Given data:
The given angle .
The given angle AOB is an obtuse angle.
Thus, third option is correct.
What is the connection between side ratios and angle in a right triangle
Trigonometric ratios are ratios between any two sides of a right triangle that can then be used to determine the measure of an angle between those two sides. Primary trigonometric ratios (in a right triangle trigonometry) are: sin (x), cos (x) and tan (x)
On the basis of any two side lengths, we may even determine the acute angle measurements in a right triangle. We may get the ratios of the lengths of the triangle's sides to an acute angle in a right triangle by knowing the acute angle's measurement.
What relationship exists between a triangle's side ratios and angle?In a triangle, the longest side is located across from the largest angle, while the shortest side is located across from the smallest angle.
Triangle Unfairness: The lengths of any two sides added together in a triangle always exceed the length of the third side.
Pythagoras Theorem, a²+b²=c² in a right triangle with hypotenuse c.
A triangle is a right triangle if its sides conform to the relationship a²+b²=c²
The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The other two inner angles add up to 90 degrees.
Remember that the Pythagorean theorem only holds true for right triangles, in which case the converse of the theorem also holds true. In other words, if a triangle's sides satisfy the connection, then it must be a right triangle.
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3. The difference of two-thirds of a number x and6 is at least -24. Which inequality represents allpossible values for x?
We will solve as follows:
The expression represented in the text is:
[tex]\frac{2}{3}x-6\ge-24[/tex]Now, we solve for x:
[tex]\Rightarrow\frac{2}{3}x\ge-18\Rightarrow2x\ge-54[/tex][tex]\Rightarrow x\ge-27[/tex]So, the solution is x >= 27. [Option D]
Angel is at a birthday party. There are 12 cupcakes where some are blue and some are green. Out of There are 8 green cupcakes. Express the number of blue cupcakes as a decimal
12 cupcakes
8 green cupcakes
To find the number of blue cupcakes subtract the green cupcakes (8) to the total cupcakes:
12 -8 = 4 blue cupcakes
To express as a decimal, divide the number of blue cupcakes by the total number of cupcakes:
4/12 = 0.33333
The points scored on a test for a sample of 39 students are summarized in the following table
the mean score of the test for sample of 39 students is 76.92.
The data is given as:
Number of students Score of each student Total score
07 90 630
17 80 1360
11 70 770
04 60 240
The total number of students = 7 + 17 + 11 + 4
n = 39
Total scores = 630 + 1360 + 770 + 240
T = 3000
Mean score = T / n
M = 3000 / 39
M = 1000 / 13
M = 76.92
Therefore, the mean score of the test for sample of 39 students is 76.92.
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I'll send you the pic
1. 5 (3) = 15
2. 4 (8) = 32
3. 6 (3/2) = 9
4. 12 ( ) = ?
Look at the models below. DO Tell whether each statement is True or False. equivalent to į because à has 2 times as many shaded parts and 2 times as many equal parts as True False 3 b. , is equivalent to because has 2 times as many parts shaded and 2 more equal parts than True 0 False 4 is equivalent to because both models have i shaded part True False d. is equivalent to because á has 2 + 6 = 8 equal parts. True False
a.
Since:
[tex]\frac{1}{3}\equiv\frac{2}{2}\times\frac{1}{3}=\frac{2}{6}[/tex]The statement is true
b.
Since:
[tex]\frac{2}{2}\times\frac{1}{4}=\frac{2}{8}\ne\frac{2}{6}[/tex]The statement is false
c.
Since:
[tex]\frac{1}{4}\equiv\frac{2}{2}\times\frac{1}{4}=\frac{2}{8}[/tex]The statement is true.
d.
Since:
[tex]\begin{gathered} \frac{2}{6}=\frac{1}{3} \\ \frac{2}{8}=\frac{1}{4} \\ \frac{1}{4}\ne\frac{1}{3} \end{gathered}[/tex]The statement is false.
(k²-7k+ 10) ÷ (k − 1)
Consider the functions g(x) = 2x + 1 and h(x) = 2x + 2 for the domain 0 < x < 5 Without evaluating or graphing the functions, how do the ranges compare?
