Christopher sold 20 cups of large 20-ounce cups of lemonade
outside his house.
What are linear and non-linear functions?A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.
Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.
An example of a non-linear function is a quadratic function.
Given, Christopher has set up a lemonade stand outside his house and sells small cups and large cups of lemonade.
Small cups sold is x and the number of large cups sold is y.
Each small cup holds 10 ounces of lemonade and each large cup holds 20 ounces of lemonade and he sold 800 ounces.
Therefore,
10x + 20y = 800...(i)
He also sold twice as many small cups as large cups.
Therefore,
2y = x...(ii)
10(2y) + 20y = 800.
20y + 20y = 800.
40y = 800.
y = 20.
So, He sold 20 cups of large lemonade.
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What is the relation between direction cosines of a vector?
The direction cosines of a vector are the cosines of the angles between the vector and the three mutually perpendicular axes of a coordinate system.
The direction cosines of a vector [tex]$\mathbf{a}$[/tex] are denoted by l, m and n. Mathematically, the relation between these direction cosines is given by:
[tex]$$\mathbf{a}=l\mathbf{\hat{i}}+m\mathbf{\hat{j}}+n\mathbf{\hat{k}}$$[/tex]
where i,j and k are unit vectors along the three axes of the coordinate system.
To calculate the direction cosines of a given vector [tex]$\mathbf{a}$[/tex] with components [tex]$a_x$, $a_y$ and $a_z$[/tex], we can use the following formula:
[tex]$$l = \frac{a_x}{\sqrt{a_x^2+a_y^2+a_z^2}}$$[/tex]
[tex]$$m = \frac{a_y}{\sqrt{a_x^2+a_y^2+a_z^2}}$$ \\ $$n = \frac{a_z}{\sqrt{a_x^2+a_y^2+a_z^2}}$$[/tex]
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Write an equivalent expression using the distributive property: 6(x-8)
Answer: 6x-48
Step-by-step explanation:
Use the distributive property
6x-48
6x-6*8
6x-48
Please answer these questions with steps explaining how to solve them. Also please go step by step explaining what you did.
x/3 - 3 = x/9 + 3
Answer:
what does x mean, like what number does it represent in this situation
Answer:
x = 27
Step-by-step explanation:
I made '3' into 9/3
x/3 - 9/3 = x/9 + 9/3
convert terms to fractions with a denominator of 9
x/3 = 3x/9
9/3 = 27/9
3x/9 - 27/9 = x/9 + 27/9
(3x-27)/9 = (x+27)/9
since each denominator equals 9 we can set the numerators equal to each other:
3x - 27 = x + 27
3x = x + 54
2x = 54
x = 27
PLEASE HELP FAST I WILL GIVE BRAINLIEST, Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Using the properties of integer exponents, match each expression with its equivalent expression.
The 5⁻³ is equivalent to 1/125, - 5⁻³ is equivalent to -1/125, (-5⁻³)⁻¹ is equivalent to -125 and (-5⁻³)⁰ is equivalent to 1
What is Expression?An expression is combination of variables, numbers and operators.
Equivalent expressions are expressions that work the same even though they look different.
5⁻³
This can be written as 1/5³ which is equal to 1/125
-5⁻³
This can be written as -1/5³ which is equal to -1/125
(-5⁻³)⁻¹
We have an exponential property
[tex](x^{a} )^{b} =x^{ab}[/tex]
So (-5⁻³)⁻¹=(-5)³=-125
(-5⁻³)⁻¹ equivalent expression is -125
(-5⁻³)⁰
=(-5)⁰=1
Hence, the 5⁻³ is equivalent to 1/125, - 5⁻³ is equivalent to -1/125, (-5⁻³)⁻¹ is equivalent to -125 and (-5⁻³)⁰ is equivalent to 1
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If loga(7)=4, what is the value of a^4
Answer:
7
Step-by-step explanation:
So the log thingy is loga(b) = c
a^c = b
So in this one, a = a
b = 7
c = 4
a^4 = 7
Can some one help me with this question its hard :( down below ill give brainliest
Answer:
B) 7^2 x 7^3
Step-by-step explanation:
B is 7^5 , everything else is 7^4
A. X=9
B. X=14
C. X=16
D. X=12
E. X=10
Answer:
Angle K is 1/2 the measure of arc JL, so JL = 228. Add arc KL to arc JL to get 268 and subtract from 360. 360 - 268 = 92. 8x - 36 = 92. X = 16.
