What is the solution set for the open sentence with the given replacement set?
2t-t=0,{1,2,3,4}
A. Null set
B. 2
C. 3
D. 4
An open sentence is a mathematical sentence that has an unknown.
The solution set for t is (a) Null set
The equation is given as:
[tex]\mathbf{2t - t = 0}[/tex]
The set is given as:
[tex]\mathbf{\{1,2,3,4\}}[/tex]
First, we solve for t in: [tex]\mathbf{2t - t = 0}[/tex]
[tex]\mathbf{t = 0}[/tex]
The above equation implies that, the value of t is 0
0 is not represented in the given set, [tex]\mathbf{\{1,2,3,4\}}[/tex]
Hence, the solution set for t is (a) Null set
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Match the expression with its name. 9x4 – 3x + 4
Answer:
Fourth-degree trinomial
Step-by-step explanation:
9x^4 – 3x + 4 is a trinomial expression because it has three parts: 9x^4, –3x and 4, and is a fourth-degree expression because four is the highest exponent applied to the variable x (the other exponents are one and zero).
Find two consecutive integers whose product is 5 less than the square of the smaller number
To find two consecutive integers whose product is 5 less than the square of the smaller number, let the smaller number be x and use algebraic equations to solve for x.
Explanation:To find two consecutive integers whose product is 5 less than the square of the smaller number, we can let the smaller number be x. The larger number would then be x + 1. The product of the two consecutive integers is x(x + 1) and the square of the smaller number is x^2. According to the problem, x(x + 1) = x^2 - 5. We can solve this equation to find the values of x and x + 1.
Expanding x(x + 1) gives us x^2 + x. So, the equation becomes x^2 + x = x^2 - 5. We can simplify this equation by canceling out x^2 on both sides, which leaves us with x = -5.
So the consecutive integers are -5 and -4.
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Summarize the steps to orderly problem solving when dealing with a mathematical chemistry problem
Fill in the blanks to write an equation in slope-intercept form representing the function shown in the table.
PLEASE HELP!!
Complete the coordinate proof of the theorem.
What are the roots of the equation? 5 x 3+45x2+70x=0
Final answer:
The roots of the equation 5x³ + 45x² + 70x = 0 are -7 and -2.
Explanation:
This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 5, b = 45, and c = 70. To find the roots of the equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values, we get:
x = (-45 ± √(45² - 4(5)(70))) / (2(5))
Simplifying further gives us:
x = (-45 ± √(2025 - 1400)) / 10
And finally, calculating the square root and applying the ± gives us the two roots:
x = (-45 ± √625) / 10
x = (-45 ± 25) / 10
which can be further simplified to:
x = -7 or x = -2
4a-3b=21 true or false
There are 13 animals in the barn. Some are chickens and some are pig's. There are 40legs in all. How many of each animal are there?
Answer:
7 pigs6 chickensStep-by-step explanation:
If all were chickens, there would be 26 legs. There are 14 legs more than that. Each pig contributes 2 additional legs, so there must be 14/2 = 7 pigs. The remaining 6 animals are chickens.
___
Check
7×4 + 6×2 = 28 +12 = 40 . . . . total legs
Answer:
easy! 27
Step-by-step explanation:
13- 40 = 27
or 13 + 27 =40
just add up 13 and 27 you'll get 40 in all
edit; btw I'm not the brightest
The formula for finding the length of an arc on a circle is L=2πr(x360) , where r is the radius of the circle and x is the measure of the central angle of the arc. Solve for x.
To solve for the measure of the central angle (x) in the arc length formula, rearrange the formula such that [tex]x = (L/2\pi r) * 360.[/tex] This method allows you to determine the degree measure of the arc once you know the arc length (L) and the radius (r) of the circle.
Explanation:Given that the formula for finding the length of an arc in a circle is [tex]L=2\pi r(x/360)[/tex], you can solve for x if L and r are known. In this formula, r stands for the radius of the circle and x represents the measure of the central angle of the arc in degrees. So, to isolate x, you would need to rearrange the formula, giving us: [tex]x = (L/2\pi r) * 360.[/tex]
This effectively means that the degree measure of the arc (x) is equivalent to the ratio of the arc length to the circumference (which is 2πr) times 360 degrees.
