Her door should be 3 cm on scale .
A ratio is defined as a comparison of two quantities of equal units, showing how much of one quantity is in the other quantity.It is given that dimension of the kitchen table is 60m by 2 m .
Let the width of the door be " x".
We given Mal's Kitchen door is 1.2 m wide .
The ratio is given by
[tex]x:1.2[/tex] ......(1)
She decides on a scale of 1 to 40 which means 1 : 40 .....(2)
Equating equation (1) and (2) , we get
[tex]x:1.2=1:40[/tex]
Representing in fraction , we get
[tex]\frac{x}{1.2} =\frac{1}{40} \\\\x=\frac{1.2}{40} \\\\x=0.03m\\x=3cm[/tex]
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The complete question is mention below :
Mai wants to make a scale drawing of her kitchen. her kitchen is a rectangle with length 6m and width 2m. She decides on a scale of 1 to 40. Mal's Kitchen door is 1.2 m wide. How wide should the door be on the scale drawing?How wide should the door be on the scale drawing?
Under her cell phone plan, Ximena pays a flat cost of $44.50 per month and $4 per
gigabyte. She wants to keep her bill at $50.10 per month. How many gigabytes of data
can she use while staying within her budget?
If Ximena pays a flat cost of $44.50 per month and $4 per gigabyte and she wants to keep her bill at $50.10 per month, then she can use 1.4 gigabyte of data while staying within her budget.
Given,
The flat cost of cell phone plan = $44.50 per month
Cost per gigabyte =$4
She wants to keep her bill amount = $50.10
Consider the number of gigabyte used as x
Then the linear inequality will become
44.50+4x≤50.10
4x≤50.10-44.50
4x≤5.6
x≤1.4
Hence, If Ximena pays a flat cost of $44.50 per month and $4 per gigabyte and she wants to keep her bill at $50.10 per month, then she can use 1.4 gigabyte of data while staying within her budget
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Guys i need help making this quadratic equation into a standard form HELP ME PLEASE, ^2 means Like 2 Square.
1.) 11x^2 - 98 = 11 + 9x
2.) (2x - 1)^2 = (x + 4) ^2
3.) 4x^2 + 2x - 9 = (x - 2)(x - 9)
4.) 0 = 6 (x + 7)^2 - 58
5.) - 1/2 ( x - 1/4 )^2 + 12 = 0
Answer:
1) 1x² - 9x - 109 = 0
2) 3x² -12x -15 = 0
3) 3x² + 13x - 27 = 0
4) 6x² + 84x + 236 = 0
5) -16x² + 8x + 383 = 0
Step-by-step explanation:
The standard form of the quadratic equation is ax² + bx + c where a, b and c are constants.
So we have to convert each of the equations into a form that resembles the above
(1) 11x² -98 = 11 + 9x
Simplify both sides of the equation.(2) (2x - 1)² = (x + 4) ²
Simplify both sides of the equation(3) 4x² + 2x − 9 = (x − 2)(x − 9)
Simplify (x−2)(x−9)(4) 0 = 6(x +7 )² - 58
Switch sides:(5) -1/2 ( x - 1/4 )² + 12 = 0
Calculate [tex]-\dfrac{1}{2} (x - \dfrac{1}{4})^2 = -\dfrac{1}{2} (x^2 - 2\(\dfrac{1}{4}x + \dfrac{1}{16})[/tex]57x23=?
What is the explanations
Answer:1311
Step-by-step explanation:
2 digit long multiplication.
__________________________________________
Long multiplication can seem very intimidating, especially if you're multiplying two numbers that are pretty large. If you take it step by step, though, you'll be able to do long multiplication in no time.
First, muiltiply the 3 by 5 and 7, and muiltiply the 2 by 5 and 7 as well.
[tex]\frac{\begin{matrix}\:\:&\:\:&5&7\\ \:\:&\times \:&2&3\end{matrix}}{\begin{matrix}0&1&7&1\\ 1&1&4&0\end{matrix}}[/tex]
(NOTE: Remember when you muiltiply two digit numbers, when you pass from the first digit to the other on the bottom side, you ALWAYS add a zero to the beginning of the result BEFORE multiplying the following digit)
Secondly, once you've multiplied, you add both results of the multiplication.
