If the sum of the measures of any two supplementary angles is 180 degrees and m[tex]m\angle L+m\angle S=180^0\text{ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1}[/tex]Also, if the measure of < L is sixty-six degrees less than five times the measure of < S, then:
[tex]m\angle L=5m\angle S-66_{--------------}2[/tex]Substitute equation 2 into equation 1 to have:
[tex](5m\angle S-66)+m\angle S=180[/tex]Simplify the result to have:
[tex]\begin{gathered} 5m\angle S-66+m\angle S=180 \\ 5m\angle S+m\angle S-66=180 \\ 6m\angle S-66=180 \end{gathered}[/tex]Add 66 to both sides of the resulting equation:
[tex]\begin{gathered} 6m\angle S-66+66=180+66 \\ 6m\angle S=246 \end{gathered}[/tex]Divide both sides of the equation by 6
[tex]\begin{gathered} \frac{\cancel{6}m\angle S}{\cancel{6}}=\frac{\cancel{246}^{41}}{\cancel{6}} \\ m\angle S=41^0 \end{gathered}[/tex]Get the measure of < L. Recall that:
[tex]\begin{gathered} m\angle L=5m\angle S-66 \\ m\angle L=5(41)-66 \\ m\angle L=205-66 \\ m\angle L=139^0 \end{gathered}[/tex]Hence the measure of < L is 139 deg. while the measure of
The beachfront path was 5,907 feet long. A tropical storm caused waves that washed away 4,806 feet from the end. How long was the path after the storm?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
5907 feet = beachfront path
4806 feet
Step 02:
beachfront path
120 100 temperature in °F 60 20 0 10 30 40 50 60 70 80 latitude in degrees North Add points that represent the predicted temperatures for each city on your scatter plot from the original cities. If you do not have a copy of your work from yesterday, you may choose to use the scatterplot above. Copy the data over or print a copy of the scatterplot here Scatterplot.pdf Upload a photo of your work in the space below. Upload Choose a File
Scatterplot is a simple graph that follows x and y coordinates.
Once you have the name of the cities, you can look up their latitude either using a printed map or online map, and that will be your x coordinate.
For your y coordinate, that will be the predicted temperature.
For example, the latitude of the Detroit is 42 degrees North (x coordinate) and has a temperature of 52 degree Fahrenheit (y coordinate), then we can have this plotted like this: (disregard the yellow line, it is only there as basis)
Another example: This is for Albuquerque. The latitude is 35.2 (x coordinate) and it's predicted temperature today is 73 degree Fahrenheit (y coordinate).
The red dot on the image above, that is where we will plot Albuquerque since it's latitude is 35.2 and its temperature is 73, as shown by the yellow lines. (Do not draw the yellow lines. It is only there for basis.)
You do the same with the rest of the cities using its corresponding latitude and predicted temperature today.
Consider a square and a regular octagon (an 8-sided figure with sides of equal length), One side of thesquare is 7 feet longer than a side of the octagon, and the two figures have the same perimeter. What arethe lengths of the sides of each figure? (Round to two decimal places if necessary.)
EXPLANATION:
We are given the following details:
A square and a regular octagon have the same perimeter. However the sides are not given. Let us assign a variable to the sides of the octagon. One side of the octagon would be represented by letter x.
Note that it is a regular octagon which means all eight sides have the same length. Next we are told that one side of the square is 7 feet longer than one side of the octagon. This means one side of the square would be 7 + x. Note that a square too has all four sides with equal length.
Therefore we would hav e the following;
[tex]\begin{gathered} Octagon=x \\ Square=7+x \end{gathered}[/tex]Next we are told the two figures have the same perimeter.
