Step-by-step explanation:
-27 [tex]\sqrt{72}[/tex] = -27 [tex]\sqrt{36*2}[/tex] = -27 (6) [tex]\sqrt{2}[/tex] = - 162 [tex]\sqrt{2}[/tex] = - 229.1
Which decimal is less than 0. 8 and greater than 0. 02
A. 0. 81
B. 0. 46
C. 0. 86
D. 0. 6
The decimal which is less than 0. 8 and greater than 0. 02 is 0. 46 (option B).
To answer this question, we need to understand how decimals work. A decimal is a number that represents a value less than one, and it is denoted by a dot or a period. The digits that come after the dot represent the number of tenths, hundredths, thousandths, etc., depending on the place value of the digit.
Now, let's consider the given options: 0.81, 0.46, 0.86, and 0.6. We need to find the decimal that lies between 0.8 and 0.02.
We can eliminate option D, 0.6, as it is less than 0.8. Similarly, we can eliminate option A, 0.81, as it is greater than 0.8.
To choose between options B, 0.46, and C, 0.86, we need to compare them with the given values, 0.8 and 0.02. We can see that 0.46 is less than 0.8 but greater than 0.02.
Therefore, the answer is option B, 0.46.
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PLEASE ANSWER ASAP
1. How many atoms are present in 8.500 mole of chlorine atoms?
2. Determine the mass (g) of 15.50 mole of oxygen.
3. Determine the number of moles of helium in 1.953 x 108 g of helium.
4. Calculate the number of atoms in 147.82 g of sulfur.
5. Determine the molar mass of Co.
6. Determine the formula mass of Ca3(PO4)2.
IT WOULD BE HELPFUL
The number of atoms present in 8.500 mole of chlorine atoms can be calculated using Avogadro's number, which is 6.022 x [tex]10^{23}[/tex] atoms per mole. Therefore:
Number of atoms = 8.500 mole x 6.022 x [tex]10^{23}[/tex]atoms/mole
Number of atoms = 5.1177 x [tex]10^{24}[/tex] atoms
Find out the mass (g) of 15.50 mole of oxygen?The mass of 15.50 mole of oxygen can be calculated using the molar mass of oxygen, which is 16.00 g/mol. Therefore:
Mass = 15.50 mole x 16.00 g/mole
Mass = 248 g
The number of moles of helium in 1.953 x [tex]10^{8}[/tex] g of helium can be calculated using the molar mass of helium, which is 4.00 g/mol. Therefore:
Number of moles = 1.953 x [tex]10^{8}[/tex] g / 4.00 g/mol
Number of moles = 4.883 x [tex]10^{7}[/tex] mol
The number of atoms in 147.82 g of sulfur can be calculated using the molar mass of sulfur, which is 32.06 g/mol, and Avogadro's number. Therefore:
Number of moles = 147.82 g / 32.06 g/mol
Number of moles = 4.608 mol
Number of atoms = 4.608 mol x 6.022 x [tex]10^{23}[/tex] atoms/mol
Number of atoms = 2.773 x [tex]10^{24}[/tex] atoms
The molar mass of Co (cobalt) is 58.93 g/mol.
The formula mass of Ca3(PO4)2 can be calculated by adding the atomic masses of each element in the compound. The atomic masses are:
Ca = 40.08 g/mol
P = 30.97 g/mol
O = 16.00 g/mol
Formula mass = (3 x Ca) + (2 x P) + (8 x O)
Formula mass = (3 x 40.08 g/mol) + (2 x 30.97 g/mol) + (8 x 16.00 g/mol)
Formula mass = 310.18 g/mol
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the ____ numbering system is base 16; in other words, 16 numerals are used to express any given number
The hexadecimal system numbering system is base 16; in other words, 16 numerals are used to express any given number.
In this system, 16 numerals are used to represent any given number. The numerals used in this system are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F, where A represents 10, B represents 11, and so on, up to F, which represents 15.
This system is commonly used in computer science, as it is more compact than the decimal system, and allows for easier conversion between binary and decimal systems. In the hexadecimal system, each digit represents a power of 16, just as each digit in the decimal system represents a power of 10.
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can someone answer my new math questions please
Answer:
yes
Step-by-step explanation:
Dilate point S by a scale factor of 1/2
PLEASE JUST TELL WHERE THE POINT MUST BE LOCATED DONT GIVE A LONG EXPLANATION AND IF U CAN UPLOAD A PIC OF THE ANSWER
The position of point S after dilating will be half of the original. The dilated point S' has been shown below.
