Answer:
The missing number is -4.---------------------------------
For the equation to have infinitely many solutions, the variables and constants should cancel and should end up with 0 = 0. It means for any value of the variable the equation is true, i.e. both sides are equal.
Given equation:
2x + ? = 2x - 4If we solve it for ? we'll get:
? = - 4Use the commutative property to write an expression 8c-1.5
Answer:
Step-by-step explanation:
i need help on that too
A rectangle piece of metal has an area of 32 square centimeters. Its perimeter is 24 centimeters. What are the dimensions of the piece
The dimensions of the piece are l = 8 and b =4.
What are dimensions?
The minimal set of coordinates required to specify any point within a mathematical space is the dimension of that space. Because only one coordinate is required to specify a point on a line, it has a dimension of one.
Here,
Let the length of a rectangular piece of metal = l cm
And the breadth of a rectangular piece of metal = b cm
Perimeter of a rectangular piece of metal = 2(l+b) = 24 cm
Or, l+b = 24/2
Or, l+b = 12 -------- (1)
Area of a rectangular piece of metal = l×b = 32 cm²
Or, l×b = 32 ------- (2)
We know that,
(l - b)² = (l+b)² - 4×l×b
(l - b)² = (12)² - 4×32
(l - b)² = 144 - 128
(l - b)² = 16
(l - b)² = 4
l - b = 4 --------- (3)
Adding equations (1) and (3), we get
l+b+l-b = 12 + 4
2l = 16
l = 8
Now, we put the value of l in equation(1) and we get
8 + b = 12
b =4
Hence, the dimensions of the piece are l = 8 and b =4.
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1. Write two expressions that are equivalent to the expression listed below. You can use the equation editor to input your answers.
(x^{1/3)²
Two index that are equivalent to the index (x^{1/3)² are:- 1) X⁽²/³⁾, 2) (∛X)²
What are index ?
An index can be assigned to a number or variable. A value raised to the power of a variable's (or a constant's) value is its index. The exponents or powers are other names for the indices. It displays how many times a particular number must be multiplied. It takes the following form:
a(m) = a × a × a ×……× a (m times)
The base in this case is a, and the index is m.
The index instructs a certain integer (or base) to be multiplied by itself a specified number of times, where the number of times is determined by the index raised to the base. It is a condensed way of expressing large sums of information and calculations.
[tex]X^b . X^A. X^n = X^b^a^n[/tex]
Example: 2^3 = 2 × 2 × 2 = 8
[tex][X^\frac{1}{3} ]^2[/tex][tex]= X^\frac{2}{3}[/tex]
We can also write the same index as;
[tex]A^\frac{1}{n}=\sqrt[n]{A}[/tex]
[tex]X^\frac{2}{3}=[\sqrt[3]{x}]^2[/tex]
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Next O Quiz 6.2
10
Select the correct answer.
According to the Dietary Guidelines for American 2015, you should limit your fat intake to what percentage of your total calories?
OA. Less than 10%
OB. 25-35%
C.
OD.
45-55%
65-75%
Reset
Next
According to the Dietary Guidelines for American 2015, you should limit your fat intake to 25% - 35% of your total calories. The correct option is B.
What is dietary guidelines?Food-based dietary guidelines also known as dietary guidelines are intended to serve as a foundation for public food and nutrition policies, health and agricultural policies, and nutrition education programs aimed at promoting healthy eating habits and lifestyles.
Calories are the units of energy released by your body when it digests and absorbs food. The higher the calorie content of a food, the more energy it can provide to your body. When you consume more calories than you require, your body stores the excess calories as fat. Even fat-free foods can be high in calories. In this case, the fay should not be more than 35%.
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Nancy's pack of pens had 80% red pens. If
there were 55 pens total in the pack, how
many were red?
Answer:
44
Step-by-step explanation:
80*55/100 = 44
Answer:78
Step-by-step explanation:
A garden table and a bench cost $703 combined. The garden table costs $47 less than the bench. What is the cost of the bench?
Answer:
375
Step-by-step explanation:
let a garben table cost x
a bench cost x+47
x+x+47=703
2x=703-47
2x=656
x=656÷2=328
bench: 328+47=375
SWIMMING Yukio is keeping track of the number of calories she
burns while swimming freestyle laps. The number of calories she
burns can be represented by a function. Sketch a graph that shows
the number of calories burned y as a function of time x, in hours.
y-Intercept: No calories burned when she has swum for 0 hours.
