Answer:
Step-by-step explanation:
We are to show that 1/1-sin theta + 1/1+cos theta = 2×sec square theta
Starting from the left hand side of the expression:
1/1-sin theta + 1/1+cos theta
Find the LCM
[tex]\frac{1}{(1 -sin \theta) (1+cos \theta)} \\\\= \frac{1+cos \theta + 1 -sin \theta ]}{(1 -sin \theta) (1+cos \theta)} \\ = \frac{2+cos \theta - sin \theta}{1+cos \theta - sin \theta - sin \theta cos \theta}[/tex]
Solve by using the quadratic formula:
x2 - 6x + 7 = 0
Final Answer: [tex]x = 3 + \sqrt{2}, 3 - \sqrt{2}[/tex]
Steps/Reasons/Explanation:
Question: Solve by using the quadratic formula: [tex]x^{2} - 6x + 7 = 0[/tex].
Step 1: Use the Quadratic Formula.
[tex]x = \frac{6 + \sqrt[2]{2} }{2}, \frac{6 - \sqrt[2]{2} }{2}[/tex]
Step 2: Simplify solutions.
[tex]x = 3 + \sqrt{2}, 3 - \sqrt{2}[/tex]
~I hope I helped you :)~ The quadratic formulaic is attached in an image.
A circular spinner for a game has a radius of 5 cm. The probability of winning on one spin of this spinner is $\frac{2}{5}$. What is the area, in sq cm, of the WIN sector? Express your answer in terms of $\pi$.
The total area of a circle is pi * radius^2
The total area of the circle is pi x 5^2 = 25pi sq. cm.
2/5 of this is success, so the answer is 2/5 * 25pi = 10 pi sq. cm.
What is the final amount if 1102 is increased by 2% followed by a further 1% increase? Give your answer rounded to 2 DP.
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
The final amount of 1102 with a 2% increase followed by a 1% increase is 1135.28.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
We have,
Amount = 1102
Percentage increase = 2%
Another percentage increase = 1%
Now,
The final amount.
= 101% of 102% of 1102
This can be written as,
= 101/100 x 102/100 x 1102
= (101 x 102 x 1102) / 10000
= 1135.28
Thus,
The final amount of 1102 with a 2% increase followed by a 1% increase is 1135.28.
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Jamie works for a construction company. Hi sorry company was hired to build some bricks. They bought 3/4 of a ton of bricks. Each brick house uses 1/5 of a ton of bricks. Using the amount that they have Howe many brick house can Jamie complete before they have to order more.
Answer:
3 3/4 brick house
Step-by-step explanation:
Total bricks bought = 3/4 of a ton
Each brick house uses = 1/5 of a ton
How many brick house can Jamie complete before they have to order more?
Number of brick house Jamie can complete with the available bricks = Total bricks bought / bricks per house
= 3/4 ÷ 1/5
= 3/4 × 5/1
= 15/4
= 3 3/4 brick house
Jamie will complete 3 3/4 brick house before they have to order more bricks
Calculate the remainder when 3456 is divided by 7
Answer:
The remainder when 3456 is divided by 7 is 6.
5 is the remainder when 3456 is divided by 7
What is Division?A division is a process of splitting a specific amount into equal parts.
We need to find the remainder when 3456 is divided by 7
3456/7
3456:7 is a ratio and 3456/7 is also called as fraction.
The number 3456 is called the numerator or dividend, and the number 7 is called the denominator or divisor.
3456 we can write as 3451+5
3451 is divided by 7 which gives 493.
5 is the remainder when 3456 is divided by 7
Hence, 5 is the remainder when 3456 is divided by 7
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 Can someone pleaseeee help if you’re correct I’ll give u brainlist
Answer:
30
Step-by-step explanation:
I asked the my math tutor lol
HELP PLS ! i’ll give brainlest is the answer is correct
Answer:
Function.
General Formulas and Concepts:
Algebra I
Vertical Line Test - each x-value must have it's own y-valueStep-by-step explanation:
If we apply the Vertical Line Test to the graph, we can see that each x-value has it's own y-value. Therefore, the graph is a function and not a relation.
