The expression x²−−6 can be factored as:
[tex]x^{2} - 6 = (x + \sqrt{6} )(x - \sqrt{6})[/tex]
What is Factoring an expression?
A numerical or algebraic expression is factored when it is written as a product of factors. The distributive property can be used to factor expressions.
The expression x²−−6 can be factored as:
[tex]x^{2} - 6 = (x + \sqrt{6} )(x - \sqrt{6})[/tex]
The solutions for this equation would be x = √6 or x = -√6. These are the values of x that make the expression equal to zero.
Factoring the expression in this way can be useful in solving related equations or in finding the roots of a quadratic function. It also helps in visualizing the graph of the function, as the factored form shows the x-intercepts, which are the points where the graph crosses the x-axis.
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What are the line segments in this rectangle?
a rectangle with the vertices labeled Q, R, S, and T
Answer:
qr rs st qt are the line hope it helped
Each worker at a store gets paid $15.90 for that first 40 hours worked. After 40 hours, they earn time and a half wages. Every employee has a 28% of his/her gross pay deducted for taxes, insurance etc. how much of a net pay does each worker take home?
Each worker would take home a net pay of $586.71.
What is the net pay?
The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.
To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.
To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.
For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:
Gross Pay for 40 hours = $15.90/hour x 40 hours = $636
For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:
Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88
Therefore, their total gross pay would be:
Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88
Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:
Total Deductions = 28% x $814.88 = $228.17
Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:
Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71
Therefore, each worker would take home a net pay of $586.71.
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Simplify fully 8c^4d^5+2c^3d^3
The expression when simplified is 2c^3d^3(4cd^2 + 1)
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
8c^4d^5+2c^3d^3
Factor out 2 from the expression
So, we have the following representation
2(4c^4d^5 + c^3d^3)
Factor out c^3d^3 from the expression
So, we have the following representation
2c^3d^3(4cd^2 + 1)
Hence, the expression is 2c^3d^3(4cd^2 + 1)
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Please help with this question I can’t seem to solve it
Answer:
X Y
0 0
2 -3
Step-by-step explanation:
The slope should look like this photo.
PLEASE HELLLP IM TAKING A QUIZ!!Cory is making popcorn. He knows that 3 identical scoops of unpopped
kernels produce 6 quarts of popcorn.
R
Which table most likely represents the total amount of popcorn, in quarts,
produced by x scoops of unpopped kernels?
Answer: C
Step-by-step explanation:
I am fairly certain this is the right answer. Good luck on your quiz!
Answer:C
Step-by-step explanation:
I remember this from class one time hope it helps:)
Complete the sentence below.
If (3x2 + 22x + 7) = (x + 7) = 3x + 1 , then (x + 7) ( ? )
＝?
The check of the polynomial division problem shows that the product of two polynomials is a polynomial.
This supports the fact that the __________ ?
property is satisfied for polynomial multiplication.
A local coffee shop is testing out new flavors of coffee: Caramel Apple Latte and Salted Minty Mocha. A poll conducted by the
coffee shop determined that 46 customers preferred only the Caramel Apple Latte, 61 customers chose only the Salted Minty
Mocha, 27 customers chose both flavors, but 18 liked neither flavor. What is the probability that a randomly selected
customer would only like the Caramel Apple Latte?
The probability that a customer selected randomly would only like Carmel apple is 23/76
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space/ total outcome
sample space is the number of customers that like caramel apple latte only = 46
The total number of customers = 46+61+27+18 = 152
Therefore The probability that a customer selected randomly would only like Carmel apple = 46/152 = 23/76
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Suppose that 7 out of the 17 doctors in a small hospital are General Practitioners, 4 out of the 17 are under the age of 45, and 2 are both General Practitioners and under the age of 45. What is the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45? Enter a fraction or round your answer to 4 decimal places, if necessary.
The probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is given by the equation P = 9/17
What is Set Theory Formula?The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
Given data ,
Let the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 be P
Now , the equation will be
The fraction of doctors who are general practitioners be n ( A ) = 7/17
The fraction of doctors who are under the age of 45 n ( B ) = 4/17
And ,
The fraction of doctors who are both n ( A ∩ B ) = 2/17
Now , from the set theory formula ,
n(A∪B) = n(A) + n(B) - n(A⋂B)
And , probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B )
Substituting the values in the equation , we get
Probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B ) = ( 7 / 17 ) + ( 4/17 ) - ( 2/17 )
On simplifying the equations , we get
Probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B ) = 9/17
Hence , the probability is 9/17
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Find the value of 15 - 8-2.
3.5
04
11
Answer:
Step-by-step explanation: Yes, that is correct. The solution to the system of equations is (x, y) = (-7, 0) which is not in the given options, so none of them are the correct answer.
Winston planned to spend no more than $150 on a helmet and goggles for skiing. After
spending $90.50 on a helmet, he bought a pair of goggles that put him over his budget.
Let x represent the cost of the goggles. Which inequality describes the problem?
90.50 + x>
150
90.50 + x <
150
Solve the inequality. Then, complete the sentence to describe the solution.
The goggles cost more than $
Submit
Answer:
(a) 90.50 +x > 150The goggles cost more than $59.50Step-by-step explanation:
You want an inequality and its solution for finding the cost of goggles that put Winston over his $150 budget when combined with the purchase of a $90.50 helmet.
Total costIf x represents the cost of the goggles, then Winston's total spending is ...
90.50 + x
If that is over is $150 budget, the relation is described by ...
90.50 +x > 150
SolutionSubtracting 90.50 from both sides gives ...
x > 59.50
This tells us the goggles cost more than $59.50.
<95141404393>
Complete the following proof.
Given: WXYZ is a parallelogram with diagonals XZ and WY intersecting at point V.
Prove: XZ bisects WY
The proof of the parallelogram has been given below
How to prove that X bisects WYWe have WXYZ as a parallelogram.
XW = ZY
XW // ZY
such that
M ∠VXW = M VZY (This is alternate interior angles,)
M∠VWX = M ∠VYZ
therefore ΔVXW ≅ Δvzy
wv = yv
Then XZ bisects WY
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Show that ∶ [– 1, 1] → ℝ, given by () =
(2+)
is one-one. Find the inverse of the function
∶ [– 1, 1] → Range . (Hint: For ∈ Range , = () =
(2+)
, for some in [– 1, 1], i.e., =
(2+)
The inverse of the given function is f(x) = 2x/(1 - x)
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.
Given function is
f(x) = x/(2+x)
Assume that y = f(x) = x/(2+x)
Solve y = x/(2+x) for x:
y = x/(2+x)
Multiply (2+x) on both sides:
y(2+x) = x
2y + xy = x
Subtract xy from both sides:
2y = x - xy
2y = x(1 - y)
x = 2y/ (1 - y)
Now replace x with y and y with x:
y = 2x/(1 - x)
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Which equation represents the graph?
a graph of a line that passes through the points 0 comma negative 1 and 1 comma negative 4
y equals negative one third times x minus 1
y = −3x − 1
y equals negative one third times x plus one third
y equals negative 3 times x plus one third
The equation that represents the graph of a line passing through the points (0, -1) and (1, -4) is y = -3x - 1.
What is graph?
A graph is a visual representation of data or information that shows the relationship between different variables or quantities. Graphs can take many forms, including bar graphs, line graphs, scatterplots, and pie charts, among others. They are widely used in many fields, including mathematics, science, economics, and social sciences, to help visualize and analyze data, identify patterns, and communicate findings to others in a clear and concise manner. By representing complex information in a simple, easy-to-understand format, graphs can provide valuable insights and help us make informed decisions.
