9x + 5y = 10
is a linear equation because all variables are raised to exponent 1.
This equation is already written in standard form (A = 9, B = 5, C = 10)
2y + 4 = 6x
is a linear equation because all variables are raised to exponent 1.
Subtracting 2y at both sides:
2y + 4 - 2y= 6x - 2y
4 = 6x - 2y
or
6x - 2y = 4
which is in standard form (A = 6, B = -2, C = 4)
A grocer mixed grape juice which costs $1.50 per gallon with cranberry juice whichcosts $2.00 per gallon. How many gallons of each should be used to make 200 gallons of cranberry/grape juice which will cost $1.75 per gallon?
Let x be the amount of gallons of grape juice we are using to get the mixture we want. Let y be the amount of gallons of cranberry juice used to get the desired mixture.
Since we are told that we want a total of 200 gallons of the new mixture, this amount would be the sum of gallons of each liquid. So we have this equation
[tex]x+y=200[/tex]To find the values of x and y, we need another equation relating this variables. Note that since we have 200 gallons of the new mixture and the cost per gallon of the new mixture is 1.75, the total cost of the new mixture would be
[tex]1.75\cdot200=350[/tex]As with quantities, the total cost of the new mixture would be the cost of each liquid. In the case of the grape juice, since we have x gallons and a cost of 1.50 per gallon, the total cost of x gallons of grape juice is
[tex]1.50\cdot x[/tex]In the same manner, the total cost of the cranberry juice would be
[tex]2\cdot y[/tex]So, the sum of this two quantites should be the total cost of the new mixture. Then, we get the following equation
[tex]1.50x+2y=350[/tex]If we multiply this second equation by 2 on both sides, we get
[tex]3x+4y=700[/tex]Using the first equation, we get
[tex]x=200\text{ -y}[/tex]Replacing this value in the second equation, we get
[tex]3\cdot(200\text{ -y)+4y=700}[/tex]Distributing on the left side we get
[tex]600\text{ -3y+4y=700}[/tex]operating on the left side, we get
[tex]600+y=700[/tex]Subtracting 600 on both sides, we get
[tex]y=700\text{ -600=100}[/tex]Now, if we replace this value of y in the equation for x, we get
[tex]x=200\text{ -100=100}[/tex]Thus we need 100 gallons of each juice to produce the desired mixture.
Which of the following is a correct way to name this angle? B, 2 ACB А, САВ D. BCA C. Z CBA
The answer is Angle ACB
The angle is form from both line A and C
Find the distance between the points (5,5) and (-3,7). Round your answer to the nearest tenth, if necessary.8.2 units11.8 units3.2 units12.2 units
The formula for the distance between two points in the plane is:
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]So:
[tex]\begin{gathered} (x_1,y_1)=(5,5) \\ (x_2,y_2)=(-3,7) \\ d=\sqrt[]{(5-(-3))^2+(5-7)^2} \\ d=\sqrt[]{(8)^2+(-2)^2} \\ d=\sqrt[]{64+4} \\ d=\sqrt[]{68} \\ d=8.2462\ldots\approx8.2 \end{gathered}[/tex]So, the distance is approximately 8.2 units.
Use the function below to find the indicated value:4x – 10,x21+12 <33
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Explain the given function
It can be seen from the function that there are three conditions which are defined below:
When x is less than 3, this states that we execute the first function for values of x less than 3
When x is between 3 and less than 7, this means that whenever x ranges from 3 to 6, we execute the second function.
When x is greater than or equals to 7, we execute the last function.
STEP 2: find f(7)
Since the value of x which is 7 is greater than or equal to 7, therefore we use the last function as seen below:
[tex]\begin{gathered} f(x)=f(7) \\ f(x)=\frac{x+1}{x-3} \\ Substitute\text{ 7 for x} \\ f(7)=\frac{7+1}{7-3}=\frac{8}{4}=2 \end{gathered}[/tex]Hence, the result is 2
Variable Systems 2solve the following showings steps neatly and organized.
