Find the value of x.
57°
79°
X
Find domain and range of this function using h interval motion
Answer:
Domain: [-1, 4)Range: [-5, 4]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
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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Any buyer of a new sports car has to pick between 2 of 5 seat colors and 3 of 4 options for dashboard accessories. How many different combinations of colors and dashboard options are available to this buyer?
Different combinations of colors and dashboard options are available to the buyer who can pick between 2 of 5 seat colors and 3 of 4 options for dashboard accessories is 40.
As given in the question,
Possible combination for any buyer of a new sports car
Pick between 2 of 5 seat colors
⁵C₂ = 5! / (2!)(5-2)!
= 5!/ (2!)(3!)
= 10
Pick between 3 of 4 options for dashboard accessories
⁴C₃ = (4!)/ (3!)(4-3)!
= (4!)/ (3!)(1!)
= 4
Total different combinations of colors and dashboard options = 10 × 4
= 40
Therefore, different combinations of colors and dashboard options are available to the buyer is 40.
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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.
2/7 of 5/6 (3 1/3 * 2/5) by 1/5 equals to
[tex] \frac{2}{7} \times \frac{5}{6} ( \frac{10}{3} \times \frac{2}{5} ) \times \frac{1}{5} \\ = \frac{2}{7} \times \frac{5}{6} ( \frac{20}{15} ) \times \frac{1}{5} \\ = \frac{2}{7} \times \frac{100}{90} \times \frac{1}{5} \\ = ( \frac{2}{7} \times \frac{10}{9}) \times \frac{1}{5} \\ = \frac{20}{63} \times \frac{1}{5} \\ = \frac{20}{315} \\ = \frac{4}{63} [/tex]
ATTACHED IS THE SOLUTION
What is the correct answer to this question
Answer:
The transversal is not part of this triangle.
The height of the real painting is 24 inches. What is the height of the painting in the scale drawing? (b)In the scale drawing, the length of the painting is 7 centimeters. What is the length of the real painting?
The scale drawing height is 4 cm and the actual drawing length is 42 in
The height of the painting in the scale drawingThe complete question is added as an attachment
From the attachment, we have the ratio to be given as
Scale ratio, 1 cm : 6 in
Rewrite as
Scale measurement : Actual measurement = 1 cm : 6 in
In this question, we have
Actual measurement = 24 inches
This means that
Scale measurement : 24 in = 1 cm : 6 in
Multiply 1 cm : 6 in by 4
Scale measurement : 24 in = 4 cm : 24 in
By comparison, we have
Scale measurement = 4 cm
Hence, the scale drawing height is 4 cm
What is the length of the real painting?Recall that
Scale ratio, 1 cm : 6 in
Rewrite as
Scale measurement : Actual measurement = 1 cm : 6 in
In this question, we have
Scale measurement = 7 cm
This means that
7 cm : Actual measurement = 1 cm : 6 in
Multiply 1 cm : 6 in by 7
7 cm : Actual measurement = 7 cm : 42 in
By comparison, we have
Actual measurement = 42 in
Hence, the actual drawing length is 42 in
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Shawn found it took him 429 steps to get from home to the outside basketball court. How many steps does it take to make 8 one-way trips? Choose the best estimate.
Based on the number of steps it took Shawn to get home from outside the basketball court, the number of steps needed for 8 one-way trips is 3,432 steps
How to find the number of steps?Each trip that Shawn takes from outside the basketball court to his house, and from his house to outside the basketball court, will take 429 steps.
If Shawn then takes 8 one - way trips, the number of steps till he gets either home or the basketball courts is:
= Number of steps per trip x Number of trips
= 429 x 8
= 3,432 steps
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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]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
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
What is the exact circumference of the circle if the diameter is 16?
$&+#84$-('-8*_($&)*85"59
q. answered
user rates 2
what is the multiplicative inverse of -7 / 5
That is the answer
any body help me please. I need answer of this question as soon as possible.
The number of ways to choose the total number of participants required by the event coordinator is 54,600.