[tex]\frac{\begin{matrix}\:\:&\textbf{\:\:}&1&\:\:&\:\:\\ \:\:&\textbf{0}&1&7&1\\ +&\textbf{1}&1&4&0\end{matrix}}{\begin{matrix}\:\:&\textbf{1}&3&1&1\end{matrix}}[/tex]
[tex]=1311[/tex] <- This is your final answer.
___________________________________________
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2 2/3 divided by 3 2/3
Answer:
8/11
Step-by-step explanation:
[tex]2\frac{2}{3} = \frac{8}{3}\\3\frac{2}{3} = \frac{11}{3} \\= \frac{8}{3} \div \frac{11}{3}\\=\frac{8\times 3}{3 \times 11} = \frac{24}{33}\\\\LCM: 3\\\\\frac{24 \div 3}{33 \div 3}\\= \frac{8}{11}[/tex]
HELP ME pls it is important
Answer:
You would want have more stock and less savings
Step-by-step explanation:
-3(x+5)=-(3x+15) solve for x
Step-by-step explanation:
Simplifying
-3(x + 5) = -1(3x + 15)
Reorder the terms:
-3(5 + x) = -1(3x + 15)
(5 * -3 + x * -3) = -1(3x + 15)
(-15 + -3x) = -1(3x + 15)
Reorder the terms:
-15 + -3x = -1(15 + 3x)
-15 + -3x = (15 * -1 + 3x * -1)
-15 + -3x = (-15 + -3x)
Add '15' to each side of the equation.
-15 + 15 + -3x = -15 + 15 + -3x
Combine like terms: -15 + 15 = 0
0 + -3x = -15 + 15 + -3x
-3x = -15 + 15 + -3x
Combine like terms: -15 + 15 = 0
-3x = 0 + -3x
-3x = -3x
Add '3x' to each side of the equation.
-3x + 3x = -3x + 3x
Combine like terms: -3x + 3x = 0
0 = -3x + 3x
Combine like terms: -3x + 3x = 0
0 = 0
Solving
0 = 0
Couldn't find a variable to solve for.
This equation is an identity, all real numbers are solutions.
Answer:
Step-by-step explanation:
-3(x+5) = -(3x+15)
-3x - 15 = -3x - 15
the 2 sides are identical so there are
INFINITE solutions.
parentheses. Write the rounded value on the line
1. 5 672 874 627
(nearest millions)
The rounded value of 5,672,874,627 is 5,673,000,000
What is a rounded value?
When a number is rounded, its value is kept relatively constant while being made easier. The outcome is simpler to use but less precise. Since 73 is closer to 70 than to 80, it is 70 when rounded to the nearest ten. But 76 increases to 80.
5,672,874,627
2 is in the million column
5,672,874,627
The nearest million could be 5,672,000,000 or 5,673,000,000.
To round to the nearest million, look at the digit in the column to the right, the hundred thousands.
5,672,874,627
The number in the hundred thousands column is 8.
The rule is, if the number is 5 or more, round up
5,673,000,000
Therefore, the rounded value of 5,672,874,627 is 5,673,000,000
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Eight times six divided by two minus nine numerical expressions
Answer:
15
Step-by-step explanation:
8 x 6 / 2 -9
48 / 2 - 9
24-9
15
Find the solution to the differential equation dzdt=7te7z that passes through the origin.
The answer is [tex]z &=-0.14\left[\ln \left(1-24.5 t^2\right)\right]\end{aligned}$$[/tex]
What do you understand by differential equation?
An ordinary derivative or a partial derivative can both be found in a differential equation. The differential equation describes the relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.
Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variables x and y are related because y is an unidentified function of x. The derivative of y is also on the equation's left-hand side.