Without evaluating or graphing the functions, it is obvious that the minimum and maximum values in the range of h(x) is greater than the minimum and maximum values in the range of g(x) by 1.
What is a domain?In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain represents the input values (x-values) to a function.
What is a range?In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values (real numbers), which are shown on the y-axis of a graph.
In conclusion, the minimum and maximum values in the range of h(x) differs from those of function g(x) by 1.
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Gaby's piggy bank contains quarters and nickels worth $7.50. If she has 58 coins in all, howmany of each does she have?
let the number of quarters = x , and the number of nickels = y
quarter = $0.25 and nickel = $0.05
So, x + y = 58
x = 58 - y
and 0.25 x + 0.05 y = 7.5
so,
0.25 (58 - y) + 0.05 = 7.5
14.5 - 0.25 y + 0.05 y = 7.5
-0.2 y = -7
y = -7/-0.2 = 35
x = 58 - 35 = 23
So, the number of quarters = 23 and the number of nickels = 35
what is the value of x would make lines l and m parrallel
We know that if l and m are parallel there might be some angles that are equal to others:
Alternate interior angles
The angles closed by a blue circle are alternate interior angles, then they should be equal if l||m.
Vertcial angles
The angles closed by an orange circle are vertical angles, because they are opposite to each other on two crossed lines.
Now, we know two angles of the triangle of the middle:
We know that the addition of all the inner angles of a triangle is 180º. This is:
50º + 55º + xº = 180º
↓
105º + xº = 180º
Now, we can find x:
105º + xº = 180º
↓
xº = 180º - 105º
xº = 75º
Answer: xº = 75ºclaudia earns overtime pay when she works more then 40 hours in a week how many hours of overtime pay did she work for the week of march 4march 4-10march 4 -- 8.5march 5 -- offmarch 6 -- 9.25march 7 -- 8.75march 8 -- 10march 9 -- offmarch 10 -- 7.75A.44.25B. 40.0C. 4.25D. 2.25
She earns overtime pay when she works more than 40 hours in one week . The number of overtime pay she works for the weeks of march 4 can be calculated below
[tex]\begin{gathered} \text{total hour worked =}8.5\text{ +9.25+8.75+10+7.75=}44.25 \\ \text{The number of overtime pay for the w}eek\text{ of march 4 is 44.25} \end{gathered}[/tex]whats the variance and the standard deviation of the data set 6,9,2,5,4,10,3,12,2,7,7,8
Given:
6,9,2,5,4,10,3,12,2,7,7,8
Required:
To find the variation and standard deviation of the given data set.
Explanation:
Now variation is
[tex]s^2=\frac{\sum_{i\mathop{=}1}^n(x_i-x)^2}{n-1}[/tex]The numerator in the above is sum of the square of the given data.
Therefore,
[tex]\begin{gathered} =(6-6.25)^2+(9-6.25)^2+(2-6.25)^2+(5-6.25)^2+(4-6.25)^2+(10-6.25)^2+ \\ (3-6.25)^2+(12-6.25)^2+(2-6.25)^2+(7-6.25)^2+(7-6.25)^2+(8-6.25)^2 \end{gathered}[/tex][tex]\begin{gathered} s^2=\frac{112.25}{12-1} \\ \\ =\frac{112.25}{11} \\ \\ =10.2045 \end{gathered}[/tex]Final Answer:
[tex]10.2045[/tex]Latrice eamns 5 points for each question she answers correctly. Her grade, g is described by g = 5c, where c is the number of questions answered correctly. What is the dependent variable-Number of points per question-total grade-number of questions missed-number of questions right
The equation that describe's Latrice grade is given by:
g = 5c
g represen
Write an equation in slope-intercept form for the line that is parallel to y = 3x + 7 and passes through the point (-4, -8).
The line parallel to y = 3x +7 and passes through the point (-4,-8) is
y=3x+4
What is a slope-intercept form?It gives the graph of a straight line and it is represented in the form
y= mx +c. It is one of the form used to calculate the equation of a straight line. We have to calculate the slope of the line from the equation. The slope calculated can be used in the slope-intercept form. It is the most popular form of a straight line.