Linear or Nonlinear: The graph of the function is linear.
Positive: for time greater than 0
Increasing: for time greater than 0
End Behavior: As the number of hours she has swum increases, the
number of calories burned increases.
The proportional relationship y = 200x, showing the number of calories y burned as a function of the time swimming of x hours, is given as follows:
What is a proportional relationship?A proportional relationship is a special case of a linear function, as even though it has a constant rate of change, the intercept is of zero.
The general format of a proportional relationship is given as follows:
y = kx.
In which the constant of proportionality k represents the constant rate of change.
Supposing that for each hour swimming, the person spends 200 calories, the constant is given as follows:
k = 200.
Hence the proportional relationship that gives the number of calories y burned as a function of the time swimming of x hours is given as follows:
y = 200x.
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Bonds Payable has a balance of $810,000, and Premium on Bonds Payable has a balance of $8,910. If the issuing corporation redeems the bonds at 102, what is the amount of gain or loss on redemption?
a. $8,910 gain
b. $8,910 loss
c. $7,290 loss
d. $7,290 gain
To determine the gain or loss on the redemption of the bonds, you need to compare the redemption price to the carrying value of the bonds. The carrying value of the bonds is the amount that the bonds are recorded as being worth on the issuing corporation's balance sheet. This is calculated by adding the Bonds Payable balance and the Premium on Bonds Payable balance.
In this case, the carrying value of the bonds is $810,000 + $8,910 = $818,910. If the bonds are redeemed at a price of $102, the gain or loss on the redemption can be calculated as follows:
Gain or loss on redemption = Redemption price - Carrying value of bonds
= $102 - $818,910
= -$817,810
Since the gain or loss on the redemption is a negative number, this indicates that the redemption price was lower than the carrying value of the bonds, resulting in a loss. The correct answer is therefore: c. $7,290 loss.
Kiana delivers sandwiches for a restaurant that charges $8.25 for each sandwich plus a $10 delivery fee. Kiana has an order that totals $59.50. Write an equation to describe this situation.
Answer: 59.50=8.25x + 10
Step-by-step explanation: so we know that It is 8.25 per sandwich making it the constant. Then we know that 10 is the the deléguente fee making it the y-intercept. Finally this all has to equal to 59.50. X represents how many sandwiches the person ordered.
In March, Delphine's house had 40\%40%40, percent more snowfall than in February. Delphine's house had fff centimeters of snowfall in February.
Which of the following expressions could represent how much snowfall Delphine had at her house in March?
Choose 2 answers:
The expressions that could represent how much snowfall Delphine had at her house in March will be:
1.4f
f + 0.4f
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Since Delphine's house had 40 percent more snowfall than in February. Delphine's house had f centimeters of snowfall in February.
The expression will be:
f + (40% × f)
f + 0.4f
= 1.4f
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If quadrilateral A' B' C' D' = D8 (ABCD), which of the following statements are true? Select all that apply.
So the correct statement is A and D
Quadrilateral A'B'C'D' and ABCD will be similar only if s>= 1 The corresponding side lengths are Related by AB = s.A'What is a Quadrilateral?
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners.
The Latin words quadra, which means four, and latus, which means sides, are combined to form the English term quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides.
These are the several kinds of quadrliaterals:
Trapezium ParallelogramSquares Rectangle Rhombus KiteQuadrilateral A'B'C'D' = D8(ABCD) as we know two quadrilateral will be congruent in case of unit length scaling factor and corresponding side length corresponds like AB,BC,CD,DA
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there is a line that includes the point (11,5) and has a slope of 8/11. what is its equation in slope intercept form?
Answer:
[tex]y=\frac{8}{11} x-3[/tex]
Step-by-step explanation:
Plug in the slope and point into the equation y=mx+b to solve for the y-value of the y-intercept. Plug in the x value for x, the y value for y, and the slope for m.
[tex]5=\frac{8}{11} (11)+b[/tex]
[tex]5=8+b[/tex]
[tex]-3=b[/tex]
After solving that, you can plug the slope and y-intercept back into the equation to solve for y.
[tex]y=\frac{8}{11} x+(-3)[/tex]
[tex]y=\frac{8}{11} x-3[/tex]
Answer:
Step-by-step explanation:
Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept. We have all the information we need except for the y-intercept, so we can plug in our point to solve for the y-intercept.