SOLUTION
perimeter of rectangle = 88cm
let the widht be x
now, according to question
lenght = 3x ( as it is triple of width)
formula of rectangle perimeter
88cm = 2* (length + width)
88cm = 2(3x+x)
88cm = 4x (2 will be transported to left )
88/2 cm = 4x
( 2 become in divide as in right it was in multiply)
44 cm = 4x
x= 44/4
x= 11cm
according to question,
width of rectangle = x = 11 cm
Choose the correct answer below
The book is not the same story or the movie is not the same story.
What is De Morgan's law?The intersection of two sets' complements is the complement of the union of two sets, and the intersection of two sets' complements is the complement of the intersection of two sets. They are referred to as De Morgan's laws. These have the name De Morgan after the mathematician.De Morgan's laws are a pair of transformation rules that can both be used as rules of inference in propositional logic and Boolean algebra. They have the name of the 19th-century British mathematician Augustus De Morgan.When attempting to demonstrate that the NAND gate is equivalent to an OR gate with inverted inputs and the NOR gate is equivalent to an AND gate with inverted inputs, we can employ De Morgan's theorems.To learn more about De Morgan's law refer to:
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Hooke's Law says that the force exerted by the spring in a spring scale varies directly with the distance that the spring is stretched. If a 20 pound mass suspended on a spring scale stretches the spring 20 inches, how far will a 29 pound mass stretch the spring? Round your answer to one decimal place if necessary.
The Hooke's law is given by:
F = k*x
Where:
F = force
k = constant factor
x = distance
If F = 20 and x = 20
20 = k*20
Solving for k:
20/20 = k
k = 1
So: how far will a 29 pound mass stretch the spring?
29 = 1* x
Solving for x:
29/1 = x
x = 29 in
what is the answer to 65y=12
In this case, we have a equation with one unknown value (y)
all you have to do is to isolate y
Let's see
65 y=12
[tex]\begin{gathered} 65y=12 \\ \text{divide each side by }65 \\ \\ \frac{65y}{65}=\frac{12}{65} \\ \\ y=\frac{12}{65} \\ \end{gathered}[/tex]so the solution is y=12/65
I really hope it helps
52. What is the 275th digit after the decimal point in therepeating decimal 0.6295 ?F. 0G. 2H. 5J. 6K. 9
Given:
The digit is 0.6295.
Required:
To find the 275th digit after the decimal point in the repeating decimal 0.6295.
Explanation:
For any non-negative integer, we have:
The 4n+1th digit after the decimal point is 6.
The 4n+2th digit after the decimal point is 2
The 4n+3th digit after the decimal point is 9
The 4n+4th digit after the decimal point is 5.
Since the repeating digit is 4 and we have to find the 275th digit.
Thus
[tex]\frac{275}{4}=68\text{ with remainder 3}[/tex]It can be written as:
275 = 4. 68 + 3
That is 275th digit after the decimal point in the repeating decimal is 9 with n= 68.
Final answer:
Thus option k is the correct answer.
graph and label each figure and it's image under the given reflection. give the new coordinates. you don't have to graph it for me, could you just helps with the coordinates
Explanation
Step 1
Let the vertices
[tex]\begin{gathered} C(-4,7) \\ D(-2,4) \\ E(-4,1) \\ F(-6,4) \end{gathered}[/tex]When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed)
[tex]P(x,y)\rightarrow reflect\text{ across y a }\xi s\rightarrow P^{\prime}(-x,y)[/tex]then, apply the rule to find the new coordinates
[tex]\begin{gathered} C(-4,7)\rightarrow C^{\prime}(4,7) \\ D(-2,4)\rightarrow D^{\prime}(2,4) \\ E(-4,1)\rightarrow E^{\prime}(4,1) \\ F(-6,4)\rightarrow F^{\prime}(6,4) \end{gathered}[/tex]I hope this helps you
The price of Stock A at 9 A.M. was $12.42. Since then, the price has been increasing at the rate of $0.12 each hour. At noon the price of Stock B was $12.92. It begins to decrease at the rate of $0.09 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
The hours when the prices of the two stocks be the same is 2.38 hours.
How to illustrate the information?From the information, the price of Stock A at 9 A.M. was $12.42 and the price has been increasing at the rate of $0.12 each hour. This will be the expressed as 12.42 + 0.12h.
