We have the next equation
42=6a
we need to clear a
a=42/6
a=7
the answer is 7
A class board with edge lengths of √80 dm and √150 dm has a square with an edge length of √3 dm how many pieces of cardboard can be placed in such a way that they do not overlap?
A) 48
B) 42
C) 35
D) 30
The total number of square cardboards that can be placed is 35 square pieces.
Length of the class board = √150dm
Length of the square side = √3 dm
Number of cardboards that can be cut = √150 ÷ √3 = 7.07 ≈ 7
Width of the square = √80 dm
Number of cardboard pieces = √80 ÷ √3 = 5.16 ≈ 5
Total number of cardboard squares = 7 × 5 = 35 pieces
A square is just a normal quadrilateral because it has four equal sides and four equal 90-degree, /2 radian, or right angles angles.
An alternative explanation is that it is a rectangle with two adjacent sides that are equal in length. It is the only uniform polygon with equal-length diagonals and identically 90° internal, central, and external angles.
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Cuatro pintores tardan 6,3 horas en pintar un almacén. Se decide contratar a 9 pintores.
a) ¿Cuánto tardarán en pintar el almacén? Expresa el resultado en formato de horas y minutos. (Como por ejemplo: 3 horas 15 minutos.)
b) ¿Cuánto hay que pagar en total por el trabajo a los nueve pintores si cada pintor cobra 8,5 euros por hora trabajada?
By using unitary method, it is obtained that
a) 9 painters took 2hours 48 minutes to paint a ware house
b) 9 painters earns 214.2 euros by working 2.8 hours
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here, unitary method is used
a) Four painters took 6.3 hours to paint a ware house
1 painter take [tex]6.3 \times 4[/tex] hours to paint a ware house
9 painters took [tex]\frac{6.3 \times 4}{9}[/tex] hours to paint a ware house
9 painters took 2.8 hours to paint a ware house
9 painters took 2hour + [tex]0.8 \times 60[/tex] minutes to paint a ware house
9 painters took 2hours 48 minutes to paint a ware house
b) Each painter earns 8.5 euros per hour worked
Each painter earns 8.5 [tex]\times[/tex] 2.8 euros by working 2.8 hours
9 painters earns 8.5 [tex]\times[/tex] 2.8 [tex]\times[/tex] 9 euros by working 2.8 hours
9 painters earns 214.2 euros by working 2.8 hours
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31n+7n-21n+12n if n=20 brainly
Answer:
580
Step-by-step explanation:
31(20) + 7(20) - 21(20) +12(20)
620 + 140 - 420 + 240
580
What is the length in units of segment cd
Answer: 7.2
Step-by-step explanation: I took the test and got it correct, I'm just trying to spread the correct answer around.
Niko uses 1212marshmallows and 88graham crackers to make 44s'mores. Drag marshmallows and graham crackers into the box to show how many Niko needs to make 33s'mores.
Solving Linear Inequalities
HELP PLEASE(┬┬﹏┬┬)
In Step 2 have a mistake in student solution so the option B is correct answer.
In the given question,
A student solved the inequality [tex]\frac{-x+4}{3} > \frac{x+1}{2}[/tex].
We have to find the error in the student solution.
To find the mistake we first solve the give inequality.
The equality is [tex]\frac{-x+4}{3} > \frac{x+1}{2}[/tex]
To solve this equality we firstly equal the denominator by multiplying and divide 2 on left side and 3 on right side.
So [tex]\frac{2}{2}\times\frac{-x+4}{3} > \frac{x+1}{2}\times\frac{3}{3}[/tex]
Now simplifying
[tex]\frac{2(-x+4)}{6} > \frac{3(x+1)}{6}[/tex]
Now simplifying the brackets of numerator ob both side using distributive property.
