In XYZ, XY=14, YZ=22, and XZ=28. What is the measure of angle Z to the nearest degree? *Law of Cosines
Answers
Solution
Draw the diagram
So using cosine rule
[tex]\begin{gathered} z^2=x^2+y^2-2xycosZ \\ \\ cosZ=\frac{x^2+y^2-z^2}{2xy} \\ \\ cosZ=\frac{22^2+28^2-14^2}{2(22)(28)} \\ \\ cosZ=\frac{67}{77} \\ \\ Z=30\degree\text{ \lparen to the nearest degree\rparen} \end{gathered}[/tex]
Related Questions
Joe has 3/4 cup of paint in a container. He uses 1/3 cup on a project and then adds another 1/2 cup. How much paint does he have now?
Answers
Answer:
Step-by-step explanation:
The cup of paint he has now is 11/12.
What is the amount of paint he has now?We are basically going to add or subtract the quantity of cup added or used respectively.
Initially, he has 3/4 cup of paint.
He uses 1/3 cup out of the 3/4 cup of paint, so we subtract 1/3 from 3/4:
= 3/4 - 1/3 = 5/12
He adds another 1/2 cup, so we add 1/2 to what we have left previously (5/12):
= 5/12 + 1/2 = 11/12
Therefore, the amount of paint he has now is 11/12 cup
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Last semester, Jim earned an A in his 4-credit MATH 128 class, a B+ in his 3-credit ENG 152 class, a C- is his 2-credit COM 210 class, and a A- in his 5-credit HIST 151 class. What was his GPA for the semester? Be sure to use the following grade values in your calculation.
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Jim's GPA for the last semester was 3.41.
What is the GPA?The Grade Point Average (GPA) is the summary of academic achievement in an academic period (semester).
GPA is computed as course unit value multiplied by grade points, divided by the sum of course units.
The Grade Point Average (GPA) may also be described as the cumulative GPA, that is, the sum of the grade points divided by the sum of the units.
Determining a student's GPA helps the school administrators to ascertain the student's academic progress, verifying areas for further improvement.
Class Course Grade Credit Hours Grade Value Total Grade
MATH 128 A 4 4.0 16 (4 x 4)
ENG 152 B+ 3 3.3 9.9 (3 x 3.3)
COM 210 C- 2 1.7 3.4 (2 x 1.7)
HIST 151 A- 5 3.7 18.5 (5 x 3.7)
Total 14 47.8
GPA = 3.41 (47.8/14)
Thus, for last semester, Jim's GPA was 3.41.
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Complete the remaining steps of the proof:given: -angle QSR is congruent to angle TRS-side PR is congruent to side PSProve:triangle QSR is congruent to triangle TRS. StatementsReasons1. Given1. PR = PSZQSR *ZTRS2. ZTSR * ZQRS 2.I3. SR RS3.4. AQSR SATRS4.Corresponding parts of congruent triangles arecongruent:: Base angles of an isosceles triangle are congruentReflexive property:: Side-Angle-Side (SAS) postulateAngle-Side-Angle (ASA) postulate
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Write out the given parameter for the proofing
Given:
[tex]\begin{gathered} \Delta QSR\cong\Delta TRS \\ \vec{}PR\cong\vec{}PS \end{gathered}[/tex]From the given parameters, it can be seen that triangle PSR is an isosceles triangle because two sides (line PR and line PS) are equal
An isosceles triangle has two equal base angles.
[tex]\angle TSR\cong\angle\text{QRS(base angles of isosceles triangle are equal)}[/tex]Triangle QSR and triangle TRS has a common side which is line SR and line RS. This property is reffered to as reflective property
[tex]\vec{}SR\cong\vec{}RS(reflective\text{ property)}[/tex]From the above proofs, it can be seen the triangle QSR and triangle TRS have a same side and same angles
Therefore,
[tex]\Delta QSR\cong\Delta TRS(angle-side-angle(ASA)postulate)[/tex]Nothing
What line gets the proportionality between y and x of 4/3
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Reason: 4/3 proportionality means y/x
y = 4, x = 3
Graph these points (3, 4) and line B crosses this coordinate
7x+19 (less than or equal too) 12
Answers
Answer:
x [tex]\leq[/tex] 17/7
Step-by-step explanation:
7x + 19 [tex]\leq[/tex] 12
Is the inequality you are trying to solve.