The perimeter of an octagon is;
[tex]\begin{gathered} Octagon: \\ Perimeter=8x \\ Where: \\ x=length\text{ of one side} \end{gathered}[/tex]For a square we have;
[tex]\begin{gathered} Square: \\ Perimeter=4x \\ Where: \\ x=length\text{ of one side} \end{gathered}[/tex]Note however that the length of the square in this instance is (7 + x), hence we can re-write this equation as;
[tex]\begin{gathered} Square: \\ Perimeter=4\left(7+x\right) \end{gathered}[/tex]Since the perimeters for both are equal, we can equate both equations and we'll have;
[tex]8x=4\left(7+x\right)[/tex]We can now solve for the variable x;
[tex]8x=4\left(7+x\right)[/tex][tex]8x=28+4x[/tex]Combine like terms;
[tex]8x-4x=28[/tex][tex]4x=28[/tex]Divide both sides by 4;
[tex]\begin{gathered} \frac{4x}{4}=\frac{28}{4} \\ x=7 \end{gathered}[/tex]This means the length of a side of the octagon is 7 feet, while the length of a side of the square is 14 feet (7 + 7).
ANSWER:
[tex]\begin{gathered} Octagon=7ft \\ Square=14ft \end{gathered}[/tex]What are the calculations for the formula below? Tan-1 (5/401)
Using a calculator, we have
[tex]\arctg(\frac{5}{401})=0.71437419575...^o[/tex]which of the following equations will produce the graph shown? (answers in photo)HELP PLEASE HELP PLEASE HELP PLEASEEEE!!! ASAPPP
From the given graph,we find that the radius of the circle with center at the origin is r=4 units.
The equation of a circle with cter at the origin is
[tex]x^2+y^2=r^2[/tex]Here, r is the radius of the circle.
Put r=4 in the above equation.
[tex]\begin{gathered} x^2+y^2=4^2 \\ x^2+y^2=16 \end{gathered}[/tex]Multiply both sides of the above equation by 2.
[tex]\begin{gathered} 2x^2+2y^2=2\times16 \\ 2x^2+2y^2=32 \end{gathered}[/tex]Therefore, the equation representing the circle is,
[tex]\begin{gathered} \\ 2x^2+2y^2=32 \end{gathered}[/tex]What is the fourth term in the sequence -7.9,-8.8.-9.7...?
Here, we are to find the fourth term in the sequence
To find the fourth term, we need to identify the rule that governs the sequence
The difference between the second and
Triangle L' is the image of triangle L under a dilation.
What is the center of the dilation?
Since triangle L' is the image of triangle L under a dilation, the center of the dilation is A.
What is dilation?In Geometry, dilation can be defined as a type of transformation which changes the size of a geometric figure, but not its shape. This ultimately implies that, the size of the geometric figure would be enlarged or reduced based on the scale factor that is applied.
What is the center of dilation?The center of dilation is also referred to as a point of dilation and it can be defined as a reference (fixed) point that is used to correctly scale the dilation of a geometric figure.
By critically observing the graph (see attachment) of triangles L and L', we can logically deduce that the point at which image of triangle L was dilated is point A because it is the reference (fixed) point.
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Given IJK is congruent to LMN, find the length of all unbiased sides and the measure of all unlabeled angles. Round all answers to the nearest tenth.
Answer
IK = 6.9 cm
m < K = 30 degrees
NM =
Given that IJK is congruent to LMN
Therefore, IJ = ML
IK = LN
JK = MN
Where, IJ = 4cm
JK = 8cm
LN = 6.9cm
m < J = 60 degrees
m < N = 30 degrees
Since IK = LN
LN = 6.9cm
Therefore, IK = 6.9cm
m< K = m< N
m < N = 30 degrees
Therefore, m < K = 30 degrees
NM = JK
JK = 8cm
Therefore, NM = 8cm
ML = IJ
IJ = 4 cm
Therefore, ML is 4cm
m < M = m < J
m< J = 60 degrees
Therefore, m < M = 60 degrees
m < I = m < L
m < I = 90 degrees
Therefore, m < L = 90 degrees
use the quadratic model y= -4x^2 + 8x + 8
Hello!
First of all, let's rewrite the quadratic equation:
[tex]y=-4x^2+8x+8[/tex]To solve it, let's replace where we have x by 100, look:
[tex]\begin{gathered} y=-4\cdot(100)^2+8\cdot(100)+8 \\ y=-4\cdot10,000+800+8 \\ y=-40,000+808 \\ \boxed{y=-39,192} \end{gathered}[/tex]Answer:y= -39,192
If $2000 is invested at 8% compounded continuously, what is the amount after 2 years?
