Consider triangle DEF , where d = 17 , e = 19 and f = 30 Determine the measure of the largest angle.
Answers
The Solution.
Certainly, the largest angle is angle F ( since it is the angle directly opposite the longest side)
By cosine rule, we have
[tex]\cos F=\frac{d^2+e^2-f^2}{2de}[/tex][tex]S\text{ubstituting 17 for d, 19 for e, and 30 for }f,\text{ we get}[/tex][tex]\cos F=\frac{17^2+19^2-30^2}{2\times17\times19}[/tex][tex]\begin{gathered} \cos F=\frac{289+361-900}{34\times19} \\ \\ \cos F=\frac{650-900}{646} \end{gathered}[/tex][tex]\cos F=\frac{-250}{646}=-0.3870[/tex]Taking the cosine inverse of both sides, we get
[tex]F=\cos ^{-1}(-0.3870)=112.77^o[/tex]Therefore, the correct answer is 112.77 degrees.
Related Questions
-5 > 5 + x/3 I am so confused on these things
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Let's solve the inequality:
[tex]\begin{gathered} -5>5+\frac{x}{3} \\ -5-5>\frac{x}{3} \\ -10>\frac{x}{3} \\ -10\cdot3>x \\ -30>x \\ x<-30 \end{gathered}[/tex]Therefore the solution for the inequality is:
[tex]x<-30[/tex]In interval form this solution is written as:
[tex](-\infty,-30)[/tex]This means that x has to be less than -30 for the inequality to be true.
how to write the indicated expression for[tex] \frac{1}{2} m \: inches \: in \: feet[/tex]
Answers
Answer:
Rewriting the given expression in feet gives:
[tex]\frac{1}{24}m\text{ feet}[/tex]Explanation:
We want to write the expression below in feet.
[tex]\frac{1}{2}m\text{ inches in f}eet[/tex]Recall that;
[tex]\begin{gathered} 1\text{ foot = 12 inches} \\ 1\text{ inch = }\frac{1}{12}foot \end{gathered}[/tex]so, converting the expression to feet we have;
[tex]\begin{gathered} \frac{1}{2}m\text{ inches =}\frac{1}{2}m\times\frac{1}{12}feet \\ =\frac{1}{2}\times\frac{1}{12}\times m\text{ f}eet \\ =\frac{1}{24}m\text{ f}eet \end{gathered}[/tex]Therefore, rewriting the given expression in feet we have;
[tex]\frac{1}{24}m\text{ feet}[/tex]Subtract and simplify: (6 + 10i) – (11 + 7i)
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Given:
an expression is given as (6 + 10i) - (11 + 7i)
Find:
we have to subtract and simplify the expression.
Explanation:
(6 + 10i) - (11 + 7i) = 6 + 10i - 11 -7i = (6 - 11) + ( 10i - 7i) = -5 + 3i
Therefore, (6 + 10i) - (11 + 7i) = -5 + 3i
An online store started its business with 15 sales per week. If their sales increased 18% each week, use an exponential model to find the week in which they exceeded 1000 sales per week. Remember, A= P(1+r)^t26 weeks31 weeks38 weeks15 weeks
Answers
Given,
The initial sale is 15.
The rate of increase of sale per week is 18 %.
The final sale is 1000.
The week at which the sales exceeds 1000 is:
[tex]\begin{gathered} 1000=15\times(1+\frac{18}{100})^t \\ \frac{1000}{15}=(\frac{118}{100})^t \\ \frac{200}{3}=(1.18)^t \\ log\text{ \lparen}\frac{200}{3})=t\text{ log\lparen1.18\rparen} \\ t=25.37 \end{gathered}[/tex]The sales of the business reach to 1000 in 25th week.
Hence, the sales of the business exceed to 1000 in 26th week.
