Let the price of each ticket be represented by
[tex]=x[/tex]The price of two tickets will be
[tex]t=2x[/tex]The tax on the price of the tickets is 6% which be represented as
[tex]\begin{gathered} =\frac{6}{100}\times t \\ =\frac{6t}{100}=0.06t \end{gathered}[/tex]The price of the two tickets after tax will be
[tex]\begin{gathered} the\text{price of the two tickets+the tax on the two tickets} \\ =t+0.06t \\ =1.06t \end{gathered}[/tex]Therefore,
The price of the tickets after adding an additional booking fee of $20 will be given below as
[tex]=1.06t+20[/tex]Since,
We were asked to get the algebraic expression person, we would therefore divide the above expression by 2
[tex]\begin{gathered} =\frac{1.06t+20}{2}=\frac{1.06t}{2}+\frac{20}{2} \\ =0.53t+10 \end{gathered}[/tex]Hence,
The algebraic expression to represent the price per person using variable t is
=0.53t + 10
1a. 100 foot-long rope is cut into 3 pieces.The first piece of rope is 3 times as long asthe second piece of rope. The third piece istwice as long as the first piece of rope.What is the length of the longest piece ofrope?
To solve the exercise, it is easier to make a drawing, like this
So, you have
[tex]\begin{gathered} z=3y \\ y=y \\ x=2z \\ z+y+x=100 \end{gathered}[/tex]Now solving
[tex]\begin{gathered} x=2z \\ x=2(3y) \\ x=6y \end{gathered}[/tex][tex]\begin{gathered} z+y+x=100 \\ 3y+y+6y=100 \\ 10y=100 \\ \frac{10y}{10}=\frac{100}{10} \\ y=10\text{ ft} \end{gathered}[/tex][tex]\begin{gathered} x=6y \\ x=6(10) \\ x=60\text{ ft} \end{gathered}[/tex][tex]\begin{gathered} z=3y \\ z=3(10) \\ z=30\text{ ft} \end{gathered}[/tex]Therefore, the length of the longest piece is 60ft.
why are whole numbers rational numbers?
Answer:
Step-by-step explanation:
A whole number can be written as a fraction that has a denominator of 1. So, the whole numbers 18, 3, and 234 can be written as the rational numbers 18/1, 3/1, and 234/1.
So, all whole numbers are rational numbers, but not all rational numbers are whole numbers.
6. Line 1 passes through the points (1,4) and (-2,5). Line 2 passes through the points (1,0) and (0,3). What is true about Line 1 and Line 2? (2 points) (A) (B) They are perpendicular. They are parallel. They both decrease. They both increase. (C) (D)
First, calculate the slope (m) of both lines.
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Line 1:
Point 1 = (x1,y1) = (1,4)
Point 2 = (x2,y2) = (-2,5)
Replacing:
[tex]m=\frac{5-4}{-2-1}=\frac{1}{-3}=-\frac{1}{3}[/tex]Line 2:
Point 1 = (x1,y1) = (1,0)
Point 2 = (x2,y2) = (0,3)
[tex]m=\frac{3-0}{0-1}=\frac{3}{-1}=-3[/tex]Lines to be parallel must have the same slope, and to be perpendicular, they must have negative reciprocal slope.
None of the slopes are equal or negative reciprocal. SO, A and B are false-
Now, for the increase/ decrease
We can see that both lines have a negative slope, so they both decrease.
Correct option: C
Solve the inequality and write the solution using:
Inequality Notation:
The solution for the given inequality is x >7.
InequalityIt is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).
The solutions for inequalities can be given by: a graph in a number line or numbers.
For solving this exercise, it is necessary to find a number and a graph solution for the given inequality.
The given inequality is [tex]1-\frac{6}{7}x < -5[/tex] . Then,
Move the number 1 for the other side of inequality and simplify.[tex]-\frac{6}{7}x < -5 -1\\ \\ -\frac{6}{7}x < -6[/tex]
Multiply both sides by -1 (reverse the inequality )[tex]-\frac{6}{7}x < -6 *(-1)\\ \\ \frac{6}{7}x > 6[/tex]
Solve the inequality for x[tex]\frac{6}{7}x > 6\\ \\ 6x > 42\\ \\ x > \frac{42}{6} \\ \\ x > 7[/tex]
You should also show the results t > 7 in a number line. Thus, plot the number line. See the attached image.
