Answer:
1. x = 55°
2. x = 11°
3. x = 30°
4. x = 19°
Step-by-step explanation:
Trigonometric Identities
[tex]\sin(x)=\cos(90^{\circ}-x)[/tex]
[tex]\cos(x)=\sin(90^{\circ}-x)[/tex]
Question 1
[tex]\begin{aligned}\implies \sin(35) & =\cos(90-35)\\ & = \cos(55)\end{aligned}[/tex]
[tex]\implies x=55^{\circ}[/tex]
Question 2
[tex]\begin{aligned}\implies \cos(79) & =\sin(90-79)\\ & = \sin(11)\end{aligned}[/tex]
[tex]\implies x=11^{\circ}[/tex]
Question 3
[tex]\begin{aligned}\cos(x)& =\sin(2x)\\\implies \cos(x)& =\sin(90^{\circ}-x)\\\\\implies 2x & = 90-x\\3x & = 90\\x & = 30^{\circ}\end{aligned}[/tex]
Question 4
[tex]\begin{aligned}\sin(x+4)& =\cos(4x-9)\\\implies \sin(\theta)& =\cos(90^{\circ}-\theta)\\\\\implies x+4 & = 90-(4x-9)\\x+4 & = 90-4x+9\\5x & = 95\\x & = 19^{\circ}\end{aligned}[/tex]
In your own words, explain the discriminant test. Use the discriminant test to decide whether the equation represents a parabola, ellipse or a hyperbola and explain why you know this is true. x^2 − 4xy + 3x + 25y − 6 = 0
A discriminant test is one that tells whether a formula has one, two or no solutions.
The equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.
What is a discriminant test?A discriminant test is a test that tells whether there are one, two or no solutions for a formula.
The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac.
The discriminant of a quadratic equation is given as ax2 + bx + c = 0
A discriminant is said to be a parabola either x or y is squared and not both unlike that of an eclipse and a hyperbola.
With the given equation, x^2 − 4xy + 3x + 25y − 6 = 0, only x is squared and not both x and y.
Thus, the equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.
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How much is Bob's net salary for the week? Question 32
Answer:
A. $152.00
Step-by-step explanation:
I'm 99% sure the net salary is just the 220 (gross salary) minus everything else taken away which is (42 + 7 + 15 + 4) = 68. 220 - 68 = 152 so Bob's net salary would be 152
A medication states that the odds of having an allergic reaction are 2 in 200. What is that probability states as a percent?
What is the area of triangle ABD?
a 4.5 cm 2
b 3.5 cm 2
c 7 cm 2
d 6 cm 2
Answer: [tex]4.5 \text{ cm}^{2}[/tex]
Step-by-step explanation:
[tex]A=\frac{1}{2} bh\\\\A=\frac{1}{2}(3)(3)\\\\\boxed{A=4.5 \text{ cm}^{2}}[/tex]
The area of the triangle will be equal to 4.5 square centimeters.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space covered by the triangle in the two-dimension is called an area of the triangle.
The area of the triangle ABD will be calculated as:-
Area = [tex]\dfrac{1}{2}[/tex] x Base x height
Area = [tex]\dfrac{1}{2}[/tex] x 3 x 3
Area = 4.5 cm.
Therefore the area of the triangle will be equal to 4.5 square centimeters.
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se the distributive property to remove the parentheses.
-(-3v-4w+1)
Hii!
[tex]\leadsto\parallel\boldsymbol{Answer.}\parallel\gets[/tex]
_________________________________________________________
3v+4w-1
__________________________________________________________
[tex]\leadsto\parallel\boldsymbol{Explanation.}\parallel\gets[/tex]
We use the distributive property to "distribute" the minus sign.
[tex]\sf -(-3v-4w+1)=-1\cdot(-3v)+(-1)\cdot(-4w)+(-1)\cdot1}[/tex].
Simplify!
[tex]\sf 3v+4w-1}[/tex]. Which is our final answer.
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]
[tex]\boldsymbol{-Greetings!-}[/tex]
_________________________________________________________
Help me with this question please and thank you!! :)
Question 1
The complement of set B is all the elements in S but that are not in B, which is [tex]\{2, 4, 5, 9, 10, 11, 12, 13, 14, 17, 19\}[/tex].