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 18 people took the trip. She was able to purchase coach tickets for $170 and first class tickets for $1010. She used her total budget for airfare for the trip, which was $10620. How many first class tickets did she buy? How many coach tickets did she buy:
Answers
Explanation
Let the number of people with coach tickets be x and the number of people with first class tickets be y. Since the trip goers contained a total of 18 people we will have;
[tex]x+y=18[/tex]A coach ticket cost $170 dollars and the first class tickets cost $1010. Also, Sarah spent a total of $10620 to buy the tickets. This would give us;
[tex]170x+1010y=10620[/tex]We will now solve the equation simultaneously.
[tex]\begin{gathered} \begin{bmatrix}x+y=18\\ 170x+1010y=10620\end{bmatrix} \\ isolate\text{ for x in equation 1}\Rightarrow x=18-y \\ \mathrm{Substitute\:}x=18-y\text{ in equation 2} \\ 170\left(18-y\right)+1010y=10620 \\ 3060+840y=10620 \\ 840y=10620-3060 \\ 840y=7560 \\ y=\frac{7560}{840} \\ y=9 \\ \end{gathered}[/tex]We will substiuite y =9 in x=18-y. Therefore;
[tex]\begin{gathered} x=18-9=9 \\ x=9 \end{gathered}[/tex]Answer: From the above, Sarah bought 9 coach tickets and 9 first-class tickets.
9+7d=16 how do i slove it
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9 + 7d = 16
________________
Can you see the updates?
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9 + 7 d = 16
1. we subtract 9 from the two sides
9 - 9 + 7 d = 16 -9
0 + 7 d = 7
2. We divide by 7 both sides
(7 d)/ 7 = 7/ /7
7/7= 1
d= 1
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Answer
9 + 7d = 16
7d= 16 - 9
d= 7/ 7= 1
d= 1
Use the long division method to find the result when 8x3 + 30x2 + 3x – 1 is divided by 4x + 1. If there is a remainder, express the result in the form q(x) + r(3) b(x)
Answers
Answer:
[tex]2x^2+7x-1[/tex]Explanation:
Given the polynomial division:
[tex]\frac{8x^3+30x^2+3x-1}{4x+1}[/tex]The long division table is attached below:
Therefore, we have that:
[tex]\frac{8x^3+30x^2+3x-1}{4x+1}=2x^2+7x-1[/tex]x[tex] {x}^{3} {y}^{8} term(x + y) ^{11} [/tex]find the coefficient of the given term in the binomial expansion
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Using the binomial theorem, we have that the expansion of (x+y)^11 is:
[tex]\begin{gathered} (x+y)^{11}= \\ x^{11}+11x^{10}y+55x^9y^2+165x^8y^3+330x^7y^4+462x^6y^5+462x^5y^6+330x^4y^7+165x^3y^8+55x^2y^9+11xy^{10}+y^{11} \end{gathered}[/tex]notice that the coefficient of the term x^3 y^8 is 165
Given: D is the midpoint of segment AC, angle AED is congruent to angle CFD and angle EDA is congruent to angle FDCProve: triangle AED is congruent to triangle CFD
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Since Angle AED is congruent to angle CFD and angle EDA is congruent to angle FDS, we can use the midpoint theorem to get the following:
[tex]\begin{gathered} D\text{ is midpoint of AC} \\ \Rightarrow AD\cong AC \end{gathered}[/tex]therefore, by the ASA postulate (angle,side,angle), we have that triangle AED is congruent to triangle CFD
For questions 5-6, g(x) is a transformation of f(x) = x2. What is the function g(x) that is represented by the graph? QUESTION 5
Answers
The transformation in question 5 shows a shift to the left by 3 units.