Step-by-step explanation:
The student is expected to determine the value of a collection of coins and bills. Which of the following is an example of a clear learning goal for the Texas Essential Knowledge and Skills (TEKS) skill stated above
With an accuracy of within $0.01, the student will be able to recognize
and determine the total worth of a given assortment of coins and bills, including pennies, nickels, dimes, quarters, half-dollars, and dollar bills.
TEKS stands for Texas Essential Knowledge and Skills. It is a set of state standards for public schools in Texas, that outline what students should know and be able to do in each grade level and subject area. The standards cover subjects such as English language arts, mathematics, science, social studies, and languages other than English.
The TEKS are used to guide the development of curriculum and instruction in Texas schools.
The clear learning goal for the Texas Essential Knowledge and Skills (TEKS) skill of determining the value of a collection of coins and bills could be: "The student will be able to accurately identify and calculate the total value of a given collection of coins and bills, including pennies, nickels, dimes, quarters, half-dollars, and dollar bills, to within $0.01."
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Select all that apply.
Which symbols could be used to make the following statement true?
-15__-19
>
<
There’s more symbols but I can’t write them
Answer:
It would be >
Step-by-step explanation:
> Means bigger than, and -15 is bigger than -19.
Think of it as a number line. On the positive spectrum,
a bigger number is bigger. On the negative side, a smaller
number is bigger.
Hope this helps!
PLEASE ASAP ILL GIVE BRAINLIEST.
Answer: 12 km\h north
Step-by-step explanation:
I actually have good guesses
Velocity = 12 km/h
-
Velocity can be defined as the division between distance traveled and the time it took for that distance to be traveled:
Velocity = Distance / Time
With the above information in mind, we can calculate the velocity of the bicycle:
Velocity = 18 km / 1.5 h
Velocity = 12 km/h
Thus the velocity of the bicycle is 12 kilometers per hour.
Find the horizontal distance x the escalator covers to the nearest tenth of a foot.
Given:
Length of escalator = 26 ft
Angle of depression = 41 degrees
To find:
The horizontal distance x the escalator covers to the nearest tenth of a foot.
Solution:
In a right angle triangle,
[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]
Using this formula for the given triangle, we get
[tex]\cos 41^\circ=\dfrac{x}{26}[/tex]
[tex]26\cos 41^\circ=x[/tex]
[tex]26(0.7547)=x[/tex]
[tex]19.6222=x[/tex]
Round the value to the nearest tenth.
[tex]x\approx 19.6[/tex]
Therefore, the escalator covers 19.6 ft horizontally.
Stefan sells Jin a bicycle for $139 and a helmet for $17 The total cost for Jin is %130 of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answer: Spent $120 originally, profited by $36
Step-by-step explanation:
The total cost Stefan earned from selling the helmet and the bicycle is $139 + $17 = $156.
130% can be rewritten as [tex]\frac{130}{100}[/tex] which is simplified to 1.3.
Set up and this equation to find 130% of this price.
[tex]1.3x = 156\\x = 120[/tex]
Stefan spent $120 on these items.
Subtract this value from the selling price and solve.
[tex]156-120 = 36[/tex]
Stefan made $36 from selling the helmet and bicycle.
Gianna has $760 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $356.46.
She buys 2 bicycle reflectors for $10.01 each and a pair of bike gloves for $20.72.
She plans to spend some or all of the money she has left to buy new biking outfits for $45.35 each.
Write and solve an inequality which can be used to determine
o
o, the number of outfits Gianna can purchase while staying within her budget.
Answer:
Gianna has $760 to spend and she has already spent $356.46 on a new bicycle, $10.01 on 2 bicycle reflectors, and $20.72 on a pair of bike gloves.
The total amount spent on these items is $356.46 + $10.01 + $20.72 = $387.19.