For instance, let's consider a circle where r=5 and the arc length L has a value of 10 units. We would substitute these values into our newly rearranged formula thus: [tex]x = (10/2\pi *5) * 360 = 36[/tex] degrees. This tells us that the central angle for this particular arc on a circle with a radius of 5 units is 36 degrees.
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What is QR ?
Enter your answer in the box.
units
Answer-
[tex]\boxed{\boxed{QR=12}}[/tex]
Solution-
Triangle Midpoint Theorem-
The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
As given in the question,
QV = SV, so V is the mid point of QS,
SU = RU, so R is the mid point of RS.
Hence, UV is the line joining the midpoints of QS and RS.
Applying Triangle Midpoint Theorem,
[tex]\Rightarrow UV=\dfrac{1}{2}QR[/tex]
[tex]\Rightarrow QR=2UV[/tex]
[tex]\Rightarrow QR=2\times 6[/tex]
[tex]\Rightarrow QR=12[/tex]
Therefore, the side length of QR is 12 units.
Susie's sushi place two orders with its fish supplier one order was for 15 lb of salmon and 8 lb of tuna the order total $228 the other order was for 12 lb of salmon and 6 lb of tuna this ordered total for 180 what is the cost for 1 lb of salmon in 1 lb of tuna
A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer very close to 12 mm and it wants to know how the area A(x) of a wafer changes when the side length x changes. Find A'(12)
The value of the derivatives is A'(12) = 24.
We have,
To find the derivative of the area function A(x) with respect to x, we can differentiate the equation for the area of a square:
A(x) = x^2
Using the power rule, we differentiate A(x) with respect to x:
A'(x) = 2x
To find A'(12), we substitute x = 12 into the derivative equation:
A'(12) = 2 * 12 = 24
Therefore,
The value of the derivatives is A'(12) = 24.
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Final answer:
To find A'(12), the rate at which the area A(x) changes when the side length x changes, take the derivative of A(x), which is 2x, and evaluate it at x = 12. The derivative of A(x) is 2x, so A'(12) = 2(12) = 24.
Explanation:
To find the rate at which the area A(x) changes with respect to a change in x, we need to take the derivative of A(x) with respect to x. In this case, A(x) represents the area of a square wafer of silicon with a side length x. The derivative with respect to x is A'(x), which represents the rate of change of the area.
We want to find A'(12), which means we want to find the rate of change of the area when the side length is 12 mm. To do this, we need to take the derivative of A(x) and then evaluate it at x = 12.
Since the side length of the wafer is very close to 12 mm, we can assume x = 12.
Let's find the derivative of A(x):
A(x) = x^2
A'(x) = 2x
Now we can evaluate A'(12):
A'(12) = 2(12) = 24
Forty-eight pounds of sand are used to fill 12 bags. Miranda uses the five-step problem-solving plan. After completing the Solve step, how many pounds of sand should she find each bag will hold?
According to the Five-pan strategy ,
Step 1 . Read given problemStep 2. Construct a plan to solve it.Step 3. Perform it.Step 4. Check answer.Step 5. Write final answer with statement.For given problem :
Step 1. 48 pounds of sand are used to fill 12 bags.
To find : how many pounds of sand should she find each bag will hold?
Step 2. We need to divide the total amount of sand require to fill 12 bags by 12.
Step 3. Amount of sand require to fill one bag = (amount of sand require to fill 12 bags) ÷ 12
= (48) ÷ 12
= 4 pounds
Step 4. Checking our answer as
Amount of sand require to fill 12 bags = 12 x (Amount of sand require to fill one bag)
= 12 x 4 = 48 pounds which is given, thus our answer is correct.
Step 5. She should fill 4 pounds of sand in each bag.
What is the perimeter of the figure?
A. 88 in.
B. 88 11/24 in.
C. 88 7/8 in.
D. 89 7/8 in.
Harper has $15.00 to spend at the grocery store. She is going to buy bags of fruit that cost $4.75 each and one box of crackers that cost $3.50. Model the problem algebraically and determine the maximum number of bags of fruit,b, Harper can buy.
Which function has a domain of x greater than equal to 5 and the range of y less than equal to 3?