------------------------------------Solving for y-intercept------------------------------------
Plugging in the point gives us [tex]5=8/11*11+b[/tex]. Simplifying this equation results in [tex]5=8+b[/tex]. To solve for b, we subtract 8 from both sides, giving us that [tex]b=-3[/tex]. We now have both the slope and the y-intercept, so our equation is y = 8/11x -3.
Feel free to contact me with any questions about my answer. I hope this helps!
Which statement is true about the diagram?
B
4
Ο Δ ABD =Δ ACB by SSS
Ο Δ ABC =Δ ABD by SAS
O A CAB DAB by SSS
O No triangles are congruent
The statement "Δ ABD = Δ ACB by SSS" is true about the diagram.
The statement "Δ ABD = Δ ACB by SSS" is true about the diagram. SSS stands for Side-Side-Side, which is a congruence postulate stating that if three sides of one triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent. In the given diagram, Δ ABD and Δ ACB are congruent because their corresponding sides AB, BD, and AC are equal in length.
This means that the triangles have the same shape and size, but they may be oriented differently. The SSS congruence allows us to conclude that all corresponding angles and other corresponding sides of the two triangles are also congruent. Therefore, we can say that Δ ABD is congruent to Δ ACB based on the Side-Side-Side congruence.
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Select the correct answer. What is the range of y = sin 0 ? Ο Α. B. C. D. [-1.1] [0,⁰0) all real numbers 277
The range of the sine function is:
R: {x ∈ R| -1 ≤ x ≤1}
It can also be written as [-1, 1], so that is the correct option.
What is the range of the sine function?For a function y = f(x) we define the range as the set of the outputs, this is, the set of the possible values of y.
In this case, our function is y = sin(θ)
Remember that the maximum value of the sine is sin(π/2) = 1
And the minimum is sin(3π/2) = -1
So the maximum value of y is 1 and the minimum is -1, thus, the range is the set of all real numbers between these two, then we can write the range as:
R: {x ∈ R| -1 ≤ x ≤1}
It can also be written as [-1, 1]
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CHALLENGE:
3. There are less than 30 students in Mr. Klein's math class. On a
test, % of the class received a "B", %4 received a "C", % received a "D",
and % failed. How many more students received a "B" than received
an "A"?
Answer: ???
Step-by-step explanation:
You have to put in the numbers for the percentages.
Now let's look at the data from all the Buffalo. If we calculate the 60% confidence interval for every buffalo's count (i.e. data sample), how many Cls do we expect to contain the true mean? Store your answer in theoretical_hits. Then we need to check our theoretical answer with our actual data. Calculate the 60% confidence interval for each buffalo's count. Then commpute how many of those Cls contain the true mean. Assume that the true mean is 25,000. Store this value in sample_hits . Does this value match the theoretical value? It may be helpful to visualize the Confidence Intervals, along with the true mean. Create a plot for the Confidence intervals for the first 40 rows of the dataframe. Also plot true_mean=25000 as a horizontal dotted line. This plot will not be graded, but may help you get a better understanding of different confidence intervals for the same underlying population. We recommend looking into the ggplot package to help with this task.
15000 Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).
Given that,
We have to calculate let's now examine the Buffalo's collective data. How many Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).
We know that,
Theoretical hits= confidence interval × total no. of buffaloes
= 0.6×(buffaloes)
Sample hits = count among total no. of buffaloes, from which how many of inside 25000, that will be sample hits.
So,
=0.6×25000
=15000
Therefore, 15000 Cls should we expect to include the true mean if we compute the 60% confidence interval for each buffalo count (i.e., data sample).
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How do i simplify
4+-2=2&1/4
what do you mean by &?
if its multiplication than
2 × 1/4 = 0.50 or 1/2
4+ (-2) = 2
so the answer is:
2 = 1/2
false
5) Is the point (2,4) a solution to the system of inequalities in the graph shown below? Explain. (Yes or No 1 point) (Explain 1 point)
y<2 x+3
y≥ -4 x+1
Yes, the point (2,4) is a solution to the system of inequalities in the graph.
How to solve inequalities?
By definition, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
The given parameters include
Points (4,2)
y<2x+3
y≥-4x+1
Solving these inequalities
y<2x+3
Let y<0
0<2x+3
-3<2x
x<-3/2
(-3/2,0)
when x<0
y<2(0)+3
y<3
(0,3)
From equation 2
y≥-4x+1
x≥0
y≥0+1
y≥1
(0,1)
y≥0
0≥-4x+1
x≥-1/4
(-1/4,0)
Using the coordinates to draw the graphs the lines cut each other at points where (4,2)
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On monday, a museum had 150 visitors. On tuesday, it had 260 visitors. Estimate the percent change in the number of visitors to the museum.
The percentage change in the number of visitors = 42.30%.
Percentage change:The prior value's increase or reduction is indicated by the percentage change. The percentage increase may be used to calculate how much it has increased if the present value exceeds the previous value.
The percentage decline may be used to calculate how much it has reduced if the current value is smaller than the prior value.
The formula for Percentage change in case of increase is given by
Percentage Increase = ( Increase/Original Number) × 100
Here we have
On Monday a museum had 150 visitors
On Tuesday it had 260 visitors
The number of visitors increased from Monday to Tuesday
= 260 - 150 = 110
By the given formula percentage of change can be calculated as given below
Percentage Increase = (110/260) × 100
= 42.30%
Therefore,
The percentage change in the number of visitors = 42.30%.
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Suppose that you have 4 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards without replacement.
The probability that two cards will be drawn at random, without replacement, is 13/18.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
According to our answer-
P(at least 1 green) = 1 - P(no green)
P(no green) = draw yellow on both draws
= P(draw yellow on 1st draw) * P( draw yellow on 2nd draw, given draw yellow on 1st draw)
= 5/9 * 4/8 = 20/72 = 5/18
P(at least 1 green) = 1 - 5/18
= 13/18
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A scientist uses a submarine to study ocean life. She begins at sea level, which is an elevation of 0 feet. She travels down 21.1 feet. She then ascends 19.1 feet. Next, she travels down a second time, 80.7 feet. How many feet must she now ascend to get back to sea level?
Based on the elevation of the scientist after descending and traveling directly up, the number of feet she needs to ascend to get to sea level will be; 82.7 feet.
How to find the elevation?To find the number of feet that the scientist needs to travel up to get back to sea level, you need to find her current elevation.
The current elevation of the scientist is:
= 0 - 21.1 + 19.1 + 80.7
= 82.7 feet
In other words, the scientist is 82.7 feet below sea level.
To get back to sea level therefore, the scientist will need to travel 82.7 feet directly up.
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in a certain hyperbola, the center is at $(-2,0),$ one focus is at $(-2 \sqrt{34},0),$ and one vertex is at $(-5,0).$ the equation of this hyperbola can be written as\[\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2}
The equation of certain hyperbola with center ( -2,0) is (x+ 2)²/25 - (y)²/ 9 = 1
According to the question,
Equation of hyperbola is given : (x-h)²/a² - (y-k)²/b² = 1
Center of hyperbola = (-2,0)
Focus = (-2√34 , 0)
vertex = (-5,0)
This hyperbola is from left to right
As center is (-2,0) means h = -2 and k = 0
Hyperbola are symmetric ,
Second focus = (-2√34 , 0)
Second vertex = ( 5,0)
Vertex are (a,b) => a = 5
Foci of general hyperbola are ( h ± ck)
=> ( h ± c, k) = (-2√34 , 0)
=> -2 ± c = -2√34
=> c = ± √34
Also , c^2 = a^2 + b^2
=> 34 = 25 + b^2
=> b^2 = 9
=> b = 3
Substituting all the values ,
Equation of Hyperbola is (x+ 2)²/25 - (y)²/ 9 = 1
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Gaspar writes the algebraic expression 5b +3.79.
It represents the total cost, in dollars, of buying 5 bagels
and a container of cream cheese. Identify any variables,
coefficients, and terms in the expression. Tell what
each represents.
Answer:
B is a variable it is a letter
5 is a coefficient because it's in front of the variable
3.79 is a term because it is just numbers by itself
Step-by-step explanation:
prove that for every integer exists a multiple of that number that is composed of only ones and zeros in the decimal system
Let n be a positive integer. Consider the n+1 integers 1,11, 111,1111,... (where the last integer in this list is the integer with n+1 - 1s in its decimal expansion).
Note that there are n possible remainders when an integer is divided by n. Because there are n+1 integers in this list, by the pigeonhole principle there must be two with the same remainder when divided by n. The larger of these integers the smaller one is a multiple of n, which has a decimal expansion consisting entirely of 0s and 1s.
For example, take n=7
we have, 1,11, 111,1111,...,11111111
The remainder possible when any number is divided by 7 is 0,1,2,3,4,5,6
These are the remainders when the numbers in the first list are divided by 7 gives 1,4,6,5,2,0,1,4.
Now you can see that we have 7 pigeonholes {0,1,2,3,4,5,6} and 8 pigeons {1,11, 111,1111,...,11111111} so there needs to be at least one pigeonhole where 2 pigeons will reside.
In this case, we have 11%7=4 and 11111111%7=4
Their difference, i.e. 11111111-11=11111100 is divisible by 7.
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Gualberto has a barrel that collects rainwater. As the rainwater evaporates,
the height of the rainwater changes from 24.83 in. to 18.08 in. over a period of
5 2/5 days. What is the average change in the height of the rainwater each day?
The average change in the height of the rainwater is 1.25 inches per day
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
The initial height of the rainwater measured = y₁
The value of y₁ = 24.83 inches
The final height of the rainwater measured = y₂
The value of y₂ = 12.08
The change in height = y₁ - y₂
Substituting the values in the equation , we get
The change in height = 6.75
The number of days = 5 2/5 days
The number of days = 27/5 days = 5.4 days
So , the equation will be
The average change in the height of the rainwater = change in height / number of days
Substituting the values in the equation , we get
The average change in the height of the rainwater = 6.75 / 5.4
The average change in the height of the rainwater = 1.25 inches per day
Hence , the average change is 1.25 inches per day
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To fill an order, the factory dyed 21 yards of silk indigo and 75 yards teal. How many yards of silk did it dye for that order?
Answer:
96
Step-by-step explanation:
21+75
[tex]\frac{1}{3}+\frac{1}{105}-\frac{1}{21}[/tex]
Determine whether the quadratic function shown below has a minimum or
maximum, then determine the minimum or maximum value of the function.
f(x) = -2(x - 5)(x-7)
The vertex (3, -16) is the maximum point on our quadratic equation.
Maximum and minimum values of the function:When we compare the given Quadratic function with the general form
ax² +bx +c,
If the value of a is positive then the Quadratic function will have a minimum value, and the graph of the function opens up.
If the value of a is negative then the Quadratic function will have a maximum value, and the graph of the function opens downwards.
Here we have
f(x) = -2(x - 5)(x-7)
f(x) = -2 [x²-7x - 5x + 35 ]
f(x) = -2 [x²-12x + 35 ]
f(x) = -2x² + 12x - 35
Compare f(x) with ax²+ bx + c
=> a = -2, b = 12, and c = - 35
Here,
a = -2 is a negative value then the function f(x) will have maximum value
And the graph of the function opens down.
The formula for the x coordinate of the vertex = -b/2a
The coordinate of x = -(12)/2(-2) = 3
Now substitute x = 3 in f(x) to find y-coordinate
=> f(3) = - 2(3)² +12(3) - 35
=> f(3) = -2(9) + 36 - 35
=> f(3) = - 16
Therefore, y-coordinate = -16
Therefore,
The vertex (3, -16) is the maximum point of the quadratic equation.
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Suppose that you roll two dice. You will be paid $20 if you roll a double. You will not receive anything
for any other outcome. How much should you be willing to pay for the privilege of rolling the dice?
Please round your answer to the nearest cent.
There are 36 possible outcomes when rolling two dice, and only 1 of those outcomes results in a double. Therefore, the probability of rolling a double is 1/36, or approximately 0.028.
If you are willing to pay $20 to roll the dice, then you are effectively paying a premium of $20 for a probability of 0.028 of winning. This means that the expected value of rolling the dice is 0.028 * $20 = $0.56.
Therefore, you should be willing to pay up to $0.56 for the privilege of rolling the dice. Rounded to the nearest cent, this is $0.56.
Preeti discovers that her roommate Shari recently experimented with methamphetamine. Preeti, worried about her roommate, informs Shari that there are risks associated with methamphetamine use, such as the induction of symptoms associated with ____.
psychosis
Preeti informs Shari that there are risks associated with methamphetamine use, such as the induction of symptoms associated with Psychosis
Psychosis is a combination of symptoms resulting in an impaired relationship with reality. It can be a symptom of serious mental health disorders. People who are experiencing psychosis may have either hallucinations or delusions.
If someone is experiencing an episode of psychosis, the main symptoms include:
hallucinationsdelusionsdisorganized behaviorAccording to the question,
Preeti discovers that her roommate Shari recently experimented with methamphetamine. Preeti, worried about her roommate, informs Shari that there are risks associated with methamphetamine use, such as the induction of symptoms associated with Psychosis
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