We need to find the slope to the line y = 3x +7.
The slope of a line is m
Here, from the equation y=3x+7, m=3
So, m=3
The slope-intercept form is,
y= mx +c
-8 = 3(-4)+c
-8=-12+c
c=4 and m=3
Now, the above equation equation becomes,
y=3x+4
The line parallel to y = 3x +7 and passes through the point (-4,-8) is
y=3x+4
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Instructions: varies indirectly with . If =7 when =−4, find when =2. Use the forward slash (i.e. "/") for all fractions (e.g. -1/2 is the same as −12).
y varies directly as x
This can be written mathematically as:
y = kx
If y = 7, x = -4
Solve for the constant k
7 = -4k
k = -7/4
The equation is:
y = -7/4 x
When x = 2
substitute x =2 anto the equatio n y = -7/4 x
[tex]\begin{gathered} y=-\frac{7}{4}\times2 \\ \\ y=-\frac{7}{2} \end{gathered}[/tex]Simple calculator test - determine the angle, θ, to the nearest whole degree from each of the following:A. cos(θ) = 0.2079B. tan(θ) = 0.2126C. sin(θ) = 0.5446
Step 1
Find the value of θ using the inverse sign of all the functions.
A)
[tex]\begin{gathered} cos(\theta)=0.2079 \\ \theta=\cos^{-1}(0.2079) \\ \theta\approx78^{\circ} \end{gathered}[/tex]B)
[tex]\begin{gathered} tan(\theta)=0.2126 \\ \theta=\tan^{-1}(0.2126) \\ \theta\approx12^{\circ} \end{gathered}[/tex]C)
[tex]\begin{gathered} sin(\theta)=0.5446 \\ \theta=\sin^{-1}(0.5446) \\ \theta\approx33^{\circ} \end{gathered}[/tex]Which values has three significant figures?14001001101.22310
a) 1400 has 2 significant figures, zeros are no consider as significant figures
b) 1001 has 4 significant figures, zeros in between two nonzero numbers are significant figures
c) 101.2 has 4 significant figures, zeros in between two nonzero numbers are significant figures. Nonzero number are significant figures
d) 2310 has three significant figures. 2,3 and 1 are significant figures.
I really don't understand this lesson can you help me please
Data:
M = Math books
E = Englisg books
TB = Total books
The total of the books is the addition of the math and english books
[tex]TB\text{ = M+ E}[/tex]The Math books are: M= E-9 (Nine less that English books (E))
So replacing this in the expression for Total Books:
[tex]TB=(E-9)+E\text{ }\Rightarrow TB=E-9+E[/tex]The final expression is:[tex]TB=2E-9[/tex]Not homework just review for test not worth any points
Recall that:
Interest is the monetary gain for lending money to a third party.
Simple interest is applying the interest to the original amount without considering the extra flow of money each time the interest is applied.
Compounded interest is applying the interest to the total amount including the extra flow of money each time the interest is applied.
1) Plan A. From the given information, in 12 months Ari will earn:
[tex]I=500\cdot0.065\cdot12=390.[/tex]dollars, therefore she will have a total of $890.00.
2) Plan B. Now we use the formula for compounded interest to compute the total amount that Ari will have after one year:
[tex]A=500(1+0.065)^{12}=500\cdot2.129096\approx1064.55.[/tex]3) From the above calculations, we conclude that Ari will make more money if she invests in plan B.
4) Ari has to leave the money for another:
Using plan B. Let t be the number of extra months Ari needs to leave the money in the fund, then:
[tex]1100=500\cdot(1.065)^{12+t}\text{.}[/tex]Solving for t, we get:
[tex]\begin{gathered} 1.065^{12+t}=2.2, \\ (12+t)ln(1.065)=\ln (2.2), \\ 12+t=\frac{\ln (2.2)}{\ln (1.065)}=12.52, \\ t=12.52-12=0.52. \end{gathered}[/tex]Then, Ari needs to leave the money for another half a month but since the interest is applied each month she needs to leave the money for another whole month.