Choose the algebraic expression that describes: 13 less than y.
Determine if the triangles, ΔUVW and ΔBAC, are similar. If so, identify the similarity criterion.
A) AA similarity
B) SAS similarity
C) SSS similarity
D) not similar
Answer:
B). SAS similarity.
Step-by-step explanation:
In Δ WVU & ΔCAB,
UV/CA = 17/34 = 1/2
&
VW/AB = 14/28 = 1/2
∵ UV/CA = VW/AB = 1/2
& ∠V = ∠A (Given)
∵ ΔWVU ≅ ΔCAB (by SAS similarity)
Help would be truly appreciated. Write the polynomial in standard form from the given zeroes of lest degree that has rational coefficients, a leading coefficient of 1.
Don't have to answer all just what you can. I would appreciate if work is shown that way I can do the same for the rest. I really just need a tutorial and I'm good. Thank you so much!!!
Answer:
1) The polynomial in standard form is f(x) = x³ - 9·x² + 23·x - 15
2) The polynomial in standard form is f(x) = x³ - (2 - 2·i)·x² + 4·i·x
3) The polynomial in standard form is f(x) = x² + (3·i - 3)·x + 2 - 6·i
4) The polynomial in standard form is f(x) = x² - (5 + √5)·x + 6 + 3·√5
Step-by-step explanation:
Given that that the polynomial is of least degree, we have;
The standard form is the form, f(x) = a·xⁿ + b·xⁿ⁻¹ +...+ c
1) The zeros of the polynomial are x = 5, 3, 1
Which gives the polynomial in factored form as_f(x) = (x - 5)·(x - 3)·(x - 1)
From which we have;
f(x) = (x - 5)·(x - 3)·(x - 1) = (x - 5)·(x² - 4·x + 3) = x³ - 4·x² + 3·x - 5·x² + 20·x - 15
f(x) = x³ - 9·x² + 23·x - 15
The polynomial in standard form is therefore f(x) = x³ - 9·x² + 23·x - 15
2) The zeros of the polynomial are x = 2, 0, 2·i
Which gives the polynomial in factored form as_f(x) = (x - 2)·(x)·(x - 2·i)
From which we have;
f(x) = (x - 2)·x·(x - 2·i) = (x² - 2·x)·(x - 2·i) = x³ - 2·i·x² + 2·x² + 4·ix
The polynomial in standard form is therefore f(x) = x³ - (2 - 2·i)·x² + 4·i·x
3) The zeros of the polynomial are x = 2, 1 - 3·i
Which gives the polynomial in factored form as_f(x) = (x - 2)·(x - 1 - 3·i)
From which we have;
f(x) = (x - 2)·(x - (1 - 3·i)) = x² - x + 3·i·x - 2·x + 2 -6·i = x² + 3·i·x - 3·x + 2 - 6·i
The polynomial in standard form is therefore f(x) = x² + (3·i - 3)·x + 2 - 6·i
4) The zeros of the polynomial are x = 3, 2 + √5
Which gives the polynomial in factored form as_f(x) = (x - 3)·(x - (2 + √5))
From which we have;
f(x) = (x - 3)·(x - (2 + √5)) = x² - 2·x - x·√5 - 3·x + 6 + 3·√5
f(x) = x² - 5·x - x·√5 + 6 + 3·√5 = x² - (5 + √5)·x + 6 + 3·√5
The polynomial in standard form is therefore f(x) = x² - (5 + √5)·x + 6 + 3·√5.
Please help me with part A B and C can you write the answers and show me how you get it in a notebook please
You can see all answers in the picture
252 = 42 x 6
Which statement does the equation represent? Answer options with 4 options
A. 42 is 6 more than 252.
B. 252 is 42 more than 6.
C. 42 is 6 times as many as 252.
D. 252 is 42 times as many as 6.
Answer:
C. 42 is 6 times as many as 252
Step-by-step explanation:
because 42×6 = 252
2. Which expression is equivalent to 1/4 n – 16?
Answer:
1/4n - 16 =
1/4(n - 64)
Step-by-step explanation:
Two expression are said to be equivalent, if after substituting the value of variable by any constant the numerical value of both original expression and equivalent expression are same.
