The postulate specifies the minimum number of points in space is, Postulate 1b: Space contains at least four points not all on one plane.
A postulate is an assumption or a claim that is made without providing any supporting evidence. The fundamental claims that are used to support other claims known as theorems are known as postulates. Once a theorem is established, it can be applied to the establishment of other theorems.
By examining each postulate, we may effectively respond to this query.
Postulate 1a: establishes that if G and H are distinct points on plane R, then R contains a third point rather than GH.
Postulate (1b): establishes the bare minimum within a space.
Postulate 1: This describes a line segment with two points, say A and B.
Postulate 2: It asserts that two points determine a line.
Postulate 3: This one explains why, for example, if one leg is shorter than the other three, a table with four legs would wobble, but a table with three legs would not wobble.
Postulate 4: When points A and B are in Q, it is confirmed that AB is in plane Q.
Postulate 5: It concerns two planes.
According to the data presented above, the appropriate response to our query is:
Postulate 1b: Space contains at least four points not all on one plane.
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The calculation for x=0x=0 corresponds to the
point where the graph crosses the______-axis.
This is the point (______)
The calculation for x=0 corresponds to the point where the graph crosses the y-axis . This is the point (0,y) .
In the question ,
it is given that x=0 ,
When x=0 in a point (x,y) means , that point lies on the y -axis , and it is called as the y intercept .
Y intercept is defined as the point where the graph of a line crosses the y-axis .
the point on the y-axis will be (0,y) ,
So , the graph will cross the y-axis when x=0 , and that point will be (0,y).
and the value of y will be called as the y intercept of the graph .
Therefore , the calculation for y=0 corresponds to the point where the graph crosses the y-axis . This is the point (0,y) .
The given question is incomplete , the complete question is
The calculation for x=0 corresponds to the point where the graph crosses the________-axis. This is the point (______) .
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Select all the correct answers.
Which functions have a range of {ye R |-∞0 < y < ∞0}?
F(x)=x^2+7x-9
F(x)=-4x+11
F(x)=2/3X-8
F(x)=2^x+3
F(x)=-(x+1)^2-4
Answer: [tex]f(x)=-4x+11[/tex] and [tex]f(x)=\frac{2}{3}x-8[/tex]
Step-by-step explanation:
All linear functions with unrestricted domains have a range of all real numbers.
(a) For each pool, write an expression for the amount of water in the
gool after x minutes
Two pools are being filled with water. To start, the first pool had 817 liters of water and the second pool was empty. Water is being added to the first pool at a
rate of 19 liters per minute water is being added to the second pool at a rate of 38 liters per minute.
Leta be the number of minutes water has been added.
Amount of water in the first pool (In liters) =
Amount of water in the second pool (in liters) =
(b) Write an equation to show when the two pools would have the
same amount of water
(a) Amount of water in the first pool (In liters) = (817 + 19x) liters
Amount of water in the second pool (in liters) = 39x liters
(b) An equation to show when the two pools would have the same amount of water is 817 + 19x = 38x.
Given:
For the First Pool :
Initial amount of water in the Pool = 817 liters
Water is being added to the first pool at a rate of 19 liters per minute.
Amount of water added after x minutes = 19x
So, Total amount of water after x minutes = (817 + 19x) liters
For the Second Pool:
It was empty initially.
Water is being added to the second pool at a rate of 38 liters per minute.
Amount of water added after x minutes = 38x
So, Total amount of water after x minutes = 38x liters
Now to determine an equation to show when the two pools would have the same amount of water.
817 + 19x = 38x
38x - 19x = 817
19x = 817
x = 817/19
x = 43 minutes
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Find the perimeter of the following figure with the indicated dimensions.
Givens.
• The diameter of the semi-circle is 9.25 yd.
,• The other two sides of the triangle are 6.83 yd and 8.66 yd long.
First, find the perimeter of the semi-circle using the circumference formula.
[tex]\begin{gathered} C_{\text{semi}}=\frac{\pi\cdot d}{2}=\frac{\pi\cdot9.25yd}{2} \\ C_{\text{semi}}\approx14.52yd \end{gathered}[/tex]Second, add the two sides of the triangle to the circumference of the semi-circle.