The equation that represents the graph of a line passing through the points (0,-1) and (1,-4) is:
y = -3x - 1
To find the equation of a line given two points, you can use the slope-intercept form:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is one of the given points.
First, we can find the slope of the line:
m = (y2 - y1) / (x2 - x1)
= (-4 - (-1)) / (1 - 0)
= -3
Next, we can choose one of the given points and substitute its coordinates and the slope into the slope-intercept form:
y - (-1) = -3(x - 0)
y + 1 = -3x
y = -3x - 1
Therefore, the equation that represents the graph is y = -3x - 1.
Option A, y = -1/3x - 1, has a slope of -1/3, which is not the slope of the line passing through the given points.
Option C, y = -1/3x + 1/3, also has an incorrect slope of -1/3, and it also does not pass through the point (0,-1).
Option D, y = -3x + 1/3, has the correct slope of -3, but it does not pass through the point (0,-1).
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Margaux pays $19 for postage. What is the mass of her parcel?
To find the mass of her parcel, you must solve the equation for the input when the output is of 19.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
For this problem, we have that the numeric value is of $19, hence the equation must be solved for the input variable to find the mass of the parcel.
Missing Information
The problem is incomplete, hence the general procedure to solve it was presented.
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These two triangles are congruent.
b
B
6 cm
1049
12 cm
9 cm
A
47°
'R
29°
29°
12 cm
с
P
a)
What is the size of angle Q?
Since the triangles are congruent. Then The size of angle Q is 47°
Congruent Angle:
Congruent angles are often used in architecture, construction, design, and art. Isometrics have the same angular measurements. For example, a regular pentagon has 5 sides and 5 angles, each measuring 108 degrees. Regardless of the size or scale of a regular polygon, the angles are always congruent.
Here is a list of rules for the congruence of angles.
1. The only condition for two angles to be congruent is if the measurements of the angles agree.
2. The lengths and orientations of the two sides of this congruent angle are not important.
According to the Question:
It is given that :
B = 6 cm, 12 cm and 9 cm
A = 47°
R' = 29°
If the triangle is congruent, then all the three sides and angles will be same.
Therefore,
Angle Q = Angle A
Therefore, Angle Q = 47°
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Point Q is located at (−6,−1) on the coordinate plane. Point Q is reflected over the x-axis to create point Q' Point Q' is then reflected over the y-axis to create point Q'' What ordered pair describes the location of Q''?
Answer:
(6, 1)
Step-by-step explanation:
When a point is reflected over the x-axis, its y-coordinate changes sign. When a point is reflected over the y-axis, its x-coordinate changes sign.
So, when point Q, located at (-6,-1), is reflected over the x-axis to create point Q', the new point has the same x-coordinate and a y-coordinate of -1 to 1 = 1. So, Q' is located at (-6, 1).
Next, when Q' is reflected over the y-axis to create Q'', the new point has the same y-coordinate and an x-coordinate of -6 to 6 = 6. So, Q'' is located at (6, 1).
So, the ordered pair that describes the location of Q'' is (6, 1).
what is the total population if 15% is 36,000 people
petra jogs 60 miles in 110 minutes, at this rate how long would her take to jog per one minutes
The speed of Petra will be 0.55 mile/minute.
What exactly is speed?
The definition of speed is:
The pace at which an object's location changes in any direction.
Speed is defined as the ratio of distance travelled to time spent travelling. Because it has just one direction and no magnitude, speed is a scalar number.
Formula for Speed
The speed formula is shown below:
s=d/t
Where,
s is the speed in metres per second, d is the distance travelled in metres, and t is the duration in seconds.
Now,
As given petra jogs 60 miles in 110 minutes
then in one minute she will jog =60/110 mile
=0.5454 mile/min
Hence,
The speed of Petra will be 0.55 mile/minute.
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11311 rounded off to the nearest 100
Answer:
11300
Step-by-step explanation:
The closest 100 to 11311 is 11300
If the number was 11351 you would round up to 11400
Given: log a 2 = 4, log a 3 = 5, log a 5 = 8. Find log a 60.
A. 2.9
B. 1.46
C. .32
D. 2.1
The solution of the logarithm expression logₐ 60 is 2.1. Therefore, the answer is D.
How to solve logarithm?The logarithm expression can be solved as follows; Using the logarithm rule,
Law of multiplication of logarithm,
logₐ x + logₐ y = logₐ xy
Therefore,
logₐ 2 = 4
logₐ 3 = 5
logₐ 5 = 8
Hence, let's find logₐ 60.
logₐ 5 + logₐ 3 + logₐ 2 + logₐ 2 = logₐ (5 × 3 × 2 × 2) = logₐ 60
Hence,
0.8 + 0.5 + 0.4 + 0.4 = 2.1
Therefore,
logₐ 60 = 2.1
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The value of log a 60 is 21. The correct option is D.
What is a Logarithm?Logarithms are another way of writing exponents.
Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only.
log a 60 = log a (12 x 5)
log a 60 = log a 12 x log a 5
log a 60 = log a (4 x 3) x log a 5
log a 60 = log a 4 x log a 3 x log a 5
log a 60 = 2 log a 2 x log a 3 x log a 5
Substituting the values for the logs
log a 60 = 2 (4) + 5 + 8
log a 60 = 21
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Refer to the accompanying data set and use the 30 screw lengths to construct a frequency distribution. Begin with a
lower class limit of 0.720 in., and use a class width of 0.010 in. The screws were labeled as having a length of 3/4 in.
Click on icon to view the data
Following is the frequency distribution table:
0.720- 0.730
0.730- 0.740
0.740- 0.750
What is Frequency Table?Any table that shows the frequency of values for one or more variables within a set of data. a table displaying each value of the variable and its accompanying frequency for a whole-number variable in a data set.
Given:
The lower limit is given as 0.720 inches.
and, The upper limit is 0.750 inches.
Also, the width of each class is 0.010 inches.
Thus, the intervals will be:
0.720- 0.730
0.730- 0.740
0.740- 0.750
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Find EF, please!!!!!!!!!!
Answer:
EF = 7
Step-by-step explanation:
You want to know the length of midsegment EF in the triangle with it labeled 43-4x and the parallel base segment labeled 32-2x.
MidsegmentThe midsegment is half the length of the base segment, so we have ...
(43 -4x) = 1/2(32 -2x)
43 -4x = 16 -x . . . . . simplify
27 = 3x . . . . . . . . add 4x-16
9 = x . . . . . . . . divide by 3
EF = 43 -4x = 43 -4(9) = 43 -36
EF = 7
The points K (1,3), L(-4,-3), M (2,-8), and N (7,-2) form quadrilateral KLMN. Where would these points be on the graph?
The location of the points for quadrilateral KLMN have been plotted in the graph shown in the image attached below.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapezoidNext, we would use an online graphing calculator to construct (plot) quadrilateral KLMN on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral KLMN on the x-coordinate and y-coordinate respectively as shown in the table.
By critically observing the graph of quadrilateral QRST, we can reasonably infer and logically deduce that it represents a parallelogram.
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You (or your parents) purchase a new car for $19,725.00 plus 4.75% sales tax. The down payment is $2,175.00 and you (or your parents) have an average credit rating. How much interest is accrued after the first month?
Answer:
$90.12
Step-by-step explanation:
The principal amount of the loan is ...
(sale price)(1 + sales tax rate) - (down payment)
= $19,725×1.0475 -2175 = $18,486.94
For a secured loan, the APR charged for an average credit rating appears to be 5.85%, so the interest for the first month is
i = Prt = ($18,486.94)(0.0585)(1/12)
i = $90.12
Plot the points (-7,5),(-4,-6),(-1,4),(-7,3) in the Cartesian plane. Is the following relation a function? Why?