What is dilation?
Using a modification known as dilation, an object can be resized. Through dilatation, the objects can be resized or enlarged. This transformation results in a shape that is a perfect replica of the original image. The form's dimensions do vary, though. An expansion or contraction of the original form is required for a dilatation. This shift is referred to as a scale factor.
We are given a graph showing position of point S.
Now, on dilating the point by a scale factor of [tex]\frac{1}{2}[/tex], we get that the point will be located at half of the original.
The point has been located and attached in the image below.
Hence, the required solution has been obtained.
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Write the point-slope form of the equation of the line that passes through the points (6, -9) and (7, 1). Include your work in your final answer. Type your answer in the box provided to submit your solution.
Therefore , the solution of the given problem of equation comes out to be 10x - y = 51 is the point-slope form of the equation of the line passing through the points (6, -9) and (7, 1).
Explain the equation.Variable words are frequently used in complex algorithms to show consistency between two arguments that are opposed to one another. Academic expressions called equations are used to show the equality of various academic figures. Take into account the details in the z + 7 proposals.
Here,
The equation for the line passing between the points (6, -9) and (7, 1) must be found in the point-slope form.
Using the equation m = (y2 - y1) / (x2 - x1), find the slope (m) of the line, where (x1, y1) and (x2, y2) are the coordinates of the two points.
=> (x1, y1) = (6, -9)
=> (x2, y2) = (7, 1)
=> m = (1 - (-9)) / (7 - 6)
=> m = 10 / 1 m = 10
Consequently, the line's slope is 10.
=> y - y1 = m(x - x1)
=> m = 10 (x1, y1) = (6, -9)
=> y - (-9) = 10(x - 6)
=> y + 9 = 10x - 60
=> 10x - y = 51
Therefore, 10x - y = 51 is the point-slope form of the equation of the line passing through the points (6, -9) and (7, 1).
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A circle with center O and radius 5 has central angle XOY. X and Y are points on the circle. If the measure of arc XY is 90 degrees, what is the length of chord XY?
The length of chord XY is 5√2.
What is the length of the chord?
It is described as the line segment that connects any two points on the circle's circumference without going through the circle's center. As a result, the diameter is the chord of a particular circle that is the longest and goes through its center. In mathematics, determining the chord's length can be crucial at times.
Here, we have
Given: A circle with center O and radius 5 has a central angle XOY. X and Y are points on the circle. If the measure of arc XY is 90 degrees.
We have to find the length of chord XY.
∠XOY = 90°
OX = OY = 5
We draw a perpendicular from the center to chord XY bisect XY at D.
Now, since OD bisects ∠XOY
∠XOD = ∠YOD = 90°/2 = 45°
Now, in ΔXOD
sin45° = XD/OX
1/√2 = XD/5
5/√2 = XD...(1)
In ΔYOD
sin45° = YD/OY
5/√2 = YD...(2)
Adding (1) and (2), we get
XD + YD = 5/√2 + 5/√2
XY = 5√2
Hence, the length of chord XY is 5√2.
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Evaluate the following.
Write an exponential function of the form y=ab^x that has the given points
1. (1,5), (2, 7)
The exponential function of the form y=ab^x that has the given points is y = (25/7)(7/5)^x
Writing the exponential functionWe can use the given points to set up a system of equations and solve for the values of a and b in the exponential function y = ab^x.
Using the point (1,5), we get:
5 = ab^1
Using the point (2,7), we get:
7 = ab^2
Now, we can solve for a and b by dividing the second equation by the first:
7/5 = (ab^2)/(ab^1
Simplifying this expression, we get:
7/5 = b
Substituting this value of b back into one of the original equations, we can solve for a:
5 = a(b^1) = a(b) = a(7/5)
Simplifying this expression, we get:
a = 25/7
So, the exponential function that passes through the points (1,5) and (2,7) is:
y = (25/7)(7/5)^x
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Consider a sequence whose first five terms are:-1.75, -0.5, 0.75, 2, 3.25
Which explicit function (with domain all integers n ≥ 1) could be used to define and continue this sequence?