Using Plan A: Let t be the number of extra months Ari needs to leave the money in the fund, then:
[tex]1100=500\cdot0.065\cdot(12+t)\text{ +500.}[/tex]Solving for t we get:
[tex]\begin{gathered} \frac{1100-500}{500\cdot0.065}=12+t, \\ t=\frac{600}{32.5}-12, \\ t=6.46. \end{gathered}[/tex]Then, Ari needs to leave the money for another 6.46 months but since the interest is applied monthly she needs to leave the money for another 7 months.
7. The manager of a local restaurant has found that his cost function for producing coffee is C(x) = .097x, where C(x) is the total cost in dollars of producing x cups. (He is ignoring the cost of the coffeepot and the cost labor.) Find the total cost of producing the following numbers of cups of coffee. (a) 1000 cups (b) 1001 cups (c) What is the marginal cost for any cup? Let C(x) be the total cost in dollars to manufacture x items. Find the average cost in exercises 8 and 9.
To solve for the total cost of producing the following numbers of cups of coffee:
[tex]\begin{gathered} C(x)=0.097x \\ \end{gathered}[/tex]where
[tex]\begin{gathered} x=nu\text{mber of cups of coff}e \\ C(x)=total\text{ cost }in\text{ dollars of producing x cups} \end{gathered}[/tex](a) The total cost of producing 1000 cups =
[tex]\begin{gathered} C(x)=0.097x \\ x=1000 \\ C(x)=1000(0.097)=\text{ \$97} \end{gathered}[/tex](b) The total cost of producing 1001 cups =
[tex]\begin{gathered} C(x)=0.097x \\ x=1001 \\ C(x)=1001(0.097)=\text{ \$97}.097 \end{gathered}[/tex](c) The marginal cost for any cup = $0.097
marginal cost can be found by taking the derivative of the function
[tex]\begin{gathered} C(x)=0.097x \\ C^1(x)=0.097=\text{ \$0.097} \end{gathered}[/tex]Solve by using substitution.=−3−3=−4−5
hdhduxhx, this is the solution to the exercise:
Multiplying by -1 the second equation, we have:
y = -3x - 3
-y = 4x + 5
____________
0 = x + 2
x = -2
_____________
Now we can solve for y in the first equation, this way:
y = - 3x - 3
y = -3 (-2) - 3
y = 6 - 3
y = 3
____________
Finally, let's prove that x = -2 and y = 3 is correct for the second equation, as follows:
y = -4x - 5
3 = -4 (-2) - 5
3 = 8 - 5
3 = 3
___________
We proved that x = -2 and y = 3 is correct.
Thinking: Two students were having a discussion. They stated:“Since we factored f(x) = 2x2 + 3x + 1 into (2x+1)(x+1) we could say this:If we let h(x) = 2x + 1 and g(x) = x + 1, then we can say f(x) = h(x)g(x)” Howmight you verify their statement?
Given:
If we let h(x) = 2x + 1 and g(x) = x + 1 and
[tex]f(x)=2x^2+3x+1[/tex]Required:
How might you verify their statement?
Explanation:
We have h(x) and g(x)
[tex]\begin{gathered} =h(x)g(x) \\ =(2x+1)(x+1) \\ =2x^2+2x+x+1 \\ 2x^2+3x+1=f(x) \\ f(x)=h(x)g(x) \end{gathered}[/tex]Answer:
Hence, verified the statement.
What are the coordinates of point P on the directed line segment from R to Q such that 5 Pis 6 the length of the line segment from R to Q? Round to the nearest tenth, if necessary. A (-3.5, 2.3 ) B. (3.5, -2.3 ) C. (-3, 2) D. (3, 2)
Answer
Option A is correct.