A shift to the left by b units has the rule:
[tex]f(x)\to f(x+b)[/tex]Therefore, the shift to the left by 3 units will yield the function:
[tex]x^2\to(x+3)^2[/tex]Hence, the function g(x) will be:
[tex]g(x)=(x+3)^2[/tex]Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
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Equations that have the roots of x = 2 and x = -2 are:
(A) x² - 4 = 0(D) 4x² = 16What exactly are equations?In mathematical formulas, the equals sign is used to indicate that two expressions are equal. A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation. Like 3x + 5 = 15, for instance. Equations come in a wide variety of forms, including linear, quadratic, cubic, and others. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.So, equations true for x = 2 and x = -2 are:
Roots of x = -2:
x² = 4x² - 4 = 0Roots of x = 2:
x² = 4Now, multiply 4 on both sides as follows:
4x² = 16Therefore, equations that have the roots of x = 2 and x = -2 are:
(A) x² - 4 = 0(D) 4x² = 16Know more about equations here:
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Correct question:
Which equations are true for x = –2 and x = 2? Select two options
A. x2 – 4 = 0
B. x2 = –4 3
C. x2 + 12 = 0
D. 4x2 = 16
E. 2(x – 2)2 = 0
Ramesh leaves 2/3 of his property for his wife and 1/4 for his son and remaining for his daughter what part does his daughter receive Help me fast
Answers
3×4 = 12
2x4 = 8
4x3= 12
1x4=4
So that would be 8/12 and 4/12
Then you would add the numerator so 8+4 = 12
so the mother and the son together get 12/12 of his property which is everything. So the daughter gets nothing.
Simplify the expression below. Share all work/thinking/calculations to earn full credit. You may want to do the work on paper and then upload an image of your written work rather than try and type your work. \sqrt[4]{ \frac{162x^6}{16x^4} }
Answers
complete the Pattern 444 4440 44,400 there are three empty lines I need to finish the pattern
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Given:
d. 444 4,440 44,400
e. 9.5 950 9500
The pattern for d as you can see all numbers have 444 but they keep adding extra 0's to each number.
So the next number should have another extra 0 after 44400.
The pattern for all parts a to e seem to be multiplying each number by 10 or dividing by 10 that is why for d. 444 has no 0's but then if you multiply by 10 you get 4440.
If you do 4440*10 you get 44400.
Answer:
The same pattern applies to e.
For the first blank divide 9.5 by 10 so then 9.5 ÷ 10 = 0.95
For the 2nd blank. Multiply by 10 to 95,000 so you get 950,000. Notice how 950,000 has an extra 0.
3rd blank should be 9500000
fing the probability of .14 .73 .03 is
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The probabilities are:
*0.14 -> 14%.
*0.73 -> 73%.
*0.03 -> 3%.
In the function rule for simple interest A(t)=P(1+rt), is P a variable? Explain.
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P is a variable in the function rule for simple interest A(t)=P(1+rt).
What is a variable?Mathematically, a variable is any number, vector, matrix, function, argument of a function, set, or element of a set.
A variable assumes any possible values in a mathematical expression, problem, or experiment.
A simple interest function showing the amount after some periods is given as A(t)=P(1+rt). In this function, P represents a variable (the principal amount) because it can change depending on the amount invested or borrowed.
Thus, P is a variable in the simple interest function because it can assume any value.
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Answer:
when buying a house
Step-by-step explanation:
-3х – 10у = -20 -5x — бу = 20
Answers
You can solve a system of equations by graphing
The solution of a system of linear equations is the intersection point both graphs
using a graphing tool
the solution is the point (-10,5)
so
x=-10
y=5
the solution is the intersection point both lines
I will solve the system by substitution
we have
-3х – 10у = -20 --------> equation A
-5x — бу = 20 --------> equation B
isolate the variable y in the equation A
10y=-3x+20
y=-0.3x+2 --------> equation C
substitute equation C in equation B
-5x-6(-0.3x+2)=20
solve for x
-5x+1.8x-12=20
-3.2x=20+12
-3.2x=32
x=-10
substitute the value of x in the equation C
y=-0.3x+2
y=-0.3(-10)+2
y=3+2
y=5
the solution is x=-10 and y=5
Find the equation of the linear function represented by the table below in slope-intercept form.xy1-52-73-94-11
Answers
Answer:
[tex]y=-2x-3[/tex]Explanation:
Given the table:
x | 1 2 3 4
y | -5 -7 -9 -11
Find the slope using the two point formula.