Given equation:
[tex]$$\begin{aligned}&e^{-7 z} d z=7 t d t \\&:(-1 / 7) e^{-7 z}=3.5 t^2+C\end{aligned}$$[/tex]
[tex]$C=-1 / 7$[/tex]
[tex]$$(-1 / 7) e^{-7 z}=3.5 t^2-1 / 7$$[/tex]
[tex]$$e^{-7 z}=1-24.5 t^2$$[/tex]
[tex]$$\begin{aligned}-7 z &=\ln \left(1-24.5 t^2\right) \\z &=-0.14\left[\ln \left(1-24.5 t^2\right)\right]\end{aligned}$$[/tex]
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A bike rental fee is $15 plus $0.25 per hour how many hours can Kristen rent a bike if she has $20?
Answer:
Kristen can ride the bike for 20 hours
Step-by-step explanation:
20 - 15 = 5
The rate is 0.25 an hour.
0.25 x 4 = 1 - Currently $4
0.25 x 4 = 1 - Currently $3
0.25 x 4 = 1 - Currently $2
0.25 x 4 = 1 - Currently $1
0.25 x 4 = 1 - No more
Add up all the 4's
She can ride the bike for 20 hours.
Solve for x 2(4-3x)=20
Answer:
x = -2
Step-by-step explanation:
2(4 - 3x) = 20
8 - 6x = 20
-8 -8
-6x = 12
÷-6 -6
x = -2
I hope this helps!
Teresa ran a 20-mile marathon. Her average speed was 5 miles per hour. Approximately how long did it take her to finish the race?
Answer:4 hours
Step-by-step explanation:
You have to figure out what times 5 would equal 20.
5x=20
5(4)=20
because 5*4=20, the answer is 4
On the following number line, what number would you plot at point B?
A number line from 4 to 5 partitioned into tenths. There is a red dot between 4 and 4.1 labeled A. There is a red dot between 4.3 and 4.4 labeled B. There is a red dot between 4.5 and 4.6 labeled C. There is a red dot between 4.7 and 4.8 labeled D
4.009
4.328
4.43
4.77
The number which corresponds to the point B is (option b) 4.328.
Given,
A number line 4 to 5 partitioned into tenths. ( image is attached below)
There are 4 red dots:
A - Between 4 and 4.1B - Between 4.3 and 4.4C - Between 4.5 and 4.6D - Between 4.7 and 4.8We have to plot the number corresponding to the point B.
Let's go through the options:
a) 4.009 : This would be between 4 and 4.1. That is, point A.
b) 4.328 : This would be between 4.3 and 4.4. That is, point B.
c) 4.43 : This would be between 4.4 and 4.5
d) 4.77 : This would be between 4.7 and 4.8. That is, point D.
So, the number which corresponds to the point B is (option b) 4.328.
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My Assuming Answer;
OPTION B;
4.328
Add-ons;
Hey again! Here's an answer to your question :) Thanks for giving that recipe. Have a nice day.
Harry tosses a nickel 4 times. The probability that he gets at least as many heads as tails is.
The probability that he gets at least as many heads as tails is half or 50%.
What is the formula for probability?Probability is obtained by dividing the number of chances that it will take to realize a result by the number of total possible chances. To get the right probability for the question asked here, we need to determine:
The number of chances is equal to 4.
The total number of possible chances is given by the equation:
4 × 2 = 8
Two is obtained by recognizing the fact that there are two sides to the coin. So, he could either get a head or a tail when he tosses the nickel.
Therefore;
4/8 = 1/2 or 50%
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6 time the complement of an
angle is 44° less than 2 times its supplement. Find all angles
The value are-
original angle = 34°complement angle = 56°supplement angle = 146°What are defined as the complement and supplement angle?If a sum of two angles is 180 degrees, they are referred to as supplementary angles because they form a linear angle when combined. If a sum of two angles is 90 degrees, they are termed to be complementary angles because they form a right angle when combined.Now, for the given question.
Let the given angle be 'x'.
Then, the complement of the angle will be: 90 - x.
6 times the complement = 6(90 - x)
6 times the complement is 44 less; 6(90 - x) - 44.
Now, the supplement of the angle is; 180 - x.
Two time the supplement = 2(180 - x)
The equation will form as;
2(180 - x) = 6(90 - x) - 44
360 - 2x = 540 - 360 - 44
Simplifying the equation;
x = 34.