A. y = root squared of x-5, +3
B. y = root squared of x+5, -3
C. y = - root squared of x-5, +3
D. y = - root squared of x+5, -3
Answer:
Option C is the answer.
Step-by-step explanation:
Option A. [tex]y=\sqrt{x-5}+3[/tex]
For domain of this function
(x - 5) ≥ 0
x ≥ 5
For range of the function
for every value of x ≥ 0
y ≥ 3
Opttion B. [tex]y=\sqrt{x+5}-3[/tex]
For Domain
(x + 5) ≥ 0
x ≥ (-5)
and for every value of x ≥ (-5) range of the function will be
y ≥ (-3)
Option C.
y = -√(x -5) + 3
For domain
x - 5 ≥ 0
x ≥ 5
For range
y ≤ 3
Option D. [tex]y=-\sqrt{x+5}-3[/tex]
For domain (x + 5) ≥ 0
x ≥ -5
For range
y ≤ (-3)
Therefore option C will be the answer.
You and a friend are looking for an apartment. There are two final choices. Apartment A has a $1000 security deposit and costs $1200 each month. Apartment B has a $1500 and costs $1175 each month. How many months, m, will it take for the costs to be the same?
The required months are x = 0.60 months where at the cost become same.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let the total cost be y and the month be x
Apartment A has a $1000 security deposit and costs $1200 each month.
y = 1200x +1000 - - - - - (1)
Apartment B has $1500 and costs $1175 each month.
y = 1175x + 1500
From equation 1
1200x + 1000 = 1175x + 1500
1200x - 1175x = 500
825x = 500
x = 500 / 825
x = 0.60 months,
y = 1200*0.60 + 1000
y = 1,720
Thus, the required months are x = 0.60 months where the cost becomes the same.
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Which linear inequality is represented by the graph?
y > 2x + 2
y ≥ x + 1
y > 2x + 1
y ≥ x + 2
Step 1
Find the slope of the line
Let
[tex]A(0,1)\\B(2,5)[/tex]
the slope is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{5-1}{2-0}[/tex]
[tex]m=\frac{4}{2}[/tex]
[tex]m=2[/tex]
Find the equation of the line
we know that
the equation of the line into slope-intercept form is
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
in this problem we have
[tex]m=2[/tex]
[tex]b=1[/tex] ------> the y-intercept is the point A
substitute
[tex]y=2x+1[/tex]
Step 2
Find the equation of the inequality
we know that
the solution is the shaded area above the dotted line
so
above dotted line---------> represent the symbol ([tex]>[/tex])
the inequality is
[tex]y>2x+1[/tex]
therefore
the answer is
[tex]y>2x+1[/tex]
The correct option is [tex]\boxed{\bf option (c)}[/tex] i.e., [tex]\boxed{y>2x+1}[/tex].
Further explanation:
The linear equation of the line is [tex]y=mx+b[/tex] where, [tex]m[/tex] is the slope of the line and [tex]c[/tex] is the [tex]y[/tex]-intercept of the line.
Suppose the line passes through the two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex].
Therefore, the slope of the line can be calculated as follows:
[tex]\boxed{m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]
The symbol [tex]>[/tex] represents the solution set lies above the dotted line and the symbol [tex]<[/tex] represents the solution set below the dotted line.
Given:
The linear inequalities are given as follows:
[tex]\boxed{\begin{aligned}y&>2x+2\\ y&\geq x+1\\ y&>2x+1\\ y&\geq x+2\end{aligned}}[/tex]
Calculation:
First we will find the equation of the line.
The line cuts the [tex]y[/tex]-axis on the coordinate [tex](0,1)[/tex] as shown in the Figure 1 (attached in the end).
Therefore, the [tex]y[/tex]-intercept is [tex]1[/tex].
Kindly refer the Figure attached to the question.
From the figure 1 (attached in the end) we can see that the line passes through the points [tex](-2,-3)\text{ and }(1,3)[/tex].
The slope of the line can be calculated as follows:
[tex]\begin{aligned}m&=\dfrac{3-(-3)}{1-(-2)}\\&=\dfrac{6}{3}\\&=2\end{aligned}[/tex]
Therefore, the value of [tex]m[/tex] is [tex]m=2[/tex] and the value of [tex]b[/tex] is [tex]b=1[/tex].