The total number of boys who want to participate in the science competition organised by the Physics Department is 15.The total number of girls who want to participate in the science competition organised by the Physics Department is 10.The number of boys required by the event coordinator is 3.The number of girls required by the event coordinator is 3.The number of ways to choose the total number of participants required by the event coordinator is calculated by choosing 3 boys out of 15 boys and 3 girls out of 10 girls.Let "n" be the required number of ways.The concept of permutations and combinations is used here.n = (15C3)*(10C3)n = 455*120n = 54,600To learn more about permutations and combinations, visit :
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the temperature at sunrise is 25° each hour the temperature rises 5° write an equation that models the temperature y in degrees Fahrenheit after x hours . what is the graph of the equation
EXPLANATION
Let's see the facts:
Sunrise temperature = 25°
Rate= 5°/hour
So, the temperature after x hours is given by the expression:
Temperature after x hours= Sunrise temperature + Number of hours*Rate
Substituting terms:
T= 25 + 5x
Now, with this relationship we can build the graph:
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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Only questions #9,13,17,21,25 please show work
THANK YOU
Simplification of the given expression to single complex number are as follow :
9. -11 +4i
13. 30 - 10i
17.20
21. (3 + 5i)/2
25. -1
As given,
To simplify the following expressions to a single complex number,
9) (- 5 + 3 i) - (6 - i)
= - 5 + 3 i - 6 + i
= - 5 - 6 +3i + i
= - 11 + 4 i
13) (6 - 2 i) 5
= (6 x 5) - (2 x 5) i
= 30 - 10 i
17) (4 - 2 i) (4 + 2 i)
= [tex]4^{2} - (2i)^{2}[/tex]
= 16 - 4 [tex]i^{2}[/tex]
= 16 - 4 (-1)
= 16 + 4
= 20
21) [tex]\frac{-5+3i}{2i} = \frac{i(-5+3i)}{2i^{2}} = \frac{-5i + 3i^{2} }{2(-1)}[/tex]
= [tex]\frac{-5i+3(-1)}{-2} = \frac{3+5i}{2}[/tex]
25) [tex]i^{6} = (i^{2})^{3} = (-1)^{3} = -1[/tex]
Note: To simplify a fraction where denominator has complex component (i) as coefficient, multiply both numerator and denominator by i to eliminate i from denominator (by converting it to real number)
Therefore, simplification of the given expression to single complex number are as follow :
9. -11 +4i
13. 30 - 10i
17.20
21. (3 + 5i)/2
25. -1
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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]
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.
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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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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The length of a swimming pool is triple the width. The area of the pool is 6627 ft2. Find the length and width of the pool.
For the given statement, the length and width of the pool are 141 feet and 47 feet respectively.
What is meant by the area of the rectangle?The area occupied by the rectangle within its perimeter can be calculated using the formula for the area of a rectangle. In the aforementioned illustration, a rectangle with dimensions of 4 inches long by 3 inches wide has a surface area of 12 square inches. 4 plus 3 equals 12, so. A rectangle's area is calculated by multiplying its length by its width. Therefore, the product "l w" is the formula for the area, "A," of a rectangle whose length and breadth are "l" and "w," respectively.
Rectangular area is equal to (length breadth) square units.
Given,
length of the pool = 3 (width of the pool)
Let width of the pool = x
Length of the pool = 3x
Area of the pool = Length × Width
6627 = x × 3x
⇒ 3x² = 6627
⇒ x² = 2209
⇒ x = 47
⇒ 3x = 47 × 3
⇒ 141
This implies that the length and width of the pool are 141 feet and 47 feet respectively.
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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
The table shows the linear relationship between the amount of water being pumped
out of a pool over time.
Based on the table, what was the rate of change of the amount of water being
pumped out of the pool over time?
The rate of change of water being pumped out of the pool over time is (C) -2.
What is a linear relationship?A straight-line relationship between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.So, the linear relationship is:
x = 1, y = 8x = 2, y = 6x = 3, y = 4x = 4, y = 2Look at the values of y: 8, 6, 4, 2
The pattern is 8 - 2 = 6; 6 - 2 = 4; 4 - 2 = 2So, the rate of change will be -2.
Therefore, the rate of change of water being pumped out of the pool over time is (C) -2.
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The complete question is given below:
The table shows the linear relationship between the amount of water being pumped out of a pool over time. Based on the table, what was the rate of change in the amount of water being pumped out of the pool over time?
(A) 2
(B) 10
(C) -2
(D) -10
Describe the transformation of f(x)=x2 represent by g. (Show Work)
Answer:
Shifty to right 1
Not shift to
2
Step-by-step explanation:
The transformation has a horizontal shift right by 1 units and vertical shift upwards by 3 units. The graph is shown below.
What do you mean by transformation of a graph ?
The modification of an existing graph or graphed equation to create a different version of the following graph is known as transformation.
The functions given are :
f(x) = x²
and
g(x) = (x - 1)² + 3
Now , we know that , the horizontal shift depends on the value of h. The horizontal shift is described as:
g(x) = f (x + h)
Then , the graph is shifted to left by h units.
and
g(x) = f (x - h)
Then , the graph is shifted to right by h units.
If we compare f(x) with g(x) , their is a difference of -1 , it meant shift is right by 1 units.
Now , we know that , the vertical shift depends on the value of k. The vertical shift is described as:
g(x) = f(x) + k
Then , the graph is shifted up by k units.
and
g(x) = f(x) - k
Then , the graph is shifted down by k units.
Here , if we compare f(x) with g(x) there is addition of 3 in g(x) , this meant the graph is shifted upward by 3 units.
The graph of the function is attached below. Here , both of the functions are graphed.
Therefore , the transformation has a horizontal shift right by 1 units and vertical shift upwards by 3 units. The graph is shown below.
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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Pls help with this !!!!!