Thus, the original angle is 34°.
complement angle = 90 - x
= 90 - 34
= 56°
Thus, complement angle = 56°
supplement angle = 180 - x
= 180 - 34
= 146
supplement angle = 146°
Thus, the values of the angles are obtained.
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The price of Stock A at 9 AM was $15.97. Since then, the price has been increasing at the rate of $0.11 each
hour. At noon the price of Stock B was $16.72. It begins to decrease at the rate of $0.15 each hour. If the two rates continue,
in how many hours will the prices of the two stocks be the same?
In about hours, the prices of the two stocks will be the same.
In roughly 127 hours the prices of the two stocks will be the same.
What do we mean by equations?A mathematical equation is a statement that uses the symbol 'equal to' to connect two expressions with equal values. 3x + 5 = 15, for example. Equations are classified into linear, quadratic, cubic, and other types.So, if we count the hours (x) after 9 a.m., the stock prices will be:
A = $15.97 + $0.11xB = $16.72 - $0.15(x - 3)The value of x when A = B can be calculated using:
A = B
$15.97 + $0.11x = $16.72 - $0.15(x - 3)$15.97 + $0.11x = $16.72 - 0.15x + 0.45$0.11x + 0.15x = $16.72 + 0.45 - $15.97$0.26x = $33.14x = 33.14/0.26= 127.4615384615385Rounding off: 127Therefore, in 127 hours roughly the prices of the two stocks will be the same.
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the expression 14x 3 represents the perimeter of the triangle. what is the length of the third side
2. Consider divided by . (a) Write a real-world problem for the division. (b) Create a model or write an equation for the division. (c) Find the quotient for the real-world problem in part (a). Show your work or explain your reasoning.
2(1/2)/0.25=x and 10 is the quotient for the real-world problem in part.
What is Division?Division is splitting a group into equal parts and it is one of the four basic math operations.
The real-world problem for the division is
2(1/2)÷)0.25=x
Wth 2.5 L of water. you can drink 0.25L litres in one mouthful.How many mouthfuls do you need to drink.
the quotient for the real-world problem in part is
2.5/0.25
=10
10 is the quotient for the real-world problem in part.
Therefore 10 is the quotient for the real-world problem in part.
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what is -3+5-11 ?? i need help
Answer:-9
Step-by-step explanation:
machine a, working alone at its constant rate, produces x pounds of peanut butter in 12 minutes. machine b, working alone at its constant rate, produces x pounds of peanut butter in 18 minutes. how many minutes will it take machines a and b, working simultaneously at their respective constant rates, to produce x pounds of peanut butter?
The total time taken by machine A and B working together to produce x amount of peanut butter is 7.2 minutes.
What is the concept of time and work?
Time and work defines the way how the particular work is done in the given time. It gives an exact relationship between the work and the number of days required to complete it.
Calculation of the total time taken by the machines A and B working together
Given that Machine A completes the entire job in 12 minutes.
So, machine A completes 1/12 of the job in one minute.
Machine B takes 18 minutes to complete the entire job.
So, machine B completes 1/18 of the job in one minute
When we combine their work, they will complete (1 / 12 + 1 / 18) job in one minute i.e. (3 + 2) / 36 = 5/36 job in one minute —---- 1
To find the time taketaken by them to produce x amount of peanut butter, we will reciprocate the result obtained in equation 1
i.e. 36 / 5 minutes to complete the entire job
i.e. 7.2 minutes
Hence, the time taken by machine A and B working together to produce x amount of peanut butter is 7.2 minutes.
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a water sprinkler is set to shoot a steam of water a distance of 12m and rotate through an angle of 40 degrees.
A) what is the ares of the lawn it waters? For r=12?
B.)what angle is required to water twice as much area. for θ=40 degree?
C)what range for the water stream is requiredto water twice as much area?
The area of the lawn is given as 50 . 24 m²
How to find the area of the lawn that the sprionkler watersArea = πr² x θ/360
r = 12m
θ = 40 degrees
Area = 3.14 x 12² * 40/360
= 50.24
Hence the area is 50 . 24 m²
b. what angle is required to water twice as much area2 x 50.26
= 100.52
Area = πr² x θ/360
The value of θ is not given
When we plug in the figures we would have
100.52 = πr² x θ/360
Then θ = 100.53 x 360 / 3.14 x 12²
= 80 degrees
c. θ = 40 degrees
100. 53 = πr² x 40/360
πr² = 100.53 x 360 / 40
r = 16.97 m
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A train car is carrying 500 TV's.
