We can replace x with any real number, positive or negative. We can also plug in x = 0. There aren't any restrictions to worry about with the input.
Examples:
Plug in x = 2 to get f(2) = 2(1/10)^2 = 0.02
Plug in x = -2 to get f(-2) = 2(1/10)^(-2) = 200
Plug in x = 0 to get f(0) = 2(1/10)^(0) = 2
The domain of the given function is "All real numbers". So, option D is correct.
What is the domain of a function?The domain of a function is the set of possible values as inputs to the function. The Domain of the exponential function is the set of all real numbers represented by R.
here, we have,
Finding the domain of the given function:
The given function is f(x) = 2×
Since this function has the variable x in the exponent, this is an exponential function.
So, its inputs are of all real numbers. And the domain is {x:x ∈ R}.
Thus, option D is true.
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Evalúe the limit. Show steps
After evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow -2 }\sqrt[3]{x+1}[/tex] as x approaches -2 is -1
What is limit?A limit in mathematics is the value that a function, sequence, or index approaches when used as an input or as an index gets closer to a specific value. In order to define continuity, derivatives, and integrals, limits must be present. Limits are also crucial to calculus and mathematical analysis.
The idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network in addition to having a connection with the category theory concepts of limit and direct limit.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit we will Evalúe the power
⇒ [tex]\lim_{x\rightarrow -2 }\sqrt[3]{x+1}[/tex]
⇒ [tex]\lim_{x\rightarrow -2 }(x+1)^{1/3}[/tex]
Evalúe 2 as x
⇒ [tex](-2+1)^{1/3}[/tex]
⇒ [tex](-1)^{1/3}[/tex]
⇒ -1
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What is the correct answer to this question
Answer:
The transversal is not part of this triangle.
Find the value of x.
57°
79°
X
Can someone help with this question?✨
The expression (-6 - 5i) + (-1 + 7i) in this form a + bi is -7 + 2i
How to evaluate an expression?The expression to be evaluated is as follows:
Therefore,
(-6 - 5i) + (-1 + 7i)
The expression can be express in the form a + bi as follows:
(-6 - 5i) + (-1 + 7i)
- 6 - 5i - 1 + 7i
Let's combine the like terms
- 6 - 5i - 1 + 7i
-6 - 1 - 5i + 7i
Let's do the arithmetic
-6 - 1 - 5i + 7i
Therefore,
-7 + 2i
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19. Which of the following equations represents a line that
passes through the points (-2, 4) and (-7, 9)?
Answer:
y = - x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 4 ) and (x₂, y₂ ) = (- 7, 9 )
m = [tex]\frac{9-4}{-7-(-2)}[/tex] = [tex]\frac{5}{-7+2}[/tex] = [tex]\frac{5}{-5}[/tex] = - 1 , then
y = - x + c ← partial equation
to find c substitute either of the 2 points into the partial equation
using (- 2, 4 )
4 = 2 + c ⇒ c = 4 - 2 = 2
y = - x + 2 ← equation of line
$&+#84$-('-8*_($&)*85"59
q. answered
user rates 2
2. A bank representative studies compound interest, so she can better serve customers. She
analyzes what happens when $2,000 earns interest several different ways at a rate of 2% for 3
years.
a. Find the interest if it is computed using simple interest.
$
LA
c. Find the interest if it is compounded continuously.
$
d. What is the difference in total interest if computed using simple interest or if compounded
continuously?
a) The interest if computed using simple interest for 3 years at 2% is $120.
c) The interest when compounded continuously for 3 years at 2% is $123.67.
d) The difference in total interest between using simple interest and continuously compounding is $3.67.
What is simple interest?Simple interest is a straightforward way of computing the interest paid on a loan.
The formula for calculating simple interest is P x R x T, where P = Principal, R = Rate, and T = Time.
The formula for continuous compounding first computes the future value (FV) from which the present value (PV) is deducted, as follows:
FV = PV x e ^ (i x t), where e is the mathematical constant approximated as 2.7183.