PLEASE HELP!!!!!
A line intersects the points (-8, -1) and
(1, 8). What is the slope-intercept
equation for this line?
y= [?}x+ _
Answer:
m=1
c=7
I hope it will be useful.
Which system of linear inequalities has the point (2, 1) in its solution set? Which system of linear inequalities has the point (2, 1) in its solution set?
y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded.
y less-than negative one-half x + 3. y less-than one-half x. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded.
y less-than-or-equal-to negative x + 3. y less-than-or-equal-to one-half x + 2 On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded.
y less-than one-half x. y less-than-or-equal-to negative one-half x + 2
Answer:
c
Step-by-step explanation:
c Which system of linear inequalities has the point (2, 1) in its solution set? Which system of linear inequalities has the point (2, 1) in its solution set?
y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded.
y less-than negative one-half x + 3. y less-than one-half x. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded.
y less-than-or-equal-to negative x + 3. y less-than-or-equal-to one-half x + 2 On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded.
y less-than one-half x. y less-than-or-equal-to negative one-half x + 2v
The system of linear inequalities x + 2y ≤ 4 and 2x - y > 0 has (2,1) in its solution set.
The solution set is given as:
[tex](x,y) = (2,1)[/tex]
The above solution set is true for x + 2y ≤ 4 and 2x - y > 0, and the proof is as follows:
Substitute 2 for x and 1 for y in x + 2y ≤ 4 and 2x - y > 0.
So, we have:
[tex]\mathbf{2 + 2\times1 \le 4 }[/tex]
[tex]\mathbf{2 + 2\le 4 }[/tex]
[tex]\mathbf{4\le 4 }[/tex] --- this is true, because 4 is less than or equal to 4
Also, we have:
[tex]\mathbf{2x - y > 0}[/tex]
[tex]\mathbf{2 \times 2 - 1 > 0}[/tex]
[tex]\mathbf{4 - 1 > 0}[/tex]
[tex]\mathbf{3> 0}[/tex] --- this is also true, because 3 is greater than 0
Hence, the system of linear inequalities x + 2y ≤ 4 and 2x - y > 0 has (2,1) in its solution set.
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answer all questions please.
In ΔRST, r = 53 inches, ∠S=6° and ∠T=58°. Find the length of s, to the nearest inch.
Answer:
s = 6 inches
Step-by-step explanation:
Given:
r = 53 inches,
∠S = 6°
∠T = 58°.
Required:
Length of s
Solution:
Use Sine Rule
Thus:
[tex] \frac{s}{Sin(S)} = \frac{r}{Sin(R)} [/tex]
<R = 180 - (58 + 6)
<R = 116°
r = 53 inches,
∠S = 6°
s = ?
Plug in the values
[tex] \frac{s}{Sin(6)} = \frac{53}{Sin(116)} [/tex]
Multiply both sides by Sin(6)
[tex] \frac{s}{Sin(6)} \times Sin(6) = \frac{53}{Sin(116)} \times Sin(6) [/tex]
[tex] s = \frac{53 \times Sin(6)}{Sin(116)} [/tex]
[tex] s = 6 inches [/tex] (nearest inch)
Find xy when x(-7,10) and y(3,4)
Answer:
Distance xy = 11.66 unit (Approx)
Step-by-step explanation:
Given:
x(-7,10)
y(3,4)
Find:
Distance xy
Computation:
Distance = √(x2-x1)²+(y2-y1)²
Distance xy = √(3+7)²+(4-10)²
Distance xy = √ 100 + 36
Distance xy = 11.66 unit (Approx)
Corrado has 27 books in his room that he has already read. He wants to give them away to his 3 younger siblings. How many books will each of Corrado's siblings receive? If b represents the number of books each sibling receives, which equation could be used to solve the problem?
Answer:
9 books each
Step-by-step explanation:
27/3=9....help!!
f(x) = x2. What is g(x)?
Answer:
g(x) = 1/2x² is the correction option.
Hence, option B is true.