Gianna has $760 - $387.19 = $<<760-387.19=372.81>>372.81 left to spend on biking outfits.
She wants to buy biking outfits that cost $45.35 each.
We can write an inequality to represent the number of outfits Gianna can purchase while staying within her budget as follows:
45.35o <= 372.81
This inequality can be solved by dividing both sides by 45.35:
o <= 8.24
Therefore, Gianna can purchase 8 biking outfits while staying within her budget.
Step-by-step explanation:
HELP THIS IS EASY I JUST DONT UNDER STAND MATH ITS ON PERCETEGES
Answer:
H 40%
Step-by-step explanation:
29+27+24=80
32/80=0.4
Answer:
Step-by-step explanation:
32/80 x 100 = 40%
Find the perimeter of the parallelogram using the Pythagorean Theorem
Answer:
The perimeter of the paralellogram is [tex]24 + 2\sqrt{34}[/tex] units.
Step-by-step explanation:
We shall use the Pythagorean Theorem to determine the length of the two oblique line of the figure. From Geometry, we know that the perimeter of the parallelogram is the sum of the lengths of the four sides of the parallelogram.
First, we calculate the length of the oblique line, that is:
[tex]l_{O} = \sqrt{5^{2} + 3^{2}}[/tex]
[tex]l_{O} = \sqrt{34}[/tex]
Second, we determine the length of the vertical line by direct observation, that is:
[tex]l_{V} = 12[/tex]
Lastly, the perimeter is determined by the following formula:
[tex]p = 2\cdot (l_{O}+l_{V})[/tex]
[tex]p = 24+2\sqrt{34}[/tex]
The perimeter of the paralellogram is [tex]24 + 2\sqrt{34}[/tex] units.
Answer: 35.7
(This is the answer squared by the way)
Step-by-step explanation:
Select the correct answer. Which logarithmic equation is equivalent to this exponential equation? 2,400=7,500 (10) ^ -x
The logarithmic equation that is equivalent to this exponential equation 2,400=7,500 (10) ^ -x is [tex]x = -log_{10} \frac{8}{25}[/tex]. Option C
How to solve for the equationfrom the question we have:
2400 = 7500(10)⁻ˣ
we would have to transform the equation that we have here into the logarithm form.
This is written as:
[tex]\frac{2400}{7500}=10^-^x[/tex]
from here we are to reduce the division
hence we would have:
[tex]10^-^x = \frac{8}{25}[/tex]
-x = log₁₀8/25
then
[tex]x = -log_{10} \frac{8}{25}[/tex]
option c is correct
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To be able to walk to the center $C$ of a circular fountain, a repair crew places a 16-foot plank from $A$ to $B$ and then a 10-foot plank from $D$ to $C$, where $D$ is the midpoint of $\overline{AB}$ . What is the area of the circular base of the fountain
The area of the circular base of the fountain is 179 square feet.
What is the area of the circular base ?A circle's area is equal to its radius, r, squared, then multiplied by the mathematical constant pi: A = pi x r2.
A cylinder has two bases that are two congruent circles at the top and bottom. The radius r of a cylinder is only the radius of the circular bases, and the height h of a cylinder is the perpendicular distance between these bases.
Combined area of the walkway and fountain: (3.14)112=379.94 ft2.
Fountain area: (3.14)8*2=200.96 feet
Walkway area: 379.94-200.96=178.98 square feet, which is also rounded to 179 square feet.
The area of the circular base of the fountain is 179 square feet.
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The mighty oak tree outside of Matt's house had to be cut down. He missed the beautiful tree and the shade it provided and wanted to replace it with an oak tree that would grow quickly. The Nuttall Oak (Quercus nuttalli), the fastest-growing oak tree, grows 7 to 8feet per year (we'll assume it grows at a constant rate). At maturity, it can be up to 50 feet tall.
Which of the following equations, where t represents time in years and h represents the height in feet, describe growth that is slower than the Nuttall Oak growth rate?
CHOICES:
A: h=5t
B: h=8.5t
C: h=10t
D: h=50t
Growth that is slower than the Nuttall Oak growth rate is h=5t.