Principal = $2,000
Rate of interest = 2%
Period = 3 years
Simple Interest = $120 ($2,000 x 2% x 3)
Continuous compounding = FV - PV
FV = $2,000 x 2.7183 ^ (0.02 x 3)
= $2,000 x 1.06183697
= $2,123.67
Interest = $123.67 ($2,123.67 - $2,000)
The difference in total interest = $3.67 ($123.67 - $120)
Thus, continuous compounding produces a difference in the interest of $3.67 when compared to simple interest.
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Write the equation of a line that passes through the points (4, 2) and
(2, 6).
WE WILL FIRST FIND THE SLOPE BETWEEN THE POINTS
[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{6 - 2}{2 - 4} \\ m = \frac{4}{ - 2} \\ m = - 2[/tex]
I WILL USE POINT (2,6) TO GET THE VALUE OF c
[tex]6 = - 2(2) + c \\ 6 = - 4 + c \\ c = 6 + 4 \\ c = 10[/tex]
since the general equation of a straight line is given by y=mx+c
[tex]y = - 2x + 10[/tex]
ATTACHED IS THE SOLUTION
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
Find the gradient of the line first.
Formula of gradient is given as y2-y1 ÷ x2-x1 or y1-y2 ÷ x1-x2, where x and y are the coordinates of the points.
Gradient = (6-2) ÷ (2-4) = -2
Eqn is y = -2x + c
Substitute either one of the coordinates of the points into the equation to find c.
2 = -2(4) + c
c = 10
Equation of the line is y = -2x + 10
algebra please help if you can
The answer of the multiplication of two polynomials after simplification is [tex](6x^{4} -7x^{3}+3x^{2}+17x -14)[/tex].
According to the question,
We have the following two polynomials:
[tex](3x^{2} -5x+7)[/tex] and [tex](2x^{2}+x-2)[/tex]
Now, multiplying these two polynomials:
[tex](3x^{2} -5x+7) (2x^{2} +x-2)\\3x^{2} (2x^{2} +x-2) -5x(2x^{2} +x-2) +7(2x^{2} +x-2)\\6x^{4} +3x^{3}- 6x^{2} -10x^{3} - 10x^{2} +10x +14x^{2} +7x-14\\6x^{4} -7x^{3}+3x^{2} +17x-14[/tex]
(Please note that the numbers with the same variables can be added and subtracted. For example, the numbers with the variable [tex]x^{2}[/tex] can only be added or subtracted with variables having [tex]x^{2}[/tex].)
(More to know: every number has to be multiplied with every number in the bracket. For example, in this case, 7 from the first polynomial has been multiplied with the second polynomial. And 7 is multiplied with every number of this polynomial.)
Hence, the result after multiplying the two polynomials and simplifying them is [tex]6x^{4}-7x^{3} +3x^{2} +17x-14[/tex].
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How do I solve this problem
Consider that each unit on the grid represents 4ft. The figure consists of 2 identical equilateral triangles and 3 identical rectangles. Calculating the area of one of each kind of shape,
[tex]\begin{gathered} A_{triangle}=\frac{1}{2}b*h=\frac{1}{2}*4*4=\frac{16}{2}=8 \\ A_{rectangle}=4*4(2)=4*8=32 \end{gathered}[/tex]Therefore, the area of a single triangle is 8in^2, while the area of a rectangle is 48in^2. Calculate the total area as shown below
[tex]A_{total}=2*8+4*32=16+128=144[/tex]The area of a sheet of plywood is
[tex]A_{plywood}=4*8=32[/tex]Then, divide the total area by the area of a sheet of plywood,
[tex]\frac{A_{total}}{A_{plywood}}=\frac{144}{32}=4.5[/tex]Thus, the answer is 4.5, option D.
Evaluate 10 exponent -8
Answer:
0.000000010
Step-by-step explanation:
If ∠1 ≅ ∠2, can you conclude that any of the lines are parallel?
Explain.
A. Yes; lines n and p are parallel because corresponding angles are congruent.
B. No; ∠1 and ∠2 show no relationship.
C. Yes; lines ℓ and m are parallel because corresponding angles are congruent.
D. No; neither angle is formed by the transversal, line q.
A. Yes; lines n and p are parallel because corresponding angles are congruent.
According to the reverse of the comparable angles theorem, lines n and p are parallel if angles 1 and 2 are congruent.