[tex]\begin{gathered} P=14.52yd+6.83yd+8.66yd \\ P=30yd \end{gathered}[/tex]Therefore, the perimeter of the figure is 30 yards.Fine the unknown quantity in the following percent problem using the formal RxB=A. Round your answer to two decimal places, if necessary.
50% of what number is 60?
Answer:
120
Step-by-step explanation:
You want to find a number such that 50% of it is 60, using the formula R×B = A.
Percent relationAn amount is found by multiplying the rate by the base. That is described by the formula ...
R × B = A
Here, we're given the amount and the rate, and we want to find the base. We can fill in the given numbers and solve for B.
50% × B = 60
B = 60/0.50 . . . . . . divide by the rate
B = 120 . . . . . . . simplify
50% of 120 is 60.
Select the three equations that pass through the points (–4, –16) and (5, 2):
y + 4 = 2(x – 16)
y – 2 = 2(x – 5)
y = 2x – 8
y + 16 = 2(x + 4)
The equation of line passing through (-4, -16) and (5, 2) are y = 2x – 8, y - 2 = 2(x - 5) and y + 16 = 2(x + 4)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
The standard form for linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
The equation of line passing through (5, 2) and (-4, -16) is:
y - 2 = [(-16-2)/(-4-5)](x - 5)
y - 2 = 2(x - 5)
y = 2x - 8
y + 16 = 2(x + 4)
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Clare follow the same workout cycle each time she goes to the gym. First, she runs for 1/3 of an hour. Then, she lifts weights for 1/6 of an hour. If Clare has 1 1/2 hours to spend at the gym, how many times can she go through her workout cycle?
Clare can go 3 times for her workout cycle
How to calculate the number of work out cycle ?Clare follows the same workout cycle each time she goes to the gym
She spends 1 1/2 hour at the gym
First, she runs 1/3 of an hour
After that, she lifts 1/3 of an hour
The first step is to convert to minutes
60 mins = 1 hour
1/2 × 60
= 30
30 + 60
= 90 mins
convert 1/3 to mins
1/3 × 60
= 20 mins
convert 1/6 to mins
1/6 × 60
= 10 mins
Total mins= 20 + 10
= 30 mins
The number of workout cycles can be calculated as follows
= 90/30
= 3
Hence Clare can go 3 times for her workout cycle
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Find an equation for the perpendicular bisector of the line segment whose endpoints are ( 8 , − 1 ) (8,−1) and ( 4 , − 9 ) (4,−9).
The equation of the perpendicular bisector of the line segment is y = - (1 / 2) · x - 2.
What is the equation of the perpendicular bisector of a line segment?
In this problem we find a line segment whose endpoints are known and we need to determine the equation of the line perpendicular such that the segment is partitioned into two segments of equal length. Now we present the procedure. First, determine the coordinates of the midpoint:
M(x, y) = 0.5 · (8, - 1) + 0.5 · (4, - 9)
M(x, y) = (6, - 5)
Second, determine the slope of the line segment:
m = [- 9 - (- 1)] / (4 - 8)
m = (- 8) / (- 4)
m = 2
Third, calculate the slope of the bisector:
m' = - 1 / m
m' = - 1 / 2
Fourth, determine the intercept of the bisector:
b = y - m' · x
b = - 5 - (- 1 / 2) · 6
b = - 5 + 3
b = - 2
The equation of the perpendicular bisector of the line segment is y = - (1 / 2) · x - 2.
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Translate the sentence into an equation.
Four more than the quotient of a number and 8 equals 9.
Use the variable x for the unknown number
Answer:
(x / 8) + 4 = 9
Step-by-step explanation:
follow the instructions of the question and then write the values
−[4.2−3(2.1)](−0.2)2+1
please help!!!!!!!!!
Answer:
I believe the first one
Step-by-step explanation:
Brainliest pls?
if f(x)=-5, what is x?
Answer:
x = -5/f
Step-by-step explanation:
a) Divide both sides by f.
fx/f = -5/f
x = -5/f
Answer:
the answer is -5/f
Step-by-step explanation:
f(x)=fx
fx=-5
Divide both sides by f
fx/f =-5/f
x=-5/f
HOPE IT HELPED
What is the translation of y=x^2 shifted left 3 units
Original equation: y = x²
Tranformation rule:
horizontal translation c units leftt = f(x + c); so:
Modified equation: y = (x + 3)²
I need help with functions
The defition of a function is a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set.