P(x, y) = (-3.5, 2.3)
Explanation
Mathematically, if a point P(x, y) divides the coordinates R(x₁, y₁) and Q(x₂, y₂) internally in the ratio m:n then point P(x, y) is given as
x = [(mx₂ + nx₁)/(m + n)]
y = [(my₂ + ny₁)/(m + n)]
For this question,
R(x₁, y₁) and Q(x₂, y₂) = R (4, -1) and Q (-5, 3)
m:n = 5:1 (5/6 of a distance divides the two parts of the distance into 5/6 and 1/6, hence, the ratio is 5:1)
x₂ = -5
x₁ = 4
y₂ = 3
y₁ = -1
m = 5
n = 1
x = [(mx₂ + nx₁)/(m + n)]
x = [(5×-5 + 1×4)/(5 + 1)]
x = [(-25 + 4)/(5 + 1)]
x = (-21/6)
x = -3.5
y = [(my₂ + ny₁)/(m + n)]
y = [(5×3 + 1×-1)/(5 + 1)]
y = [(15 - 1)/(5 + 1)]
y = (14/6)
y = 2.3
P(x, y) = (-3.5, 2.3)
Hope this Helps!!!
Consider the quadratic function.What are the x-intercepts and y-intercept?What is the equation of the axis of symmetry?What are the coordinates of the vertex?Graph the function on the coordinate plane. Include the axis of symmetry.
Kindly check below
1) Let's do it in parts.
a) We can find the x-intercepts by using the factor zero property from each factor. Like this:
[tex]\begin{gathered} -(x+4)=0\Rightarrow-x-4=0\Rightarrow-x=4\Rightarrow x=-4 \\ (x-1)=0\Rightarrow x=1 \end{gathered}[/tex]The best way to find the y-intercept with this factored form is by plugging into that equation x=0
[tex]\begin{gathered} f(x)=-\left(x+4\right)\left(x-1\right) \\ y=-\left(x+4\right)\left(x-1\right) \\ y=-(0+4)(0-1) \\ y=-(4)(-1) \\ y=4 \end{gathered}[/tex]b) Expanding those factors by distributing them (FOIL) we can find this:
[tex]\begin{gathered} f(x)=-\left(x+4\right)\left(x-1\right) \\ f(x)=-\left(xx+x\left(-1\right)+4x+4\left(-1\right)\right) \\ f(x)=-x^2-3x+4 \end{gathered}[/tex]So now, let's find the x-coordinate of the vertex V(h,k):
[tex]\begin{gathered} h=\frac{-b}{2a}=\frac{-(-3)}{2(-1)}=\frac{3}{-2}=-\frac{3}{2} \\ Axis\:of\:symmetry:x=-3/2 \end{gathered}[/tex]c) The coordinates of the vertex can be found by plugging the x-coordinate into the quadratic function. This way:
[tex]\begin{gathered} f(x)=-\left(x+4\right)\left(x-1\right) \\ f(-\frac{3}{2})=-(-\frac{3}{2}+4)(-\frac{3}{2}-1)=\frac{25}{4} \\ \\ V(-\frac{3}{2},\frac{25}{4}) \end{gathered}[/tex]d) Finally, we can plot that function by setting a table:
So plotting these points (-2,6),(-1,6), (0,4), (1,0),(2,-6) and opening down the parabola for a is -1 we can plot this:
in the diagram pq and St find the slope of st
1) Looking at that diagram, we can see that Point S shares the same x-coordinate from point Q since they are on the same Vertical Line. So, it's safe to say that the x-coordinate of Point S is x=-2
2) And point S is at the same horizontal axis of point P. So for the same principle, we can say that the y-coordinate of point S is y=4
S(-2,4)
3) So let's find the Fourth point of that figure, so let's find the slope of PQ
[tex]\begin{gathered} m_{PQ}=\frac{4-1}{1-(-2)}=\frac{3}{-1+2}=\frac{3}{3}=1 \\ \\ m_{ST}=-1 \end{gathered}[/tex]Since PQ is perpendicular to ST then the slope is the opposite reciprocal of 1, i.e. -1
The ratio of the length of an airplane wing to its width is 9 to 1. If the length of a wing is 43.9 metérs, how wide must it be? The airplane wing must be ____ meters wide. (Round to the nearest hundredth.)
To compute the width of the wing, we can use the next proportion
[tex]\frac{9\text{ meters long}}{43.9\text{ meters long}}=\frac{1\text{ meter wide}}{x\text{ meters wide}}[/tex]Solving for x,
[tex]\begin{gathered} 9\cdot x=1\cdot43.9 \\ x=\frac{43.9}{9} \\ x=4.88 \end{gathered}[/tex]The airplane wing must be 4.88 meters wide.