When solving an inequality, we solve it like a regular equation and do inverse operations by looking at the number and doing the opposite of whatever its operation is. Whatever happens on one side happens to the other. So you would first subtract 19 on both sides.
1. 7x + 19 [tex]\leq[/tex] 12
-19 -19
7x [tex]\leq[/tex] -17
the reason we subtracted was because the opposite operation to addition is subtraction as the number 19 had had a plus sign behind it
--
We would now divide as the operation opposite to multiplication is division and 7x is 7 times x
2. 7x [tex]\leq[/tex] -17
÷7 ÷7
x [tex]\leq[/tex] [tex]\frac{17}{7}[/tex] OR 2 [tex]\frac{3}{7}[/tex]
--
The answer is:
x [tex]\leq[/tex] 17/7
Hope this helped!
Larissa invested $19,000 in an eleven-year CD giving 7.5% interest, but needed to withdraw $2,500 after four years. If the CD’s penalty for early withdrawal was one year’s worth of interest on the amount withdrawn, how much money did Larissa have when the CD reached maturity, not including the amount she withdrew?
Answers
Answer:
$32190
Step-by-step explanation:
19,000 x 1.3 = 24700
24700-2500=22200
22200 x 1.45 = 32190
Suppose a normal distribution has a mean of 18 abd a standard deviation of 4. A value of 24 is how many standard deviations away from the mean
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Normal Distribution
The normal distribution can be described by two parameters: the mean and the standard deviation.
We are given the parameters of a normal distribution as follows:
Mean = 18
SD = 4
A value of 24 is 24 - 18 = 6 units away from the center of the distribution, or the mean value.
Calculating the ratio of 6 units by 4 units, we get 6 / 4 = 1.5
This means the given value is 1.5 standard deviations away from the mean
Graph they given functions FNG in the same rectangular coordinate system describe the graph of G is related to the graph of F
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Functions given:
[tex]f(x)=4x[/tex][tex]g(x)=4x-4[/tex]Using a graphing calculator, we can find the graph of both functions:
The red line is representing f(x) graphically, while the blue line is representing g(x) graphically.
As they have the same slope, then f(x) is parallel to g(x).
Answer:
The functions are parallel.
calculate the the population standard division of the data set 5,4,5,3 to 6 round to the nearest hundred
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Do you have a picture of your question?
OPTION ONE GRAGH A GRAGH B OPTION TWO APPERAS TO INCREASE LESSAPPERAS TO INCREASE MOREIS LESSINCREASES MOREINCREASES LESS
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To emphasize the slow increase in profits, it would be best for Bradley to use Graph A for his presentation.
Bradley should use this graph for his presentation because the profit appears to increase less on this graph (regardless both graphs show the same information)
Determine the constant of proportionality for the relationship.
p equals 2 over 150
p = 0.0133
p = 75
p = 150
Answers
The constant of proportionality for the relationship is p = 75.
How to express proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent.
In other words, a proportional relationship is one in which two quantities vary directly with each other.
It can be represented as follows:
y = px
where
p = constant of proportionalityx and y are the variablesTherefore, when we are given the variables the constant of proportionality can be found as follows:
where
y = 150
x = 2
p = y / x
p = 150 / 2
Therefore,
p = 75
Complete question: Determine the constant of proportionality for the relationship: y = px where y = 150 and x = 2
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The ratio of boys to girls in Ms. Cunningham’s class is 2 to 3. There are 18 girls in the class. What is the TOTAL number of students in Ms. Cunningham’s class?
Responses
Answers
The total number of students(boys and girls) in Ms. Cunningham’s class are 30.
Number of girls in the class =18
The ratio of boys to girls in Ms. Cunningham’s class is 2 to 3
i.e. Ratio of boys and girls =2:3
Boys : Girls = 2 : 3
B/G = 2/3 -------1.
B/18 = 2/3
B = (18 x 2)/3
Boys = 12
Number of boys in the class = 12
Boy = 2x
12 = 2x
x = 12/2 = 6
number of girls in the class is 3x
3 x 6 = 18
Therefore, total number of students =12+18=30
The total number of students(boys and girls) in Ms. Cunningham’s class are 30.