If each set weighs 12.85 pounds, what is the
weight of the entire load?
Answer:
6425
Step-by-step explanation:
12.85x500=6425
Which number is less than 2.167 × 10?
A. 9,978
B. 1.1 x 10
C. 56,344,000
D. 2.468 × 10
Answer:
A, B, C
Step-by-step explanation:
question what is an expression equivalent to 6(24) using the distributive property? drag and drop the appropriate number into each box.
The following can be used to rewrite the provided expression: 6(24) = 6(20 + 4).
What in mathematics is a distributive property?The distributive Property states in that it is necessary to multiply every one of the two numbers by the factor before performing the addition operation when a factor is multiplied by that of the sum or addition of two terms. The distributive law, which states that in elementary algebra, equality is always true, is generalized by the distributive principle of binary operations.
According to the given data:The following generic form can be used to specify the distribution property:
a(b+c) = ab + bc
the following expression:
6(24)
We can observe the following by contrasting this to the general form:
a = 6
b + c = 24
Consequently, we must identify two integers from the options whose sum is 24.
These numbers, out of the options provided, are 20 and 4.
The following can be used to rewrite the provided expression: 6(24) = 6(20 + 4).
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You can find the net force F on an object
by using the formula F = ma, where m is
the mass of the object in kilograms and
a is its acceleration in meters per second
squared. What is the mass of an object
that has a net force of 65 kg m/s² and an
acceleration of 5 m/s²?
Answer: m = 13 kg
Step-by-step explanation:
This question gives us the formula to use. We will plug-in the values we know and solve for the unknown (mass).
Given:
F = ma
Plug-in known values:
(65 kg m/s²) = m(5 m/s²)
Divide both sides of the equation by 5 m/s²:
The m/s² unit cancel out, so we are left with kg.
m = 13 kg
The mass of the object is 13 kg.
1. Which of the drawings described below would create a line of reflection that takes the point A to point B?
a.
Draw the perpendicular bisector of segment AB.
b. Draw a line through B perpendicular to segment AB.
c. Draw the line passing through A and B.
d. Draw a line parallel to line AB.
The drawing that creates a line of reflection that takes the point A to point B is; D: Draw a line parallel to line AB.
How to create a line of reflection
A line of reflection is a line that lies in a position between two identical mirror images so that any point on one image is the same distance from the line as the same point on the other flipped image.
Let us look at the given options;
A) Draw the perpendicular bisector of segment AB; A perpendicular bisector will NOT create a line of reflection that takes point A to point B but rather it will divide the line AB in two equal parts
B) Draw a line through B perpendicular to segment AB; A line through B perpendicular to segment AB will NOT Create a line of reflection that takes point A to point B
C) Draw the line passing through A and B;
A line passing through A and B will NOT create a line of reflection that takes point A to point B but rather will create Line A and B again and not its reflection
D) Draw a line parallel to line AB;
A line parallel to line AB will create a line of reflection that takes point A to point B because a parallel line never meet thereby creating the direct imagery of Line AB.
Thus, the drawing that create a line of reflection that takes the point A to point B is; D: Draw a line parallel to line AB.
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A group of friends wants to go to the amusement park. they have $327.75 to spend on parking and admission. parking is $13.75, and tickets cost $39.25 per person, including tax. how many people can go to the amusement park?
The total number of people who can go to the amusement park in the given scenario is 6. This problem is based on the basic mathematical formulae.
Formulae are mathematical statements comprising expressions, numbers, and variables to ease complex calculations.
Given that
The total amount for the expenditure = [tex]\[/tex]327.75.
Cost of parking per person = [tex]\[/tex]13.75,
Cost of tickets per person = [tex]\[/tex]39.25.