So, Your ques
Identify The Function Family Sketched Below
The function family sketched is exponential function.
From the graph, we can find certain values of the function for certain x-values.
When x = 0, the function has value 1.
When x = 2, the function has value 4
When x = 3, the function has value 8.
When x = 4, the function has value 16
From this we can identify the function as the exponential function, f(x) = eˣ
because e⁰ = 1. i.e., exponential function has value 1 when x = 0 which satisfy the sketch of the function given.
Also the other options given as piecewise function, linear function and quadratic function.
A piecewise function will not have a continuous sketch, but here the sketch of the function is continuous. So it cannot be a piecewise function. A linear function will have the sketch as a straight line, but here it is not. So it is not a linear function. The function values given in the sketch does not satisfy the quadratic function also.
So the only option is the sketch is of the exponential function.
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fill in the missing number to form equivalent fraction
20/?=?/6=10/?=?/900=8/12
Missing numbers are 30, 4, 30 and 300.
What is equivalent fraction?Equivalent fractions are those that, despite their visual differences, reflect the same value. You will have consumed half of a cake, for instance, if you have one, divide it into two equal pieces, and then eat one of the pieces. Two or more fractions that are equal despite having dissimilar numerators and denominators are said to be equivalent. Every time, the fraction is written as "one half" in its simplest form.
Given Data
20/?=?/6=10/?=?/900=8/12
Fraction which is given
[tex]\frac{8}{12}[/tex]
= [tex]\frac{2}{3}[/tex]
As they are equivalent fraction, so their simplest form will be equal
Let the missing numbers be x
1) [tex]\frac{20}{x}[/tex]
= [tex]\frac{20}{30}[/tex]
2) [tex]\frac{x}{6}[/tex]
= [tex]\frac{4}{6}[/tex]
3) [tex]\frac{10}{x}[/tex]
= [tex]\frac{10}{30}[/tex]
4) [tex]\frac{x}{900}[/tex]
= [tex]\frac{600}{900}[/tex]
Missing numbers are 30, 4, 30 and 300.
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need help asap!!
Q: The length of a pipe in a panpipe L, in ft, is inversely proportional to its pitch p, in hertz. The inverse variation is modeled by the equation p = 497/L. Find the length of pipe required to produce a pitch of 220 Hz.
Answer:
hajajJzjzjzjzjzjzkzkzkzkzksk
eatmyass
The length of pipe required to produce a pitch of 220 Hz is 2.26 feet.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
The length of a pipe in a panpipe L, in ft, is inversely proportional to its pitch p, in hertz.
The inverse variation is modeled by the equation p = 497/L.
The length of pipe required to produce a pitch of 220 Hz,
= 497/220
= 2.26 feet
Therefore, the length is 2.26 feet.
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A funky 6-sided die with faces labeled 1, 2, 3, 4, 5, and 6 has a chance of 1/12 landing on each face and a 1/24 chance of landing on each edge. When Kira rolls the die, if it lands on a face, she records the number on top. If she lands on an edge, she records the sum of the two numbers on top. If Kira rolled the die infinitely many times and averaged the result, what is the expected value of the number recorded?
From the statement, we know that there are two possible scenarios:
A) Kira rolls the die and gets a face with a 1, 2, 3, 4, 5 or 6.
• The probability of this event is P(A) = 1/12.
,• Kira will write the number of the face in this case.
B) Kira rolls the die and gets an edge.
• The probability for this event is 1/24.
,• Kira will write the sum of the numbers that share the top edge.
,• There are multiple values for the result of the sum.
We must take into account that:
• 1 and 5 are on opposite faces,
,• 2 and 3 are on opposite faces,
,• 4 and 6 are on opposite faces.
The possible values of the sum and the forms to get it are:
0. 3, = 1 + 2 → P(B'_1) = 1/24
,1. 4, = 1 + 3 → P(B'_2) = 1/24
,2. 5, = 1 + 4 → P(B'_3) = 2/24
,3. 6, = 2 + 4 → P(B'_4) = 2/24
,4. 7, = 1 + 6 = 2 + 5 = 3 + 4 → P(B'_5) = 3/24
,5. 8, = 2 + 6 = 3 + 5 → P(B'_6) = 2/24
,6. 9, = 3 + 6 = 4 + 5 → P(B'_7) = 2/24
,7. 11, = 5 + 6 → P(B'_9) = 1/24
We have 8 possible results for the sum.