In Distributive Property: a(b+c)=ab+bc
[tex]\frac{2\times(-x)+2\times4}{6} > \frac{3\times x+3\times1}{6}[/tex]
[tex]\frac{-2x+8}{6} > \frac{3x+3}{6}[/tex]
Since the both side have same numerator. So we can write the inequality as
-2x+8 > 3x+3
Subtract 8 on both side
-2x+8-8 > 3x+3-8
-2x > 3x-5
Subtract 3x on both side
-2x-3x > 3x-5-3x
-5x > -5
Divide by -5 on both side
-5/-5 x > -5/-5
x > 1
Hence the value of x is greater than 1.
Now we see the step on student.
We can see that in step 2 has mistake. In step 2 student doesn't use distributive property to solve the bracket.
Hence, we can say that option 2 is correct.
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Graph the function h(x)=. I have a picture of the problem
Let's begin by listing out the given information
[tex]\begin{gathered} h(x)=-\frac{2}{3}x-2 \\ h(x)=y \\ y=-\frac{2}{3}x-2 \end{gathered}[/tex]We will graph the function by assuming values for the independent variable (x = -3, 0, 3
[tex]\begin{gathered} y=-\frac{2}{3}x-2 \\ x=-3 \\ y=-\frac{2}{3}(-3)-2=2-2=0 \\ (x,y)=(-3,0) \\ x=0 \\ y=-\frac{2}{3}(0)-2=0-2=-2 \\ (x,y)=(0,-2) \\ x=3 \\ y=-\frac{2}{3}(3)-2=-2-2=-4 \\ (x,y)=(3,-4) \end{gathered}[/tex]We will plot the ordered points (shown below)
Priya creates a scatter plot showing the relationship between the number of steps she takes and her heart rate. The correlation coefficient of the line of best fit is 0.88.Are they correlated? Explain your reasoning.
Correlation coefficient: statistical measure of the strength of the relationship between the relative movements of two variables.
• If a correlation coefficient has an exact value of one, it has a perfect positive relationship between the two variables
,• If a correlation coefficient has an exact value of minus one, there is a perfect negative relationship between the two variables.
,• Analysts in some fields of study do not consider correlations important until the value surpasses at least 0.8. However, a correlation coefficient with an absolute value of 0.9 or greater would represent a very strong relationship.
Thus, they have a weak correlation.
factor out the coefficient of the variable term 4x-20
the given expression is,
4x - 20 = 0
here 4 is the coefficient of variable x
4x = 20
x = 20/4
x = 5
thus, the value of x is 5
what needs to be corrected in this constr of a line parallel to line AB passing through C
The corrected form is second arc should be centered at C.
Assuming the goal is to construct a line parallel to AB that passes through given point C.
-Draw a line through C and across AB at an angle creating D.
- With the compass width about half of DC, and center D, draw the first arc to cross both lines.
-Using the same compass width , draw the second arc with center C.
-Then set the compass width to the lower arc (the first arc)
- Move the compass to the second arc. Mark off an arc to make point E
-Draw a straight line through C and E
Thus the line CE will be parallel to line AB
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A recipe calls for 5 teaspoons of orange juice. A can of orange juice is 21 fluid ounces. How many teaspoons of juice is in the can?
Answer:
21 fluid ounces = 126 teaspoons
Step-by-step explanation:
1 teaspoons is 0.166667 fluid ounces
Now we just have to think 0.166667 * x = 21
21 ounces = 126 teaspoons
Hope this helped :)
Answer: the can contains 126 teaspoons in the can of range juice.
Step-by-step explanation:
given,
no. of teaspoons of orange juice is the call= 5 teaspoons
ounces in the orange juice can= 21 fluid ounces
if 1 ounce = 6 teaspoons
then, 21 ounces= 126 teaspoons.