We want to find the intersection of set A and the complement of set B, which is the set of all elements that both sets contain.
This is {2, 9, 10, 12}, meaning there are 4 elements.
Question 2
Following a similar logic as the last problem, the complement of set A is [tex]\{1,3,4,5,6,7,11,13,14,15,17,18,19\}[/tex].
Therefore, the desired set is [tex]\{1,3,6,7,15,18\}[/tex], and thus there are 6 elements.
Urgent
find the values of x and y 8x+5y=-5 7x-3y=3
Answer:
x= 0, y= -1
Step-by-step explanation:
To obtain the values of x and y from a system of equations, start by labelling the given equations.
8x +5y= -5 -----(1)
7x -3y= 3 -----(2)
Let's solve by elimination.
Here, I will be working to eliminate the y term. This is done by ensuring both equations have the same numerical value in the coefficient of y.
(1) ×3:
24x +15y= -15 -----(3)
(2) ×5:
35x -15y= 15 -----(4)
Add the two equations together since the coefficient of y has opposite signs.
(3) +(4):
24x +15y +35x -15y= -15 +15
59x= 0
Divide both sides by 59:
x= 0
Now, substitute the value of x into any equations to find the value of y.
Substitute x= 0 into (1):
8(0) +5y= -5
5y= -5
Divide both sides by 5:
y= -5 ÷5
y= -1
Additional:
For similar questions on system of equations, do check out the following!
https://brainly.com/question/4346392Four students were asked to write an expression which has terms that have a greatest common factor of ab. The
expressions provided by the students are shown below.
Olivia
20ab-14abc
Michelle
16a+3b
Michelle
Naomi
Which student wrote the correct expression?
O Olivia
O Peyton
Naomi
18abc-13abc
Peyton
15abc+ 14ab
Answer: Peyton
Step-by-step explanation:
Michelle: Greatest common factor is 1
Naomi: Greatest common factor is abc
Olivia: Greatest common factor is 2ab
Peyton: Greatest common factor is ab
the price for each ticket is 7.99 one person thinks the total for all eight people will be around 50.00 is this a reasonable estimate. why?
Answer:
No
Step-by-step explanation:
no because just muiltiplying 7.00 * 8 is 56 not inculuding the 99 cents it is already over 50. The answer is 63.92 so a reasonable estimate would be around $60
(X+p)(x+q) what part of the trinomial will equal the product of p and q?
The part of the trinomial that will equal the product of p and q is the constant part
How to determine the part?The expression is given as:
(x + p)(x + q)
From the expression, p and q are both constants.
When a constant is multiplied to another, the result is a constant
This means that:
pq = constant
Hence, the part of the trinomial that will equal the product of p and q is the constant part
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From this diagram, select the
pair of lines that must be
parallel if 24 = 23. If there
is no pair of lines, select
"none."
O is parallel to q
let's take the angle opposite to angle 4 is alpha
angle 4 = angle alpha ( vertically opposite angles)
angle alpha = angle 3 ( as angle 4 = angle 3).
hence o is parallel to q as both the angles are equal
The graph of (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of (in red).
The blue graph shows a upward translation by 4 units and horizontal translation by 3 units to have the equation h(x) = -1/2(x -3)² + 4
Translation of coordinates and functionThe given graph is a quadratic graph. Given the function of the blue parabola expressed as:
f(x) = -1/2x²
The blue graph shows a upward translation by 4 units and horizontal translation by 3 units to have the equation
h(x) = -1/2(x -3)² + 4
Note that the upward translation will be positive while the horizontal shift to the right will be negative
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The Candle Factory is producing a new candle. It has a radius of 3 inches and a height of 5 inches. How much wax is needed to make the candle? Use 3.14 for Pi. Round to the nearest whole cubic inch.
A cylinder with a radius of 3 inches and height of 5 inches.
Recall the formulas S A = 2 pi r squared + 2 pi r h and V = pi r squared h.
141 cubic inches
236 cubic inches
443 cubic inches
565 cubic inches
Answer:
141 cubic inches
Step-by-step explanation:
The candle can be modeled as a cylinder.
To find how much wax is needed to make the candle, calculate the volume of the cylinder.