Step-by-step explanation:
+ 1.25
every new term is the previous term + 1.25.
with starting value -1.75
f(n) = 1.25n - 1.75
PLEASE HELP ME
I’LL GIVE YOU BRAINLIEST
The profit function of the company is given by P(x)=-4x^3 + 32x^2 - 64, where x is the number of toys sold in hundreds, and P(x) is the profit in thousands of dollars.
How to explain the graphThe key features of the graph of the profit function are the following:
The degree of the polynomial function is 3, which means that the graph is a cubic curve.
The coefficient of the leading term is negative (-4), which means that the graph opens downwards.
The coefficient of the quadratic term is positive (32), which means that the graph is concave up.
The y-intercept of the graph is -64, which means that the company will incur a loss of $64,000 if it does not sell any toys.
It should be noted that to find the maximum profit, we need to evaluate the profit function at x = 5.33:
P(5.33) = -4(5.33)^3 + 32(5.33)^2 - 64 = 23.78
Therefore, the maximum profit that the company can make is $23,780.
In summary, the graph of the profit function reveals that the company will incur a loss if it does not sell any toys, but it can make a profit if it sells at least some toys. The profit function has a cubic shape that opens downwards, indicating that the profit decreases as the number of toys sold increases beyond a certain point. The maximum profit occurs at x = 5.33, where the profit is $23,780.
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I need a bit of help please
The slope of the line in the reduced form is 4 / 7.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
Therefore,
slope = m = change in y / change in x
slope = m = y₂ - y₁ / x₂ - x₁
P = (2, 3)
Q = (9, 7)
x₁ = 2
x₂ = 9
y₁ = 3
y₂ = 7
Therefore,
slope = 7 - 3 / 9 - 2
slope = 4 / 7
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Can someone help me asap? It’s due tomorrow. I will give brainiest if it’s all correct.
Answer:
1.a
2.c
3.d
4.b
Step-by-step explanation:
Find the nearest 10th the cylinder is 22 inches and 12.5 inches what is the lateral surface ?
Rounding the result off to the nearest 10th, the lateral surface area of the cylinder is 822 inches².
What is surface area?Surface area is the total area of the exposed surfaces of a three-dimensional object. It is measured in square units such as square centimeters (cm2) or square meters (m2). Surface area is an important concept in mathematics, science, and engineering, as it is the total area that determines properties such as friction, heat transfer, and fluid dynamics. For example, a larger surface area can increase the rate of heat transfer and allow for more efficient cooling. Similarly, a larger surface area can increase the friction between two objects, allowing them to grip better. Surface area is also important in chemistry, as it affects the amount of gas or liquid that can be absorbed or released by a given object.
The cylinder has a radius of 11 inches and a height of 12.5 inches. To find the lateral surface area of a cylinder, the formula used is A = 2πrℎ, where r is the radius and h is the height of the cylinder. After plugging in the values, the lateral surface area of the cylinder is 821.75 inches². Rounding the result off to the nearest 10th, the lateral surface area of the cylinder is 822 inches².
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5. This solid was created by joining two right rectangular prisms.
4½ cm
8 cm
4 cm
-9 cm
10½ cm
Enter the volume of the solid, in cubic centimeters.
The volume of the solid as shown in the diagram is 540 cm².
What is volume?Volume is the space occupied by a solid shape.
To calculate the volume of the of the solid, we use the formula below
Formula:
V = LWH+lwh............................ Equation 1Where:
V = Volume of the solid L = Length of the bigger prismW = Width of the bigger prismH = Height of the bigger prisml = Length of the smaller prismw = Width of the smaller prismh = Height of the smaller prismFrom the diagram in question,
Given:
L = 10.5 cmW = 9 cmH = 4 cml = 9 cmw = 4.5 cmh = 4 cmSubstitute these values into equation 1
A = (10.5×9×4)+(9×4.5×4)A = 378+162A = 540 cm³Hence, the volume is 540 cm³.
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can you give me a simple fast answer
The mapping that is a function will be B). X
How to explain the functionEvery function got a set of input values called " Domain " and a set of respective output values as " Range"
And function worked as Function( Input value ) = Output value
There are basic rules for function :
1. There always exist output value for every single input value.
2. Every input value should have one and only one output value
For W : Rule 2 is violated
Here, Input value 6 result to two output value 2 and 4
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Which inequality is true when the value of w is -3?
Beau is building 9 puppy bots and 6 kitty bots. Each bot needs 4 wheels. How many wheels does beau need in all
According to unitary method, Beau needs 60 wheels in all to build 9 puppy bots and 6 kitty bots.
