is $10 per t-shirt, and the profit from hats is $12 per hat. Therefore, 10T + 12H = $246 (total profit).
We can now set up the equations:
T + H = 23
10T + 12H = $246
From the first equation, we can express H in terms of T: H = 23 - T.
Substitute H = 23 - T into the second equation:
10T + 12(23 - T) = $246
Simplify and solve for T:
10T + 276 - 12T = $246
-2T + 276 = $246
-2T = $246 - 276
-2T = -$30
T = 15 (number of t-shirts sold)
Now, we can find the number of hats by substituting T back into H = 23 - T. Since T is 15, H = 23 - 15 = 8 (number of hats sold).
Therefore, the basketball team sold 15 t-shirts and 8 hats.
What is 265,200 rounded to the nearest hundred thousand
265,000
Hope this helps!
Because the number in the ten thousands place is over 4, it’s going to turn the 2 in the hundred thousands place into a 3, making the answer 300,000
What is the domain of the function?
y= sqrt 5x-10
I don't know if this will help but I found this on YAHOO!
Answer: Domain of definition of a function is the set of numbers which the variable attains and for which the function is defined.
Step-by-step explanation:
f(x) = sqrt (5x-10)
Here x can have value equal to any real number >=2 because if x attains value less that 2, 5x-10 becomes negative and sqrt(5x-10) has no real value.
therefore the domain of the function f(x) is (2, infinity) inclusive of 2.
The domain of the above function is (2, ∞) .
What is a Domain ?Let y = f(x) be a function with an independent variable x and a dependent variable y.
If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.
For the given function [tex]y = \sqrt{5x-10[/tex]
The domain will be the value that satisfies the function and produces a value of y
For any value less than 2 , the value of v will be an imaginary number .
As the square root of a negative number will be an imaginary number.
Therefore (2, ∞) is the domain of the above function.
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A right triangle △ABC with right angle C is inscribed in a circle. Find the radius of this circle if: Given m∠C = 90°, k(O, r) inscribed in △ABC, AC = 8 cm, BC = 6 cm. Find r.
Answer:
The radius is [tex]r=5\ cm[/tex]
Step-by-step explanation:
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<C =(1/2)[arc\ AB][/tex]
[tex]m<C =90\°[/tex]
substitute
[tex]90\°=(1/2)[arc\ AB][/tex]
[tex]arc\ AB=180\°[/tex]
That means----> The length side AB of the inscribed triangle is a diameter of the circle
Applying Pythagoras Theorem
Calculate the length side AB
[tex]AB^{2}=AC^{2}+BC^{2}[/tex]
[tex]AB^{2}=8^{2}+6^{2}[/tex]
[tex]AB^{2}=100[/tex]
[tex]AB=10\ cm[/tex] -----> is the diameter
Find the radius
[tex]r=10/2=5\ cm[/tex] -----> the radius is half the diameter
Give some examples of perpendicular lines inside or outside your classroom.
Answer: Well for example two roads that are meeting with each other and they form a right angle,
Step-by-step explanation:
Answer:
1. A Christian cross.
2. Roads that meet at intersections
3. Hospital crosses.
Step-by-step explanation:
Perpendicular lines are lines that touch each other, or are slanted in a way that they will eventually touch each other. The examples I used are all crosses, which are two line that cross.
5. Solve by using the square root property.
(x - 3)² +6=1
Answer:
x = 3 + i+√5
x = 3 + i-√5
OR
x= 4 - √6
x= 4 +√6
Step-by-step explanation:
(x - 3)² +6=1
(x - 3)² + 6 = 1
-6 -6
sq root > (x - 3)² = -5
x-3 = i±√5 (i because neg. number)
x = 3 + i±√5
since its ±
two possible answers
x = 3 + i+√5
x = 3 + i-√5
Or
(x - 3)² +6=1
(x-3)+ √6= √ 1
x-3 = 1 - (±) √6
x= 4 - (±) √6
Answers
x= 4 - √6
x= 4 +√6
how many times would you expect the result to be a number less than 6
Answer:
5 if its a dice.
Step-by-step explanation:
On a dice, 5. The probability of it landing on 6 is 1/6
The circle below is centered at the point (5,3) and has a radius of length 4. What is it’s equation
[tex] {x}^{2} + {y}^{2} - 10x - 6y + 18 = 0[/tex]
Answer:
[tex](x-5)^2 + (y-3)^2= 16[/tex] is the equation of a circle
Step-by-step explanation:
The circle below is centered at the point (5,3) and has a radius of length 4
To find the center form of equation, we use formula
[tex](x-h)^2 + (y-k)^2= r^2[/tex]
where (h,k) is the center and 'r' is the radius of the circle
given center is (5,3)
h=5 and k =3
radius r= 4, plug in all the values in the equation
[tex](x-h)^2 + (y-k)^2= r^2[/tex]
[tex](x-5)^2 + (y-3)^2= 4^2[/tex]
[tex](x-5)^2 + (y-3)^2= 16[/tex] is the equation of a circle
The width of a rectangle is 12 cm less than the length. The area is 64cm^2 find the length and width. Use quadratic equations by factoring.
