To find the distance from a point P to a plane defined by three points Q, R, and S, we can use the following formula:
distance = |(A * x + B * y + C * z + D) / √(A^2 + B^2 + C^2)|
where (A, B, C) are the coefficients of the normal vector of the plane, (x, y, z) are the coordinates of the point P, and D is the constant in the equation of the plane.
To find the coefficients of the normal vector, we can use the cross product of two vectors lying in the plane, say, QR and RS.
Let's first find the vectors QR and RS:
QR = (5 - 0, 0 - (-1), 3 - 7) = (5, 1, -4)
RS = (7 - 0, 5 - (-1), 0 - 7) = (7, 6, -7)
Next, we find the cross product of QR and RS:
cross product of QR and RS = (B, C, A) = (7, -30, 15)
So, the normal vector of the plane is (15, -30, 7).
Now we substitute the values for the coefficients and the coordinates of the point P into the formula:
distance = |(15 * 3 + (-30) * 1 + 7 * 7 + D) / √(15^2 + (-30)^2 + 7^2)|
To find the value of D, we can use any of the three points on the plane and substitute their coordinates into the equation of the plane in the form Ax + By + Cz + D = 0.
Let's use the point Q:
15 * 5 + (-30) * 0 + 7 * 3 + D = 0
Expanding and solving for D, we get:
75 + 21 + D = 0
D = -96
Finally, substituting the values back into the formula for distance, we get:
distance = |(15 * 3 + (-30) * 1 + 7 * 7 + -96) / √(15^2 + (-30)^2 + 7^2)|
distance = |(-24 + -30 + 49 - 96) / √(15^2 + (-30)^2 + 7^2)|
distance = |(-101) / √(15^2 + (-30)^2 + 7^2)|
distance = |(-101) / √(15^2 + (-30)^2 + 7^2)|
distance = |(-101) / √(225 + 900 + 49)|
distance = |(-101) / √1274|
distance = |(-101) / 35.6|
distance = 2.85
So, the distance between the point P and the plane is approximately 2.85.
A group consisting of 23 aggressive zombies quadruples in size every hour. Which equation matches the number of zombies after 2 hours
Answer:
The equation that matches the number of zombies after 2 hours would be:
23 × 4^2 = 23 × 16 = 368
So after 2 hours, there would be 368 aggressive zombies.
How many pounds are in 1
1⁄2 pounds and 8 ounces?
There are
pounds in 1 pounds and 8 ounces.
The solution is
n ID:
The number of pounds in [tex]1\frac{1}{2}[/tex] pounds and and 8 ounces is 2 pounds.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that 1 pound = 16 ounces.
As there are [tex]1\frac{1}{2}[/tex] pounds=1.5×16= 24 ounces.
The total number of ounces in [tex]1\frac{1}{2}[/tex] pounds and 8 ounces is
24+8
32 ounces.
Now let us convert Ounces to pounds.
we divide the number of ounces by 16.
Therefore, 32 ounces is equal to 32/16 = 2 pounds.
Hence, 2 pounds will be there in [tex]1\frac{1}{2}[/tex] pounds and 8 ounces
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In ΔGHI, i = 800 cm, m m∠G=26° and m m∠H=122°. Find the length of h, to the nearest 10th of a centimeter.
Answer:
For the nearest 10th of a centimeter, the value of h is 460 cm
Step-by-step explanation:
To find length of h we can use Law of Sines . The Law states that for a triangle with sides a, b, and c and angles A, B, and C opposite to those sides, the following equation holds:
a/sin A = b/sin B = c/sin C
In ΔGHI, let h be the length of the side opposite angle H, and let i be the length of the side opposite angle I.
Now:
h/sin 122° = i/sin 26°
We can find h by cross multiplying:
h = i * sin 122° / sin 26°
=459.9
Here,
h = 459.9 cm
By taking approximation we get 460 cm
Answer:
This answer is actually 1280.3
Step-by-step explanation:
Suppose that 22 inches of wire costs 66 cents. At the same rate, how much (in cents) will 49 inches of wire cost?
Answer: 147 cents
Step-by-step explanation:
Unit rate is what we need here: i.e., how much does 1 inch of wire cost?
22in --> 66cents
1 in --> 66/22 = 3
3 cents per inch!
so 49 inches will cost 49 x 3 = 147 cents
Consider the graph of the function f(x)=log4(x-2)+2. What are the domain and the range of function f?
For the function f(x) = log4(x - 2) + 2, the domain is (2,∞) and range is (-∞,∞).