Total cost per person = Cost of parking per person + Cost of tickets per person
Total cost per person = [tex]\[/tex]13.75 + [tex]\[/tex]39.25
= [tex]\[/tex]53
So,
Number of persons = [tex]\frac{The total amount for the expenditure}{Total cost per person }[/tex]
= [tex]\frac{327.75}{53}[/tex] = 6.18.
So, 6 people can go to the amusement park.
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Logic puzzle help solve pleaseeeeeeeee
Answer:
Many challenging questions do not involve numerical or geometrical considerations but call for deductive inferences based chiefly on logical relationships. Such puzzles are not to be confounded with riddles, which frequently rely upon deliberately misleading or ambiguous statements, a play on words, or some other device intended to catch the unwary. Logical puzzles do not admit of a standard procedure or generalized pattern for their solution and are usually solved by some trial-and-error method. This is not to say that the guessing is haphazard; on the contrary, the given facts (generally minimal) suggest several hypotheses. These can be successively rejected if found inconsistent, until, by substitution and elimination, the solution is finally reached. The use of various techniques of logic may sometimes prove helpful, but in the last analysis, success depends largely upon that elusive capacity called ingenuity. For convenience, logic problems are arbitrarily grouped in the following categorie
John goes to the bank to get a $15,000 loan.The loan has a simple interest rate of 6% and is 4 years long.What is the TOTAL amount John has to pay?
The total amount John has to pay in repaying the loan and interest is $18,600
What makes up the total amount John has to pay?
The total amount that John has to pay comprises of the loan principal of $15,000 and the interest on the loan which is computed at the simple interest rate of 6% for the loan duration of 4 years
I=PRT
I=interest for 4 years=unknown
P=loan principal=$15,000
R=interest rate=6%
T=number of years of loan=4
I=$15,000*6%*4
I=$3,600
A=P+I
A=$15,000+$3,600
A=$18,600
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Jarome is making pizza. He uses 2 1/2 cups of cheese for
every 2 3/4 pizzas. He has 6 1/4 cups of cheese left in the
bag. How many pizza pies can he make with the leftover
cheese?
Jarome can make 6 whole pizzas with the leftover cheese.
Given that Jarome uses 2 1/2 cups of cheese for every 2 3/4 pizzas. He has 6 1/4 cups of cheese left in the bag.
We need to determine the number of pizza pies can he make with the leftover cheese.
To find out how many pizza pies Jarome can make with the leftover cheese, we need to determine how many sets of 2 3/4 pizzas can be made using 6 1/4 cups of cheese.
Let's start by finding the number of sets of 2 3/4 pizzas that can be made from 6 1/4 cups of cheese:
Number of sets = Total cheese available / Cheese per set
Number of sets = 6 1/4 cups / 2 1/2 cups per set
To make the calculation easier, let's convert all the mixed numbers to improper fractions:
6 1/4 cups = (4 x 6 + 1) / 4 = 25/4 cups
2 1/2 cups = (2 x 2 + 1) / 2 = 5/2 cups
Number of sets = (25/4) / (5/2)
Now, to divide fractions, we invert the divisor (5/2) and multiply:
Number of sets = (25/4) x (2/5)
= (25 x 2) / (4 x 5)
= 50/20
= 5/2
So, Jarome can make 5/2 sets of 2 3/4 pizzas with 6 1/4 cups of cheese.
Now, let's see how many pizzas he can make with the leftover cheese:
To calculate the number of pizzas in 5/2 sets, we multiply it by the number of pizzas per set (2 3/4 pizzas):
Number of pizzas = (5/2) x (2 3/4)
Again, let's convert all the mixed numbers to improper fractions:
2 3/4 pizzas = (4 x 2 + 3) / 4 = 11/4 pizzas
Number of pizzas = (5/2) x (11/4)
Now, when multiplying fractions, we simply multiply the numerators together and the denominators together:
Number of pizzas = (5 x 11) / (2 x 4) = 55/8
So, Jarome can make 55/8 pizzas with the leftover 6 1/4 cups of cheese.
Now, let's simplify the fraction:
55/8 = 6 7/8
Therefore, Jarome can make 6 7/8 pizzas with the leftover 6 1/4 cups of cheese.
Since we can't make a fraction of a pizza, he can make 6 whole pizzas with some cheese left over.
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