Substitute [tex]2[/tex] for [tex]m[/tex] and [tex]1[/tex] for [tex]b[/tex] in the equation of the line [tex]y=mx+b[/tex].
Second we will find the equation of the inequality.
The shaded region is shown in Figure 1 above the dotted line .
Therefore, the solution set of the line lie above the dotted line and it will represented by the symbol [tex]>[/tex].
Thus, the inequality [tex]y>2x+1[/tex] satisfies the given graph.
Therefore, the correct option is [tex]\boxed{\bf option (c)}[/tex] i.e., [tex]\boxed{y>2x+1}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Linear inequalities
Keywords: Linear equations, linear inequality, equation, line, slope, intercept, dotted line , coordinate, shaded region, solutions set, graph, curve.
One box of crackers costs $1.75. The crackers are advertised as “3 boxes for $5.25.” Which proportion can be used to represent the cost of the crackers?
Add: 4/100 + 2/10 = A) 6/10 B) 6/100 C) 24/100 D) 42/100
Which of the following prefixes would be best to use when measuring your own mass? need help.
Milli
Centi
Deci
Kilo
A spinner is divided into 4 equal sections the probability of landing on A is 1/4 Norma spins the spinner 16 times how many times can she expect the spinner to land on A
Final answer:
Norma can expect the spinner to land on section A 4 times after spinning it 16 times, based on the probability of [tex]\frac{1}{4}[/tex].
Explanation:
The question asks about the expected number of times Norma can anticipate the spinner to land on section A after spinning it 16 times, given that the probability of landing on A is [tex]\frac{1}{4}[/tex]. To find this, we use the concept of expected value, which in this context is the probability of an event happening multiplied by the number of trials. Since the probability of landing on A is [tex]\frac{1}{4}[/tex] and there are 16 spins, the expected number of times landing on A is calculated as [tex]\frac{1}{4}[/tex] multiplied by 16.
Expected number of landings on A = Probability of landing on A × Number of spins = [tex]\frac{1}{4}[/tex] × 16 = 4.
Therefore, Norma can expect the spinner to land on section A four times after spinning it 16 times.
Mr. Vella can build a brick wall in 4 days. His apprentice can build the same wall in 6 days. After working alone for 3 days, Mr. Vella became ill and left the job for his apprentice to complete. How many days did it take the apprentice to finish the wall?
Apprentice will take [tex]1\frac{1}{2}[/tex] days to finish the wall.
What is work?" Work is defined as when force is applied to move an object in the direction of displacement."
According to the question,
Number of days taken by Vella to build a brick = 4 days
Work done by Vella in 1 day = [tex]\frac{1}{4}[/tex]
Work done by Vella in 3 days = [tex]\frac{3}{4}[/tex]
Number of days taken by apprentice to build same brick = 6 days
Total days taken by apprentice to complete 3/4 of work = [tex]\frac{3}{4} of 6[/tex]
= [tex]\frac{3}{4}[/tex] × 6
=[tex]\frac{9}{2}[/tex]
= [tex]4\frac{1}{2}[/tex] days
Number of days apprentice take to finish the wall is = 6 - [tex]4\frac{1}{2}[/tex]
= [tex]1\frac{1}{2}[/tex]
Hence, apprentice will take [tex]1\frac{1}{2}[/tex] days to finish the wall.
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Which estimate best describes the area under the curve in square units?
10 units²
15 units²
25 units²
30 units²
Find the derivative of f(x) = 8x + 4 at x = 9
The distance between two cities on a map is 13 cm. What is the actual distance between the cities if the map is drawn at a scale of 1:50,000?
Answer:
6.5 km
Step-by-step explanation:
1:50,000
13 cm on a map, multiply both sides by 13 which leaves us with:
13:650,000
However, we need to calculate the distance in kilometers, not centimeters. To do that, we have to divide 650,000 by 100,000 which leaves us with 6.5 km
PLZ HELP! :) ASAP. Which of these sets of numbers contains no irrational numbers?
Steve had 7 more than twice as many quarters as dimes. if the total value of her coins was $10.15, how many of each kind of coin did she have?
If angle 3 is 45 degrees, what is the measure of it's supplement?
A) 45
B) 90
C) 205
D) 135