Take the points (1, -5) and (2, -7).
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-7-(-5)}{2-1} \\ =\frac{-7+5}{1} \\ =-2 \end{gathered}[/tex]Substitute the value of the slope into the slope-intercept form y = mx+c.
[tex]y=-2x+c[/tex]Plug the point (1, -5) into y = -2x+c to find c.
[tex]\begin{gathered} -5=-2+c \\ c=-5-(-2) \\ =-3 \end{gathered}[/tex]Thus, y = -2x - 3, which is the required equation of the given linear function.
find the value of x,y,z
Answers
Answer: x =116 degrees
y = 88 degrees
Explanation:
[tex]\begin{gathered} \text{ Find the value of x, y, and z} \\ To\text{ find z} \\ \text{Opposite angles are supplementary in a cyclic quadrilateral} \\ 101\text{ + z = 180} \\ \text{Isolate z} \\ \text{z = 180 - 101} \\ \text{z = 79 degre}es \\ To\text{ find x} \\ 2(101)\text{ = x + 86} \\ 202\text{ = x + 86} \\ \text{Collect the like terms} \\ \text{x = 202 - 86} \\ \text{x = 116 degr}ees \\ \text{ find y} \\ 2z\text{ = y + 70} \\ z=\text{ 79} \\ 2(79)\text{ = y + 70} \\ 158\text{ = y + 70} \\ \text{y = 158 - 70} \\ \text{y = 88 degre}es \end{gathered}[/tex]Therefore, x = 116 degrees, y = 88 degrees, and z = 79 degrees
step by step guide I am stuck at the part where you have to divide, I have split them up into 2 and got GCF for p on first term and 6 on second term
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We have the next expression:
[tex]pq\text{ - pr + 6q-6r}[/tex]Factorize using factor by grouping.
First, let's find the common terms. The one who is in all terms or majority terms.
In this case, let's use p:
[tex]p(q-r)+6q-6r[/tex]Factorize the common term 6.
[tex]p(q-r)+6(q-r)[/tex]Look at the expressions, both are multiply by (q-r), so we can rewrite the expression like this:
Factorize the common term (q-r)
[tex](q-r)(p+6)[/tex]You have a $250 gift card to use at a sporting goods store. a) Write an inequality that represents the possible numbers x of pairs of socks you can buy when you buy 2 pairs of sneakers. PRIO *12 SALE PRICE $80 b) Can you buy 8 pairs of socks? Explain.
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Sale price 12
number of socks =X
Sneakers sprice 80
Amount disposable 250
Then
Part a)
250 - 2•80 = 12X
250 - 160 = 12X
90 ≥ 12 X
Part b)Can buy 8 pairs?
Answer NO , because 90 < 12•8
Drag each expression to the correct location on the model. Not all expressions will be used.552 + 25r + 2071
Answers
Given
[tex]\frac{5x^2+25x+20}{7x}[/tex]To find: The equivalent rational expression.
Explanation:
It is given that,
[tex]\frac{5x^2+25x+20}{7x}[/tex]That implies,
[tex]\frac{5x^2+25x+20}{7x}[/tex]what is the scale factor from triangle PQR to triangle STU
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To find the scale factor from one triangle to another we need to divide the measurements of the second triangle by the corresponding measurements of the first triangle.
Since we need the scale factor from triangle PQR to triengle STU we need to divide the measurements of STU by the corresponding measurements of triangle PQR.
Sides PR and SU are corresponding sides, so we sivide 12 by 8:
[tex]\frac{12}{8}=\frac{3}{2}[/tex]To confirm, we also divide the measurements of sides UT and RQ:
[tex]\frac{9}{6}=\frac{3}{2}[/tex]Thus, the scale factor is: 3/2 = 1.5
If f(x) = -2x + 8 and g(x) = v* + 9, which statement is true?