At noon the price of Stock B was $12.92. It begins to decrease at the rate of $0.09 each hour. This will be:
= 12.92 - 0.09h
where h = number of hours
Equate both equations. This will be:
12.42 + 0.12h = 12.92 - 0.09h
Collect like terms
12.92 - 12.42 = 0.12h + 0.09h
0.21h = 0.50
h = 0.50 / 0.21
h = 2.38 hours.
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A rectangular room is 1.8 times as long as it is wide, and its perimeter is 29 meters. Find the dimension of the room. The length is : meters and the width is meters.
Let's say x is going to be the number meters of the width of the room:
x: width
Since its lenght is 1.8 as it is width, then it will be 1.8 · x long:
1.8x: lenght
Step 2: relating the expressions for each side to its perimeterWe know that the perimeter of a rectangle is given by
Perimeter = 2· (width + lenght)
We know that the perimeter is 29 meters, then
Perimeter = 29
↓
29 = 2· (width + lenght)
We do know an expression for its width and lenght, we replace them:
29 = 2· (width + lenght)
↓
29 = 2· (x + 1.8x)
Step 3: finding xSince x + 1.8x = 2.8x:
29 = 2· (x + 1.8x)
↓
29 = 2· (2.8x)
↓ 2· 2.8 = 5.6
29 = 5.6x
↓ dividing both sides by 5.6
29/5.6 = 5.6x/5.6
5.2 = x
Final step: finding its dimensionsSince
x: width
then
Width = 5.2 meters
Since
1.8x: lenght
then
Lenght = 1.8 · 5.2 meters = 9.36 meters
Answer: the dimensions of the room are Width = 5.2 meters and Lenght = 9.36 meters
Omoro bought 2 2/3 pounds of takis that he is going to bring to school for lunch each day in plastic bags that carry 1/8 of a pound.how many bags can omoro fill completely ?
Given:
Amount of takis bought = 2⅔ pounds
Amount the plastic bag can carry = 1/8 pounds
First convert 2⅔ to a simple fraction:
2⅔ = 8/3
To find the amount of bags Omoro can fill completely, we have to divide the amount of takis bought by the amount of takis the plastic bag can carry:
(8/3) ÷ (1/8)
[tex]\begin{gathered} =\text{ }\frac{8}{3}\text{ }\ast\text{ }\frac{8}{1} \\ =\text{ }21.3\text{ bags} \end{gathered}[/tex]Therefore, Omoro can fill approximately 21 bags completely
ANSWER:
21 bags
help meeeeeeeeee pleaseee !!!!!
The total number of toys sold if the daily sales of the toy is $6.50 is 2750 toys.
Functions and valuesEach element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The independent values are known as the domain while the dependent are the codomain.
Given the function that represents the price-sales relationship for number of toys as;
y = 6000 - 500x
If the daily sales of the toy is $6.50, the total toys sold will be:
y = 6000 - 500 (6.50)
y = 6000 - 3250
y = 2750 toys
This gives the total number of toys sold.
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14. Construction workers are laying out the rectangular foundation for a new building.They want to check that the corner is 90°. They measure the diagonal as shown to be 9.5 m. Is the angle 90° Explain your reasoning.
Explanation: We can see on the image that the two sides and the diagonal represent a triangle. We also know that this triangle to have a 90 degrees angle is will be called a right triangle. Finally, all right triangles obey the Pythagorean equation
[tex]h^2=a^2+b^2[/tex]NOTE:
h = hypotenuse
a and b = other sides
Step 1: Once we know the length of the two sides we can use the Pythagorean equation to find the length of the hypotenuse for the triangle to be a right triangle and consequently have an angle that measures 90 degrees.
Step 2: Let's calculate as follows
[tex]\begin{gathered} h^2=a^2+b^2 \\ h=\sqrt[]{8^2+6^2} \\ h=10 \end{gathered}[/tex]Step 3: We can see above, that to have an angle that measures 90 degrees (right triangle) the triangle have to have a hypotenuse = 10 which is different from 9.5.
Final answer: So the angle does not measure 90°.