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The function y=f(x)is graphed below. What is the average rate of change of the function f(x) on the interval−4≤x≤−1
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STEP - BY - STEP EXPLANATION
What to find?
The average rate of change of the given function.
Given:
Step 1
State the average rate of change formula.
[tex]Average\text{ rate of change=}\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]Step 2
Determine the values of the function at the given interval.
Let x₁ = -4 and x₂ = -1
Locate f(x₁) and f(x₂) on the graph given.
f(x₁) = 4 and f(x₂)= -2
Step 3
Substitute the values into the formula and simplify.
[tex]Average\text{ rate of change=}\frac{-2-4}{-1+4}[/tex][tex]=\frac{-6}{3}[/tex][tex]=-2[/tex]ANSWER
Average rate of change = -2
3k-18 written as a product of 3
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The answer is 6
If you divide 18 by 3 it's 6
19. Put these numbers in order from least to greatest: V36, V27, V16, V10, V8, V64(2 pts.)-2520 adenotto
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EXPLANATION
Putting the numbers from least to greast give us:
8, 10, 16, 27, 36, 63
Assume the point (10,20) belongs to the graph of f(x) what point belongs to the graph of y = f( x - 5 )(15,20) (10,25) (5,20) (10,15)
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Answer:
(15, 20)
Explanation:
If the point (10,20) belongs to the graph of f(x), a function that satisfies this point for example could be:
[tex]f(x)=2x[/tex]When x is replaced with x-5, we have:
[tex]\begin{gathered} f(x-5)=2(x-5) \\ =2x-10 \end{gathered}[/tex]Therefore, when x=15
[tex]\begin{gathered} f(x-5)=2(15)-10 \\ =30-10 \\ =20 \end{gathered}[/tex]A point that belongs to the graph of y = f(x-5) is (15, 20).
help me please
thank you
Answers
Part (a)
[tex]P(0)=0.7166(0)^2+6.267(0)+1.344 \approx 1.3[/tex]
Part (b)
[tex]P(5)=0.7166(5)^2+6.267(5)+1.344 \approx 50.6[/tex]
Part (c)
[tex]P(10)=0.7166(10)^2+6.267(10)+1.344 \approx 135.7[/tex]
You can make 8 pancakes with 5g of butter. How much butter do you need for 12 pancakes.
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1. find how many grams of butter it takes to make 4 pancakes; 8 / 2= 4
2. divide the number of grams by the number you just divided by (2)
3. solve 5 / 2 = 2.5
4. acknowledge 8 + 4 = 12, so do 5 + 2.5 = 7.5
You need 7.5 grams of butter
Help needed! please help math
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The Mercury is 5.745 × 10^9 kilometers closer to the sun.
In this question, we have been given the approximate average distance from the sun to Neptune and Mercury.
Mercury : 5.79 × 10^9 kilometers
Neptune : 4.5 × 10^7 kilometers
We need to find how much Mercury is closer to the sun.
To find the distance by which Mercury is closer to the sun, consider the difference (5.79 × 10^9) - (4.5 × 10^7)
In the above difference the exponents of 10 are different.
So, we consider the 10^7
we write 5.79 × 10^9 as 579 × 10^7
So the difference would be,
(579 × 10^7) - (4.5 × 10^7)
= (579 - 4.5) × 10^7
= 574.5 × 10^7 km
= 5.745 × 10^9 km
Therefore, the Mercury is 5.745 × 10^9 kilometers closer to the sun.
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What property of real numbers does each statement demonstrate? a + (-a) = 0 A Additive Inverse B Commutative Property of Addison c Associative Property of Addron o Distributive Property
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solution
For this case the best way to solve this problem
a +(-a)=0
Is using the :
A. Additive inverse property
18 red marbles; 6 to 9
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27 blue marbles are there in the bag.
How to find the number of blue marbles?Given,
A bag contains 18 red marbles.
The ratio of red marbles to blue marbles is 6:9
Solution:
From the given ratio of 6:9,
If 6 part is red marble, then 1 part = 18/6 =3
Therefore,
The number of blue marbles is 9*3 = 27
Thus, there are 27 blue marbles in the bag.