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helpppppppppppppppppppppppppppppppppppppp
Answer:
[tex]\large \text{$f^{-1}(x) = 3x -6$}[/tex]
Graphs attached
Step-by-step explanation:
Your inverse function is correct. So not sure what additional information you need
I am not familiar with the graphing tool you have been provided with. My graph is attached. I used a free online graphing tool
mr dudzic has above ground swimming pool thatbis a circular cylinder. the diameter of the pool is 25 ft. and the height isb4.5 ft. in order to open he needs to shock it with chlorine. if one gallon of liquid chlorin treats 3000 gallons of water, how many full gallons will he need to buy. (1 foot^3=7.48 gallons)
The volume of the cylinder is
[tex]V=\pi\text{ }\times r^2\times h[/tex]The diameter of the cylinder is 25 feet, then
The radius of it = 1/2 x diameter
[tex]r=\frac{1}{2}\times25=12.5ft[/tex]Since the height is 4.5 ft
Substitute them in the rule above
[tex]\begin{gathered} V=3.14\times(12.5)^2\times4.5 \\ V=2207.8125ft^3 \end{gathered}[/tex]Now we will change the cubic feet to gallons
[tex]\because1ft^3=7.48\text{ gallons}[/tex]Then multiply the volume by 7.48 to find the number of gallons
[tex]7.48\times2207.8125=16514.4375gallons[/tex]Now let us divide the number of gallons by 3000 to find how many gallons of liquid chlorin he needs to buy
[tex]\frac{16514.4375}{3000}=5.5048125[/tex]Then he has to buy 6 full gallons
PLEASE HELP ASAP! What is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola?
A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.
What is hyperbola?A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set. A hyperbola is made up of two mirror images of one another that resemble two infinite bows.These two sections are known as connected components or branches. A series of points in a plane that are equally spaced out from a directrix or focus is known as parabolas. The difference in distances between a group of points that are situated in a plane and two fixed points—which is a positive constant—is what is referred to as the hyperbola.Therefore, a hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.
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To find the area of a shape region:Find the area of the entire region:Fimd the area of the unshaded region(s)Subtract the area of the unshape region from the area of the entire region
IN order to find the area of the shaded region, proceed as follow:
calculate the area of the right triangle:
A = b·h/2
A = (21 yd)(34 yd)/2 = 357 yd²
next, calculate the area of the circle:
A' = π r²
A' = (3.1415)(7 yd)² = 153.93 yd²
next, subtract the area of the circle to the area of the rectangle:
AT = A - A' = 357 yd² - 153.93 yd²
AT = 203.07 yd²
Hence, the area of the shaded region is 203.07 yd²
Please can I have the answer for number 12?Thanks a lot
Given:
length of the piece of string = 3/4 inches
length of the piece that we need = 1/8 inches
The number of smaller piece that we can get from the original piece of string can be calculated using the formula:
[tex]\text{Number }of\text{ smaller piece = }\frac{length\text{ of original piece}}{length\text{ of smaller piece}}[/tex]Applying this formula:
[tex]\begin{gathered} \text{Number of smaller piece = }\frac{3}{4}\div\text{ }\frac{1}{8} \\ \end{gathered}[/tex]If the number of pieces is represented as n:
[tex]n\text{ = }\frac{3}{4}\div\text{ }\frac{1}{8}[/tex]Answer:
find the lowest common denominator of - not graded !
Given:
There are two equation given in the question.
Required:
We have to find the lowest common denominator of both equation.
Explanation:
[tex]\frac{p+3}{p^2+7p+10}and\frac{p+5}{p^2+5p+6}[/tex]are given equations
first of all we need to factorization both denominator
[tex]\begin{gathered} p^2+7p+10and\text{ }p^2+5p+6 \\ (p+5)(p+2)and\text{ \lparen p+3\rparen\lparen p+2\rparen} \end{gathered}[/tex]so here (p+2) is common in both so take (p+2) for one time only
so now the lowest common denominator is
[tex](p+5)(p+2)(p+3)[/tex]Final answer:
The lowest common denominator for given two equations is
[tex](p+5)(p+2)(p+3)[/tex]
Attached is a photo of my written question, thank you.
Given:
The function is,
[tex]f(x)=-2x^2-x+3[/tex]Explanation:
Determine the function for f(x + h).
[tex]\begin{gathered} f(x+h)=-2(x+h)^2-(x+h)+3 \\ =-2(x^2+h^2+2xh)-x-h+3 \\ =-2x^2-2h^2-4xh-x-h+3 \end{gathered}[/tex]Determine the value of expression.
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-2x^2-2h^2-4xh-x-h+3-(-2x^2-x+3)}{h} \\ =\frac{-2h^2-4xh-h}{h} \\ =-2h-4x-1 \end{gathered}[/tex]So exprression after simplification is,
-2h - 4x - 1
Enter your solution as an ordered pair, with no spaces and with parentheses. OR the answer could be: Infinitely many OR No Solution
Given the equation system:
[tex]\begin{gathered} 1)y=4x \\ 2)3x+2y=55 \end{gathered}[/tex]The first step is to replace the first equation in the second equation
[tex]3x+2(4x)=55[/tex]With this, we have a one unknown equation. Now we can calculate the value of x:
[tex]\begin{gathered} 3x+8x=55 \\ 11x=55 \\ \frac{11x}{11}=\frac{55}{11} \\ x=5 \end{gathered}[/tex]Now that we know the value of x, we can determine the value of y, by replacing x=5 in the first equation
[tex]\begin{gathered} y=4x \\ y=4\cdot5 \\ y=20 \end{gathered}[/tex]This system has only one solution and that is (5,20)
1) K thinks of a number, then doubles the number ,and then multiplies the result by 3 . If her final number is 65 more than her original number, then what was her original number?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The original number is 13.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 2x = 4 is an equation.
We have,
Let the number be K.
K thinks of a number, then doubles the number, and then multiplies the result by 3.
This can be written as:
(2 x k) = 2k ____(1)
3 x (2k) = 6k ____(2)
If her final number is 65 more than her original number can be written as:
6k = 65 + k _____(3)
From (3) we get,
6k = 65 + k
Subtract k on both sides.
6k - k = 65 + k - k
5k = 65
Divide both sides by 5.
5k / 5 = 65 / 5
k = 13
Thus,
The original number is 13.
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need help with image
Step by step explanation:
sum of co-exterior angle is 180°
(10x-48)+(6x)=180°
4x-48=180°
4x=180-48
4x=132
x=132/4
x=33
5. How would you solve the system of equations y = 5x + 1 and -2x + 3y =-10 ? What is the solution? *
SOLUTION:
Step 1:
In this question, we are given the following:
Solve the system of equations y = 5x + 1 and -2x + 3y =-10 ?
What is the solution?
Step 2:
The solution to the systems of equations:
[tex]\begin{gathered} y\text{ = 5x + 1 -- equation 1} \\ -2x\text{ + 3y = -10 -- equation 2} \end{gathered}[/tex]check:
Given y = -4 , x = -1
Let us put the values into the equation:
y = 5x + 1 and -2x + 3y = -10
[tex]\begin{gathered} y\text{ = 5x + 1} \\ -4=5(-1)\text{ + 1} \\ -4=-5+1 \\ -4\text{ = - 4 (COR}\R ECT) \end{gathered}[/tex][tex]\begin{gathered} -2x+3y\text{ = -10} \\ -2(-1)+3(-4)_{}_{} \\ 2-12=-10\text{ (COR}\R ECT) \end{gathered}[/tex]CONCLUSION:
The solution to the system of equations are:
[tex]\begin{gathered} \text{x = -1} \\ y=-4 \end{gathered}[/tex]
the sum of interior angle measures of a polygon with n sides is 2340 degrees. find n15
the measure of each angle will be 2340/n then if n=15 the measure of each one of the angles will be 2340/15=156 degrees
Brandon's car used 10 gallons to travel 310 miles. At what rate does the car use gas, in miles per gallon?On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
Given:
At 10 gallons, the car is able to cover 310 miles.
Find: At 1 gallon, the car can travel ____ miles.
Solution:
First, let's fill in the number line with the given values.
To solve for the question mark at 1 gallon, simply divide 310 by 10.
[tex]310\div10=31[/tex]Hence, the car uses gas at 31 miles per gallon.
find the area of the circle with a circumference of 30π. write your solution in terms of π
we know that
the circumference of a circle is giving by
[tex]C=2\pi r[/tex]we have
C=30pi
substitute
[tex]\begin{gathered} 30\pi=2\pi r \\ \text{simplify} \\ r=\frac{30}{2} \\ r=15\text{ units} \end{gathered}[/tex]Find the area of the circle
[tex]A=\pi r^2[/tex]substitute the value of r
[tex]\begin{gathered} A=\pi(15^2) \\ A=225\pi\text{ unit\textasciicircum{}2} \end{gathered}[/tex]the area is 225π square units95-a(b+c) when a= 9, b = 3 and c=7.4 I don’t get how to solve this please put an explanation
Notice that in the statement of the exercise are the values of a, b and c. Then, to evaluate the given expression, we replace the given values of a, b, and c. So, we have:
[tex]\begin{gathered} a=9 \\ b=3 \\ c=7.4 \\ 95-a\mleft(b+c\mright) \\ \text{ We replace the given values} \\ 95-a(b+c)=95-9(3+7.4) \\ 95-a(b+c)=95-9(10.4) \\ 95-a(b+c)=95-93.6 \\ 95-a(b+c)=\boldsymbol{1.4} \end{gathered}[/tex]Therefore, the result of evaluating the given expression when a = 9, b = 3, and c = 7.4 is 1.4.
What is the value of sinθ given that (3, −7) is a point on the terminal side of θ?
Solution
[tex]\begin{gathered} \text{ using pythagoras theorem} \\ \\ OB=\sqrt{OA^2+AB^2}=\sqrt{3^2+7^2}=\sqrt{58} \\ \\ \Rightarrow\sin\theta=\frac{AB}{OB}=-\frac{7}{\sqrt{58}}=-\frac{7\sqrt{58}}{58} \end{gathered}[/tex]divide and Simplify 7/5 ÷7/9
What we have is a fractional division, this is following expression
[tex]\frac{(\frac{7}{5})}{(\frac{7}{9})}[/tex]For this procedure, it says to multiply the top and bottom ends to get the numerator, and the middle numbers to get the denominator
[tex]\frac{7\cdot9}{7\cdot5}=\frac{9}{5}[/tex]In conclusion after splitting and simplifying this, the answer is 9/5
J is the midpoint of CT if CJ=5x-3 and JT=2x+21 find CT
Since J is the midpoint of the CT segment, then:
[tex]\begin{gathered} CJ=JT \\ 5x-3=2x+21 \end{gathered}[/tex]Now, you can solve the equation for x:
[tex]\begin{gathered} 5x-3=2x+21 \\ \text{ Add 3 from both sides of the equation} \\ 5x-3+3=2x+21+3 \\ 5x=2x+24 \\ \text{ Subtract 2x from both sides of the equation} \\ 5x-2x=2x+24-2x \\ 3x=24 \\ \text{ Divide by 3 from both sides of the equation} \\ \frac{3x}{3}=\frac{24}{3} \\ x=8 \end{gathered}[/tex]Replace the value of x into the equation for segment CJ or segment JT to find out what its measure is. For example in the equation of the segment CJ:
[tex]\begin{gathered} CJ=5x-3 \\ x=8 \\ CJ=5(8)-3 \\ CJ=40-3 \\ CJ=37 \end{gathered}[/tex]Finally, you have
[tex]\begin{gathered} CJ=37 \\ CJ=JT \\ 37=JT \\ \text{ Then} \\ CT=CJ+JT \\ CT=37+37 \\ CT=74 \end{gathered}[/tex]Therefore, the measure of the segment CT is 74.
Martin and Isabelle go bowling. Each game costs $10, and they split that cost. Martin has his own bowling shoes, but Isabelle pays $3 to rent shoes.Which graph shows a proportional relationship? Explain why.
We have the following:
Martin's graph is good and correct, although it is not totally straight, but the relationship that it keeps is totally proportional.
On the other hand, Isabelle's graph, although it is totally straight, is wrong, because she must start from 3, which is the rental value of the shoes, and her graph starts at 0, therefore it is wrong, despite of which shows a proportional relationship.
Therefore the correct answer is Martin's graph.
Answer:
Step-by-step explanation:
a line with a slope of 1/3 and containing the point (-4,7)
An equation of line with a slope of 1/3 and containing the point (-4,7) is
y = 1/3 x + 25/7
In this question, we have been given
slope (m) = 1/3
and a point (-4, 7)
We need to find an equation of a line with a slope of 1/3 and containing the point (-4,7)
Using the formula for the slope-point form of equation of line,
y - y1 = m(x - x1)
y - 7 = 1/3(x + 4)
y - 7 = (1/3)x + 4/3
y = (1/3)x + 4/3 + 7
y = 1/3 x + 25/7
Therefore, an equation of line with a slope of 1/3 and containing the point (-4,7) is y = 1/3 x + 25/7
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1+——>1/12 write. Fraction to make each number sentence true, answer I got is 1/1
c) Set x to be the number we need to find; therefore, the inequality to be solved is
[tex]\begin{gathered} 1+x>1\frac{1}{2}=1+\frac{1}{2}=\frac{3}{2} \\ \Rightarrow1+x>\frac{3}{2} \\ \Rightarrow-1+1+x>-1+\frac{3}{2} \\ \Rightarrow x>\frac{1}{2} \end{gathered}[/tex]Therefore, any number greater than 1/2 (greater, not equal to) satisfies the inequality; particularly 1/1=1>1/2. Thus, 1/1 is a possible answer
A 35-foot wire is secured from the top of a flagpole to a stake in the ground. If the stake is 1 feet from the base of the flagpole, how tall is the flagpole?
The figure for the height of flagpole, wire and ground is,
Determine height of the pole by using the pythagoras theorem in triangle.
[tex]\begin{gathered} l^2=b^2+h^2 \\ (35)^2=(14)^2+h^2 \\ 1225-196=h^2 \\ h=\sqrt[]{1029} \\ =32.078 \\ \approx32.08 \end{gathered}[/tex]Thus, height of the flagpole is 32.08 feet.
Please help with this question
The average velocities of the stone are: i) 12.96 m / s, ii) 13.20 m / s, iii) 13.20 m / s, iv) 13 m / s. The instantaneous velocity is approximately equal to 13 meters per second.
How to find the average velocity and the instantaneous velocity of a stone
The average velocity (u), in meters per second, is the change in the height (h), in meters, divided by the change in time (t), in seconds. And the instantaneous velocity (v), in meters per second, is equal to the average velocity when the change in time tends to zero.
a) Then, the average velocities are determined below:
Case i)
u = [f(1.05) - f(1)] / (1.05 - 1)
u = (18.748 - 18.1) / 0.05
u = 12.96 m / s
Case ii)
u = [f(1.01) - f(1)] / (1.01 - 1)
u = (18.232 - 18.1) / 0.01
u = 13.20 m / s
Case iii)
u = [f(1.005) - f(1)] / (1.005 - 1)
u = (18.166 - 18.1) / 0.005
u = 13.20 m / s
Case iv)
u = [f(1.001) - f(1)] / (1.001 - 1)
u = (18.113 - 18.1) / 0.001
u = 13 m / s
The fourth option offers the best estimation for the instantaneous velocity at t = 1 s. Then, the instantaneous velocity is approximately equal to 13 meters per second.
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A box contains 6 red pens, 4 blue pens, 8 green pens, and some black pens. Leslie picks a pen and returns it to the box each time. the outcomes are: number of times a red pen is picked: 8number of times a blue pen is picked: 5 number of times a green pen is picked: 14number of times a black pen is picked: 3Question: if the theoretical probability of drawing a black pen is 1/10, how many black pens are in the box?
We have:
x = total pens
n = number of black pens
so:
[tex]x=6+4+8+n=18+n[/tex]and for black pen:
[tex]\begin{gathered} \frac{1}{10\text{ }}=0.1\text{ (probability)} \\ \text{then} \\ \frac{n}{18+n}=0.1 \\ n=0.1(18+n) \\ n=1.8+0.1n \\ n-0.1n=1.8+0.1n-0.1n \\ 0.9n=1.8 \\ \frac{0.9n}{0.9}=\frac{1.8}{0.9} \\ n=2 \end{gathered}[/tex]answer: 2 black pens
15 = a/3 - 2
what is a?
Answer: a is 51
Step-by-step explanation:
Hope this help.
Answer:
a==51
Step-by-step explanation:
15=a/3-2
a/3-2+2=15+2
a/3=17
a=17*3
a=51
Help pleas Which statement best completes the diagram.
The statement which best completes the cause and effect diagram is that: A. British leaders limit the ability of colonists to expand westward.
What is a cause and effect graphic organizer?A cause and effect graphic organizer is also referred to as cause and effect diagram and it can be defined as a type of chart which highlights and shows the relationship between two things, phenomenon, or events in which an occurrence of one (cause) typically leads to the occurrence of another (effect).
During the late 18th to mid 19th centuries, the United States of America began to grow westward and this led to the emigration of Native American tribes who had in this geographical region for thousands of years before the arrival of European colonists.
Consequently, conflict developed between them which was known as "The French and Indian War" and this caused British leaders to limit the ability of many European colonists to continue expanding westward.
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Complete Question:
Which statement best completes the diagram?
A. British leaders limit the ability of colonists to expand westward.
B. British merchants refuse to buy raw materials from the colonies.
C. British military forces are ordered to leave North America.
D. British leaders end policies that strictly controlled the colonies.