---------------------
Now, we want to know the value of the expected value of the numbers recorded by Kira.
By definition, the expected value is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values.
The expected value of the number recorded by Kira will be:
[tex]E=\sum_{i\mathop{=}1}^6A_i\cdot P(A_i)+\sum_{i\mathop{=}1}^8B_i\cdot P(B_i)[/tex]Where:
• A_i represents the result of event A_i and P(A_i) its probability,
,• B_i represents the result of event B_i and P(B_i) its probability.
Using the data from above, we compute each of the sums.
A) For the first sum, we take into account that each event A_i has the same probability:
[tex]\sum_{i\mathop{=}1}^6A_i\cdot P(A_i)=(1+2+3+4+5+6)\cdot\frac{1}{12}=\frac{7}{4}=1.75.[/tex]B) For the second sum, we use each of the values of the sum and the probabilities of each sum:
[tex]\begin{gathered} \sum_{i\mathop{=}1}^8B_i\cdot P(B_i) \\ =3\cdot\frac{1}{24}+4\cdot\frac{1}{24}+5\cdot\frac{1}{24}+6\cdot\frac{1}{24}+7\cdot\frac{3}{24}+8\cdot\frac{2}{24}+9\cdot\frac{2}{24}+11\cdot\frac{2}{24}=\frac{95}{24}. \\ \end{gathered}[/tex]Summing the results of each sum, we get the following result for the expected value:
[tex]E=\frac{7}{4}+\frac{95}{24}=\frac{42}{24}+\frac{95}{24}=\frac{137}{24}\cong5.71.[/tex]AnswerThe expected value for the number recorded is 137/24 or approximately 5.71.
1/5 (x-2)= 1/10 (x +6)
Answer: The answer is 10
Step-by-step explanation:
Distribute 1(x-2)/5 = 1(x+6)/10
x-2/5 = x+6/10
Multiply by 10 on each side
2(x - 2) = x + 6
Distribute
2x - 4 = x + 6
Add 4 on each side
2x= x + 10
Subtract x
x = 10
Answer: x=10
Step-by-step explanation:
1/5(x-2)=1/10(x+6)
Distribute and multiply first
(1/5*x) -(1/5*2)=(1/10*x) +(1/10*6)
1/5x-2/5=1/10x+6/10
We do not have the same denominators on both sides. 5 goes into 10 two times so we will multiply everything on the left by 2 to get a common denominator.
2/10x-4/10=1/10x+6/10
Subtract 1/10x from both sides
1/10x-4/10=6/10
Add 4/10 to both sides
1/10x=10/10
1/10x= 1
Multiply both sides by 10/1 (the fraction inverse) to get rid of the fraction.
(10/1)(1/10x) =(1)(10/1)
x= 10
Check work:
1/5(x-2)=1/10(x+6)
Substitute your answer for x
1/5(10-2)=1/10(10+6)
1/5(8)=1/10(16)
8/5=16/10
Simplify 16/10 by dividing by 2
8/5=8/5
help me please
The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
The water pressure on a submerged object is given by P = 64d, then the value d is 10.5 feet.
a. D = P/64 is the solution to the formula's "d" subject.
b. The depth of a submerged object at a pressure of 672 pounds per square foot is 10. 5 feet.
What is a function?A function can be defined as an expression, law or rule that shows the relationship between two variables.
Given the role as;
P = 64d
Where;
P stands for pressure in pounds per square foot.
The object's depth, d, is expressed in feet.
Now let's center the formula on the variable "d."
Both sides of the equation are divided by the variable "d64-based "'s coefficient. This is carried out so that the variable can stand on its own.
We have.
P/64 = 64d/64
d = P/ 64
If there is pressure, P is equivalent to 672 pounds per square foot.
When the value of the variable is inserted into the formula, we obtain;
d = P/64
Then,
d = 672/64
Discover the quotient.
d = 10. 5 ft.