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Find the x -intercept and the y-intercept of the graph of the equation.-x+2 y=-7Good evening I am having a hard time getting this math is there any way you can help me?
Answers
Answer:
• x-intercept =7
,• y-intercept = -3.5
Explanation:
Given the linear equation
[tex]-x+2y=-7[/tex]x-intercept
The x-intercept is the value where the line crosses the x-axis.
We calculate this by setting y=0
[tex]\begin{gathered} \text{When y=0} \\ -x+2y=-7 \\ -x+2(0)=-7 \\ -x=-7 \\ x=7 \end{gathered}[/tex]The x-intercept is 7.
y-intercept
The y-intercept is the value where the line crosses the y-axis.
We calculate this by setting x=0
[tex]\begin{gathered} \text{When x=0} \\ -x+2y=-7 \\ -0+2y=-7 \\ 2y=-7 \\ Divide\text{ both sides by 2} \\ \frac{2y}{2}=-\frac{7}{2} \\ y=-3.5 \end{gathered}[/tex]The y-intercept is -3.5.
Is 2x-y=44x-2y=6 A Consistent and dependent?
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Solution
We are given the two equations
[tex]\begin{gathered} 2x-y=4\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1) \\ 4x-2y=6\ldots\ldots\ldots.\ldots\ldots\text{.}(2) \end{gathered}[/tex]Now, equation (1) x 2
[tex]\begin{gathered} 4x-2y=8\ldots\ldots.\ldots\ldots\ldots\ldots\ldots(1) \\ 4x-2y=6\ldots\ldots\ldots\ldots\ldots\ldots.\ldots(2) \end{gathered}[/tex]Equation (1) - equation (2)
[tex]\begin{gathered} (4x-4x)+(-2y-(-2y))=8-6 \\ 0+0=2 \\ 0=2 \end{gathered}[/tex]Which is never possible!
Therefore, the system of equation is NOT consistent.
Note:
Let us also draw the graph of the eqautionm given
Therefore, the system of equation is Inconsistent and Independent
Find the coordinates of the midpoint of a segment with the given endpoints.C(0,5) and D(-4,-5)
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We have the following:
[tex]m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})_{}[/tex]resolving:
[tex]\begin{gathered} m=(\frac{0+(-4)_{}}{2},\frac{5+(-5)_{}}{2})_{} \\ m=(-\frac{4}{2},\frac{0}{2}) \\ m=(-2,0) \end{gathered}[/tex]Therefore, the midpoint is:
[tex]m=(-2,0)[/tex]Need to know if I’m doing this right and understanding it
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Solution
Intercepts : (0 , ) and (160, 0 )
Symmetry: x = 60
positive: (0 , 120)
negaive: (--∝ , 0) U (120 , +∝)
Increasing: (-∝ , 60)
Decreasng ; (60 , +∝)
Relatve extrema: (150
factor each trinomial if the trinomial cannot be factored write prime. show ALL work1.) 2x^2+5x-122.) 6x^2-23x+7
Answers
1) the initial expression is:
[tex]2x^2+5x-12[/tex]To factor this expression we can use the cuadratic formula that is:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4(a)(c)}}{2(a)} \\ a=2 \\ b=5 \\ c=-12 \end{gathered}[/tex]so we replace the values and we get:
[tex]\begin{gathered} x=\frac{-5\pm\sqrt[]{5^2-4(2)(-12)}}{2\cdot2} \\ x=\frac{-5\pm\sqrt[]{121}}{4} \\ x=\frac{-5\pm11}{4} \end{gathered}[/tex]So now we have two solutions so:
[tex]\begin{gathered} x_1=\frac{-5+11}{4}=\frac{6}{4}=\frac{3}{2}=1.5 \\ x_2=\frac{-5-11}{4}=-\frac{16}{4}=-4 \end{gathered}[/tex]so the factor expression will be:
[tex](x-\frac{3}{2})(x+4)[/tex]2) the initial expression is:
[tex]6x^2-23x+7[/tex]so we repeat the same procedure so:
[tex]\begin{gathered} x=\frac{23\pm\sqrt[]{23^2-4(6)(7)}}{2(6)} \\ x=\frac{23\pm\sqrt[]{529-168}}{12} \\ x=\frac{23\pm\sqrt[]{361}}{12} \\ x=\frac{23\pm19}{12} \end{gathered}[/tex]So the two possible solutions are:
[tex]\begin{gathered} x_1=\frac{23+19}{12}=\frac{42}{12}=\frac{7}{2}=3.5 \\ x_2=\frac{23-19}{12}=\frac{4}{12}=\frac{2}{6}=\frac{1}{3}=0.33 \end{gathered}[/tex]so the factor form is:
[tex](x-\frac{7}{2})(x-\frac{1}{3})[/tex]Macy babysits the children in her neighborhood. For each family, she charges a flat fee plus a per hour charge as described by the data in the table.Which equation represents the total amount Macy charges for each family where x represents the number of hours she babysits? A. y = 4x + 71 B. y = 9x + 7 C. y = 4x + 36 D. y = 13x + 117
Answers
Answer:
B. y=9x+
Explanation:
To deermine tehe equation, pick two pairs of points from the table.
