4-2x≤-3 so basically you are trying to find x so the best inequality for this equation would be less than or equal to hoped this helped have a great day :)
Answer:
4 - 2x < 3
Step-by-step explanation:
Given,
The measured temperature in Toronto = 4°C,
∵ the temperature started dropping 2°C every hour,
So, the decrement in temperature after x hours = 2x degree celsius,
∴ The total temperature after x hours = original temperature - decrement in the temperature,
= 4 - 2x
According to the question,
Total temperature would be below -3°C,
4 - 2x < 3
Which is the required inequality.
Which operation is NOT closed for polynomials?
A) add a trinomial to a trinomial
B) divide a binomial by a trinomial
C) multiply a binomial by a binomial
D) subtract a binomial from a trinomial
Answer:
Option B is the correct choice.
Step-by-step explanation:
Since we know that polynomials are closed under addition, subtraction and multiplication but not under division because division of two polynomials is not necessarily a polynomial.
Dividing a binomial by a trinomial will result in a rational expression and it will have negative exponent. Negative exponents are not allowed in polynomials.
Therefore, option B is the correct choice.
The variable, usually on the x-axis, which is used to predict y-values, is called the ____ variable. It is also sometimes called the explanatory variable.
Answer: Independent variable
Step-by-step explanation:
The variable usually on the x-axis, which is used to predict y-values, is called the Independent variable.
Discussion:
In most mathematical relations including linear programming problems; we usually have a combination of two variables namely;
Dependent andIndependent variableThe variable whose value determines the value of other variables is termed the independent variable and is usually plotted on the x-axis.
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put the following decimals in order from least to greatest 4.08; 4.3; 4.803; 4.038
Answer:
4.038 < 4.08 < 4.3 < 4.803
Step-by-step explanation:
We are given four decimal numbers and we have to arrange them in increasing order:
The numbers are 4.08, 4.3, 4.803, 4.038
The expanded form of these decimal numbers are:
[tex]4.08 = 4 + \displaystyle\frac{8}{100}[/tex]
[tex]4.3 = 4 + \displaystyle\frac{3}{10}[/tex]
[tex]4.803 = 4 + \displaystyle\frac{8}{10} + \displaystyle\frac{3}{1000}[/tex]
[tex]4.038 = 4 + \displaystyle\frac{3}{100} + \displaystyle\frac{8}{1000}[/tex]
Thus, the increasing order is:
4.038 < 4.08 < 4.3 < 4.803
2 times 5 times 10 to the 5th power
2x5x10^5=1000000. You do the exponent first,10^5 = 100000. Then you multiply that by 5, 5x100000=500000. Then by 2, 500,000x2= 1000000.
Write the equation of the line in slope intercept form that passes through the points (-1,1) and (2,13)
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-1, 1) and (2, 13). Substitute:
[tex]m=\dfrac{13-1}{2-(-1)}=\dfrac{12}{3}=4[/tex]
Therefore the equation of a line is
[tex]y=4x+b[/tex]
Put the coordinates of the point (2, 13) to the equation of a line:
[tex]13=4(2)+b[/tex]
[tex]13=8+b[/tex] subtract 8 from both sides
[tex]5=b\to b=5[/tex]
Answer: y = 4x + 5Compare 2.3 and 2.03
Twenty-seven is the product of three and a number
It’s the product of three and nine.
A function follows the rule y = -75 - 5 x . When the function's output is 25, the equation is 25 = -75 - 5 x . What is the function input when the output is 25? 20 -20 10 -10
Answer: C. -20
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What is 2/5 - [-4 7/10]
Answer: 5 1/10
Solution:
2/5-[-4 7/10]
2/5-[-(4*10+7)/10]
2/5-[-(40+7)/10]
2/5-[-47/10]
2/5+47/10
2*2/(5*2)+47/10
4/10+47/10
(4+47)/10
51/10
(50+1)/10
50/10+1/10
5 1/10
estimate 771 divided by 3.6
Final answer:
To estimate the division of 771 by 3.6, round 3.6 to 4 and divide 771 by 4 to get an approximate result of 192.75.