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Pleaseeeee helpppppp meeeee
The coordinates of the vertex and the range of the function y = |3 · x + 6| - 4 are (x, y) = (- 2, - 4) and y ≥ - 4, respectively. (Correct choice: B)
What is the vertex and the range of a function?In this problem we have an absolute value function of the form y = |a · x + b| + c, of which we need to determine the coordinates of the vertex and the range of the function. The coordinates of the vertex is the point of the function such that:
x-Coordinate
|a · x + b| = 0
a · x + b = 0
x = - b / a
y-Coordinate
y - c = 0
y = c
And the range of the function is:
y ≥ c
If we know that a = 3, b = 6 and c = - 4, then the coordinates of the vertex and the range of the function are, respectively:
Coordinates of the vertex
(x, y) = (- 2, - 4)
Range of the function
y ≥ - 4
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PLEASEEEEEEEEEEE HELP!!!!!!!
Answer:
answer y=-5/3x+5
Step-by-step explanation:
The slope is decreasing so the slope is negative
Rise is 5 run is 3 so its 5/3 but the slope is negative so its -5/3
Y intercept is located at 0,5 so it equals 5
y=-5/3x+5
The equation of line will be;
⇒ y = - 5/3x + 5
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The equation of line is decreasing.
The rise will be 5.
The run will be 3.
Now,
Since, The equation of line is decreasing.
Hence, The slope of the line is negative.
Here, The rise will be 5.
The run will be 3.
So, The slope = Rise / Run
= 5/3
Thus, The slope = - 5/3
So, The equation of line in point-slope form will be;
⇒ y = mx + b
⇒ y = - 5/3x + 5
Thus, The equation of line will be;
⇒ y = - 5/3x + 5
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What is an equation of the line that passes through the point (2,-5)(2,−5) and is parallel to the line x-2y=16x−2y=16?
The slope intercept form of the required line is x -2y = 12
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
The given line is
[tex]x - 2y = 16\\2y = x - 16\\y = \frac{1}{2}x - \frac{16}{2}\\[/tex]
Slope of the line = [tex]\frac{1}{2}[/tex]
Slope of the line parallel to this line = [tex]\frac{1}{2}[/tex]
The line passes through (2, -5).
Equation of the required line-
[tex]y - (-5)= \frac{1}{2}(x - 2)\\2y + 10 = x - 2\\ x - 2y = 10 + 2\\x-2y = 12[/tex]
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Question 7After Anishing his workout,Justin's heart rate decreased 3beats per minute for each of thenext 4 minutes. What was thechange in Justin's heart rateafter 4 minutes?
Justin"s heart rate decreased 3 beats per minute for each of next 4 minutes
Let his heart rate be be 1
For the first minutes
1 minute his heart rate was 1 - 3 = -2
This is because the heart rate is decreasing 3 beats per minutes
2minutes later, his heart beat will be -2 -3
-2 - 3 = -5
3 minutes later, his heart beat will be -5 - 3
-5 - 3 = -8
4 minutes later, -8 - 3
-8 - 3 = -11
Change = Final heart beat - initial heart beat / initial heart beat
Change = -11 -2 / -2
Change = -13/-2
Change = 13/2
= 6.5
Jaylene works at a book store. She is paid an hourly rate plus 10% commission on everything she sells. One week she was paid $381.25 for working 15 hours and selling $1,225 worth of books. What is her hourly rate?
She is paid an hourly rate plus 10% commission on everything she sells
Total amount she get = Hourly rate + 10% on sale price of the objects
One week she was paid $381.25 for working 15 hours and selling $1,225 worth of books.
Let the hourly wages is x
She paid $381.25 for working 15 hours
for hourly rate divide the amount by number of hours :
[tex]\begin{gathered} \text{ Hourly Rate=}\frac{381.25}{15} \\ \text{ Hourly rate=25.416} \end{gathered}[/tex]The hourly rate is $25.416
Answer : The hourly rate is $25.416
One popular smoothie recipe uses 2/3 oz of acai juice to make one smoothie. Acai juice typically comes in a 5-oz container, and you want to know how many smoothies can be made from one container. (Write both a multiplication equation and division equation that represents this scenario) (Determine the number of smoothies can be made from one oz of acai)
You can make one and a half smoothies from one oz of acai juice
How to write multiplication equation and division equation?