Answer:
length=16, width=4
Step-by-step explanation:
Use l as length and make an equation:
64 = x*(x-12)
Solve using quadratics, x=16.
Subtract 12 and get 4.
Tim mails two boxes of cookies to friends. One box weighs 1 3/4 pounds, and the other weighs 2 2/3 pounds. What is the total weight of the two boxes?
the answer would be 4 5/12 pounds
The total weight of the two boxes will be 4 and 5/12 pounds.
What is Algebra?Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.
Tim mails two boxes of cookies to friends. One box weighs 1 and 3/4 pounds, and the other weighs 2 and 2/3 pounds.
Then the total weight of the two boxes will be
Total weight = 1 + 3/4 + 2 + 2/3
Total weight = 3 + 17/12
Total weight = 3 + 1 + 5/12
Total weight = 4 + 5/12
The total weight of the two boxes will be 4 and 5/12 pounds.
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what is the inverse of y=cos(x-pi/2)
Answer:
[tex]f^{-1}(x)=\cos^{-1} x+\frac{\pi}{2}[/tex]
Step-by-step explanation:
The given function is
[tex]y=\cos(x-\frac{\pi}{2})[/tex]
To find the inverse of this function, we interchange x and y.
[tex]x=\cos(y-\frac{\pi}{2})[/tex]
Take the inverse cosine of both sides to obtain;
[tex]\cos^{-1} x=y-\frac{\pi}{2}[/tex]
[tex]\cos^{-1} x+\frac{\pi}{2}=y[/tex]
Therefore the inverse of the given cosine function is;
[tex]f^{-1}(x)=\cos^{-1} x+\frac{\pi}{2}[/tex] where [tex]-1\le x\le 1[/tex]
Answer:
the answer is B
y=tanx- pie/2
Consider the net of a triangular prism where each unit on the coordinate plane represents four feet. If a sheet of plywood measures 4 ft x 8 ft, how many sheets of plywood will a carpenter need to build the prism?
A) 3
B) 3.5
C) 4
D) 4.5
Answer:
B) 3.5 ^_^
Step-by-step explanation:
PLS HELP!!!!What are the sine, cosine and tangent ratios of
angle W in the triangle below
Step-by-step explanation:
Remember SOH-CAH-TOA:
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
The side adjacent to W is 4. The side opposite of W is 3. The hypotenuse is 5.
Therefore:
Sine = 3 / 5
Cosine = 4 / 5
Tangent = 3 / 4
A parabola opening upward shifted 7 units rights and 4 units down
Answer:
y + 4 = a(x - 7)^2
Step-by-step explanation:
The standard vertex form of a parabola with vertex at (h, k) is
y - k = a(x - h)^2
and if we start with the simplest case, y = a(x)^2 and translate its graph 7 units to the right and 4 units down, we get y - {-4] = a(x - 7)^2, or
y + 4 = a(x - 7)^2
The answer is y + 4 = a(x - 7)^2.
The standard vertex form of a parabola with vertex at (h, k) is
y - k = a(x - h)^2
And if we start with the simplest case,
y = a(x)^2 and
translate it Into 7 units to the right and 4 units down,
we get
y - {-4] = a(x - 7)^2
then we get the equation is y + 4 = a(x - 7)^2.
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which of the following statements is true about the question ?
Answer:
second one :p
Second one I think ;-;
Kara rotates a square around its horizontal axis of symmetry to make a solid figure. Which of following could be the shape of a horizontal cross section of the solid figure
Answer:
I am pretty sure the answer is square
Given that (x,y)=(5,10), find r
ANSWER
[tex]r = 5 \sqrt{5 } [/tex]
EXPLANATION
Given that (x,y)=(5,10), we want to find r.
We use the relation:
[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]
We substitute x=5 and y=10 into the formula to get,
[tex]r = \sqrt{ {5}^{2} + {10}^{2} } [/tex]
This implies that,
[tex]r = \sqrt{ 25+ 100 } [/tex]
[tex]r = \sqrt{125} [/tex]
[tex]r = 5 \sqrt{5 } [/tex]
what is the solution to 8(y + 7) > 8y + 3
Answer:
y can be any real number
Step-by-step explanation:
8(y + 7) > 8y + 3
Distribute
8y+56 > 8y+3
Subtract 8y from each side
8y-8y +56 > 8y-8y +3
56 > 3
This is always true so the inequality is always true
y can be any real number
Find the surface area of the composite solid. Round the answer to the nearest hundredth
Answer:
135.39
Step-by-step explanation:
The solid consist of 4 triangles and a 5 rectangles.
Formula to calculate area of triangle is
1/2 (height) (base)
Formula to calculate area of rectangle is
length x width
so
Total surface area of the composite solid is
2( 4(4) + 6(4) + 1/2(√13)(4) + 1/2(2√2)(6) ) + 6(4)
111.39 + 24
135.39
Answer:
Total area = 135 .39 square yard
Step-by-step explanation:
Given : composite figure.
