Lucky's Market purchased a new freezer for the store.When the freezer door stays open, the temperatureinside rises. The table shows how much thetemperature rises every 15 minutes. Find the unit rate.temperature (°F) =10number of minutes =15(answer) °F per minute
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Notice that the information in the table can be modeled using a linear function. To find the slope (rate of change) given two points, use the formula below
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow slope=m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} (15,10),(30,20) \\ \Rightarrow slope=\frac{20-10}{30-15}=\frac{10}{15}=\frac{2}{3} \end{gathered}[/tex]Related Questions
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
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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.
CRITICAL THINKING Describe two different sequences of transformations in which the blue figure is the image of the red figi 1 1 2 B I y ET
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1) rotation 90° clockwise over the origin and a reflection over the x-axis
2) rotation 90° counter clockwise over the origin and reflection over y-axis
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.
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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°.
Variable Systems 2solve the following showings steps neatly and organized.
Answers
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
Question 8 of 10What is the slope of the line described by the equation below?y=-x+ 8A. 8B. 1OOOC. -8O D.-1SUBMIT
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We have the following equation
y = -x + 8
this equation is writen in slope intercept form
y = mx + b
where m is the slope
From the above, we can see that the slope is m = -1
Can you please help me
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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 mm2Order the numbers from least (1) to greatest (10).ITEM BANK-Move to Battom3.564.034.212V12mor
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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.
Question 3 (9 points)Find Pred then green)What is the probability that you select a red marble, then a green marbleP (red) -P (then Green) - (Total of marbles will be 1 less)P (red then green) = *Hint: Multiply
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Solution
Step 1
Write out an expression for the probability
[tex]\text{The probaility of an event occurring= }\frac{\text{Number of required events}}{\text{Total number of events}}[/tex]Step 2
Define terms
Total number of events = 8 marbles
Number of required events = red then marble
Number of red = 2 marbles2
Number of green = 2 marbles
Note: The question is without replacement.
Step 3
Get the required probabilities and the answer
[tex]\begin{gathered} Pr(\text{red marble) = }\frac{2}{8} \\ Pr(\text{green marble without replacement) =}\frac{2}{7} \end{gathered}[/tex]Hence the Pr(of red then green) is given as
[tex]\begin{gathered} =Pr(\text{red) }\times Pr(green\text{ without replacement)} \\ =\frac{2}{8}\times\frac{2}{7}=\frac{1}{14} \end{gathered}[/tex]Hence the probability of picking a red marble then a green marble = 1/14
[tex]6x - 9y - 7x + - 6y[/tex]simplify please
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6x - 9y - 7x + -6y
To simplify the expression add the like terms
The like terms are the terms which have the same variable and same degree
6x, -7x are like terms
-9y, -6y are like terms
So let us add them
(6x + -7x) + (-9y + -6y)
6 + -7 = -1
6x + -7x = -x
-9 + - 6 = -15
-9y + -6y = -15y
(6x + -7x) + (-9y + -6y) = -x + -15y
Remember (+)
If f (x) = 4x^3 - 25x^2 – 154x+ 40 and (x - 10) is a factor, what are the remaining factors?
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Find the slope of the line defined by each pair of points.:( points :(-1,4). Points. (-1,-5)
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Notice that the x coordinate of both points is the same, therefore the line is a vertical line.
Answer: The slope is undefined.
Parking spaces in a parking lot are parallel to each other. Find the measure of the two
unknown angles and explain your reasoning.
measure of angle m:
measure of angle n:
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Answer:
m = 70° , n = 110°
Step-by-step explanation:
m and 110° are same- side interior angles and sum to 180°
m + 110° = 180° ( subtract 110° from both sides )
m = 70°
n and 110° are corresponding angles and are congruent , then
n = 110°
O EQUATIONS AND INEQUALITIESSolving a decimal word problem using a linear equation with th.