The probability that VSU and KSU both win a basketball game in the same week is 47%. Theprobability that VSU wins is 50%. What is the probability that KSU will win given that VSUhas already won?
EXPLANATION
Let the probability that KSU will win a game be Pr(A), and let the probability that VSU wins be Pr(B). Therefore;
[tex]\begin{gathered} Pr(A\cap B)=0.47 \\ Pr(B)=0.5 \end{gathered}[/tex]We can then use the conditional probability formula below.
[tex]Pr(A|B)=\frac{Pr(A\cap B)}{Pr(B)}[/tex]Therefore, the probability that KSU will win given that VSU has already won becomes
[tex]Pr(A|B)=\frac{0.47}{0.50}=0.94[/tex]Answer: 0.94
the sum of 2 numbers is 75. the second number is 3 less than twice the first. find the numbers
SOLUTION
Let one of the numbers be x
Using the statement: The second number is 3 less than twice the first
Then the second number is
[tex]2x-3[/tex]Since, the sum of 2 numbers is 75
It follows:
[tex]x+2x-3=75[/tex]Solve for x
[tex]\begin{gathered} 3x=75+3 \\ 3x=78 \\ x=\frac{78}{3} \\ x=26 \end{gathered}[/tex]Therefore the first number is 24
The second number is
[tex]\begin{gathered} 2(26)-3 \\ =49 \end{gathered}[/tex]therefore the numbers are 49 and 26.
will you kindly assist me pls. work math step by step answer in numbers pls. to work how you got the answer
Translating for numbers, we have:
[tex]\frac{1}{5}=0,2\rightarrow3\frac{1}{5}=3,2[/tex]This way, we can make what follows:
[tex]Day_1+Day_2=3\frac{1}{5}+4=3,2+4=7,2_{}[/tex]Calculating now the amount is needed to complete the 9 miles:
[tex]Day_3=9-7,2\text{ = 1,8}[/tex]--------------------------------------------------------------------------------------------------------
And from here, the solution with the fractions.
We can start with the sum of what Shelly has biked in the first two days:
[tex]Day_1+Day_2=3\frac{1}{5}+4=7\frac{1}{5}_{}[/tex]This is the amount of mile she has already biked. But we know she needs to complete all the 9 miles in the third day. So, the difference from 9 and the amount she already did is the amount she needs to bike in the third day.
[tex]\text{Day}_3\text{ = 9 - 7}\frac{1}{5}\text{ = 1}\frac{4}{5}[/tex]Not ConnectedThunde...lt BridgeNot Connected2 (07.01 HC)answer the following question. Find the value of sin x and cosy. What relationship do the ratios of sin x® and cos yº share?
The given triangle is a right-angled triangle.
Consider PO is Hypotenuse.
By using the Pythagoras formula, we get
[tex]PO^2=8^2+6^2[/tex][tex]PO^2=64+36[/tex][tex]PO^2=100=10^2[/tex][tex]PO=10[/tex]Consider the angle x:
Recall the sine formula
[tex]\sin \theta=\frac{Opposite\text{ side}}{\text{Hypotenuse}}[/tex]Substitute Opposite side =6 and Hypotenuse=10, we get
[tex]\sin x^o=\frac{6}{10}[/tex][tex]\sin x^o=\frac{3}{5}[/tex][tex]\text{Use sin }36.869=\frac{3}{5}[/tex][tex]\sin x^o=\sin 36.869[/tex][tex]x^o=37[/tex]Consider the angle y:
Recall the sine formula
[tex]\sin \theta=\frac{Opposite\text{ side}}{\text{Hypotenuse}}[/tex]Substitute Opposite side =8 and Hypotenuse=10, we get
[tex]\sin y^o=\frac{8}{10}[/tex][tex]\sin y^o=\frac{4}{5}[/tex][tex]\text{Use }\sin 53.13^{}=\frac{4}{5}[/tex][tex]\sin y^o=\sin \text{ 53.13}[/tex][tex]y^o=53^{}[/tex]Hence the required values are
[tex]x^o=37^o[/tex][tex]y^o=53^o[/tex]