The unitary method is a mathematical technique used to solve problems by finding the value of one unit and then calculating the value of the required quantity by multiplying or dividing it with the given value of units.
Given that each bot needs 4 wheels, we can find the number of wheels required to build one bot. Using the unitary method, we can say that one bot needs 4 wheels. Therefore, 9 puppy bots will need 9 times 4 wheels, which is 36 wheels.
Similarly, 6 kitty bots will need 6 times 4 wheels, which is 24 wheels. To find the total number of wheels required to build all the bots, we can add the number of wheels required for puppy bots and kitty bots
Total number of wheels required = 36 + 24 = 60
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A line intersects the points (-3, 4) and
(-2, 3). What is the slope-intercept
equation for this line?
y = -x + [?]
The slope-intercept equation of line is -1 and equation will be y = -x - 1.
What is the slope?
m = (y2 - y1) / (x2 - x1) is the formula for calculating slope from two points on a line, (x1, y1) and (x2, y2). Here,
m = the line's slope
x1 is equal to the initial point's x-coordinate.
y1 is the first point's y-coordinate.
x2 is equal to the second point's x-coordinate.
The second point's x-coordinate is equal to y2.
x1 = -3, y1 = 4; x2= -2, y2=3
m = (3-4)/(-2 - (-3))
= -1 / (-2+3)
= -1/1
m = -1
Substitute the value in given equation:
y = -x + (-1)
y = -x - 1
Hence, the slope-intercept equation of line is -1 and equation will be y = -x - 1.
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What is the missing length of a rectangular prism where the height and width are both 9 cm and the surface area is 432 cm2?
The missing length is 7.5 cm.
What is a rectangular prism?
A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.
Here, we have
Let the missing length be x cm.
The formula for the surface area of a rectangular prism is:
SA = 2lw + 2lh + 2wh
We are given that the height and width are both 9 cm, so we can substitute those values and simplify:
432 = 2(x)(9) + 2(x)(9) + 2(9)(9)
432 = 18x + 18x + 162
432 - 162 = 36x
270 = 36x
x = 270/36
x = 7.5
Hence, the missing length is 7.5 cm.
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match the answers to the questions. ⚠️due tmr!
Below is the correct matching of the questions to the right answers
Mean average deviation - (C) The average deviation of the data from the mean.Range of a data set - (E) The difference between the highest value and the lowest value in a numerical data set.First quartile - (AB) The median in the lower half of the rank-ordered data.Second quartile - (B) The median value in the data set.Third quartile - (A) The median in the upper half of the rank-ordered data.Interquartile range - (D) The distance between the first and third quartiles of the data set.What you should know about statistical measuresThe statistical measures listed in the previous question are often used to describe and analyze statistical variables.
For instance, the range of a data set is a measure of the spread of values in a variable, while the quartiles and interquartile range provide information about the distribution of the variable. Mean average deviation is a measure of the variability of the variable around its mean value.
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1. Mean average deviation - The average deviation of the data from the mean.
2. Range of a data set - The difference between the highest value and the lowest value in a numerical data set.
3. First quartile - The median in the upper half of the rank-ordered data.
4. Second quartile - The median value in the data set.
5. Third quartile - The median in the lower half of the rank-ordered data.
6. Interquartile range - he distance between the first and third quartiles of the data set.
What you should know about statistical measures?The statistical measures are often used to describe and analyze statistical variables. For instance, the range of a data set is a measure of the spread of values in a variable, while the quartiles and interquartile range provide information about the distribution of the variable. Mean average deviation is a measure of the variability of the variable around its mean value.
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If you were to use the substitution method to solve the following
system, choose the new equation after the expression equivalent to x
from the second equation is substituted into the first equation.
3x + 2y = -21
x-3y = 4 (6 points)
Answer:
Step-by-step explanation:
Making x the subject in the second equation gives:
x = 4+3y
substituting x = 4 +3y into the first one gives:
3(4 + 3y) + 2y = -21
12 + 9y +2y = -21
11y = -33
y = -3
Verify that the segments are parallel.
10. CD || AB
This means that the corresponding sides of the two triangles are in proportion, and therefore CD is parallel to AB, as required.
What is triangle?A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is often used in mathematics, science, engineering, and art. Triangles can be classified into different types based on the length of their sides and the size of their angles. Triangles are used in various applications, such as in the construction of buildings, bridges, and other structures, as well as in navigation and surveying. They are also important in various fields of mathematics, including trigonometry and geometry.