The converse of the corresponding angles theorem is what?
According to the corresponding angles theorem, the corresponding angles on each line that a transversal cuts are congruent if the two lines are parallel to one another.
In contrast, lines that fall on those angles are parallel to one another if two corresponding angles are congruent to one another.
The diagram's angles 1 and 2 relate to one another.
In light of the converse of the equivalent angles theorem, lines n and p are parallel if angles 1 and 2 are congruent.
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A rectangular plot of ground is 10 m longer than it is wide. It’s area is 10,000 square meters.
Based on the fact that the rectangular plot has a length that is 10 m longer than the width, the equation that will help to find area of the rectangular plot of land is 10x + x² = 10,000
How to find the area of the plot of land?To find the area of the plot of land is the same as finding the area of a rectangle which is:
Area of a rectangle = Length x Width
Assuming the width of the rectangular plot of ground is x, then the length would be:
= 10m + x
= 10 + x
The area of the rectangular plot of ground can therefore be found by the formula:
Area of a rectangle = Length x Width
10,000 square meters = (10 + x) × x
10,000 square meters = 10x + x²
10x + x² = 10,000
In conclusion, an equation that can help you to find the dimensions of the plot of ground is 10x + x² = 10,000.
Rest of the question is:
What equation will help me find the dimensions?
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A principal of $3100 is invested at 3.75% interest, compounded annually. How much will the investment be worth after 9 years? Use the calculator provided and round your answer to the nearest dollar
he Solution:
iven:
[tex]\begin{gathered} P=Principal=\text{ \$}3100 \\ \\ r=rate=3.75\text{\%} \\ \\ t=time=9years \end{gathered}[/tex]We are required to find the amount the investment will be worth after 9 years.
he Compound interest formula:
[tex]A=P(1+\frac{r}{100})^n[/tex]In this case:
[tex]\begin{gathered} A=amount=? \\ P=\text{ \$3100} \\ r=3.75\text{ \%} \\ n=9\text{ years} \end{gathered}[/tex]Substitute:
[tex]A=3100(1+\frac{3.75}{100})^9=3100(1.0375)^9=4317.7217\approx\text{ \$}4318[/tex]Therefore, the correct answer is $4318
To prove two triangles are congruent, you must have at least one pair of congruent sides
True or false
Answer: The angles in an equilateral triangle are always 60°. When a triangle has two congruent sides it is called an isosceles triangle. The angles opposite to the two sides of the same length are congruent. A triangle without any congruent sides or angles is called a scalene triangle.
Step-by-step explanation:
The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent. When all the sides of two triangles are congruent, the angles of those triangles must also be congruent. This method is called side-side-side, or SSS for short.
what is the multiplicative inverse of -7 / 5
That is the answer
I need help simplifying rational expressions and finding the excluded values
SOLUTION:
Step 1:
In this question, we are meant to find the value of:
[tex]\frac{x^2-x}{x+2}dividedby(x^2_{}+2x-3)[/tex]Step 2:
The details of the solution are as follows:
CONCLUSION:
The final answer in rational expression is:
[tex]\begin{gathered} \frac{\text{x }}{(x+2)(x+3)} \\ \text{The excluded values are: x=-2, x = -3} \end{gathered}[/tex]Solve for x and graph.|x+5| = .01
We need to solve the following equation:
[tex]|x+5|=0.01[/tex]There are two possibilities for the absolute operator, we have the possibility that the argument is positive or negative. Therefore:
[tex]\begin{gathered} x+5=0.01 \\ x=0.01-5=-4.99 \\ \end{gathered}[/tex][tex]\begin{gathered} -(x+5)=0.01 \\ -x-5=0.01 \\ -x=0.01+5 \\ -x=5.01 \\ x=-5.01 \end{gathered}[/tex]The solution is -4.99 and -5.01.