Step-by-step explanation:
Please check the attached graph.
The blue line represents f(x) = x²The red line represents f(x) = 1/2x²It means when we multiply the parent function by a number 'b' which is less than 1, then the parent function f(x) = x² is vertically compressed by b.
Here, the graph is vertically compressed by 1/2, therefore we conclude that g(x) = 1/2x² is the result of vertical compression of the parent function by 1/2.
Therefore, g(x) = 1/2x² is the correction option.
Hence, option B is true.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I know its not that hard im just doing this for fun lol
Answers:
0.210.226.50.680.6240.230.10130.200.1916plus all rounded so i don't cuffuse anyone
Find X
Coordinates are: 3x, 3x+10, 2x+10
Answer:
D. 20
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Geometry
All angles in a triangle add up to 180°Step-by-step explanation:
Step 1: Set Up Equation
3x + 3x + 10 + 2x + 10 = 180
Step 2: Solve for x
Combine like terms: 8x + 20 = 180Isolate x term: 8x = 160Isolate x: x = 20solve: 4y - 6 = 2y + 8
Answer:
y = 7
Step-by-step explanation:
Given
4y - 6 = 2y + 8 ( subtract 2y from both sides )
2y - 6 = 8 ( add 6 to both sides )
2y = 14 ( divide both sides by 2 )
y = 7
can someone help me plz .. Use these lengths to find cos B, tan B, and sin B.
Answer:
cos B = [tex]\frac{7}{25}[/tex]
tan B = [tex]\frac{24}{7}[/tex]
sin B = [tex]\frac{24}{25}[/tex]
Step-by-step explanation:
In the right triangle, there are three sides and 2 acute angles
Hypotenuse ⇒ the opposite side of the right angleLeg1 and Leg 2 ⇒ the sides of the right angleThe trigonometry functions of one of the acute angles Ф are
sin Ф = opposite leg/hypotenusecos Ф = adjacent leg/hypotenusetan Ф = opposite leg/adjacent legIn Δ ACB
∵ ∠C is the right angle
∴ AB is the hypotenuse
∵ AC is the opposite side of ∠B ⇒ leg1
∵ CB is the adjacent side of ∠B ⇒ leg2
→ By using the ratios above
∴ cos B = [tex]\frac{CB}{AB}[/tex] , tan B = [tex]\frac{AC}{CB}[/tex] , sin B = [tex]\frac{AC}{AB}[/tex]
∵ CB = 7, AB = 25, AC = 24
∴ cos B = [tex]\frac{7}{25}[/tex]
∴ tan B = [tex]\frac{24}{7}[/tex]
∴ sin B = [tex]\frac{24}{25}[/tex]
Conceded goals: 0,1,2,3,4 Frequency:2,8,4,10,6 What is the mean number of goals conceded
Answer:
2.333
Step-by-step explanation:
Given that:
Conceded goals: 0,1,2,3,4
Frequency:2,8,4,10,6
Mean(m) = Σ(fx) / Σf
Σfx = (0*2) + (1*8) + (2*4) + (3*10) + (4*6) = 70
Σf = (2 + 8 + 4 + 10 + 6) = 30
Hence,
Mean = 70 / 30
Mean = 2.333
Identify the following division expressionS that have a quotient of 25. (MORE THAN ONE ANSWER)
(A) 125/5
(B) (100/20) + (100/5)
(C) (100/5) + (25/5)
(B) 125/25
(MULTIPLE CHOICE BRAINLIST IF RIGHT)
Answer:
a and c are correct
Step-by-step explanation:
i hoped this helped
GUYSSS HELPPP MEEE IM SUPPOSED TO SUBMIT IT IN 20 MINS AND I HAVE NO IDEA!!
PLEASE HELP
1. f(x) = x² + x + 4
f(x) = 0
0 = x² + x + 4
-4 = x² + x
2. linear equation
one solution
A young sumo wrestler goes on a special diet to gain weight.