Given:
P=$2000
r=8% = 0.08
t=2 years
Then, if the interest is compounded continuously for t years at a rate of r per year, then the compounded amount is given by:
[tex]A=P\cdot e^{rt}[/tex]Therefore:
[tex]A=2000\cdot e^{(0.08)(2)}=2000\cdot e^{0.16}=2347.02[/tex]Answer: $2347.02
Lamar received 7/8 of the 160 votes cast for class treasure how many votes did he receive
160 is 1
x is 7/8
[tex]\frac{\frac{7}{8}\times160}{1}=\frac{7}{8}\times160=140[/tex]ANSWER
He received 140 votes
1,000 raffle tickets were sold. There will be one first prize of $1,000 and one second prize of $500. The rest of the tickets will win nothing. Use the chart to calculate the expected value.
The value of the Variance is $1,247.75 and the value of Standard Deviation is $35.32.
What is meant by standard deviation ?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.
Karl Pearson is credited with giving SD the name "standard deviation." I wouldn't guess anything more than that he wanted to suggest it as a benchmark. If anything, standardization references either stand alone or make an indirect reference to SD.
Therefore the value of variance is $1,247.75 and the value of Standard Deviation is $35.32.
The complete question is :1,000 raffle tickets were sold. There will be one first prize of $1,000 and one second prize of $500. The rest of the tickets will win nothing. Use the following table to calculate the variance and standard deviation. μ = $1.50.
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At a middle school, 74 students have freckles. There are 258students in the school. To the nearest tenth of a percent,what percent of the students have freckles?
The answer is 28.7% of the students have freckles (approximated to the nearest tenth of a percent).
The point P = (x, — 5/7) lies on the unit circle shown below. What is the value of xin simplest form?
The point (x,y) on unit circle is
[tex](x,y)=(\cos \theta,\sin \theta)[/tex]We know y is "sin theta" and sin is "opposite" over "hypotenuse". Thus, we can draw a triangle
We see that "5" is opposite of theta and 7 is the hypotenuse.
To get x, we use the pythagorean theorem:
[tex]\begin{gathered} \text{leg}^2+\text{AnotherLeg}^2=\text{Hypotenuse}^2 \\ x^2+5^2=7^2^{} \\ x^2+25=49 \\ x^2=49-25 \\ x^2=24 \\ x=\sqrt[]{24} \\ x=2\sqrt[]{6} \end{gathered}[/tex]From unit circle formula, we know value of x is cos. Thus, we take the cosine ratio, adjacent over hypotenuse.
Adjacent is 2 Sqrt(6) and Hypotenuse is 7 Thus,
[tex]x=\frac{2\sqrt[]{6}}{7}[/tex]
Use mental math to find the equations that are true Select all that apply.
A. 400 ÷ 80 = 50
B. 4,000 ÷ 80 = 5
C. 400÷8= 50
D. 40,000 800 = 50
E. 40,000 ÷ 80 = 500
3 correct answers
True equations are C. 400 ÷ 8= 50, D. 40,000 ÷ 800 = 50, and E. 40,000 ÷ 80 = 500. A division or divisions into which a whole can or is divided A method of division is a method of dividing something.
What is division?Division is one of the four fundamental arithmetic operations, or how numbers are combined to create new numbers. Multiplication, addition, and subtraction are the other operations.In mathematics, division is the process of dividing a sum into equal parts. For example, we could divide a group of 20 people into four groups of five, five groups of four, and so on.The divisional process or act; the divisional state b: the act, procedure, or occurrence of dispersing among a number of people: distribution. A division or divisions into which a whole can or is divided A method of division is a method of dividing something. The division methods are classified into three types based on their difficulty level.These are the grouping method, also known as division by repeated subtraction, the short division method, also known as the bus stop method, and the long division method.To learn more about division refer to:
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show work!!What value of x makes the equation 33x=11 true33x=11
The value of x that makes the equation true is 1/3
Explanation:[tex]\text{33x = 11}[/tex]The value of x that will make the equation true will be a value when substituted will give same value on the right and left side of the equation.