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The logarithmic function f(x) = log4(x - 2) + 2 is defined only for x-2 > 0, or equivalently, x > 2.
So, the domain of the function is all real numbers greater than 2, or -
Domain: x > 2
Now let's consider the range of the function.
The logarithmic function takes positive values for positive inputs, and it approaches negative infinity as x approaches zero from the right.
Since f(x) = log4(x-2) + 2, the function takes values greater than 2 when x is greater than 4, and it approaches 2 as x approaches 2 from the right.
So, the range of the function is -
Range: -∞ > f(x) > ∞
Therefore, the function has range and domain as (-∞,∞) and (2,∞) respectively.
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Cone B is the image of cone A after dilation by a scale factor of 1/4.
If the volume of cone B is 1 m³, find the volume of cone A, the preimage.
The volume of the Cone A will be 4m³.
What is a cone?
A cone is a shape constructed by connecting a common point, known as the apex or vertex, to all the points of a circular base using a collection of line segments (which does not contain the apex). The height of the cone is the distance from the vertex to the base. The radius of the circular base has been measured. The slant height is the length of the cone from the apex to any point on the perimeter of the base. Based on these values, formulae for the cone's surface area and volume have been developed. The cone in the illustration is characterised by its height, radius of base, and slant height.
Volume of cone=πr²h where r=radius of base and h=height of cone
Curved surface area=πrL , where L=slant height
Now,
As given Cone B is the image of cone A after dilation by a scale factor of 1/4. If the volume of cone B is 1 m³
After dilation volume also decreases/increases with respect to scale factor of dilation. Here scale factor is 1/4
and Then volume of A=1*4
=4 m³
hence,
The volume of the Cone A will be 4m³.
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Answer: it is actually 64m^3
Step-by-step explanation:
i did it and this was the right answer
Y = -6x + 2
Y = -6x - 8
Answer:
Flase, no real numbers (2+-8)
Step-by-step explanation:
First, you conjoined the equations (-6x+2=-6x-8). Then you conjoined the variables first, (-6x+6x=0). Now you have 2=-8, which is not true.
tell how the communative and associative properties of adddition can help you evsaluate the expression using mental math? 8+(-8-5)
Using commutative and associative properties of addition, the solution for given expression is -5.
What is commutative and associative property?
The associative and commutative characteristics are universal principles that apply to addition and multiplication. The associative property states that rearranging the numbers will get the same result, while the commutative property states that rearranging the numbers will yield the same result.
These properties tell that one can add in any order, the result will always be the same.
We are given an expression as 8+(-8-5).
So, in this instead of adding from left to right, we can see that the 8 + (-8) will be zero and only -5 will be left as an answer.
Hence, the solution for given expression is -5.
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cos(y) = sin(0)
what is the value of 0?
EASY POINTS!
Answer from the screenshot :)
Vertex A will be located at (-1, 0) after a rotation of -90°
Vertex B will be located at (-5, 3) after a rotation of 90°
Vertex C will be located at (6, -7) after a -180° rotation
Vertex D will be located at (1, -4) after a 270° rotation
How to find the new locations?The transformation rule for rotation of -90°
(x, y) → (y, -x)
A (0, -1) → (-1, 0)
The transformation rule for rotation of 90°
(x, y) → (-y, x)
B (3, 5) → (-5, 3)
The transformation rule for rotation for -180°
(x, y) → (-x,-y)
C (-6, 7) → (6, -7)
The transformation rule for rotation for 270° rotation
(x, y) → (-y, x)
D (-4, -1) → (1, -4)
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PLS help fast this is the last day for my test solve the system of linear equations. check your solution. 3y+4y=-10 y=-3/4x - 5/2
This equation has infinitely many solutions.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Here, we have
Given: 3x+4y = -10...(1),
y = -3/4x - 5/2....(2)
We solve this linear equation and we get
We multiply equation (2) by 4 and we get
4y + 3x = -5(2)
4y + 3x = -10
Hence, this equation has infinitely many solutions.
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Find the average rate of change
Please helppppp
Step-by-step explanation:
please review the attachment. That's the answer.
Painted Pots lets customers choose and paint their own potter
y. The store has teapots in multiple sizes. Rebecca chose to paint the largest teapot offered, which cost $18. She also painted 4 small teacups to go with her teapot. Rebecca spent a total of $42 on pottery.
Which equation can you use to find c, the cost of each teacup?