Here,
To use similarity theorems to show that CD is parallel to AB, we need to first establish that triangles AEB and CED are similar. If we can show that these triangles are similar, then we can use the corresponding angles theorem, which states that if two pairs of corresponding angles are congruent, then the lines containing the sides are parallel.
Let's compare the two triangles AEB and CED:
Angle AEB is congruent to angle CED (both are vertical angles).
Angle EAB is congruent to angle ECD (both are alternate interior angles formed by a transversal cutting parallel lines AB and CD).
Angle BAE is congruent to angle DCE (both are alternate interior angles formed by a transversal cutting parallel lines AB and CD).
Therefore, we have established that triangles AEB and CED are similar by the angle-angle-angle similarity theorem.
Now that we have shown that the triangles are similar, we can use the corresponding sides theorem, which states that the corresponding sides of similar triangles are in proportion, to find out if CD is parallel to AB.
The corresponding sides of AEB and CED are:
AE/CE = AB/CD
Substituting the given values, we have:
AC + CE / CE = AB / BD
4 + 12 / 12 = AB / (14/3)
16/12 = AB / (14/3)
AB = (16/12) x (14/3)
= 56/9
Now we can use the corresponding sides theorem to find the length of CD:
AE/CE = AB/CD
Substituting the values we have found, we get:
4/12 = (56/9)/CD
CD = (56/9) x (12/4)
= 14
Since we have found that AB = 56/9 and CD = 14, we can see that:
AB/CD = (56/9)/14
= 4/3
This means that the corresponding sides of the two triangles are in proportion, and therefore CD is parallel to AB, as required.
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What is the value of x?
Right triangle. Vertices are not labeled. The length of one side equals 18.15. The length of the second side equals 17.39. The length of the hypotenuse is unknown, and is labeled x.
Round your final answer to the nearest tenth.
Answer:
x=25.1
Step-by-step explanation:
by using Pythagorean theorem, [tex]a^{2} +b^{2}=c^{2}[/tex] where c is the hypotenuse
[tex]18.15^{2}[/tex]= 329.4225
[tex]17.39^{2}[/tex]= 302.4121
since those two side lengths are the legs, the sum of the numbers is the length of the hypotenuse squared
therefore, 631.8356 (the sum) = [tex]c^{2}[/tex]
by taking the square root of 631.8356, you will get approx 25.1 for the hypotenuse (aka x)
Plssss help it is asking to find the surface area of this triangular prism
The total surface area of the triangular prism is calculated to be equal to 608 square centimeters.
How to calculate for the total surface area of the triangular prismThe triangular prism can be observed to be a large rectangle and two identical triangles, so we shall calculate for the total surface area as follows:
area of one triangle = 1/2 × 8 cm × 12 cm
area of one triangle = 48 cm²
area of the two triangle faces = 2(48) = 96 cm²
area of the large rectangle face = (10 + 12 + 12) cm × 16 cm = 512 cm²
Total surface area of prism = 96 cm² + 512 cm² = 608 cm²
Therefore, the total surface area of the triangular prism is calculated to be equal to 608 square centimeters.
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Which graph shows the solution to the inequality Negative 3 x minus 7 less-than 20 Group of answer choices A number lines goes from negative 10 to positive 10. An open circle appears at positive 9. The number line is shaded from positive 9 through negative 10. A number line goes from negative 10 to positive 10. An open circle appears at positive 9. The number line is shaded from positive 9 through positive 10. A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10. A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through negative 10.
The solution is all values of x greater than -9.
What is the correct graph for the given inequality?The correct graph for the given inequality "Negative 3x - 7 < 20" is:
From negative 10 to positive 10, a number line runs. An open circle shows up at negative 9. From negative 9 to positive 10, the number line is shaded.
To chart the arrangement, we initially confine the variable by adding 7 to the two sides of the imbalance:
Negative 3x - 7 + 7 < 20 + 7
Negative 3x < 27
Next, we divide both sides by -3, remembering to flip the inequality sign since we're dividing by a negative number:
Negative 3x/-3 > 27/-3
x > -9
Therefore, the arrangement is all upsides of x more prominent than - 9. Since these are the values that satisfy the inequality, we graph this by drawing an open circle at -9 on the number line and shading all values to the right of -9.