To find : Find the surface area of the composite solid. Round the answer to the nearest hundredth.
Solution : We have given a composite figure with rectangle base and four triangles .
Base of two triangle = 4 yd .
Height of two triangle = √13 yd .
Base of other two triangle = 6 yd .
Height of other two triangle = 2√2 yd .
Area of rectangle = length * width .
Area of rectangle = 6 *4
Area of rectangle = 24 square yard .
Area of all rectangle = 3 *24 = 72 square yard
Area of two square = 2( 4*4) = 32 square yard.
Area of triangle = [tex]\frac{1}{2} base * height[/tex].
Area of triangle= [tex]\frac{1}{2} 4 *√13 [/tex].
Area of triangle = 2√13 .
Area of two triangle = 2 * 2√13 .
Area of two triangle = 4√13 square yard.
Area of other triangle = [tex]\frac{1}{2} 6 * 2√2 [/tex].
Area of other triangle = 3* 2√2
Area of other triangle = 6√2.
Area of other two triangle = 2 *6√2.
Area of other two triangle = 12√2 square yard.
Total area = Area of 3 rectangle + Area of two triangle + Area of other two triangle + area of square
Total area = 72 + 4√13 + 12√2 + 32
Total area = 135 .39 square yard.
Therefore, Total area = 135 .39 square yard.
9. Which of the following is the representation of a decimal number? A. 1/2 B. 23 C. 33/10 D. .25
Answer:
B because there is a dot in front of the 25 which is also known as a decimal point.
For this case we have that by definition, a decimal number is a number that is composed of a whole part, which can be zero, and by another lower than the unit, separated from the whole part by a point.
Examples:
0.05
1.76
According to the options given, we have:
A. [tex]\frac {1} {2},[/tex] it is a fraction
B. 23, is a whole number
C.[tex]\frac {33} {10}[/tex], it is a fraction
D. 0.25, is a decimal number.
Answer:
Option D
ABCD is a rhombus. = 8 cm, and = 3.5 cm. What is the area of the rhombus? A. 14 cm2 B. 21 cm2 C. 28 cm2 D. 56 cm2
Answer:
A) 14 cm^2
Step-by-step explanation:
Given
Rhombus ABCD
let the given length be diagonal 1, a= 8cm
diagonal 2,b= 3.5cm
Area of ABCD=?
Area of rhombus= ab/2
Putting the values in above :
Area of ABCD= 8(3.5)/2
=28/2
=14 !
Answer:
14cm^2
Step-by-step explanation:
Given: EFGH inscribed in k(O) m∠FHE = 45°, m∠EGH = 49° Find: m∠FEH
Answer:
[tex]m<FEH=86\°[/tex]
Step-by-step explanation:
we know that
The inscribed angle measures half that of the arc comprising
step 1
Find the measure of arc EF
[tex]m<FHE=\frac{1}{2}(arc\ EF)[/tex]
we have
[tex]m<FHE=45\°[/tex]
substitute
[tex]45\°=\frac{1}{2}(arc\ EF)[/tex]
[tex]arc\ EF=90\°[/tex]
step 2
Find the measure of arc EH
[tex]m<EGH=\frac{1}{2}(arc\ EH)[/tex]
we have
[tex]m<EGH=49\°[/tex]
substitute
[tex]49\°=\frac{1}{2}(arc\ EH)[/tex]
[tex]arc\ EH=98\°[/tex]
step 3
Find the measure of arc FGH
[tex]arc\ FGH=360\°-(arc\ EH+arc\ EF)[/tex]
substitute the values
[tex]arc\ FGH=360\°-(98\°+90\°)[/tex]
[tex]arc\ FGH=172\°[/tex]
step 4
Find the measure of angle FEH
[tex]m<FEH=\frac{1}{2}(arc\ FGH)[/tex]
we have
[tex]arc\ FGH=172\°[/tex]
substitute
[tex]m<FEH=\frac{1}{2}(172\°)=86\°[/tex]
CAN SOMEONE HELP ME ANSWER THIS
Answer:
5 timesStep-by-step explanation:
[tex]30\cdot\dfrac{1}{6}=\dfrac{30}{6}=5[/tex]
Compare the three functions below. Which has a greater period? A) y = 3cos(2x+1), B) y=5cos(4x +8), and C) y=cos(2x+4) (4.3)
Comparing the periods of the given cosine functions indicates that functions A) and C) both have the greatest period of π, which is longer than the period of function B), π/2.
Explanation:To compare the periods of the given functions, let's first understand what the general form of a cosine function tells us about its period.
The general form is y = A cos(Bx + C), where A is the amplitude, B affects the period, and C is the phase shift.
The period of such a function is given by 2π / |B|.
For function A) y = 3cos(2x+1), B = 2, thus its period is π.
For function B) y=5cos(4x +8), B = 4, yielding a period of π/2.
Lastly, for function C) y=cos(2x+4) (4.3), assuming the (4.3) is an unrelated notation and focusing on the given cos component with B = 2, its period is also π.
The function with the greatest period among A, B, and C is thus A) and C), both having the same period of π, which is greater than the period of B).