What was the cost of each teacup
The value of the equation is y = 4c + 18 , where c is the cost of each teacup and c = $ 6
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The total cost Rebecca spend on teacups = $ 42
The cost of the large teapot = $ 18
The cost of small teacups be = c
The number of small teacups = 4
So , the equation will be
Total cost Rebecca spend on teacups = cost of the large teapot + ( number of small teacups x cost of small teacups )
Substituting the values in the equation , we get
42 = 18 + 4c
y = 4c + 18 be equation (1) , where y is the total cost
On simplifying the equation , we get
Subtracting 18 on both sides of the equation , we get
4c = 24
Divide by 4 on both sides of the equation , we get
c = $ 6
Therefore , the cost of each teacup is $ 6
Hence , the equation is y = 4c + 18
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when will my dad come back? it has been approx 6 years
Answer:
he had to go to china for the milk and while he was there he got kidnapped so it might be a while
sorry bro
Step-by-step explanation:
Answer:
Step-by-step:
he is just trying to find the best milk he can don't even worry about it just become rich he's sure to come back then-
Determine whether the statement is true or false. 1. A census is a count of part of a population.. O True O False
The statement regarding the census in this problem is classified as a True statement.
What are the concepts of population and sample?Population: Collection or set of individuals or objects or events whose properties will be studied.
Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.
A Census is when a group of the population is chosen, that is, a sample is chosen, hence the statement for this problem is true.
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What is the solution to the system of equations?
{2x−3y=−5
{3x+y=−2
The solution to the system of equations is x = -1 and y = 1.
What is system of equations?A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."
The system of equation is given as:
2x - 3y = -5 .........(1)
3x + y = -2 ........(2)
Equation 2 can be written as:
y = -2 - 3x
Substituting the value of y in equation 1 we have:
2x - 3(-2 - 3x) = -5
2x + 6 + 9x = -5
11x + 6 = -5
11x = -5 -6
11x = -11
x = -1
Substituting the value of x in equation 2 we have:
3x + y = -2
3(-1) + y = -2
-3 + y = -2
y = -2 + 3
y = 1
Hence, the solution to the system of equations is x = -1 and y = 1.
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Determine the value of each. Round all answers to the nearest hundredth
AC =
a=
0=
The values for the length AC and the angles of the right-angled triangle ABC are AC = 12.37, α = 75.96 , and θ = 14.04 using the trigonometric ratios of tangent.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering the right-angled triangle ABC, we shall calculate for the angle B and side lengths a and b as follows:
AC² = 3² + 12² {Pythagoras rule}
AC = √(9 +144)
AC = √153
AC = 12.3693
tanα = 12/3 {opposite/adjacent}
α = tan⁻¹(4) {cross multiplication}
α = 75.9638
tanθ = 3/12 {opposite/adjacent}
θ = tan⁻¹(1/4){cross multiplication}
θ = 75.9638
Therefore, the values for the length AC and the angles of the right-angled triangle ABC are AC = 12.37, α = 75.96 , and θ = 14.04 using the trigonometric ratios of tangent.
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How many numbers of the form x15y are divisible by 15
Shermanos changes $15 for a supreme pizza how much will you pay for 2 supreme pizzas including 8.875% tax?
The sales tax rate is 4.5%. How much sales tax will you pay on a $125 purchase?
Work Shown:
4.5% of 125 = 0.045*125 = 5.625
That rounds to 5.63
Answer:
5.625
Step-by-step explanation:
A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.08.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 22-year period.
The probability that there are fewer than 2 tornadoes in a 22-year period is, 0.214
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
Since the probability of a tornado in any given year is 0.08,
the probability of no tornado in any given year is;:
= 1 - 0.08
= 0.92.
Let X be the number of tornadoes in a 22-year period.
X follows a binomial distribution with n = 22 and p = 0.08.
We want to calculate the probability that there are fewer than 2 tornadoes in a 22-year period.
This can be written as:
P(X < 2) = P(X = 0) + P(X = 1)
Using the binomial probability formula, we can calculate:
P(X = 0) = (22 choose 0) x (0.08)⁰ x (0.92)²² ≈ 0.038
P(X = 1) = (22 choose 1) x (0.08)¹ x (0.92)²¹ ≈ 0.176
Therefore,
P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.214
So the probability that there are fewer than 2 tornadoes in a 22-year period is approximately 0.214 or 21.4%.
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Find the lengths of the sides of a triangle if two of the sides are equal, the third side is 1 1/3 cm longer than the others, and its perimeter is 5 2/5 cm. The two equal sides of the triangle are (blank)cm. The third side is (blank) cm.