Explanation:
To estimate 771 divided by 3.6, we can round 3.6 to the nearest whole number, which is 4. The estimation calculation would then be 771 ÷ 4. Dividing 771 by 4 can be done by breaking down 771 into 760 + 11. Now, 760 ÷ 4 equals 190, and 11 ÷ 4 is approximately 2.75. Adding these two results, we get an estimated total of 192.75. Therefore, the estimated result of 771 ÷ 3.6 is approximately 192.75.
A building company used 24 workers to prepare a building site. The site measured 30 acres and the work was completed in 10 days.
a) The company is asked to prepare another site measuring 45 acres. The company must complete the work on the new site in 12 days. How many extra workers must they use if they are to meet the deadline?
b) What assumption have you made in your calculations? How does this affect your answers?
Answer:
30 workers are required.
Step-by-step explanation:
If the site measured 30 acres and was completed in 10 days, then it can be said that on average [tex]\frac{30}{10} = 3\frac{acres}{day}[/tex] were made.
Then, 24 workers completed 3 acres / day.
Then, [tex]\frac{24.workers}{\frac{3acres}{day}} = \frac{8..Workers * days}{acre}[/tex]
8 workers can complete 1 acre per day
Now to know how many workers are needed to complete 45 acres in 12 days, we multiply:
[tex]8\frac{Workers * days}{acre}*\frac{45}{12} \frac{acres}{days} = 30.workers[/tex].
Finally, 30 workers are required.
To solve this problem it was assumed that everyone worked at the same pace, which may not be true, the fact that some work at a slower or faster pace than another could alter the result, causing them to finish less or more acres by day.
how many planes can two distinct lines have in common
either 0 or 1 plane(s)
Compare 4 x 10^6 and 2 x 10^7.
A) 2 x 10^7 is 7 times larger than 4 x 10^6
B) 2 x 10^7 is 6 times larger than 4 x 10^6
C) 2 x 10^7 is 5 times larger than 4 x 10^6
D) 2 x 10^7 is 3 times larger than 4 x 10^6
Answer:
C. [tex]2\times 10^7[/tex] is 5 times larger than [tex]4\times 10^6[/tex]
Step-by-step explanation:
We want to compare [tex]4\times 10^6[/tex] and [tex]2\times 10^7[/tex].
In order to determine how many times
[tex]2\times 10^7[/tex]
is larger than
[tex]4\times 10^6[/tex],
we need to divide [tex]2\times 10^7[/tex] by [tex]4\times 10^6[/tex] to obtain;
[tex]\frac{2\times 10^7}{4\times 10^6} =\frac{10}{2} =5[/tex]
Therefore we can see that;
[tex]2\times 10^7[/tex] is 5 times larger than [tex]4\times 10^6[/tex]
The correct answer is C.
Simplify the following expression.
12 - 5[(4 + 2)/\2 - (22 + 10)]
A.
-198
B.
-238
C.
-18
D.
-98
12 - 5[(4 +2)² - (22 + 10)]
Remember to follow PEMDAS. First, solve both parenthesis
12 - 5[(4 +2)² - (22 + 10)]
12 - 5[(6)² - (32)]
Next, solve the exponent
(6)² = 6 x 6 = 36
12 - 5[(36) - (32)]
Then, solve the bracket.
36 - 32 = 4
12 - 5[4]
Next, multiply
-5 x 4 = -20
Finally, subtract.
12 - 20 = -8
None of the above. The answer is -8. Please check the answers and the question again
~Rise Above the Ordinary
HELP ASAP!!!!!!!!!!!!!!
What is an equation of the line that is parallel to y=3x−8 and passes through (1, 8) ?
Im pretty sure its y = 3x - 17
Would you consider these shapes congruent??
no it would not be congruent
Hello!
Answer:No, these shapes would not be considered congruent. In geometry, figures would only be congruent if they have the same size and shape. In the above image, the two figures have the same shapes, but they do not have the same size.
Peter is trying to buy fencing for the perimeter of his garden. His garden is in the shape of a rectangle with a length of 2(x+6)feet and a width of 3.5x feet. How many feet of fencing will he need to buy? Write and simplify an expression to represent this situation? What properties did you use?