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Given:
[tex]PlanA=0.16\text{ for each minutes of calls}[/tex][tex]PlanB=25\text{ monthly fee plus 0.12 for each minute of calls}[/tex]To Determine: The numbers of calls for the which the two plans are equal
Solution
Let x be the number of minutes of calls for which the two plans are equal
The cost of plan A is
[tex]C_{ost\text{ of plan A}}=0.16x[/tex]The cost of plan B
[tex]C_{ost\text{ of plan B}}=25+0.12x[/tex]If the cost for the two plans are equal, then
[tex]0.16x=25+0.12x[/tex]Solve for x
[tex]\begin{gathered} 0.16x-0.12x=25 \\ 0.04x=25 \\ x=\frac{25}{0.04} \\ x=625 \end{gathered}[/tex]Hence, the number of minutes of calls for which two plans are equal is 625 minutes
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?
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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.
Solve the following compound inequalities. Use both a line graph and interval notation to write each solution set.
t+1-5 ort+1> 5
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The value of the inequality expression given as t + 1 < -5 or t + 1 > 5 is (-oo, -6) u (4, oo)
How to determine the solution to the inequality?The inequality expression is given as
t + 1 < -5 or t + 1 > 5
Collect the like terms in the above expressions
So, we have
t < -5 - 1 or t > 5 - 1
Evaluate the like terms in the above expressions
So, we have
t < -6 or t > 4
Hence, the solution to the inequality is t < -6 or t > 4
Rewrite as an interval notation
(-oo, -6) u (4, oo)
See attachment of the number line
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Please help this is due tomorrow!!
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The expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The given polynomial expression below is:
⇒ 10x⁵y⁷/5x⁵y · 3x⁴y⁸/3x⁻³y¹⁰
Apply the division operation in the constant terms
⇒ 2x⁵y⁷/x⁵y · x⁴y⁸/x⁻³y¹⁰
Apply the arithmetic operation in the Exponents of the same base variables
⇒ 2y⁶ · x⁷y⁻²
⇒ 2y⁶⁻² · x⁷
⇒ 2y⁴ · x⁷
⇒ 2x⁷· y⁴
Therefore, the expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.
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There are two points (-7,6) and (7,2) the upper part is a shaded circle the ordered pairs that are solutions to the inequality on the graph.This is the line -- - - - - - - -- - -- - - - - - - -- - - - - - --- - - - - - -You can use DESMOS(6,3)(-6,6)(5,0)(2,4)
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SOLUTION
Incomplete question
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.
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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
If the snow is falling at a rate of 1 inches per hour, how many hours will it take to snow 12 inches?
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Imagine the following, we will place a tube under the snow. So we have the following
After one hour, the tube will be filled with 1 inch of snow.
After 2 hours, we will have one inch more
So, one way to calculate the amount of snow after a specific amount of hours, is simply multiplying the hours by the rate at which the height of the snow changes. IN here, the height changes 1 inch per hour. So after x hours the height of the snow would be
[tex]1\cdot\text{ x }[/tex]We want to find x, such that the height of the snow is 12.
So we have the equation
[tex]1\cdot x\text{ = 12}[/tex]which gives us that in 12 hours we will have 12 inches of snow.
Mrs. Smith stores water in different size bottles. she has 4 containers that are 2 1/2 quarts each and 3 containers that are 425 cups each. how many fluid ounces of water does she have?