The variable www models the wrestler's weight (in kilograms) after the wrestler has been on a special diet for ttt months.
w=80+5.4tw=80+5.4tw, equals, 80, plus, 5, point, 4, t
How much weight does the wrestler gain every 222 months?
kilograms
Answer:
10.8 kg
Step-by-step explanation:
w = 80 + 5.4t
At time 0, when he starts the diet, his initial weight is
w = 80 + 5.4(0)
w = 80
80 kg.
After 2 months, t = 2. His weight is
w = 80 + 5.4t
w = 80 + 5.4(2)
w = 80 + 10.8
w = 90.8
90.8 kg.
His gain in 2 months was 90.8 kg - 80 kg = 10.8 kg
Answer: 10.8 kg
The wrestler gains 10.8 kg every 2 months.
What is an equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
For given question,
We have been given an equation that models the wrestler's weight (in kilograms) after the wrestler has been on a special diet for t months.
w = 80 + 5.4t
We need to find his weight after 2 months.
At time t = 0, when he starts the diet, the wrestler's initial weight would be,
⇒ w = 80 + 5.4(0)
⇒ w = 80 kg
After 2 months, t = 2 the wrestler's weight weight would be,
⇒ w = 80 + 5.4(2)
⇒ w = 80 + 10.8
⇒ w = 90.8 kg
We need to find the weight gain in 2 months.
90.8 - 80 = 10.8 kg
Therefore, the wrestler gains 10.8 kg every 2 months.
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1) Anna and Jason have summer jobs stuffing envelopes for two different companies. Anna earns $20 for every 400 envelopes she finishes. Jason earns $10 for every 250 envelopes he finishes.
A) Create tables, draw graphs, and write equations that show the earnings, y, as functions of the number of envelopes stuffed, x, for both Anna and Jason.
B) Who makes more from stuffing the same number of envelopes? Explain how you know using the information above.
C) Anna has savings of $100 at the beginning of the summer and she saves all of her earnings from her job. Graph her savings as an equationof the number of envelopes she’s stuffed, n. How does this graph compare to her previous earnings graph? What is the meaning of the initial value and slope in each case?
D)You survey 6 other employees and findthe following data on envelopesstuffed (x) and dollars earned(y). Plot a trend lineon the graph. Find the equation of the trend line.
Answer:
The answer is below
Step-by-step explanation:
A) i)
For Anna initially, she has $0 from making 0 envelopes. Anna earns $20 for every 400 envelopes. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{20-0}{400-0}(x-0)\\\\y=\frac{1}{20} x[/tex]
The table is:
x: 200 400 600 800 1000
y: 10 20 30 40 50
ii)
Jason has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:
[tex]y-0=\frac{10-0}{250-0}(x-0)\\\\y=\frac{1}{25} x[/tex]
x: 200 400 600 800 1000
y: 8 16 24 32 40
The graph is plotted using geogebra online graphing
b) From the table of Anna and Jason we can see that Anna makes more stuffing than Jason for the same number of envelopes.
c) Anna has a savings of $100 initially. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{20-0}{400-100}(x-0)\\\\y=\frac{1}{15} x+100[/tex]
Therefore from the graph there is a y intercept at 100. That is the earnings starts initially is $100.
The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value of y at x = 0)
For the first graph, the slope is 1/20 with an initial value of 0 while for the second graph the slope is 1/15 with an initial value of 100
D) The trend line pass through the points (10, 10) and (100, 40), hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{40-10}{100-10}(x-10)\\\\y-10=\frac{1}{3} (x-10)\\\\y=\frac{1}{3}x+\frac{20}{3}[/tex]
how many solutions does the nonlinear system of equations graphed below have
a. one
b. four
c. zero
d. two
Answer:
The nonlinear system of equations has 4 solutions ⇒ B
Step-by-step explanation:
The number of solutions of a system of equations equal to the number of points of intersection of the graphs of the equations of the system
Let us use this note to solve the question
From the given figure
∵ The nonlinear system of equations represented by two curves and a circle
∵ Each curve intersects the circle into two points
∴ The number of the points of intersection is 4
→ By using the note above
∵ The number of intersection points equal to the number of solutions
∴ The number of solutions is 4
∴ The nonlinear system of equations has 4 solutions