• The points are (8, 79) and (12, 115)
Substitute these points into the lope-ointercept form of the equation of a line.
[tex]y=mx+b[/tex]At (8,79): x=8 and y=79
[tex]79=8m+b[/tex]At (12, 115): x=12 and y=115
[tex]115=12m+b[/tex]Solve the two equations siultaneously fror m and b.
[tex]\begin{gathered} 79=8m+b \\ 115=12m+b \\ Subtract \\ -36=-4m \\ \implies m=\frac{-36}{-4}=9 \end{gathered}[/tex]Next, substitute m=9 into the first equation to solve for b:
[tex]\begin{gathered} 79=8m+b \\ 79=8(9)+b \\ b=79-72 \\ b=7 \end{gathered}[/tex]Substitute m=9 and b=7 into the slope-intercept form:
[tex]y=9x+7[/tex]The equation that represents the total amount Macy charges for each family where x represents the number of hours she babysits is:
[tex]y=9x+7[/tex]Option B is correct.
For installation with a 300-kVA, 3-phase transformer, a 480-volt primary, and a 240-volt secondary. Calculate the maximum overcurrent protection value (not the fuse or circuit breaker rating) using the protection method for primary-only protection. (Round the FINAL answer to two decimal places.)
Answers
By using the protection method for primary-only protection, the maximum overcurrent protection (MOCP) is equal to 451.59 Amperes.
What is MOCP?In Electrical engineering, MOCP is an abbreviation for maximum overcurrent protection and it can be defined as the maximum allowable current rating that is required for any circuit breaker or fuse, in order to properly protect an electrical equipment, especially under uncertain or anticipated fault conditions.
Mathematically, the amount of current flowing through the primary winding of a three-phase transformer can be calculated by using this mathematical expression:
Current, I = 3-phase KVA/(1.73 × Voltage)
Substituting the given parameters into the formula, we have;
Current, I = 300,000/(1.73 × 480)
Current, I = 300,000/830.4
Current, I = 361.27 Amperes.
By using the protection method for primary-only protection, the maximum overcurrent with 25% above the current is given by:
Maximum overcurrent = 125% × Current
Maximum overcurrent = 125/100 × 361.27
Maximum overcurrent = 45,158.75/100
Maximum overcurrent = 451.5875 ≈ 451.59 Amperes.
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If you own a larger lawn, you must use more water to hydrate it.
Identify the independent variable.
Answers
Answer:
the independent variable is the lawn size
Step-by-step explanation:
Answer: The lawn size
Step-by-step explanation: The independent variable is the input which causes the output to change.
The table shows Mr. Blackwell's total earnings as a car salesman for different sale amounts.
Graph the points on the coordinate plane and connect them with a straight line.
Answers
A graph of the points on the coordinate plane with a straight line is shown in the image attached below. An equation in slope-intercept to represent the relationship is y = 125x + 500.
How to calculate the slope of a line?In order to determine the equation of this line in slope-intercept, we would first of all calculate its slope. Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope, m = (3,000 - 1,750)/(20 - 10)
Slope, m = 1,250/10
Slope, m = 125.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.c represents the intercept.At point (10, 1,750), we have;
y - 1,750 = 125(x - 10)
y - 1,750 = 125x - 1,250
y = 125x - 1,250 + 1,750
y = 125x + 500
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Answer:
Step-by-step explanation:
