There are 6 people going to the movie
Jan, her 3 children, 2 neighbor children
(1+3+2)
Each costs 3 dollars to get in
Total cost = number of people * cost
Total cost = (1+3+2) * 3
= 6*3
= 18
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
Width = 5.7 ft, Length = 10.5 ft
Step-by-step explanation:
Let the width be [tex]w[/tex]. Then, the length is [tex]2w-0.9[/tex].
[tex]w(2w-0.9)=59.85 \\ \\ 10w(20w-9)=5985 \\ \\ 200w^2-90w-5985=0 \\ \\ 40w^2-18w-1197=0 \\ \\ (4w+21)(10w-57)=0 \\ \\ w=5.7 (w>0) \\ \\ \implies 2w-0.9=2(5.7)-0.9=10.5[/tex]
The sum of two numbers is 38 and their product is 165. Find the larger number. PLEASE HELP
Answer:
The larger number is 33
Step-by-step explanation:
Writing and solving a system of equations
Let x and y be the numbers
sum of two numbers is 38
x+y = 38
their product is 165
xy = 165
x = 38-y
Substitute this into xy =165
(38-y) * y = 165
38y - y^2 = 165
-y^2 + 38y -165 = 0
Multiply by -1
y^2 - 38y + 165 =0
Factor
( y-33) ( y-5) = 0
Using the zero product property
y -33 =0 y-5 =0
y =33 y=5
Now we can find x for each solution
x = 38-33 =5 x = 38-5 = 33
The two numbers are 33 and 5
The larger number is 33
PLEASE HELP ME OUT 12x^2+4x-1
Answer:
(6x-1)(2x+1)
Step-by-step explanation:
12x²+4x-1 (find two numbers that when you add or subtract them the ANS will be the coefficient of x and those same numbers when you multiply them the ANS will be the product of 12 and -1) then replace the middle term with those numbers.
12x²+6x-2x-1
(12x²+6x)(-2x-1)
6x(2x+1)-1(2x+1)
(6x-1)(2x+1)
Susie makes bracelets to sell at a local craft fair. At each craft fair, she sells 16 more bracelets than the last time. At her first craft fair, she sold 82 bracelets. At her second craft fair, she sold 98 bracelets. At her third craft fair, she sold 114 bracelets. If this pattern continues, how many bracelets will she sell at her sixth craft fair? 120 bracelets 130 bracelets 146 bracelets 162 bracelets
Answer:
162 bracelets
Step-by-step explanation:
1st - 82 bracelets
2nd - 98
3rd - 114
4th - 130
5th - 146
6th - 162
The height of a bridge is given by y=-3x² + x, where y is the height of the bridge (in miles) and x is the number of miles from the base of the bridge.
A. How far from the base of the bridge does the maximum height occur?
B. What is the maximum height of the bridge?
Answer:
A. (1/6) mile is the maximum height.
B. The maximum height occurs (3/36) miles from the base of the bridge.
Step-by-step explanation:
The answer of (1/6) mile to the point of maximum height is correctly given by 001466952. I'll add a little more perspective as well as a second approach in addition to graphing.
Graphing
As suggested by 001466952, one may graph the function and look for the point at which the maximum (vertex) is located. The attached graph shows this approach. The maximum height of 0.83 miles is also found on the graph [point (0.1667, 0.083)].
First Derivative
One may also take the first derivative of the function. The first derivative will provide the slope at any point x on the original curve. The slope at the vertex will be 0 (the top point where the slope turns from positive to negative). The slope will be zero at the very top.
y = -3x^2 + x
dy/dx = -6x + 1
0 = -6x+1
x = (1/6) mile
Use x = (1/6) in the original equation to find the height at this point.
y = -3x^2 + x
y = -3(1/6)^2 + (1/6)
y = (-3/36) + (6/36)
y = 3/36 or 0.083 miles from the bridge's base.
The solution is
a) The maximum height occurs at x = 1/6 where x is the number of miles from the base of the bridge
b) The maximum height of the bridge is ( 1/12 ) miles
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the height of the bridge be represented by the equation ,
y = -3x² + x be equation (1)
where y is the height of the bridge
and x is the number of miles from the base of the bridge
Now , to find the number of miles at which the maximum height occurs
Take the first derivative of the function and substitute it to 0
So , ( dy / dx ) = 0 ( at maximum height )
On simplifying the equation , we get
dy / dx = -6x + 1
when ( dy / dx ) = 0 ( at maximum height )
-6x + 1 = 0
Adding 6x on both sides of the equation , we get
6x = 1
Divide by 6 on both sides of the equation , we get
x = 1/6
Now , the maximum height of the bridge is at when x = 1/6
Substitute the value of x = 1/6 in equation (1) , we get
y = -3x² + x
y = -3 ( 1/6 )² + 1/6
y = -3/36 + 1/6
On simplifying the equation , we get
y = 3/36 miles
y = 1/12 miles
Hence , the maximum height of the bridge is 1/12 miles
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
15. An object that weighs exactly 1pound is placed on a digital scalethat measures weight in ounces. Ifthe scale is precise but notaccurate, what weight might beshown on the scale?
The rate of conversion between pounds and ounces is shown as;
16 ounces = 1 pound
Then you have a digital scale that measures weight in ounces. If you put an object that weighs "exactly 1 pound" on the digital scale, its supposed to display 16 ounces.
However the scale has been described as "not accurate," which implies that the calibration (fine tuning) has been altered either accidentally or on purpose. This also implies that the result would not be 100 percent correct, but it might be a little over or below 16 ounces. Hence the scale might display what in mathematics is termed as "plus or minus" and is denoted by the sign ±
The scale therefore might display 15 ounces or 17 ounces (that is ± 16)
±
A bottle rocket is launched straight up. Its height in feet (y) above theground x seconds after launch is modeled by the quadratic function: y =-16x2 + 132x + 6.How many seconds did it take the rocket to reach its maximum height?
Answer:
(C)4.125 seconds
Explanation:
The quadratic function modeling the rocket's movement is:
[tex]y=-16x^2+132x+6[/tex]To determine the number of seconds it takes the rocket to reach its maximum height, we are being asked to find the equation of the line of symmetry.
For a quadratic function of the form y=ax²+bx+c, the equation of the line of symmetry is:
[tex]x=-\frac{b}{2a}[/tex]In the given equation:
a = -16, b = 132
Therefore:
[tex]\begin{gathered} x=-\frac{132}{-2\times16} \\ x=4.125 \end{gathered}[/tex]It takes the rocket 4.125 seconds to reach its maximum height.
Annie's mother asked Annie to go buy oranges, dog food, and bug spray. Each square's side length is 1 block. How many blocks will Annie have to walk in all if she visits the fruit stand, the pet store, and the supermarket, in that order, before returning home?
Here using the length of square, it is obtained that
Annie walked 14 blocks in total.
What is a square?
Square is a two dimensional four sided figure.
Here,
Length of each side of one square = 1 block
From Annie's home to the supermarket, Annie will have to walk 1 block
From Supermarket to pet store, Annie will have to walk 1 block straight and then 2 blocks to the left
From pet store to the fruit vendor, Annie will have to walk 1 block straight and then 2 blocks to the left
Total number of blocks walked by Annie from home = 1 + 1 + 2+ 1 + 2
= 7 blocks
Total number of blocks walked by Annie while returning home
= 1 + 1 + 2+ 1 + 2
= 7 blocks
Total number of blocks walked by Annie = 7 + 7 = 14 blocks
To learn more about square, refer to the link-
https://brainly.com/question/25092270
#SPJ1
Complete Question
The figure has been attached
Eight minus six and two-fifths
Answer:
1 and three-fifth or 1.6
Can someoen answer this please
Answer:
n general, greater frequency and intensity of climate hazards are more likely to prompt people to migrate when the population is more vulnerable and has a lower capacity to adapt. Climate events can be divided into fast- and slow-onset events.
Step-by-step explanation:
Hi, can you help me answer this question please, thank you
Given:
The test claims that the proportion of men who own cats is smaller than the proportion of women who owns cat.
The null and atlernative hypothesis is given as,
[tex]\begin{gathered} \mu_M=\text{ Men who own cats} \\ \mu_F=\text{ Women who own cats} \end{gathered}[/tex]So,
[tex]\begin{gathered} H_0\colon\mu_M=\mu_F_{} \\ H_1\colon\mu_M<\mu_F \end{gathered}[/tex]Answer: option c)
Answer:
what he said^^
Step-by-step explanation:
because of blablablablabla
Use the dilation to find the value of y.
According to definition of dilation and the characteristics of the geometrical system in the picture, we find that the misssing side has a length of 25 units. (Correct choice: C)
How to determine the length of the missing side associated to two proportional triangles
The figure shows a geometrical system of two proportional right triangles generated about the point C, in which two pairs of sides related to the same side ratio for a dilation. Mathematically speaking, a dilation is defined by the following expression:
k = AB / A'B'
Where:
k - Scale factorAB - Original sideA'B' - Dilated sideThe ratio formula associated to the figure is shown below:
y / 35 = 15 / 21
y = (15 / 21) · 35
y = 25
The missing length is equal to 25.
To learn more on dilations: https://brainly.com/question/13176891
#SPJ1
Lindsey bought a picnic basket originally priced at $40 but on sale for 50% off. After 10% sales tax, what was the total cost?
$
The total cost price of the basket is $22.
What is Discount ?
The discount is determined by dividing the purchase price by the item's par value. The discount is a type of cost price reduction or deduction for a product. It is primarily employed in consumer interactions when discounts on various goods are offered to customers. A percentage represents the discount rate.
Here ,
Original cost price of the basket = $40
After 50% offer the cost price of the bag is,
=> 40- 50% of 40
=> 40 - 20
=> $20.
Now the sales tax is 10% then,
=> 20+ 10% of 20
=> 20+ 2
=>$22
Therefore the total cost is $22 after discount.
To learn more about discount
https://brainly.com/question/24711235
#SPJ1
Can you please help me
Step 1: Write out the formula for finding the area of a rhombus
[tex]\begin{gathered} \text{Area }=\frac{AC\times DB}{2} \\ \text{ Where} \\ AC\text{ and DB are the diagonals of the rhombus } \end{gathered}[/tex]Step 2: Substitute the given values to find AC
[tex]\begin{gathered} \text{ Area }=45\text{ square units} \\ DB=6\text{units} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{6AC}{2}=45 \\ 3AC=45 \\ \text{ Dividing both by 3, we have} \\ \frac{3AC}{3}=\frac{45}{3} \\ AC=15 \end{gathered}[/tex]Hence, AC is 15 unitsTwo points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 60 yd from B and 105 yd from A, with angle ACB measuring 69.3 . How far apart are A and B (to the nearest yard)?A. 101 yardsB. 110 yardsC. 119 yardsD. 128 yards
Let's draw a diagram of this problem:
This triangle can be seen as follows:
We can use the Law of Cosines to find the length of side c, since we know the measure of angle C:
[tex]c^2=a^2+b^2-2ab\cos (C)[/tex]In our case:
[tex]c^2=105^2+60^2-2(105)(60)\cos (69.3)[/tex][tex]c^2=11025+3600-12600\cos (69.3)=14625-12600\cos (69.3)[/tex]Taking the square root of both sides we get:
[tex]c=\sqrt[]{14625-12600\cos (69.3)}[/tex]which, using a calculator or online resource to calculate the right side of the equation will give us:
[tex]c=100.9[/tex]To the nearest yard, A and B are 101 yards apart, so option A. is correct.
If you make $75.00 a week at your job and want to save $250.00 over 3 months, saving an equal amount each week, how much spending money will you have each week?
The amount of spending money you will have each week is $54.17 .
How to find the spending money available?You make $75.00 a week at your job and want to save $250.00 over 3 months, saving an equal amount each week.
The amount of spending money available each week can be calculated as follows:
Therefore,
3 months = 12 weeks
let
x = amount saved every week.
Therefore,
12x = 250
x = 250 / 12
x = 20.83 dollars
Hence,
Amount of spending money each week = 75 - 20.83
Amount of spending money each week = $54.17
learn more on savings here:https://brainly.com/question/2871328
#SPJ1
PLEASE HELP QUICK 25 POINTS
Solve the following system of equations algebraically:
y = x² - 14x + 23
y=-3x + 5
Answer:
x=9, x=2
Step-by-step explanation:
Since both expressions (x^2 - 14x + 23 and -3x+5) are equal to y, set those expressions equal to each other and solve for x.
x^2 - 14x + 23 = -3x + 5
subtract 5 from both sides
x^2 - 14x + 23 - 5 = -3x + 5 - 5
x^2 - 14x + 18 = -3x
add 3x to both sides
x^2 - 14x + 3x + 18 = -3x + 3x
x^2 - 11x + 18 = 0x
factor.
(x-9)(x-2) = 0
Because the product of these two things equals 0, we know that one of these terms must equal to zero.
x-9 = 0 or x-2 = 0
it can be either, so solve for both.
x-9 + 9 = 0 + 9 or x-2 + 2 = 0 + 2
x = 9 or x=2
One number is chosen from the list 2,4,6, and 8. Another is selected from the list 6, 7 and 8. Find the probability that they are the same. a. 0 b.1/6 c. 2/3 d. 1/3
There are 2 options to get the same number, they choose 6 from both lists or they choose 8 from both lists.
Then, the probability to select 6 from the first list is:
[tex]\frac{1}{4}[/tex]Because we have 4 options ( 2, 4, 6, 8) and 1 of then is number 6. At the same way, the probability to select 6 from the second list is:
[tex]\frac{1}{3}[/tex]Because there are 3 numbers and one of them is 6.
Finally, the probability to choose 6 from both lists is the multiplication of the probabilities above, so:
[tex]P_6=\frac{1}{4}\cdot\frac{1}{3}=\frac{1}{12}[/tex]We can also calculate the probability to choose 8 from both lists as:
[tex]P_8=\frac{1}{4}\cdot\frac{1}{3}=\frac{1}{12}[/tex]Because 1/4 is the probability to choose 8 from the first list and 1/3 is the probability to select 8 from the second list.
Therefore, the probability that both numbers are the same is the sum of the probability to choose 6 from both lists and the probability to choose 8 form both lists.
[tex]\begin{gathered} P=P_6+P_8 \\ P=\frac{1}{12}+\frac{1}{12} \\ P=\frac{1}{6} \end{gathered}[/tex]Answer: b. 1/6
Simplify the expression.
negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths
The actual solution of the mathematical statement is -6.93
How to determine the actual solution?From the question, we have the following statement that can be used in our computation:
negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths
Mathematically, this statement can be expressed as
-15 + -3.7 + 9.15/5 * 3² - 4.7
Evaluate the quotient and the exponents in the expression'
So, we have
-15 + -3.7 + 1.83 * 9 - 4.7
Evaluate the product exponents in the expression'
So, we have
-15 + -3.7 + 16.47 - 4.7
Evaluate the sum and the difference
-6.93
Hence, the solution is -6.93
Read more about expressions at
brainly.com/question/4344214
#SPJ1
PLEASE ANSWER. I REALLY NEED THIS A+++
Answer: the first one is yes and the second one is no
Step-by-step explanation: that’s the answer i took the test
Consider the following solutions Please help on my question I’m confused
The function f(x) and g(x) is given as follows:
[tex]f(x)=4x+5;\; g(x)=2x-1[/tex]The composite function is defined as:
[tex](f\circ g)(x)=f(g(x))[/tex]Replace x with g(x) in the expression given for f(x):
[tex]f(g(x))=4(g(x))+5[/tex]Substitute g(x)=2x-1 into the right-hand side of the equation:
[tex]\begin{gathered} f(g(x))=4(2x-1)+5 \\ \Rightarrow f(g(x))=8x-4+5=8x+1 \end{gathered}[/tex]Recall that,
[tex]\begin{gathered} (f\circ g)(x)=f(g(x)) \\ \Rightarrow(f\circ g)(x)=8x+1 \end{gathered}[/tex]Notice that the composite function is a polynomial function of degree one (linear).
Recall also, that the domain of all polynomial functions is the set of real numbers.
Hence, the domain of the composite function (fog)(x) is the set of real numbers.
The set of real numbers in interval form is:
[tex](-\infty,+\infty)[/tex]The answer is:
[tex]\begin{gathered} (f\circ g)(x)=\boxed{8x+1} \\ \text{The domain of }(f\circ g)(x)\text{ is }\boxed{(-\infty,+\infty)} \end{gathered}[/tex]Write an equation of the line that passes through the point (-2,6) and is parallel to the line that passes through the points (0,-4) and (3,2)
We have the points:
p(0,-4) & q(3,2)
then, our directional vector will be:
pq(3,6)
now we have the equation of the line that we need to be parallel with:
(x,y)=(0,-4)+t(3,6)
We get (3,6) as follows:
we determine the directonal vector using the two point given:
p(0,-4) & q(3,2)
pq(3-0,2+4) =>pq=(3,6)
Now, the point of the line that is parallel to the one we got is: (-2,6):
Since a condition for being parallel is that the directional vector from one line is a product of the other, then:
(x,y) = (-2,6) + t(6,12)
As can be seen, the directional vector is parallel to the one found before (one is multiple of the other)
As for before, the equation of the line that passes by the point (-2,6) and is parallel to the line (x,y) = (0,-4) + t(3,6) is:
[tex](x,\text{ y) = (-2,6) + t(6,12)}[/tex]show your stepsWhat is the solution of the equation?SEE IMAGE
Given the equation
[tex]\begin{gathered} 3\text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ + 3 = 27} \\ \end{gathered}[/tex]Subtract 3 from both sides
[tex]\begin{gathered} 3\text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ + 3-3 = 27}-3 \\ \\ 3\text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ = }24 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ = }\frac{24}{3} \\ \text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ = 8} \\ \end{gathered}[/tex]Raise both sides to power 5 to remove the 5th root on the left hand side
[tex]\begin{gathered} \text{ (}\sqrt[5]{(x+2)^3\text{ }})^5=8^5 \\ \\ (x+2)^3=(8^{})^5 \\ (x+2)^3=\text{ 32768} \\ \end{gathered}[/tex]Take the cube root of both sides
[tex]\begin{gathered} \sqrt[3]{(x+2)^3}^{}=\sqrt[3]{32768} \\ (x+2\text{ )= 32} \\ \end{gathered}[/tex]Subtract 2 from both sides
x + 2 = 32
x = 32 - 2
x = 30
The solution to the equation is x = 30
8(y+4)-2(y-1)=70-3y
solve for y
Answer:
y = 4
Step-by-step explanation:
8(y + 4) - 2(y - 1) = 70 - 3y ← distribute parenthesis and simplify left side
8y + 32 - 2y + 2 = 70 - 3y
6y + 34 = 70 - 3y ( add 3y to both sides )
9y + 34 = 70 ( subtract 34 from both sides )
9y = 36 ( divide both sides by 9 )
y = 4
What is the purpose of the vertical line test for functions?