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Answer:
The total volume of fluid ounces of water she have is;
[tex]422\text{ ounces}[/tex]Explanation:
Given that she has 4 containers that are 2 1/2 quarts each
[tex]\begin{gathered} V_1=4\times2\frac{1}{2}\text{ quarts} \\ V_1=10\text{ quarts} \end{gathered}[/tex]Recall that to convert quarts to ounce;
[tex]1\text{ quart }=32\text{ ounces}[/tex][tex]\begin{gathered} V_1=10\text{ quarts }=10\times32\text{ ounces} \\ V_1=320\text{ ounces} \end{gathered}[/tex]Also, she has 3 containers that are 4.25 cups each;
[tex]\begin{gathered} V_2=3\times4.25\text{ cups} \\ V_2=12.75\text{ cups} \end{gathered}[/tex]To convert cups to ounces;
[tex]1\text{ cup}=8\text{ ounces}[/tex]So;
[tex]\begin{gathered} V_2=12.75\text{ cups }=12.75\times8\text{ ounces} \\ V_2=102\text{ ounces} \end{gathered}[/tex]The total volume of fluid ounces of water she have is;
[tex]V=V_1+V_2[/tex]substituting the values;
[tex]\begin{gathered} V=320+102\text{ ounces} \\ V=422\text{ ounces} \end{gathered}[/tex]Therefore, the total volume of fluid ounces of water she have is;
[tex]422\text{ ounces}[/tex]8x +1312x + 7X == [?]Enter
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The two angles given in the problem lie the opposite of each other with respect to the transversal line. This means that these two angles are supplementary angles. The sum of the two angles will be equal to 180 degrees, hence, we can set up an equation solving for x. We have
[tex]8x+13+12x+7=180[/tex]Solve for x, we have
[tex]\begin{gathered} 20x+20=180 \\ 20x=180-20 \\ \frac{20x}{20}=\frac{160}{20} \\ x=8 \end{gathered}[/tex]The value of x
Choose the correct answer below
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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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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.
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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
On a circle of radius 9 feet, what angle would subtend an arc of length 7 feet?
_____ degrees
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The angle subtend an arc length of 7 feet is 44.56°
Given,
Radius of a circle = 9 feet
Arc length of a circle = 7 feet
Arc length :
The distance between two places along a segment of a curve is known as the arc length.
Formula for arc length:
AL = 2πr (C/360)
Where,
r is the radius of the circle
C is the central angle in degrees
Now,
AL = 2πr (C/360)
7 = 2 × π × 9 (C/360)
7 = 18 π (C/360)
7/18π = C/360
C = (7 × 360) / (18 × π)
C = (7 × 20) / π
C = 140 / π
C = 44.56°
That is,
The angle subtend an arc length of 7 feet is 44.56°
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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)
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Using solving systems using elimination addition method3x-7y=5-3x+7y=-9help
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In the elimination method, we need to eliminate one of the variables using addition or subtraction.
In this case, if we add both equations, we have that:
Since we obtained a FALSE result, we can say that this system of linear equations has NO SOLUTIONS.
In summary, using the elimination method, we add both equations. The result for that was a false r
Determine the prime factorization of 350
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define Prime factorization.
Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number itself. Examples of prime numbers are 2,3,5,7...etc.
STEP 2: Find the prime factors of the given number
Prime factorization of any number means to represent that number as a product of prime numbers.
We start by dividing the number by the lowest possible prime numbers.
STEP 3: Express 350 as a product of its prime factors
[tex]\begin{gathered} \text{Prime factors}=2,5,5,7 \\ \text{Product of prime factors=}2\times5\times5\times7 \\ =2\times5^2\times7 \end{gathered}[/tex]Hence, the prime factorization of 350 is given as:
[tex]2\times5^2\times7[/tex]Simplify using the laws of exponents. Use the box to the right of the variable as it’s simplified exponent.
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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]The figure on the right is a scale drawing of the figure on the left. What is the scale factor?
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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.
Find the equation of the linear function represented by the table below in slope-intercept form.xy1-82-123-164-20
Answers
Given :
The table for y and x is given as
Explanation :
The slope-intercept form is determined as
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]First find the slope of the equation using the coordinates from the table.
[tex]m=\frac{-12-(-8)}{2-1}=\frac{-12+8}{1}=-4[/tex]Now substitute the values in the slope-intercept form.
[tex]\begin{gathered} y-(-8)=-4(x-1) \\ y+8=-4(x-1) \\ y=-4x+4-8 \\ y=-4x-4 \end{gathered}[/tex]Answer:
Hence the equation of line is determined as
[tex]y=-4x-4[/tex]