To get x, we will divide both sides by the coefficient of x. The coefficient of x is 33. So we will divide both sides by 33:
[tex]\begin{gathered} \frac{33x}{33}\text{ = }\frac{11}{33} \\ x\text{ =}\frac{11}{33} \\ x\text{ = }\frac{1}{3} \end{gathered}[/tex]To determine if the value of x we got is right, we will substitute in the equation given:
[tex]\begin{gathered} 33x\text{ = 11} \\ 33(\frac{1}{3})\text{ = 11} \\ 11\text{ = 11} \\ left\text{ hand side = right hand side} \\ \\ Hence,\text{ the value of x that makes the equation true is }\frac{1}{3} \end{gathered}[/tex]solve 7c+10=17c A.) c=1B.) c=-1C.) C= -[tex] \frac{5}{12} [/tex]D.) c= -[tex] \frac{5}{12} [/tex]
A) c = 1
Explanations:The given equation is:
7c + 10 = 17c
Collect like terms:
17c - 7c = 10
10c = 10
Divide both sides by 10:
10c / 10 = 10 / 10
c = 1
Omar needs to read 5 novels each month. Let N be the number of novels Omar needs to read in M months. Write an equation relating N to M. Then graph your equation using the axes below
If Omar needs to read 5 novels each month, then we can express it as 5M because M represents months, and this expression is equal to N because it represents the number of novels Omar needs to read.
Therefore, the equation that represents this situation is 5M = N.Now, to graph the expression, we have to evaluate it when M = 1 and M = 2.
[tex]\begin{gathered} 5\cdot1=N\Rightarrow N=5 \\ 5\cdot2=N\Rightarrow N=10 \end{gathered}[/tex]So, the ordered pairs are (1,5) and (2,10), let's graph them to then draw the line through those points.
Need help with this one 3 tutors have canceled I been on it for 30 min
Answer: We have to find the JK, the simple answer is as follows, it is calculated by first finding the angle M and then using a trigonometric ratio to calculate the JK.
The simple and brief steps are as follows:
[tex]\begin{gathered} \angle M=\theta_T=\sin^{-1}(\frac{LJ}{LM})=\sin^{-1}(\frac{12}{20})=36.869897646^{\circ} \\ \\ \theta=\frac{\theta_T}{2}=18.434948823^{\circ}\approx18.435^{\circ} \end{gathered}[/tex]Therefore the JK is:
[tex]\begin{gathered} \tan(\theta)=\frac{JK}{JM}\rightarrow\tan(18.435^{\circ})=\frac{JK}{16} \\ \\ \\ JK=16\tan(18.435^{\circ})=5.3333333\approx5.34 \\ \\ \\ JK\approx5.34 \end{gathered}[/tex]Therefore JK is 5.34.
* 1. If [x] = 8, then what are the values of x?
Answer:
x = 8, x = -8
Explanation:
The absolute value function gives the magnitude of a number, i.e its distance from zero
|x| = 8 tells us that the number x is 8 units away from zero on the number line. Now there are two numbers that are 8 units away from zero. One is x = 8 and the other is x = -8.
Drag each volume of a prism to match a rectangular prism on the left with the given dimensions.54 cu. in.72 cu. in.36 cu. in.80 cu. in.Dimensions of Rectangular PrismVolume of Rectangular Prism 4 in., 3 in., 6 in. 6 in., 3 in., 2 in. 4 in., 5 in., 4 in. 2 in., 9 in., 3 in.
We need to determine the volume of each of the given rectangular prisms.
We know that the volume V of a rectangular prism with dimensions a, b, and c is given by:
[tex]V=a\cdot b\cdot c[/tex]Thus, to find the volume of each rectangular prism, we need to multiply its dimensions.
We obtain:
[tex]\begin{gathered} 4in,3in,6in\Rightarrow V=4in\cdot3in\cdot6in=(4\cdot3\cdot6)(in\cdot in\cdot in)=72in^{3} \\ \\ 6in,3in,2in\Rightarrow V=6in\cdot3in\cdot2in=(6\cdot3\cdot2)in^{3}=36in^{3} \\ \\ 4in,5in,4in\Rightarrow V=4in\cdot5in\cdot4in=(4\cdot5\cdot4)_{}in^{3}=80in^{3} \\ \\ 2in,9in,3in\Rightarrow V=2in\cdot9in\cdot3in=(2\cdot9\cdot3)in^{3}=54in^{3} \end{gathered}[/tex]Therefore, dragging each volume to its respective place, we obtain:
which of the following is not an ordered pair form the function f(x) = 5x - 6?
the function is.