A circle has a radius of .10 in. Find
the increase in area when the radius is increased by 2 in. Use
3.14 for
The increase in area of the circle when the radius is increased by 2 is 13.8 in.
How to calculate area of circle?Area of a circle can be described as the region that is been taken by the circle.
The area of the circle can be expressed as A=πr^2
We were told that the radius of the circle is been given as 0.10 in.
Then we can calculate the are of the circle by input the given radius into the formula above as:
A=πr^2
r= radius of the circle
A= area of the circle
A=3.14 (0.10)^2 =0.0314 in.
Then we were told that the radius is increased by 2 in.
Then the area of the circle will now be A=3.14* (2.10)^2 =13.85 in.
Then the the increase in area can be calculated as : (13.85 in. - 0.0314 in.) = 13.8 in.
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The table shows the fraction of students from differentgrade levels who are in favor of adding new items tothe lunch menu at their school. Which list shows the grade levels in order from the greatest fraction of students to the least fraction of students ?
First, write all the fractions using the same denominator. To do so, find the least common multiple of all denominatos. The denominators are:
[tex]50,20,25,75,5[/tex]The least common multiple of all those numbers is 300.
Use 300 as a common denominator for all fractions to be able to compare their values.
5th grade
[tex]\frac{33}{50}=\frac{33\times6}{50\times6}=\frac{198}{300}[/tex]6th grade
[tex]\frac{13}{20}=\frac{13\times15}{20\times15}=\frac{195}{300}[/tex]7th grade
[tex]\frac{18}{25}=\frac{18\times12}{25\times12}=\frac{216}{300}[/tex]8th grade
[tex]\frac{51}{75}=\frac{51\times4}{75\times4}=\frac{204}{300}[/tex]9th grade
[tex]\frac{3}{5}=\frac{3\times60}{5\times60}=\frac{180}{300}[/tex]Now, we can compare the numerators to list the fraction from greatest to lowest:
[tex]\begin{gathered} \frac{216}{300}>\frac{204}{300}>\frac{198}{300}>\frac{195}{300}>\frac{180}{300} \\ \Leftrightarrow\frac{18}{25}>\frac{51}{75}>\frac{33}{50}>\frac{13}{20}>\frac{3}{5} \\ \Leftrightarrow7th\text{ grade}>8th\text{ grade}>5th\text{ grade}>6th\text{ grade}>9th\text{ grade} \end{gathered}[/tex]Therefore, the list of grade levels in order from the greatest fraction of students to the least fraction of students, is:
7th grade (18/25)
8th grade (51/75)
5th grade (33/50)
6th grade (13/20)
9th grade (3/5)
Simplify using the laws of exponents. Use the box to the right of the variable as it’s simplified exponent.
Given:
[tex](15m^8)\placeholder{⬚}^3[/tex]To find:
to simplify using laws of exponents
First, we need to expand the expression:
[tex]\begin{gathered} In\text{ exponent laws, a}^3\text{ = a }\times\text{ a }\times\text{ }a \\ \\ Applying\text{ same rule:} \\ (15m^8)\placeholder{⬚}^3\text{ = \lparen15m}^8)\times(15m^8)\text{ }\times(15m^8) \\ =\text{ 15 }\times\text{ }m^8\times\text{15 }\times\text{ }m^8\times\text{15 }\times\text{ }m^8\text{ } \\ \\ collect\text{ like terms:} \\ =\text{ 15 }\times\text{ 15 }\times15\text{ }\times m^8\times\text{ }m^8\times\text{ }m^8\text{ } \end{gathered}[/tex][tex]\begin{gathered} Simpify: \\ 15\times15\times15\text{ = 3375} \\ \\ m^8\text{ }\times\text{ m}^8\text{ }\times\text{ m}^8 \\ when\text{ multiplying exponents with same base, } \\ \text{we will pick one of the base and add the exponents together } \\ m^8\text{ }\times\text{ m}^8\text{ }\times\text{ m}^8\text{ = m}^{8+8+8} \\ =\text{ m}^{24} \end{gathered}[/tex][tex]\begin{gathered} 15\times15\times15\times m^8\times m^8\times m^8\text{ = 3375 }\times\text{ m}^{24} \\ \\ =\text{ 3375m}^{24} \end{gathered}[/tex]in the lab Dale has two solutions that contain alcohol and is mixing them each other.she uses four times as much solution A as solution B.solution a is 20% of alcohol and solution B is 15% of alcohol. how many milliliters of solution B does he use, if the was resulting mixtures has 570 milliliter of pure alchohol.number of milliliters of solution B__?