What is equation?An equation is a mathematical statement that expresses two values as being equal. It is the basic building block of algebra and can be used to solve for unknown values, or to show the relationships between two or more values. Equations use mathematical operators such as addition, subtraction, multiplication, and division, as well as symbols and numbers, to express relationships between values. An equation can be written in the form of an expression, a system of equations, or a single equation. In all cases, an equation requires both sides of the equation to be equal in order to be valid and have a solution.
This equation describes growth that is slower than the Nuttall Oak growth rate because it has a lower rate of growth of 5 feet per year. The Nuttall Oak grows 7 to 8 feet per year, so any equation with a growth rate lower than that would be slower. Choices B, C, and D have higher growth rates than the Nuttall Oak, so they would not be slower than the Nuttall Oak growth rate.
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JKLM is a parallelogram. what is m
A shoe store recorded the number of customers who made a purchase out of a sample of 100 customers who entered the store each day. The boxplot shown summarizes the recorded data for one year. Based on the boxplot, which of the following statements is true?
A. The range of the number of customers making a purchase is greater than 32.
B. The interquartile range of the number of customers making a purchase is 25.
C. The number of days that had at least 26 customers making a purchase is greater than the number of days that had at most 11 customers making a purchase
D. The number of days that had from 11 to 26 customers making a purchase is equal to the number of days that had at most 14 customers making a purchase.
E.The difference between the median and the lower quartile for the customers making a purchase is less than 2.
Explain your thinking.
Less than 2 units separate the median from the lower quartile for customers making purchases.
What is meant by quartile deviation?The three values known as quartiles divide sorted data into four equal-sized portions, each with an equal number of observations. An example of a quantile is a quantile. First quartile: Also referred to as the lower quartile or Q1. The median or second quartile is also referred to as Q2. Third quartile: Also referred to as the higher quartile or Q3.
Half of the difference between the upper and lower quartiles can be used to define the quartile deviation analytically. Here, the upper quartile (Q3) and lower quartile (Q1) can be used to depict quartile deviation as the letters QD. The term "quartile deviation" is sometimes used to refer to the semi-interquartile range.
The coefficient of quartile deviation serves as a gauge for a collection of data's variability or spread. It is determined by taking the square root of the difference between the upper and lower quartiles, squaring the result, and dividing it by two. Comparing data sets is simple because it is expressed as a percentage.
Therefore, the correct answer is option E. The difference between the median and the lower quartile for the customers making a purchase is less than 2.
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A plane flying with an air speed of 300 mph at 50 degrees and it crosses the jet stream, which is blowing at 200 mph at an angle of 160 degrees. The plane's actual velocity with respect to the ground is the vector sum of these two velocities. Find the actual velocity to the nearest whole mph and degree (add the sum of the vectors).
Answer:
298.24 mph at an angle of 89 degrees
Step-by-step explanation:
[tex]v_p[/tex] = Velocity of plane = 300 mph at 50 degrees
[tex]v_j[/tex] = Velocity of jet stream = 200 mph at 160 degrees
The velocity of the plane in component form is
[tex]v_p=300\cos50^{\circ}\hat{i}+300\sin50^{\circ}\hat{j}[/tex]
The velocity of the jet stream in component form is
[tex]v_j=200\cos160^{\circ}\hat{i}+200\sin160^{\circ}\hat{j}[/tex]
Resultant velocity is given by
[tex]v=(300\cos50^{\circ}+200\cos160^{\circ})\hat{i}+(300\sin50^{\circ}+200\sin160^{\circ})\hat{j}\\\Rightarrow v=4.9\hat{i}+298.2\hat{j}[/tex]
Magnitude is given by
[tex]|v|=\sqrt{4.9^2+298.2^2}\\\Rightarrow |v|=298.24\ \text{mph}[/tex]
Angle is given by
[tex]\theta=\tan^{-1}\dfrac{298.2}{4.9}=89^{\circ}[/tex]
The velocity of the plane is 298.24 mph at an angle of 89 degrees.
A small business makes bottles of
temonade. Today, they have 528 ounces
of lemonade to bottle. Each bottle holds
24 ounces of lemonade. They sell each
bottle for $2.