SHOW ALL WORK
Given dimensions of a rectangular garden are:
length = 2(x+6) feet
width = 3.5x feet
using the distributive property on length we get, length = 2x+12
Perimeter of a rectangle is 2(length+width)
So, P = 2(2x+12+3.5x)
Solving it we get,
P = 2(5.5x +12) ..............adding like terms
P = [tex](2\times5.5)+(2\times12)[/tex] .............multiplying and adding
P = 11x+24
So, perimeter is 11x+24 feet. This value of fencing will be needed.
Britt has 4 full boxes plus 12 extra CDs, and Jim has 3 full boxes and 5 extra CDs. If the number of CDs in each box is represented by c, Write an expression that shows the total number of CDs that Britt and Jim have.
This is actually quite easy.
Britt=4c+12 because 4 boxes and 12 extra
Jim=3c+5 because 3 boxes and 5 extra
Final answer:
The total number of CDs that Britt and Jim have is represented by the expression 7c + 17, where c is the number of CDs in each full box.
Explanation:
The total number of CDs that Britt and Jim have can be expressed using the variable c, which represents the number of CDs in each full box. Britt has 4 full boxes and 12 extra CDs, so her total is given by the expression 4c + 12. Jim has 3 full boxes plus 5 extra CDs, so his total is 3c + 5. To find the combined total number of CDs for both Britt and Jim, we add their individual totals:
Total CDs = Britt's CDs + Jim's CDs
Total CDs = (4c + 12) + (3c + 5)
By combining like terms, we get:
Total CDs = 7c + 17
This expression represents the total number of CDs that Britt and Jim have together in terms of c, the number of CDs per box.
I dont understand this please help me
A.) 34.68
hope this helps
A is your answer. Take the $289 and multiply that by 0.12.
Hope this helps & good luck. :)
How would u do -6-(-1)=
The answer would be -5 because:
-6-(-1)
Keep Change Flip
-6 + 1
Different signs Subtract..so the answer would be 5 but then you add the negative to it because -6 is greater than the positive 1
A chain 5 links long is joined to a chain 7 links long. How many links long is the resulting chain
12 links long because 5 + 7 = 12
Rachel earns $21 per day for 22a-22d select true or false for each statement
22a. False
22b. True
22c. True
22d. False
For each scenario, we multiply Rachel's daily earnings ($21) by the number of days worked to find her total earnings.
In 22a, Rachel earns 21 × 20 = $420, not $421 as stated.
In 22b, Rachel indeed earns 21 × 15 = $315, making the statement true.
Similarly, in 22c, Rachel earns 21 × 13 = $273, confirming the statement as true.
However, in 22d, Rachel's earnings for 13 days amount to 21 × 13 = $273, not $250, rendering the statement false.
Therefore, the true statements are 22b and 22c, while 22a and 22d are false.
Complete Question:
A certain triangle has 30 angle and 60 angle which much be a true statement about the triangle
Answer:
D
Step-by-step explanation:
The longest side is twice as long as the shortest side because lets suppose I have a triangle that has vertices with angles 30 and 60, the last one has to be 90 because the total is 180 degrees. Now for a 30 60 triangle, if the hypotenuse has a length of 2, the following ratios will hold true for the other two sides. The side that shares the 90 degrees and 60 degrees corners will be of length 1 and the side that shares the 30 degrees and 90 degrees corners (vertices) will be of length sqrt(3). This is true all the time. In this case the correct answer is that the longest side is twice as long as the shortest side because the longest side is the hypotenuse with length 2 and the shortest side will be the one that shares the 90 degrees and 60 degrees corners and is of length 1.
Answer:
A
Step-by-step explanation:
Select from the drop down menus to correctly complete each statement. - 15 < -13 - 13 < - 11 is - 13 located to the right or to the left of -15 on the number line. is - 11 located to the left or the right of - 13 on a number line.
On the number line, smaller numbers are located to the left of larger numbers, which are located on the right.
So, if you have two numbers x and y on the number line, the smaller of the two will be on the left, the larger one on the right.
So, -13 is located to the right of -15, because it's larger.
For the same reason, -11 is located to the right of -13.
On the number line, you would have something like
<--------(-15)-------(-13)--------(-11)---------->
On a number line, negative values decreases as we move to the left while positive values increases to the right. Hence,
-13 is located to the right of - 15 -11 is located to the right of - 13Starting from 0 to the left, we have - 1, - 2, - 3,... which continues in that sequence as decreases as we move to the left of the number line.