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
r = 3 inh = 5 inπ = 3.14Substitute the given values into the formula and solve for V:
[tex]\implies \sf V=3.14 \cdot 3^2 \cdot 5[/tex]
[tex]\implies \sf V=3.14 \cdot 9 \cdot 5[/tex]
[tex]\implies \sf V=28.26 \cdot 5[/tex]
[tex]\implies \sf V=141.3\:in^3[/tex]
Therefore, the amount of wax needed to make the candle is 141 cubic inches (nearest whole cubic inch).
A phone company offers a monthly cellular
phone plan for $25. The plan includes 250
anytime minutes, and charges $0.20 per minute
above 250 min. Write a piecewise-defined
function for C(x), the cost for using x minutes in
a month.
The function will be given as C(x) = 25 + 0.2(x) here x is in minutes.
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
Given that:-
A phone company offers a monthly cellular phone plan for $25. The plan includes 250 anytime minutes and charges $0.20 per minute above 250 min.The cost of the 250 minutes is $25 and if the time extends from 250 minutes then the function will be expressed in the form of.
C(x) = 25 + 0.2 (x)
Here C(x) is the total cost and the x is in minutes.
Hence the function will be given as C(x) = 25 + 0.2(x) here x is in minutes.
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DRaw the graph of f (x) = 1/2 x² -2x where -2 < x < 4
Answer:
Graphs Attached Below
Step-by-step explanation:
Hello!
Standard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]
From our Equation:
a = 1/2b = -2c = 0There are several values that are needed to drawing a parabola:
y - interceptAxis of Symmetry (AOS)Vertexx - interceptsY-interceptStandard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]
The y-intercept is the "c" value. Given that our equation has a "c" value of 0, the y -intercept is 0.
Axis of SymmetryA parabola is always symmetrical vertically. The line in which the fold happens is the Axis of Symmetry.
To calculate the AOS, we use the formula [tex]AOS = \frac{-b}{2a}[/tex], from the values of the equation.
Calculate
[tex]AOS = \frac{-b}{2a}[/tex][tex]AOS = \frac{-(-2)}{2(0.5)}[/tex][tex]AOS = \frac{2}{1}[/tex][tex]AOS = 2[/tex]The Axis of Symmetry is a vertical line, so the AOS is the line x = 2.
VertexThe vertex is the highest or lowest point on the graph of a parabola. It resides on the AOS of the graph.
To calculate the vertex, we simply have to find the y-value, given that we have the x-value from the AOS. We can find the y-value by plugging in the AOS for x in the original equation.
Calculate
[tex]f(x) = \frac12x^2 - 2x[/tex][tex]f(x) = \frac12 (2)^2 - 2(2)[/tex][tex]f(x) = 2 - 4[/tex][tex]f(x) = -2[/tex]The y-value is -2. The vertex is (2, -2).
X-interceptsThe x-intercepts are the points where the graph intersects the x-axis (y = 0).
Solve by Factoring
[tex]f(x) = \frac12 x^2 - 2x[/tex][tex]0 = \frac12x(x - 4)[/tex][tex]x = 0, x = 4[/tex]The roots are (0,0) and (4,0).
GraphNow we just draw the y-intercept, vertex, AOS, and the x-intercepts, and draw a curved line between them.
Image Attached
Domain RestrictionsThe Domain (x-values) are being restricted to all x-values that are greater than or equal to -2 and less than 4.
That means we remove the parts of the line that don't belong in that domain.
Image Attached
Outside of the United States, many countries use ____ for their accounting standard.
A. the Common Market accounting methods
B. the international agreement on taxes and tariffs
C. the International Financial Reporting Standards
D. generally accepted accounting practices
Find the domain and range of the following graph
Write your answer as an interval.
Answer:
Domain: [1, infinity)
Range: All real numbers or (- infinity, + infinity)
Step-by-step explanation:
Hope this helps
Which equation describes the same line as y-5=-2(x+4)
i need help please very fast thanks
a dog is moving at a constant speed of 8 m/s. what is the dog’s acceleration
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Acceleration_{dog} = 0[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
A dog is moving at a constant speed of 8 m/s, that concludes that there's no change in its speed with respect to time.
And Acceleration is define as rate of change in velocity, but since velocity/speed is constant. change in velocity = 0
Henceforth, Acceleration of dog is 0 as well.
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer: Acceleration = 0 ✅
Step-by-step explanation:
Hii, let me help you out! (:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part 1Acceleration means "change in speed (which is also known as velocity, V, in physics) per a specific amount of time.