Write two equations with variables that
can be used to find how many dollars
the business will receive by selling all of
the bottles.
The amount of money that the business will receipt is $44.
given:
Small business makes bottles of lemonade today they have 528 oz of lemonade to the bottle each bottle holds 24 oz of lemonade they sell each bottle for $2 how much money will the business receipt
From the above question:
24oz of Lemonade = 1 bottle
528 oz of Lemonade = x
Cross Multiply
24 × x = 528
x = 528/24
x = 22 bottles
We are told that: they sell each bottle for $2
Hence:
1 bottle = $2
22 bottles = y
Cross Multiply
y = 22 × $2
y = $44
Therefore, the amount of money that the business will receipt = $44
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I need help on this question: Triangle ABC is similar to triangle XYZ. What is the length of AC in inches?
Answer: 3√13
Step-by-step explanation:
To find the length of AC we need to use the Pythagorean theorem.
Which is AC^2 = BC^2 + AB^2
AC^2 = 6^2 + 9^2
AC^2 = 36 + 81
AC^2 = 117
AC = √117
Select the theorem that can be used to prove that RST = VUT
There are 3 people in Lee's family
The range of their shoe sizes is 3
2 people in the family wear shoe size 6
Lee's shoe size is not 6 and it is not 3
What is Lee's shoe size
Answer:
9
Step-by-step explanation:
the range is the difference between the lowest and the highest number on the series
here the range is 3 two members have size 6 different from 6 and 3 which range its 3
What is the volume of the composite shape to the nearest whole number? (Pls answer, due today!)
A. 1,178 in^3
B. 1,035 in^3
C. 960 in^3
D. 2,138 in^3
Answer:
2,138 in^3
Step-by-step explanation:
I know this is old but other people can find this helpful
Which area model represents the factorization x2+3x+2=(x+2)(x+1)?
The factorization of the polynomial x² + 3x + 2 gives (x + 1)(x + 2)
What is an equation?An equation is an expression that shows how numbers and variables relate with each other.
A polynomial is an expression consisting of variables and their exponents with operations of addition and subtraction. Polynomials are classified based on degree as linear, quadratic and cubic.
The standard form of a quadratic equation is:
y = ax² + bx + c
where a, b and c are constants.
Given the polynomial:
x² + 3x + 2
Factorizing the polynomial:
x² + 2x + x + 2
= x(x + 2) + 1(x + 2)
= (x + 1)(x + 2)
The factorization gives (x + 1)(x + 2)
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Please graph the question in the image.
Answer:
I used desmos to make the graph
Step-by-step explanation:
Hopefully this helps!
Angel missies 4% of the free throws he attempts in a season. How many total free throws did he attempt if he missed 55
Answer:
Step-by-step explanation:
55 times 25, making Angel attempt 1375 free throws
Answer:
Step-by-step explanation:
Its 700% because 7x3 = 11
NEED HELP ASAP - Algebra 2 (5 Questions, 15 Points Each)
In question 1;
The student multiplied without flipping the second expression.
In second question;
The negative should only be distributed to the numerator.
In third question,
3/2 should be remove from the x - value which make the expression undefined.
In fourth student;
Neither student is correct.
In fifth question,;
Sarah didn't cancel incorrectly in step 3.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
In question 1;
The expression is,
⇒ x² + 2x - 3 / (x² - 3x - 10) ÷ (2x + 12) / (8x + 16)
= (2x³ + 16x² + 18x - 36) / (8x³ - 8x² - 128x - 100)
Cleary, The student multiplied without flipping the second expression.
In question 2;
⇒ (-2y - 2) / (y² + 2y - 8) - (y - 1) / (2 - y)
⇒ (-2y - 2) / (y² + 2y - 8) + (-y + 1) / (-2 + y)
Clearly, The negative should only be distributed to the numerator.
In Question 3;
The student make mistake is ''3/2 should be remove from the x - value which make the expression undefined.''
In fourth student;
Neither student is doing correct solution.
In fifth question,;
Sarah didn't cancel incorrectly in step 3.
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