The graph of the points can be seen at the end, and the relation is not a function.
How to graph the points on a coordinate axis?
The coordinate axis has two axis with numbers labeled. For any point (x, y), you need to find the value x on the horizontal axis and the value y on the vertical axis.
Then the graph of the points (-7,5), (-4,-6), (-1,4), (-7,3) will be like the one at the end of the answer.
Now, is this a function?
Not, it is not, because we can see that the input -7 is being mapped into two different outputs, and a relation is a function only if each input is mapped into a single output.
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Determine the domain and range of the given
function.
The domain is
The range is
domain = all real numbers
range = y > -2
y=x²-2
range is y is -2
domain is x is
A line with a slope of 7 passes through the points (-7, 5) and (g, -2). What is the value of g?
g=
[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{g}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{g}-\underset{x_1}{(-7)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 7 }\implies \cfrac{-7}{g+7}=7\implies -7=7(g+7) \\\\\\ \cfrac{-7}{7}=g+7\implies -1=g+7\implies \boxed{-8=g}[/tex]
Some candles are in the shape of a right circular cylinder. For one such candle, the radius is 9 cm and the height is 26.5 cm. Find the volume of the candle. Round your answer to the nearest whole number. Do not type the units in the space below. (Be sure to use the pi button on your calculator to do the calculation.)
The volume of the candle is 6740 cubic cm
How to find the volume of the candle.From the question, we have the following parameters that can be used in our computation:
Radius, r = 9 cm
Height, h = 26.5 cm
The volume of a cylinder is calculated as
Volume = πr²h
substitute the known values in the above equation, so, we have the following representation
Volume = 3.14 * 9² * 26.5
Evaluate the products and exponents
Volume = 6740 cubic cm
HEnce, the volume is 6740 cubic cm
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*Please help, I will mark brainest*
A chemical manufacturer wants to lease a fleet of 25 railroad tank cars with a combined carrying capacity of 532,000 gallons. Tank card with three different carrying capacities are available: 7,000 gallons, 14,000 and 28,000. How many of each type of tank car should be leased?
Fill in the blank: There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations x1=_t+(_), x2=_t+(_) & x3=t
Answer:
Let's call the number of 7,000 gallon tank cars "x1", the number of 14,000 gallon tank cars "x2", and the number of 28,000 gallon tank cars "x3".
We can write the following constraints based on the total carrying capacity of the fleet:
7,000x1 + 14,000x2 + 28,000x3 = 532,000
x1 + x2 + x3 = 25
x1, x2, x3 >= 0 (since we can't have a negative number of tank cars)
This is a linear programming problem, which can be solved using simplex method or the graphical method.
By using the graphical method, we find that there are multiple optimal solutions. For example, one solution is x1 = 11, x2 = 7, and x3 = 7. This means that the manufacturer should lease 11 7,000 gallon tank cars, 7 14,000 gallon tank cars, and 7 28,000 gallon tank cars to meet the total carrying capacity requirement of 532,000 gallons.
So, the answer to the question is: There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations x1 = 11 + 7t, x2 = 7 + 7t, and x3 = 7 + 7t.
A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 16 ft, its width is 7 ft, and its surface area is 500 ft2. (In the figure, h=height. Assume that the given surface area includes that of the top lid of the box.)
Answer:
Step-by-step explanation:
The surface area of a rectangular box can be calculated as follows:
Surface area = 2lw + 2lh + 2wh
Where l is the length, w is the width, and h is the height.
We are given the surface area (500 ft2) and the length and width (16 ft and 7 ft respectively), so we can use these values to solve for the height:
500 = 2 * 16 * 7 + 2 * 16 * h + 2 * 7 * h
500 = 224 + 32h + 14h
500 = 238h + 224
276 = 238h
h = 276 / 238
h = 1.16 ft
So the height of the box is approximately 1.16 feet.