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We have the function;
[tex]f(x)=-2x+8[/tex]and
[tex]g(x)=\sqrt[]{x+9}[/tex]Let's obtain f(g(x) before we make conclusions on the statements.
[tex]f^og=-2(\sqrt[]{x+9})+8[/tex]The domain of f(g(x) starts from x= - 9, this is where the function starts on the real line.
But - 6 < -9 , and thus,
The answer is - 6 is in the domain of the function.
Toy It Examine the worked problem and solve the equation. 4 4 1 (x) 1 = 9 3 3 1 1 + 3 3 4 3 :9+ 3 3 28 The solution is x=
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Given:
[tex]\frac{4}{3}(x)-\frac{1}{3}=9[/tex]Let's evaluate and solve for x.
First step:
Add 1/3 to both sides of the equation
[tex]\begin{gathered} \frac{4}{3}(x)-\frac{1}{3}+\frac{1}{3}=9+\frac{1}{3} \\ \\ \frac{4}{3}(x)=\frac{28}{3} \end{gathered}[/tex]Cross multiply:
[tex]\begin{gathered} 4x(3)\text{ = 28(3)} \\ \\ 12x\text{ = }84 \end{gathered}[/tex]Divide both sides by 12:
[tex]\begin{gathered} \frac{12x}{12}=\frac{84}{12} \\ \\ x=7 \end{gathered}[/tex]ANSWER:
x = 7
Express the following expression in the form of a + bi : (16 + 6i) ((12 - 10i) - (2 - 5i))
Answers
Given:
There is an expression given as below
[tex]\left(16+6i\right)(\left(12-10i\right)-(2-5i))[/tex]Required:
We need to simplify the given expression and express in form of a+ib
Explanation:
[tex]\begin{gathered} (16+6i)((12-10i)-(2-5i)) \\ =(16+6i)(12-10i-2+5i) \\ =(16+6i)(10-5i) \\ =160-80i+60i+30 \\ =190-20i \end{gathered}[/tex]Final answer:
a + ib = 190 - 20i
how do I solve this linear equations by substitution x=5 x + y = 4
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Substitute 5 for x in the equation x+y=4 to obtain the value of y.
[tex]\begin{gathered} 5+y=4 \\ y=4-5 \\ =-1 \end{gathered}[/tex]So solution of the equations is (5,-1).
find all other zeros of p (x)= x^3-x^2+8x+10, given that 1+3i is a zero. ( if there is more than one zero, separate them with commas.)edit: if possible please double check answers would high appreciate it.
Answers
Since we have that 1 + 3i is one zero of p(x), then we have that its conjugate is also a root, then, we have the following complex roots for p(x):
[tex]\begin{gathered} x=1-3i \\ x=1+3i \end{gathered}[/tex]also, notice that if we evaluate -1 on p(x), we get:
[tex]\begin{gathered} p(-1)=(-1)^3-(-1)^2+8(-1)+10=-1-1-8+10 \\ =-10+10=0 \end{gathered}[/tex]therefore, the zeros of p(x) are:
x = 1-3i
x = 1+3i
x = -1
Which point on the number line below best represents V30?
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We should try different squared numbers that are bigger and smaller than 30 as:
[tex]\begin{gathered} \sqrt{16}=4 \\ \sqrt{25}=5 \\ \sqrt{36}=6 \end{gathered}[/tex]Since 30 is between 25 and 36, the square root of 30 is going to be between 5 and 6. So the point that best represents the square root of 30 is M.
Answer: Point M
How many terms are in 6b+b2+5+2b-3f
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In that polynomial there are 5 terms, they are separated by signs.
If we simplify the new number of terms is 4
6b + b^2 + 5 + 2b - 3f
8b + b^2 + 5 - 3f