If Kerel has 9 quarters and nickels in his pocket, and they have a combined value of 125 cents, how many of each coin does he have?
nickels
quarters
By using substitution method, if Kerel has 9 quarters and nickels in his pocket and they have a combined value of 125 cents, then he has 4 quarters and 5 nickels
Total number of coins = 9
Consider the number of quarters as x and number of nickels as y
Then the equation will be
x+y =9
x= 9-y
The combined value of the coins = 125 cents
We know
1 quarter = 25 cents
1 nickel = 5 cents
Then the equation will be
25x+5y = 125
Here we have to use the substitution method
Substitute the value of x in the equation
25(9-y)+5y = 125
225-25y+5y = 125
-20y = -100
y = 5
Substitute the value of y in the first equation
x = 9-y
x = 9-5
x= 4
Hence, by using substitution method, if Kerel has 9 quarters and nickels in his pocket and they have a combined value of 125 cents, then he has 4 quarters and 5 nickels
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The total measure of two adjacent angles is 168°. If one of the adjacent angles measures 107.6°, determine the measure of the other adjacent angle.
275.6°
197.6°
72.4°
60.4°
Answer: The answer is 60.4
Step-by-step explanation: I got it right
Which of the following expressions are equivalent? Justify your reasoning.Question 5
Answer:
Explanation:
A) Given the below expression;
[tex]\sqrt[4]{x^3}[/tex]The above can be written as;
[tex]\sqrt[4]{x^3}=(x^3)^{\frac{1}{4}}[/tex]Recall the below law of exponent;
[tex](a^n)^m=a^{nm}[/tex]Applying the above law of exponent to the expression, we'll have;
[tex](x^3)^{\frac{1}{4}}=x^{\frac{3}{4}}[/tex]B) Given the below expression;
[tex]\frac{1}{x^{-1}}[/tex]Recall the below law of exponent;
[tex]\frac{1}{a}=a^{-1}[/tex]Applying the above law of exponent to the expression, we'll have;
[tex]\frac{1}{x^{-1}}=x^{-1(-1)}=x^1=x[/tex]C) Given the below expression;
[tex]\sqrt[10]{x^5\cdot x^4\cdot x^2}[/tex]Recall the below laws of exponents;
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ (a^n)^m=a^{^{nm}} \end{gathered}[/tex]Applying the above law of exponent to the expression, we'll have;
[tex]\begin{gathered} \sqrt[10]{x^{5+4+2}}=\sqrt[10]{x^{11}}^{}^{} \\ =(x^{11})^{\frac{1}{10}}=x^{\frac{11}{10}}^{}^{} \end{gathered}[/tex]D) Given the below expression;
[tex]x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}[/tex]Recall the below law of exponents;
[tex]a^n\cdot a^m=a^{n+m}[/tex]Applying the above law of exponent to the expression, we'll have;
[tex]x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}=x^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=x^{\frac{1+1+1}{3}}=x^{\frac{3}{3}}=x^1=x[/tex]We can see from the above that the below expressions are equivalent because they both yield the same result as x;
[tex]\begin{gathered} A)\sqrt[4]{x^3} \\ D)x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}\cdot x^{\frac{1}{3}} \end{gathered}[/tex]I need an answer please
the answer is 40 degrees
Step-by-step explanation:
DCB+DCE+ACE =180
DCB+100+ACE=180 (degrees)
DCB+DCB=180-100
2 DCB = 80 (degrees)
DCB=80÷2
DCB = 40 Degrees
City workers are using a snowplow to clear a street. A tire on the snowplow is 3.2 ft in diameter and has to turn 47 times in traveling the length of the street. How long is the street?
Use the value 3.14 for π. Round your answer to the nearest tenth. Do not round any intermediate steps.
If a tire on the snowplow with a diameter of 3.2 ft turns 47 times then, the length of the street is 472.3 feet.
To clear a street the city workers use a snowplow. The diameter of the tire of the snowplow is 3.2 ft.
The tire has to turn 47 times to cover the total length of the street.
Now, we know that the circumference of a circle is given as:
C = 2πr where r is the radius of the circle. And the radius of a circle is half of its diameter.
Therefore, the circumference of the circle can be written as:
C = πD where D is the diameter of the circle.
Now, to calculate the total length of the street we will find the product of the circumference and the number of times the tire has to turn to cover the street.
Therefore,
Length of the street, L = nC
L = nπD
L = 47 × 3.14 × 3.2 ft
L = 472.256 ft
L = 472.3 ft
Hence, the length of the street is 472.3 feet.