Moving towards the left, - 13 appears before - 15 ; Hence - 13 is located relative to the right of - 15 on the number line
Similary, - 11 appears before - 13 ; Hence - 11 is located relative to the right of - 13 on the number line.
Therefore, - 13 and - 11 are located to the right of - 15 and - 13 respectively on the number line.
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What is the solution of the equation when solved over complex numbers? x^2+27=0
the solution of the equation x²+27 = 0 is 3√3 i
What are real and imaginary roots ?
A real root to an equation is a real number. A complex root to an equation is an imaginary root represented as complex numbers.
In other words real roots can be represented in a number line where as imaginary roots can not.
In order to determine the simplification, we have to know the rule of the imaginary numbers.
The imaginary numbers are the same than real numbers, but they add just one term more, which is :
√-1 = i
So, to implicate this term, we have to use the rules of the roots:
given equation is :
x²+27 = 0
solving for x by Subtracting 27 from both sides
x²+27 -27 = -27
x² = -27
To remove square root , take square root on both sides
√x² = √-27
x = √-27
The value of √-1 is 'i' therefore,
x = i√27
x =3√3 i
Therefore, The solution of the equation x²+27 = 0 is 3√3 i
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Keisha solved the following equation: 4x − 2x + 8 = 6(x + 4) Step Work Justification 1 2x + 8 = 6(x + 4) Combine like terms 2 2x + 8 = 6x + 24 Associative property of multiplication 3 −4x + 8 = 24 Subtraction property of equality 4 −4x = 16 Addition property of equality 5 x = −4 Division property of equality
4x - 2x + 8 = 6(x + 4) Given
(4x - 2x) + 8 = 6(x + 4)
2x + 8 = 6(x + 4) Combine like terms
2x + 8 = (6)(x) + (6)(4)
2x + 8 = 6x + 24 Distributive Property
2x - 6x + 8 = 6x - 6x + 24
-4x + 8 = 24 Subtraction Property of Equality
-4x + 8 - 8 = 24 - 8
-4x = 16 Subtraction Property of Equality
-4x : (-4) = 16 : (-4)
x = -4 Division Property of Equality
spencer hits a tennis ball past his opponent. the height of the tennis ball in feet is modeled by the equation h(t)=-0.075t^2+0.6x+2.5 where t is the time since the tennis ball was hit meausured in seconds. how long does it take for the ball to reach its maximum height?
The quadratic function is given by the equation [tex]h(t)=-0.075t^2+0.6t+2.5.[/tex]
The maximal height will be at vertex. Find t-coordinate of the parabola vertex:
[tex]t_{vertex}=-\dfrac{b}{2a}=-\dfrac{0.6}{2\cdot (-0.075)}=4\text{ seconds.}[/tex]
At t=4,
[tex]h(4)=-0.075\cdot 4^2+0.6\cdot 4+2.5=-1.2+2.4+2.5=3.7\text { feet. }[/tex]
Answer: it will take 4 seconds for the ball to reach the maximal height of 3.7 feet.
I need this today ASAP!!!!
-4 1/2 + 1/3
The answer of this expression is - 4 1/6
simplify the following expression into the form a+bi where a and b are rational numbers
(3+7i) (-2-2i) -4i(5-9i)
Answer:
- 28 - 40i
note that i² = (√-1)² = - 1
expand product of factors using FOIL
= - 6 - 6i - 14i - 14i² - 20i + 36i²
= - 6 - 6i - 14i + 14 - 20i - 36
= - 28 - 40i
Step-by-step explanation:
Got right on PLATO
The solution to the complex expression (3+7i) (-2-2i) -4i(5-9i) is -28 - 40i
What is a complex number?A complex number is a number of the form a + bi, where a and b are real numbers, and i = √-1
i² = (√-1)² = -1
Given the expression:
(3+7i) (-2-2i) -4i(5-9i)
= -6 - 14i -6i + 14 - 4i(5 - 9i)
= 8 - 20i - 20i - 36
= -28 - 40i
The solution to the complex expression (3+7i) (-2-2i) -4i(5-9i) is -28 - 40i
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what is the value of (x+3) folders at $0.10 each
7+3 =10 or 3(10) 30