Answer:
The purpose of the vertical line test is to determine if the function is in fact a function. (Option C)
Explanation:
Once a vertical line is drawn to every part of the function and it only hit one point on the graph, then it is a function. For example,
If the vertical line hits two points or more on the graph, then the graph is not a function. For example, a circle is not a function.
A café has 60 tables. 35% of the tables have 2 chairs at each table. The remaining 65% of the tables have 4 chairs at each table. How many tables have 4 chairs?
The value for 39 tables have 4 chairs.
What is percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Percentage formula = (Value/Total value) × 100
Given,
total number of tables = 60
Percentage of tables have 4 chairs = 65%
Number of tables have 4 chairs = 65(60)/100
= 39
To know more about percentage, visit:
https://brainly.com/question/27574467
#SPJ1
If the charge for shipping and handling is 8%, what is the total charge for an online order of $45?
We need to calculate the 8% of $45
[tex]45\cdot\frac{8}{100}=3.60[/tex]The total charge will be
[tex]45+3.60=48.60[/tex]ANSWER
The total charge is $48.60
is у = 3х3 – 3 linear?
Given the equation :
[tex]y=3x^3-3[/tex]It is a cubic function because the power of x = 3
The cubic function is not linear function
The linear function has the form : y = m * x + b
The power of x for the linear function = 1
so, the answer is : No
Graph the equation on the coordinate plane. y=12x−3
In order to draw a straight line on a graph at least two points are needed.
The graph for the given straight line is shown in the diagram.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The given equation is as below,
y = 12x − 3
Substitute x = 0 in the above equation to get,
y = 12 × 0 - 3
=> y = -3.
Substitute y = 0 in the above equation to get,
0 = 12x - 3
=> x = 3 / 12
=> x = 1 / 4
Now, draw a line through these two points on the coordinate plane to get the graph of y = 12x − 3.
The graph of y = 12x − 3 is given in the following diagram.
Hence, the graph of the given equation is drawn by finding the intercepts.
To know more about straight line equation click on,
brainly.com/question/21627259
#SPJ1
Write a quadratic function that fits the points (0, 6), (2, 4), and (3, 6).
The quadratic equation y = x² - 3 · x + 6 fits the points (0, 6), (2, 4) and (3, 6).
How to find a quadratic equation that fits a set of three points
Herein we find a set of three points that fits in a quadratic equation, that is, a polynomial of the form y = a · x² + b · x + c, where a, b, c are real coefficients. It is possible to find a quadratic equation as the number of points is equal to the numbers of real coefficients.
First, obtain the system of linear equations by substituting the values of x and y on each case:
(x, y) = (0, 6)
a · 0² + b · 0 + c = 6
c = 6
(x, y) = (2, 4)
a · 2² + b · 2 + c = 4
4 · a + 2 · b + c = 4
(x, y) = (3, 6)
a · 3² + b · 3 + c = 6
9 · a + 3 · b + c = 6
Second, solve the system of linear equations by numerical methods:
(a, b, c) = (1, - 3, 6)
Third, write the resulting quadratic equation:
y = x² - 3 · x + 6
To learn more on quadratic equations: https://brainly.com/question/1863222
#SPJ1