Let:
• A ,be the number of millilitres (mL) of solution A used.
,• B ,be the number of mL of solution B used.
We know that Dale uses four times as much solution A as solution B, meaning
[tex]A=4B[/tex]Now, we know that we will end up with 570 mL of pure alcohol in the final solution. Using the dilution of both A and B (20% means 0.2 and 15% is 0.15) we would have that:
[tex]0.2A+0.15B=570[/tex]We would have the following system of equations:
[tex]\begin{cases}A=4B \\ 0.2A+0.15B=570\end{cases}[/tex]Substituting equation 1 in equation 2 and solving for B :
[tex]\begin{gathered} 0.2A+0.15B=570 \\ \rightarrow0.2(4B)+0.15B=570 \\ \rightarrow0.8B+0.15B=570 \\ \rightarrow0.95B=570\rightarrow B=\frac{570}{0.95} \\ \Rightarrow B=600 \end{gathered}[/tex]Substituting in equation 1 and solving for A:
[tex]\begin{gathered} A=4B \\ \rightarrow A=4(600) \\ \Rightarrow A=2400 \end{gathered}[/tex]This way, we can conclude that 2400 mL of solution A and 600mL of solution B were used.
Sarah wants to take a vacation that will cost 2,562 if sarah plans to save for 9 months, then how much needs to be saved per month
Let:
x = Number of months
y = Total savings
a = Savings per month
so:
[tex]\begin{gathered} y=ax \\ where \\ y=2562 \\ x=9 \\ so\colon \\ 2562=9a \\ solve_{\text{ }}for_{\text{ }}a\colon \\ a=\frac{2562}{9} \\ a\approx284.67 \end{gathered}[/tex]She needs to save approximately $284.67 per month
7. Which expression is equivalent to the distance between -2 and -15 on a number line? Select all that apply. OT-15 - (-2)] O 1-15-2 O 1-15+ (-2) 1-2 + (-15) 1-2-(15)
Can you please help me
we have that
the area of parallelogram is equal to
A=b*h
we have
b=14 mm
Find the value of h
tan(60)=h/7 -----> by opposite side divided by the adjacent side
Remember that
[tex]\tan (60^o)=\sqrt[]{3}[/tex]so
h=7√3 mm
substitute
A=14(7√3 )
A=98√3 mm2Nathalie is finishing a workout on the treadmill. She speeds up before slowing down to a stop. Nathalie draws a graph to represent her workout.
As the x-axis increases uniformly the y-axis increase and decreases so the horizontal axis must be labeled with time and the vertical axis with speed so option (A) is correct.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
The graph is easy to understand the behavior of the graph.
The graph of a treadmill workout has been plotted.
We all know that the speed of the treadmill keep fast initially but after some time the speed reduces and it goes to zero lineary.
Therefore,the horizontal axis wich is uniform changes cause to vertical axis with first increase and then decrease shown.
Hence "As the x-axis increases uniformly the y-axis increase and decreases so the horizontal axis must be labeled with time and the vertical axis with speed".
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First use the Pythagorean theorem to find the exact length of the missing side. Then find the exact values of the six trigonometric functions for angle 0.
The trigonometric functions are given by the following formulas:
[tex]\begin{gathered} \sin \theta=\frac{a}{h} \\ \cos \theta=\frac{b}{h} \\ \tan \theta=\frac{a}{b} \\ \cot \theta=\frac{b}{a} \\ \sec \theta=\frac{h}{b} \\ \csc \theta=\frac{h}{a} \end{gathered}[/tex]Where we call a to the opposite leg to the angle θ (the side whose measure equals 20), b is the adjacent leg to angle θ (the side whose measure equals 21) and we call h to the hypotenuse (the larger side, whose measure equals 29).