Answer:
Step-by-step explanation:
Here's a step by step solution with more details:
Let's call the length of the two equal sides of the triangle as x.
The third side, which is 1 1/3 cm longer, will have a length of x + 1 1/3 cm.
The perimeter of the triangle is 5 2/5 cm, so we can write an equation using the lengths of the sides:
x + x + (x + 1 1/3) = 5 2/5
Simplifying the equation:
2x + 1 1/3 = 5 2/5
Subtracting 1 1/3 from both sides:
2x = 4 1/5
Dividing both sides by 2:
x = 2 2/5
So the two equal sides of the triangle are 2 2/5 cm and the third side is 2 2/5 + 1 1/3 = 3 7/15 cm.
Answer:
One equal side = [tex]1\frac{16}{45}[/tex]cm and third side is [tex]2\frac{31}{45}[/tex]cm
Step-by-step explanation:
This is describing an isosceles triangle
1[tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]
5[tex]\frac{2}{5}[/tex] = [tex]\frac{27}{5}[/tex]
Let
x = one of the two equal sides of the triangle
∴ Third side of triangle = [tex]\frac{4}{3} + x[/tex]
Perimeter of a triangle = Sum of all three sides:
[tex]\frac{27}{5}[/tex] [tex]= x + x + (\frac{4}{3} + x)[/tex]
Expand the parenthesis using the Distributive Law and bring all the like terms together:
[tex]=\frac{27}{5} = 2x + \frac{4}{3} + x[/tex]
[tex]= \frac{27}{5} = 3x + \frac{4}{3}[/tex]
[tex]= \frac{27}{5} -\frac{4}{3} = 3x[/tex]
The two denominators of the two fractions have to be manipulated to be made the same:
[tex]= (\frac{3}{3})(\frac{27}{5}) - (\frac{5}{5})(\frac{4}{3}) = 3x[/tex]
[tex]= \frac{81}{15} - \frac{20}{15} = 3x[/tex]
[tex]= \frac{81 - 20}{15} = 3x[/tex]
[tex]= \frac{61}{15} = 3x[/tex]
Cross-multiplication is added:
[tex]= (61)(1) = (15)(3x)[/tex]
[tex]= 61 = 45x[/tex]
Isolate x and make it the subject of the formula:
x = [tex]\frac{61}{45}[/tex]
x = One of the two equal sides = [tex]1\frac{16}{45}[/tex]cm
∴Third side:
= [tex]\frac{61}{45} + \frac{4}{3}[/tex]
= [tex]\frac{61}{45} + (\frac{15}{15})(\frac{4}{3})[/tex]
= [tex]\frac{61}{45} + \frac{60}{45}[/tex]
= [tex]\frac{61 + 60}{45}[/tex]
= [tex]\frac{121}{45}[/tex]
= [tex]2\frac{31}{45}[/tex]cm
Use the information provided to write the equation of the circle. Center: (-8,11) Radius:2
Use the information provided to write the equation of the circle Center (-8, 11) Radius is 2 is equal to (x + 8)² + (y - 11)² = 4.
What is equation of the circle?
To write the equation of a circle, we need to know its center and radius. If we have the center at point (a, b) and the radius is r, the equation of the circle is:
(x - a)² + (y - b)² = r²
If you have the specific values of a, b, and r, you can plug them into this equation to get the equation of the circle.
The general equation of a circle with center (h, k) and radius r is:
(x - h)² + (y - k)²= r²
Using the given information, we can substitute the values into the equation:
(x - (-8))² + (y - 11)² = 2²
Simplifying, we get:
(x + 8)² + (y - 11)² = 4
Therefore, the equation of the circle with center (-8, 11) and radius 2 is:
(x + 8)² + (y - 11)² = 4
This equation represents all the points that are 2 units away from the center (-8, 11).
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When an accountant records_ on hand, they are noting a company's ____
A. human resources; total liquid assets
B. cash; total of amount dollars, money orders, checks, and other forms of
money
C. supplies; materials that need to be purchased soon
D. inventory; number of employees on payroll
Answer: Choice B
Explanation: The phrase "cash on hand" means the amount of money the company has. It could be literal cash as the phrase directly implies. Or it could be near equivalents to cash. A near equivalent is something you can convert to cash fairly easily, meaning a bank would readily accept it. The only drawback is that it's not actual cash so its not as liquid as cash itself. Also, you would need to take into account the delay time between deposit and when the bank balance is updated.