[tex]f(x)=5x-6[/tex]So to solve it we need to replace the order pair and see if the equation have sence so:
For (3,9)
[tex]\begin{gathered} 9=5\cdot3-6 \\ 9=15-6 \\ 9=9 \end{gathered}[/tex]So A is correct
For (1,-1)
[tex]undefined[/tex]What angle (in racians) between 0 and 2(pi) has the same cosine as [tex] \binom{6\pi}{11} [/tex]
180 degrees is equivalent to pi radians
[tex]\begin{gathered} \text{ }\pi\text{ = 180} \\ \\ \frac{6\text{ }\pi\text{ }}{11}\text{ = p} \end{gathered}[/tex]p = (6 x 180) / 11
[tex]98.18^0[/tex]Of the 100 people who tested three(3) sodas, 60 people preferred soda A. What fraction of the people preferred soda A? (Express As Fraction)
please help!!!! the options for the select part are x or y
We are given the graph of a function, which we are told that is polynomial of degree 4.
Recall that the domain of a function is the values of x for which the the function is defined. Using the graph, the domain is the set of x coordinates of the point s of the graph.
On the other side, recall that the range of a function is the set of values that the function takes. So, using the graph, the range is the set of y coordinates of the points of the graph.
Since we know that the graph is from a polynomial of degree 4, we recall that polynomials of any degree are defined for every value of x. Then, the domain of this graph is (-infinity, infinity).
On the other side, to determine the range. we take a look at the y coordinates of the graph. So the highest value from the graph is 7. Also, we see that the polynomial decreseases its value as x gets bigger or smaller. This behavior stays true globally, so, we can say that the range of the function is the interval (-infinity,7].
What are your thoughts? Is mathematics important in getting a good paid career?
Based on the statistics shown, we can see that 8 out of the 9 of the best-paying college majors are engineers, and in engineering, there is a lot of math involved, which means that math is important in getting a good-paid career.
Answer: mathematics is important in getting a good-paid career.
The figure shows a child estimating the height of a tree by looking at the topof the tree with a mirror. Assuming that both the child and the tree form rightangles with the ground, which of the following proportions can be used toestimate the height of the tree?h ft4 ftk5 ft12 ftisDC124
To get the height of the tree, we will apply the principle of similar triangles
For similar triangles, we can take ratios of similar sides of the two triangles
The sketch is given below
We can now compare similar sides as follow
[tex]\frac{h}{4}=\frac{12}{5}[/tex]Thus, the answer is option D
In the picture, point C is a point of tangency.158AEDA =DE=
we have that
If point C is a point of tangency
then
triangle ACD is a right triangle
so
Applying Pythagorean Theorem
DA^2=AC^2+CD^2
we have
AC=8 units
CD=15 units
substitute
DA^2=8^2+15^2
DA^2=64+225
DA^2=289
DA=17 unitsPart 2
Find DE
we have that
DA=DE+EA ------> by addition postulate theorem
we have
DA=17 units
EA=AC=8 units
substitute
17=8+DE
DE=9 unitssimplify 38-87. I dont know
To check if we can simplify the fraction 38/87, we need to decompose the numerator and the denominator in their prime factors:
[tex]\begin{gathered} 38=2\cdot19 \\ 87=3\cdot29 \end{gathered}[/tex]If the two numbers have any prime factor in common, we can divide both numbers by this prime factor. But in this case, the two numbers don't have prime factors in common, so we can't simplify the fraction further.
So the fraction 38/87 is already in the simplest fraction form.
Cost of Steak: Justin is purchasing two top sirloin steaks. The meat costs $4.00 per pound, and each steak weighs 6 lb 4 oz. What is the cost of the steak?The steak costs $.
Note thae 1 pound = 16 ounces
4 oz x 1/16 = 0.25 lb
The total weight of steak now is 6 lb + 0.25 lb = 6.25 lb
Multiply this weight by the cost per pound :
6.25 lb x $4 = $25
The answer is $25