Given that:
smoothie recipe uses 2/3 oz of acai juice to make one smoothie and
Acai juice comes in a 5-oz container
In order to know how many smoothies can be made from one container, you divide the volume of the Acai juice container by the volume needed to make one smoothie. Thus the equation is:
No. of smoothies = volume of container/volume needed for one smoothie
The number of smoothies that can be made from one oz of acai is:
No. of smoothie = 1/(2/3) = 1 1/2 smoothies
Therefore, the number that can be made from one oz is one and half smoothies
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help please will give brainliest
The factored form of the quadratic equation 2x² + 25x + 50 is (2x + 5)(x + 10)
How to factor quadratic equations?Factoring quadratics is a method of expressing the quadratic equation ax² + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax² + bx + c = 0.
Therefore, let's factor the equation 2x² + 25x + 50.
2x² + 25x + 50
The two numbers one can multiply and add to get 100 and 25 respectively are 20 and 5.
Therefore,
2x² + 20x + 5x + 50
2x(x + 10)+ 5(x + 10)
Therefore,
(2x + 5)(x + 10)
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the school cafeteria orders for cartons of regular milk for every three cartons of chocolate milk a. complete the bar diagram to show the ratio b. the school ordered 120 cartons of regular milk. Divide 120 cartons of regular milk by underscore_because there are__boxes in the top row c.write the value of each box in both rows of the bar diagram d.how many cartons of chocolate milk did the school order?
1) Gathering the data
a) Since each Regular milk has four cartons and chocolate 3. If we multiply by 30 we get 120 for Regular Milk and 90 for Chocolate Milk
Regular Milk 4
Chocolate Milk: 3
Regular Milk: 120
Chocolate Milk: 90
The ratio is 4/3, 4 cartons of regular milk for every 3 cartons of chocolate milk.
b) Divide the 120 cartons by 30 because there are 4 boxes in the top row
c) write the value of each box in both rows of the bar diagram
d) According to the bar graph the School ordered 90 cartons of chocolate milk
How to find the products of binomials
Answer:
FOIL Method! (EXPLAINED BELOW)
Step-by-step explanation:
FOIL MEANS First Out In Last.
For example:
Binomial: (a+b) (a+b)
STEP 1: Multiply the first term of each bracket.
(a+b) (a+b)
So, a * a = [tex]a^{2}[/tex]
The number would be positive since both terms are positive.
STEP 2: Multiply the outer terms.
(a+b) (a+b)
So, a * b = ab
The number would be positive since both terms are positive.
STEP 3: Multiply the inner terms.
(a+b) (a+b)
So, a * b = ab
The number would be positive since both terms are positive.
STEP 4: Multiply the last terms.
(a+b) (a+b)
So, b * b = [tex]b^{2}[/tex]
The number would be positive since both terms are positive.
STEP 5: Put them together with the appropriate signs.
[tex]a^{2} + 2ab + b^{2}[/tex]What did you like most about CodeMonkey?
The thing that I like most about CodeMonkey is that it makes it easier for children to learn computer coding and that it also boost their intelligence.
What is the advantage of using CodeMonkey?CodeMonkey is a computer coding educational environment that teaches beginners computer programming concepts and languages. CodeMonkey is designed for students aged 6 to 14.
Students who use critical thinking, problem solving, reasoning, logic, computational, and algorithmic thinking perform better in class. Because these abilities carry over into their daily learning, the skills they develop integrate with core subjects.
Computer programming is the process of carrying out a specific computation, typically by designing and constructing an executable computer program. Programming tasks include analysis, algorithm generation, algorithm accuracy, and resource consumption profiling, and algorithm implementation.
CodeMonkey is a fantastic learning tool for people of all ages! The courses cover the entire curriculum for grades K-8. It is best to start teaching code at a young age. Anyone can learn to code, and it can be enjoyable.