By replacing 20 for a, 21 for b and 29 for h into the above formulas, we get:
[tex]\begin{gathered} \sin \theta=\frac{20}{29} \\ \cos \theta=\frac{21}{29} \\ \tan \theta=\frac{20}{21} \\ \csc \theta=\frac{29}{20} \\ \sec \theta=\frac{29}{21} \\ \cot \theta=\frac{21}{20} \end{gathered}[/tex]Identify the graph that has a vertex of (-1,1) and a leading coefficient of a=2.
To determine the vertex form of a parabola has equation:
[tex]f(x)=a(x-h)^2+k[/tex]where V(h,k) is the vertex of the parabola and 'a' is the leading coefficient.
From the question, we have that, the vertex is (-1, 1)
and the leading coefficient is a = 2
We substitute the vertex and the leading coefficient into the vertex form to
get:
[tex]\begin{gathered} f(x)=2(x+1)^2\text{+}1 \\ f(x)=2(x+1)^2+1 \end{gathered}[/tex]The graph of this function is shown in the attachment.
Hence the equation of parabola is
[tex]f(x)=2(x+1)^2+1[/tex]Hector is thirsty and opens up the refrigerator and finds a half full gallon of milk. Hector drinks 2/5 of the milk Later kevin opens up the refrigerator and finds some milk left in the gallon. He drinks 1/3 of what is left. Draw a picture of the situation above. Include the amount of milk before hector drank any, after hector drank some, and then after kevin drank some. What fraction is the entire gallon did kevin drink What fraction of the entire gallon is left after both hector and kevin drink some milk?
When Hector opens up the refrigerator he finds the next :
He drinks 2/5 of the milk he found, then he drank:
[tex]\frac{1}{2}\times\frac{2}{5}=\frac{1\times2}{2\times5}=\frac{2}{10}=\frac{1}{5}gallon[/tex]And he left in the bottle of milk:
[tex]\frac{1}{2}-\frac{1}{5}=\frac{5-2}{2\times5}=\frac{3}{10}gallons\text{ of milk}[/tex]And after that Kevin open up the refrigerator and finds the next:
Kevin drinks 1/3 of what is left, then he drinks:
[tex]\frac{3}{10}\times\frac{1}{3}=\frac{3\times1}{10\times3}=\frac{3}{30}=\frac{1}{10}\text{gallon of milk}[/tex]And then he left:
[tex]\frac{3}{10}-\frac{1}{10}=\frac{3-1}{10}=\frac{2}{10}=\frac{1}{5}[/tex]And the milk he left in the bottle is:
I’m trying to understand where I should shade a graph given the narrative
we have the system
[tex]\begin{gathered} x+y\leq4 \\ y\leq-x+4 \end{gathered}[/tex]The solution to the first inequality is the shaded area below the solid line y=-x+4
[tex]x\ge2[/tex]The solution to the second inequality is the shaded area to the right of the solid vertical line x=2
therefore
The solution to the system is the shaded area below the solid line y=-x+4 and to the right of the solid vertical line x=2
using a graphing tool
see the attached figure below
The solution is the triangular area
Order the numbers from least (1) to greatest (10).ITEM BANK-Move to Battom3.564.034.212V12mor
To order these numbers, we begin with the whole part of each number. In the case of having two numbers with equal whole part, we look for the greatest tenth. So, the order would be
[tex]3.56;4.03;4.2;12[/tex]Notice that, 4.03 is less than 4.2, because its tenth is less.
Choose all true inequalities from the list below.3 < 8-8 < -3-5 < -2118 > 4
ANSWER and EXPLANATION
We want to identify which of the inequalities are correct.
For the inequality to be correct, the left and right-hand sides of the inequality must agree with
The figure on the right is a scale drawing of the figure on the left. What is the scale factor?
In order to find the scale factor, we just need to divide one side of the right figure by the corresponding side in the left figure.
So, taking the sides SU and PR, we have:
[tex]\text{scale}=\frac{SU}{PR}=\frac{12}{8}=1.5[/tex]So the scale factor is 1.5.