Part 1 is Successfully completed!
↪
Part 2Our Dog ProblemNow let's focus on finding the acceleration of the dog.
Like I said above, [tex]\sf Acceleration=change\;in\;speed\;per\;a\;specific\;amount\;of\;time[/tex]
Well, we are provided with the information that the dog's speed is constant. This means that it doesn't change. So the dog keeps on moving at a speed of 8 m/s. This means that its speed doesn't change, so the change in speed is 0. And this means that its acceleration is 0.
Voila! There's our answer, cheers! (:
___________________Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
[tex]\underbrace[/tex]
Mitch needs to do his laundry. It takes him 75 minutes to do each load
when he washes and dries the load. It takes him 43 less minutes if he
hangs up his laundry to dry. He decides to hang up one load of laundry
to dry.
Mitch writes the equation 75r -43 = 332, where x is the number of loads
of laundry he needs to do in order to determine how long it is going to
take him.
The next step Mitch wrote to solve the equation is shown here: 75r = 375
Which property did he use to get to this step?
A
addition property of equality
B
distributive property
C
subtraction property of equality
D
combining like-terms
Answer: [A] addition property of equality
Step-by-step explanation:
Mitch used the addition property of equality because he added 43 to both sides of the equation.
75r - 43 = 332
43 + (75r - 43) = (332) + 43
75r = 375
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the density of some steel is7.98gm/cc.how much does 60cc weigh?
Substituting into the formula d=m/v,
[tex]7.98=\frac{m}{60}\\\\m=\boxed{478.8 \text{ gm}}[/tex]
g(x)=f(x)-3 which statement best describes the graph of g(x) with the graph of f(x)
Answer: The graph of g(x) is the graph of f(x) shifted 3 units down.
What amount would u have if u deposited 1800 a year for 30 years at 7% compounded annually
Answer: $183,731
Step-by-step explanation:
After 30 years, the interest is $183,731
21% of hospital patients stay for less than 1 day. If 1,134 patients in January stay less than 1 day what total of number of patients did the hospital treat in January?
Can anyone Help I have 25 questions, 2hr 40mins remaining,
Combining the like-terms, the result of the addition of polynomials f(x) and g(x) is given by:
[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]
How do we add polynomials?We add polynomials combining the like-terms, that is, adding terms with the same exponent.
In this problem, the polynomials are:
[tex]f(x) = 3x^{\frac{1}{2}} + 7x^{-\frac{1}{4}} + 8x^{-4}[/tex][tex]g(x) = -\frac{7}{4}x^{\frac{1}{2}} + 12x^{-\frac{1}{4}} - 21x^3[/tex]Combining the like terms, the addition is given by:
[tex]f(x) + g(x) = \left(3 - \frac{7}{4}\right)x^{\frac{1}{2}} + (7 + 12)x^{-\frac{1}{4}} + 8x^{-4} + 21x^3[/tex]
[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]
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Help asap !………………………
Answer:
c
Step-by-step explanation:
dvdywuwhfuwi eurue wuid
PLEASE HELP WITH THIS PROBLEM!
Answer: Options 1 and 2
Step-by-step explanation:
To model exponential decay, the base of the exponential has to be less than 1.
Model exponential decay equation are
y = 0.34(0.98)^x
y = 8 (0.28)^x
Model exponential decay equation
Model exponential decay equation has the base value which is less than 1.Exponential decay is the process of reducing amount by consistent percentage rate over a time period. It can be expressed by the equation y=a(1-b)x where y is the final amount, a original amount, b decay factor, and x is the amount of time that has passed.Option C and D have the base value greater than 1. So it can't be model exponential decay equation.
Hence, the model exponential decay equation are
y = 0.34(0.98)^x
y = 8 (0.28)^x
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What is the simplified form of √ 144x36?
Answer:
12x^18
Step-by-step explanation:
please help! write D u E and D n E using interval notation.
Part 1
[tex]D \cup E[/tex] denotes the union of the two sets (in other words, all the elements in both sets).
This means it is [tex](-\infty, 4) \cup [7, \infty)[/tex]
Part 2
[tex]D \cap E[/tex] denotes the elements shared between both sets.
This means the answer is [tex](4, 7][/tex]