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Plot points between and beyond each x-intercept and vertical asymptote. Find the value of the function at the given value of x.
f(x)= 2/ x^2+3x-10
the points we plotted are (-6, -1/2), (-4, 1/2), (0, -1/5), (3, 1/2), and (6, 1/5).
What is function?
a function is a relationship or expression involving one or more variables. It has a set of input and outputs.
To find the x-intercepts, we set the numerator of the function equal to zero:
[tex]2 / (x^2 + 3x - 10) = 0[/tex]
This is only true if the numerator is equal to zero, so:
2 = 0
This is not possible, so the function has no x-intercepts.
To find the vertical asymptotes, we look for values of x that make the denominator equal to zero:
[tex]x^2 + 3x - 10 = 0[/tex]
We can factor the quadratic as:
(x + 5)(x - 2) = 0
This means that the function has vertical asymptotes at x = -5 and x = 2.
Now, let's plot some points between and beyond each x-intercept and vertical asymptote:
When x = -6, f(x) = 2 / (-6)² + 3(-6) - 10 = -1/2
When x = -4, f(x) = 2 / (-4)² + 3(-4) - 10 = 1/2
When x = 0, f(x) = 2 / (0)² + 3(0) - 10 = -1/5
When x = 3, f(x) = 2 / (3)² + 3(3) - 10 = 1/2
When x = 4, f(x) = 2 / (4)² + 3(4) - 10 = -1/2
When x = 6, f(x) = 2 / (6)² + 3(6) - 10 = 1/5
Therefore, the points we plotted are (-6, -1/2), (-4, 1/2), (0, -1/5), (3, 1/2), and (6, 1/5).
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CAN SOMEONE PLEASE HELP ME WITH THIS :((
What is the value or arc PQ? Only enter numerical values.
The value of arc PQ is 110°
What is circumference of a circle?The circumference of a circle is the length of the 360 degree arc of that circle. Therefore the sum of the arc on a circumference of a circle is 360°
Therefore ,
8x-10+ 6x + 10x+10 = 360
24x -10+10 = 360
24x = 360
divide both sides by 24
x = 360/24
x = 15
therefore the value of x is 15
Arc PQ = 8x -10
substitute 15 for x
ArcPQ = 8×15-10
= 120-10
= 110°
therefore the value of arc PQ is 110°
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how do i write an inequality for this?
The inequality expression representing the area of the shaded region, indicating both the shaded area and the broken line is; y > 0
What is an inequality?An inequality is a mathematical statement consisting two expressions joined with inequality symbols, which includes; '<', '>', '≠', '≤', and '≥'.
The area of the shaded region is the part of the coordinate plane above the x-axis.
The region shaded can therefore be indicated by the area y > 0
The x-axis on the coordinate plane representing the boundary of the shaded region consists of broken line, which indicates that the line is not included in the shaded region.
The inequality representing the area of the shaded region is therefore;
y > 0
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PLEASE HELP, WILL MARK BRAINLY!!
3. Twice the difference of a number and three is the sum of that number and four.
4. Three times a number is two times the difference of that number and one.
Answer:
3. 2(x - 3) = x + 4
2x - 6 = x + 4
x = 10
4. 3x = 2(x - 1)
3x = 2x - 2
x = -2
The cost, in dollars, of a single-story home can be approximated using the formula
C = klw, where is the approximate length of the home and w is the approximate
width of the home. Find the units for the coefficient k.
The unit for the coefficient k would be dollars per unit of length squared.
Units of a variableTo find the units for the coefficient k in the formula C = klw, we need to analyze the units of each variable.
C represents the cost of the home, which is measured in dollars.
l represents the length of the home, which is measured in some units of length, such as feet or meters.
w represents the width of the home, which is also measured in some units of length, such as feet or meters.
Therefore, we can determine the units for k by analyzing how the units for C, l, and w combine in the formula C = klw.
Starting with the left-hand side of the equation, we know that C represents dollars.
On the right-hand side of the equation, we have k times l times w. To determine the units of k, we need to figure out what units would make the entire right-hand side of the equation equal to dollars.
Since we are multiplying three quantities (k, l, and w), the units of k must cancel out the units of length in l and w in order to leave us with units of dollars.
This means that the units of k must be dollars per unit of length squared. We can write this as:
k = $/length^2
So, the units for the coefficient k in the formula C = klw are dollars per unit of length squared.
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