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1. How many total engineers liked science 2. Which type of engineer was surveyed the most 3. P(mechanical engineer)4. P(engineer who liked math)5. P(engineer who liked science or is a chemical engineer)6. P(electrical or chemical engineer)7. P(mechanical engineer who liked science)8. P(engineer who liked math and is an electrical engineer)Answer the following problems about two way frequency tables fill in the missing cells of each table make sure to reduce your fraction.
Step 1; Complete the table
1. The number of engineers that like science are 266
2. The engineer surveyed the most is Electrical Engineers
3. Pr(mechanical Engineer) is
[tex]\begin{gathered} \frac{total\text{ number of mechanical engin}er}{\text{total}} \\ \text{Total number pf mechanical engine}er\text{ =170} \\ \text{Total =516} \\ =\frac{170}{516} \\ =0.33 \end{gathered}[/tex]4. Pr(engineer who liked maths ) is
[tex]\frac{Total\text{ number of engin}er\text{ who liked maths }}{ground\text{ total}}=\frac{254}{516}=0.49[/tex]5. Pr( Engineer who like science or is a chemical engineer) is
Let Pr(engineer like science)=E and Pr(a chemical engineer)=S
The Pr( Engineer who like science or is a chemical engineer) is given as
[tex]\begin{gathered} Pr(E)+Pr(S)-Pr(\text{EnS)} \\ \text{where Pr(E)=}\frac{262}{516},\text{ Pr(S)=}\frac{171}{516},\text{ Pr(EnS)=}\frac{91}{516} \end{gathered}[/tex]Hence, we have
[tex]\begin{gathered} \frac{262}{516}+\frac{171}{516}-\frac{91}{516} \\ =\frac{262+171-91}{516}=\frac{342}{516}=0.66 \end{gathered}[/tex]6. Pr( Electrical or chemical) is
[tex]\begin{gathered} Pr(\text{Electrical) +Pr(chemical)} \\ Pr(\text{electrical)}=\frac{175}{516},\text{ Pr(chemical)}=\frac{171}{516} \\ \text{hence,} \\ \frac{175}{516}+\frac{171}{516}=\frac{346}{516}=0.67 \\ \end{gathered}[/tex]7. Pr(Mechanical engineer who liked science) is given as
[tex]\begin{gathered} Pr(M|S)=\frac{Pr(MnS)}{Pr(S)} \\ Pr(MnS)=\frac{81}{516},\text{ Pr(S)=}\frac{262}{516} \\ Pr(M|S)=\frac{81}{516}\times\frac{516}{262}=\frac{81}{262}=0.31 \end{gathered}[/tex]8. Pr(an engineer who liked maths and is an electrical engineer)
[tex]\frac{85}{175}=0.49[/tex]Write the slope-intercept form of an equation for
the line of fit. Use points (1997, 683) and (2003, 56).
Answer:
y = −209/332x + 644129/332
Step-by-step explanation:
Determine whether the dilation from A to B is an enlargement or a reduction. Then find the scale factor of the dilation.
From the figure we notice that the figure B is smaller than figure A, hence the dilation is a reduction.
Now, to find the dilation factor we notice that the right side of figure A has length 6; the same side for figure B has length 2; then we need to find a factor that fullfils:
[tex]6k=2[/tex]solving for k we have that:
[tex]\begin{gathered} 6k=2 \\ k=\frac{2}{6} \\ k=\frac{1}{3} \end{gathered}[/tex]Therefore the scale factor of the dilation is 1/3
john must saves at least 25.50 to buy a hat. if he saves 80 cents per day, how many days will it take him to save enough?
represent the days as a variable
days= x
remeber that 80c is the same as $0.80
write an equation that models this situation
[tex]0.80x>25.50[/tex]solve the equation for x
[tex]\begin{gathered} \text{0}.80x=25.50 \\ x>\frac{25.50}{0.80} \\ x>31.875 \end{gathered}[/tex]according to this, after 31.875 days he will have enoght for the hat
Answer:
32 days
Step-by-step explanation:
25.50 / (.80 /day)= 31.875 days <=== so after 32 days he will have enough
What is the value of x-9 if x = -24?