Therefore,
The water pressure on a submerged object is given by P = 64d, then the value d is 10.5 feet.
a. D = P/64 is the solution to the formula's "d" subject.
b. The depth of a submerged object at a pressure of 672 pounds per square foot is 10. 5 feet.
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5) Roland has a basket of 24 fruits. If 3) out of 8 of these fruits are oranges, how many oranges are in Roland's basket? a) 5 b) 8 c) 9 d) 15
Answer:
The answer would be C or 9.
Step-by-step explanation:
Figure out how many times 8 can fit into 24.(That would be 3 times) Then multiply 3 by the number of times 8 fit into 24 and get to your answer! (Please let me know if I am wrong)
Answer:
[C] 9
Step-by-step explanation:
Given:
Roland has a basket of 24 fruits. If 3 out of 8 of these fruits are oranges, how many oranges are in Roland's basket?
Solve:
" 3 out of 8 " is the same things as "⅜"
Therefore,
24 × ⅜
Now solving 24 × ⅜:
24 is the same as 24/1 since 24 divided by 1 is 24.
Hence, the problem will be like this:
[tex]\frac{24}{1}\times\frac{3}{8}[/tex]
Multiply the numerators together (24 x 3 = 72) and multiply the denominators together (1 x 8 = 8) and make it into one fraction like so:
[tex]\frac{72}{8}[/tex]
Now we have to find the GCF: GCF = Greatest Common Factor;
The greatest common factor of 72 and 8 is 8.
Dividing the numerator and the denominator by its greatest common factor to get:
[tex]\frac{9}{1}[/tex]
Convert the improper fraction above to a whole number to get the answer:
[tex]\frac{9}{1}=9[/tex]
Hence, there are 9 oranges in Roland's basket.
As a result, [C] 9 is the correct answer.
Kavinsky~
The table below represents an exponential function, g, that has been vertically shifted from the parent function, f(x) = 2x.
x 0 1 2 3 4
g(x) -11 -10 -8 -4 4
Determine the size of the shift from function f to function g. Then, plot the points of a function that is shifted only half as much as g from the parent function, f. Use the same x-values as used in the table for function g.
Drawing Tools
Select
Point
PLS SHOW GRAPH
The size of the shift from function f to function g is 12 units down
How to calculate the size of the shift?The table of values is given as
x 0 1 2 3 4
g(x) -11 -10 -8 -4 4
From the question, we understand that the function g(x) is an exponential function
The parent function of an exponential function in this case, is represented as
f(x) = 2^x
When represented on a table of values, we have
x 0 1 2 3 4
f(x) 1 2 4 8 16
So, we have
x 0 1 2 3 4
f(x) 1 2 4 8 16
g(x) -11 -10 -8 -4 4
Notice that the difference between the values of f(x) and g(x) is 12
This means that
g(x) = f(x) - 12
So, we have
g(x) = 2^x - 12
Hence, the size of the shift is 12 units down
See attachment for the graphs of f(x) and g(x)
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Are these rational numbers?
1) -1098.15
2) -2,784.75
Yes, these -1098.15 and -2,784.75 are rational numbers.
Rational number is the one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively
What is a rational numbers?A rational number is the one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. Every integer (e.g., 5 = 5/1) and, for instance, the number 3/7 are rational numbers. Boldface Q, also known as blackboard bold, is typically used to signify the set of all rational numbers, also known as "the rationals," the field of rationals, or the field of rational numbers.
Real numbers are those that are sensible. The rational real numbers are those whose decimal expansion either ends after a finite number of digits (for instance, 3/4=0.75) or eventually starts to repeatedly repeat the same finite sequence of digits (9/44=0.204545454). This assertion is accurate not just in base 10, but also in every other integer base, such as the binary and hexadecimal ones
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James bought a plant and planted it in a pot near a window in his house. The initial height of the plant was 6 inches and it grew at a rate of 3 inches per month. Make a table of values and then write an equation for H, in terms of t, representing the height, in inches, of the plant t months after James bought the plant.
initial height = 6
Rate of growth = 3 inches per month
Table:
Month height 1
96+3(3) = 91
2 6 + 3 (2)=12
3 6+3 (3) = 15
Apply the formula:
H = H0 + rt
Where:
H0 = initial growth
r = growing rate
t= number of months
Replacing:
H(t) = 6 + (3 t)
The graph of an absolute value function f(x) = a|x| includes the point (1, 8). Complete the following statements.Another point on the graph is ( ?, 8).The value of a is
In a absolute value graph the value of y is the same in -x and x.