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What is the exact circumference of the circle if the diameter is 16?
Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production
process. Assume a production process produces items with a mean weight of 15 ounces.
a. The process standard deviation is 0.20, and the process control is set at plus or minus 0.75 standard deviation. Units with
weights less than 14.85 or greater than 15.15 ounces will be classified as defects. What is the probability of a defect (to 4
decimals)?
In a production run of 1000 parts, how many defects would be found (round to the nearest whole number?
b. Through process design improvements, the process standard deviation can be reduced to 0.07. Assume the process control
remains the same, with weights less than 14.85 or greater than 15.15 ounces being classified as defects. What is the probability of
a defect (round to 4 decimals; if necessary)?
In a production run of 1000 parts, how many defects would be found (to the nearest whole number)?
c. What is the advantage of reducing process variation, thereby causing a problem limits to be at a greater number of standard
deviations from the mean?
Using the normal distribution, it is found that:
a) The probability of a defect is of 0.4532, and out of 1000 parts, 453 will be classified as defective.
b) The probability of a defect is of 0.0324, and out of 1000 parts, 32 will be classified as defective.
c) The reduction in the variability also reduces the number of defective parts.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.For item a, the mean and the standard deviation are given as follows:
[tex]\mu = 15, \sigma = 0.2[/tex]
The proportion of defectives is two times the p-value of Z when X = 14.85, as 14.85 and 15.15 are the same distance from the mean and the normal distribution is symmetric, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (14.85 - 15)/0.2
Z = -0.75
Z = -0.75 has a p-value of 0.2266.
2 x 0.2266 = 0.4532 = 45.32%
Out of 1000, the number of defectives is:
0.453 x 1000 = 453.
For item b, we have that [tex]\sigma = 0.07[/tex], hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (14.85 - 15)/0.07
Z = -2.14
Z = -2.14 has a p-value of 0.0162.
2 x 0.0162 = 0.0324.
Out of 1000, the number of defectives is:
0.032 x 1000 = 32.
For item c, we can see that the reduction of variability will make the parts having measures closer to the desired, hence reducing the number of defectives.
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if a plane is flying at a speed of 800km/hr how long would it take to travel a distance of 1.200 km
Answer: 1.5 hour
speed=distance/ time
800=1200/time
time=1200/800
time=1.5 hour
Step-by-step explanation:
speed=distance/ time
800=1200/time
time=1200/800
time=1.5 hour
Use the properties of operations to multiply the expressions. (10.3y)(4y)
By using the properties of operations, the result of the expression (10.3y)(4y) is [tex]41.2y^{2}[/tex]
The expression is given = (10.3y)(4y)
Here we have to multiply the given expression using the properties of operations
The integers has mainly five properties of operation, closure property, associative property, commutative property, distributive property and the identity property. Each property has four integer operations. The four integer operations are addition operation, subtraction operation, multiplication operation and division operation
The given expression = (10.3y)(4y)
Multiply the given expression using the properties of operation
(10.3y)(4y) = [tex]41.2y^{2}[/tex]
Hence, by using the properties of operations, the result of the expression (10.3y)(4y) is [tex]41.2y^{2}[/tex]
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There are 4 squares and 16 triangles. What is the simplest ratio of squares to triangles?
Answer:
1 is to 4
Step-by-step explanation:
Find lowest common factor of the numbers, which is 4, then divide it into both numbers
Calculate the distance between the points E = (-4 , 5) and L=(1 , -3) in the coordinate plane. Give an exact answer (not a decimal approximation).
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ E(\stackrel{x_1}{-4}~,~\stackrel{y_1}{5})\qquad L(\stackrel{x_2}{1}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ EL=\sqrt{(~~1 - (-4)~~)^2 + (~~-3 - 5~~)^2} \implies EL=\sqrt{(1 +4)^2 + (-3 -5)^2} \\\\\\ EL=\sqrt{( 5 )^2 + ( -8 )^2} \implies EL=\sqrt{ 25 + 64 } \implies EL=\sqrt{ 89 }[/tex]
Pls help with this !!!!!