A. 33
B. 15
C. -15
B. -33
Answer:
D
Step-by-step explanation:
don't forget to follow rate like
Answer:
The second B) - 33
Step-by-step explanation:
-24 - 9 = -33.
Question 1 Which expression is equivalent to r-1.y? a Ob y? Ос ty-2 Od xy2
Step 1
State a law of indices that can be used to simplify the problem
[tex]\begin{gathered} a^{-1\text{ }}=\frac{1}{a^{-1}} \\ \end{gathered}[/tex]Step 2
Apply this to the question and get the solution
[tex]\begin{gathered} x^{-1\text{ }}=\text{ }\frac{1}{x} \\ \text{Hence} \\ \frac{1}{x}.y^2^{} \\ =\frac{y^2}{x} \end{gathered}[/tex]Hence option B
Jacob invests $8,634 in a savings account with a fixed annual interest rate of 2.67% compounded continuously. What will be the account balance be after 6 years?
Answer:
$10134.12
Step-by-step explanation:
Pe^(rt)
8634e^(0.0267)(6)
8634e^(0.1602)
= 10134.12
I hope this helps!
Jayson reads the first 48 pages of a 480-page book in 3 days. marcus reads the first 50 pages of a 400-page book in 4 days. nina reads the first 120 pages of a 600-page book in 5 days. check your work on zearn. 1. if they continue to read at these rates, who will finish first? will finish the book first. 2. how many days will each student take to finish his or her book? it will take jayson days to finish his book. it will take marcus days to finish his book. it will take nina days to finish her book.
Nina will take the shortest time finishing her book.
What is division ?Division is the opposite of multiplication. If you divide 12 into three equally sized groups, you will get four in each group if the three groups of four sum up to 12, which they do when you multiply. The main goal of division is to count the total number of evenly distributed groups or the total number of people in each group following a fair distribution.
CalculationLet's calculate how many pages each person reads in one day:
Jayson ⇒ 48 pages / 3 days = 16 pages/dayMarcus ⇒ 50 pages / 4 days = 12.5 pages/dayNina ⇒ 120 pages / 5 days = 24 pages/dayThen we divide the number of pages of each book by reading speed of the respective person:
Jayson ⇒ 480 pages ÷ 16 pages/day = 30 daysMarcus ⇒ 400 pages ÷ 12.5 pages/day = 32 daysNina ⇒ 600 pages ÷ 24 pages/day = 25 daysThus Nina will take the shortest time finishing her book.
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Simplify the expression positive exponents only 17C^9d^4 - 2c^3d^9 (times) 3C^6d^5
The value of the expression, [tex]17c^{9} d^{4} -2c^{3} d^{9} .3c^{6} d^{-5}[/tex], after simplification with only positive exponents is [tex]11c^{9} d^{4}[/tex].
According to the question,
We have the following expression:
[tex]17c^{9} d^{4} -2c^{3} d^{9} .3c^{6} d^{-5}[/tex]
Now, we know that we will first solve terms in multiplication and we also that if numbers with same base are in multiplication then their powers are added.
So, we will have the following expression:
[tex]17c^{9} d^{4} -6c^{3+6} d^{9-5\\}\\17c^{9} d^{4} -6c^{9} d^{4}[/tex]
Now, they have the same variables so the terms can be easily subtracted.
(More to know: if the variables would have been different in these two terms then they could not have been subtracted.)
[tex]11c^{9} d^{4}[/tex]
Hence, the value of the expression, [tex]17c^{9} d^{4} -2c^{3} d^{9} .3c^{6} d^{-5}[/tex], after simplification with only positive exponents is [tex]11c^{9} d^{4}[/tex].
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