Then if the coordinates (x,y) one point is (1, 8), the graph have another point in (- 1, 8).To find the value of a you use one of the points (x,y) in the general form of absolute value:
( 1 , 8) x=1 f(x)= y=8
[tex]8=a\lvert1\rvert[/tex]As:
[tex]\lvert\pm a\rvert=a[/tex]You get:
[tex]8=a\cdot1[/tex]Then:
[tex]a=8[/tex]The equation for the graph with points (1 , 8) and ( -1, 8) is:
[tex]f(x)=8\lvert x\rvert[/tex]a= 8417 x 25 in partly product?
ANSWER
10425
EXPLANATION
We want to multiply the numbers given by using product of parts.
To do this, we will split the number into hundred, tens and units. That is:
[tex](400\text{ + 10 + 7) }\cdot\text{ 25}[/tex]So that will be:
[tex]\begin{gathered} (400\cdot\text{ 25) + (10 }\cdot\text{ 25) + (7 }\cdot\text{ 25)} \\ =\text{ 10000 + 250 + 175} \\ =\text{ 10425} \end{gathered}[/tex]That is the answer.
Ozzie filled up the gas tank of his truck and headed out on a road trip. The x- axis on the graph below shows the number of miles Ozzie drove since filling up. The y- axis represents the number of gallons of gas in the truck’s gas tank. Find the x- and y- intercepts. Explain what the x- and y- intercepts mean for Ozzie.
Okay, here we have this:
Considering the provided information, we are going to find the x- and y- intercepts and explain its meaning. So we obtain the following:
Since the x-intercept is the point where the Graph intersects the x-axis (y=0) and the y-intercept is the point where the Graph intersects the y-axis (x=0), we have that:
x-intercept=(300, 0)
y-intercept=(0, 16)
Since the y-axis represents the number of gallons, and the x-axis time, then the y-intercept indicates that when filling the tank it was left with 16 gallons, and the x-intercept indicates that when emptying the tank had traveled 300 miles.
can you help me please
The given expression is 4.9 x 10⁻¹¹.
What is a mathematical expression?
An expression, often known as a mathematical expression, is a limited collection of symbols that have been well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and groupings can all be represented by mathematical representations, which can also be used to indicate the logical syntax's sequence of operations and other features. However, in contemporary mathematics, and particularly in computer algebra, formulae are seen as expressions that, depending on the values supplied to the variables present in the expressions, can be evaluated to true or false.
The given expression can be solved as follows
(7x10⁻⁶)(7x10⁻⁶)
= (7x7) x (10⁻⁶x10⁻⁶)
= 49 x 10⁻¹²
= 4.9 x 10⁻¹¹
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5. Solve for x using any method you'd like. Round to the hundredth. Show all your work. (2 points each) C. 5x^5 + 16 = 41
x = 1.37 after solving the given equation.
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.So, the equation here is: 5x⁵ + 16 = 41
Now, solve the equation normally as follows:
5x⁵ + 16 = 415x⁵ = 41 - 165x⁵ = 25x⁵ = 25/5x⁵ = 5Now, take the roots on both sides and solve as follows:
x⁵ = 5x = [tex]\sqrt[5]{5}[/tex]In decimal form:
x = 1.37972966Therefore, x = 1.37 after solving the given equation.
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W QUESTIONS 100 POINTS WILL GIVE BRAINLYEST
The areas for this problem are given as follows:
3. 681.25 ft².
4. 193 m².
Item 3The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:
A = lw.
For this problem, a rectangular deck of dimensions l = 18.75 ft and w = 15 ft is added, hence the area of the deck is:
A = 18.75 x 15 = 281.25 ft².
This area is added to the previous area, hence the total area is of:
A = 400 ft² + 281.25 ft² = 681.25 ft².
Item 4The figure is composed by:
A rectangle of dimensions 10 m and 18 m.A triangle of base 13 m and height 2 m.The area of the triangle is half the base times the height, while the area of the rectangle was presented in the previous item, hence the total area of the figure is:
A = 10 x 18 + 0.5 x 13 x 2 = 180 + 13 = 193 m².
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