5x-4>12 or 12x+5<-4
The solution is the union of the solutions from both inequalities. That is, x is either greater than 3.2 or less than -0.75. So, the final solution is: -0.75 < x < 3.2.
What is inequalities?
An inequality is a mathematical statement that represents a comparison between two values, and indicates the relationship of one value being greater than, less than, or equal to the other. It is usually represented using symbols such as ">" (greater than), "<" (less than), ">=" (greater than or equal to), "<=" (less than or equal to), and "≠" (not equal to). For example, the inequality "2x + 3 > 7" expresses that the value of the expression "2x + 3" is greater than 7 for some values of x.
Inequalities are used to describe a range of values that satisfy a certain condition. The solution to an inequality is a set of values that make the inequality true.
To solve the inequality "5x - 4 > 12 or 12x + 5 < -4", we can start by solving each inequality separately and then combining the solutions to find the final solution.
Solving the first inequality: 5x - 4 > 12Adding 4 to both sides, we get 5x > 16
Dividing both sides by 5, we get x > 3.2
So, the solution to this inequality is x > 3.2
Solving the second inequality: 12x + 5 < -4Subtracting 5 from both sides, we get 12x < -9
Dividing both sides by 12, we get x < -0.75
So, the solution to this inequality is x < -0.75
Final solution: Combining the solutions from both inequalities:
Since "or" is used in the inequality, the solution is the union of the solutions from both inequalities. That is, x is either greater than 3.2 or less than -0.75. So, the final solution is: -0.75 < x < 3.2.
So the solution to the inequality "5x - 4 > 12 or 12x + 5 < -4" is -0.75 < x < 3.2.
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There are 20 circles and 8 squares. What is the simplest ratio of squares to circles?.
When there are 20 circles and 8 squares, the simplest ratio of squares to circles is equals to the 2/5.
We have some numbers of circles and squares. The number of circles = 20
The number of squares = 8
Ratio is number which expressed that how many times one number is contains other one. The symolically represention of ratio is "/" or " : ". If a and b are two numbers then "a/b or a : b " represents 'a' ratio 'b'. For example, if we consider eight apples and six mangoes in a bowl of fruit, then the ratio of apples to mangoes is equal eight to six, i.e., 8 : 6 or 4:3. Now, we have to determine the ratio of squares to circles. Comparing the square and circles with a and b then the ratio of squares to circles is 8 : 20 or 8/20. But we want simplfy form of ratio so,
simplfy it by dividing the upper and lower parts of ratio with the common factor of 8, 20 that is 4.
=>( 8/4)/(20/4)
=> 2/5
Hence, required ratio is 2/5.
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simplify 3-2(b-2)=2-7b solve for b
The required value of the given expression which satisfy it is b = 3/5.
What is Simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
According to question:We have,
3 - 2(b - 2) = 2 - 7b
= 3 - 2b - 4 = 2 - 7b
= 5b = 3
= b = 3/5
Thus, required value of the b for the given function is b = 3/5.
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If 3250 was increased by 46%, the result would be
3
Select the correct answer.
Exponential function fis represented by the table.
X -1 0 1 2 3 4
f(x) 80 26 8 2 0 -2/3
Function g is an exponential function passing through the points (0,7) and (3,0).
Which statement correctly compares the two functions on the interval (0, 3)?
A) Both functions are positive and increasing on the interval.
B) Both functions are positive and decreasing on the interval.
C) Both functions are positive on the interval, but one function is increasing while the other is decreasing.
D) One function is positive on the interval, while the other is negative.
Option A: Both functions are positive and decreasing on the interval.
How to determine the function?The table shows that f(x) decreases when x increases in the interval (0,7) and (0, 3)
All the values of f(x) are positive in the interval (0,3).
For the exponential function that passes through the points (0, 27) and (3, 0), we also see that f(x) is decreasing when x increases: when x goes from 0 to 3, f(x) goes from 27 to 0.
Also all the values of f(x) are positive in the interval.
Then, both functions are positive and decreasing in the interval.
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The sum of one and six times a number is 151. What is the number?
This is a word problem and the value of the unknown number is equal to 25
Word problems in mathematicsWord problems are mathematical problems which involves the use of ordinary words, instead of mathematical symbols.
Let us represent the unknown number with the letter x so that we derive the equation;
1 + 6x = 151
we subtract 1 from both sides of the equation
1 - 1 + 6x = 151 - 1
6x = 150
divide through by the coefficient of x which is 6
6x/6 = 150/6
x = 25
Therefore, the value of the unknown number for the word problem is equal to 25
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