Answer:
r + s - 19
General Formulas and Concepts:
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
r - 7 + s - 12
Step 2: Simplify
Combine like terms [constants]: r + s - 19(4-1) + (6 + 5) = help plz
E. The ratio of monthly income to savings of a family is 7:2. If the savings is Rs. 500, find the monthly income and expenditure.
Step-by-step explanation:
Since the ratio of monthly income to savings of the family is 7:2, we assume that the income be 7t and savings be 2t
Now, we are given that the savings is =Rs 500
So, According to our assumption, 2t=500
⇒t=250
Hence, the income of the family is =7×250=Rs 1750
And the expenditure is =Income−Savings
=Rs 1750−Rs 500
=Rs 1250
40% of what number is 16.6?
Prove the following identities : i) tan a + cot a = cosec a sec a
Step-by-step explanation:
[tex]\tan \alpha + \cot\alpha = \dfrac{\sin \alpha}{\cos \alpha} +\dfrac{\cos \alpha}{\sin \alpha}[/tex]
[tex]=\dfrac{\sin^2\alpha + \cos^2\alpha}{\sin\alpha\cos\alpha}=\dfrac{1}{\sin\alpha\cos\alpha}[/tex]
[tex]=\left(\dfrac{1}{\sin\alpha}\right)\!\left(\dfrac{1}{\cos\alpha}\right)=\csc \alpha \sec\alpha[/tex]
Question :
tan alpha + cot Alpha = cosec alpha. sec alphaRequired solution :
Here we would be considering L.H.S. and solving.
Identities as we know that,
[tex] \red{\boxed{\sf{tan \: \alpha \: = \: \dfrac{sin \: \alpha }{cos \: \alpha} }}}[/tex][tex] \red{\boxed{\sf{cot \: \alpha \: = \: \dfrac{cos \: \alpha }{sin \: \alpha} }}}[/tex]By using the identities we gets,
[tex] : \: \implies \: \sf{ \dfrac{sin \: \alpha }{cos \: \alpha} \: + \: \dfrac{cos \: \alpha }{sin \: \alpha} }[/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin \: \alpha \times sin \: \alpha }{cos \: \alpha \times sin \: \alpha} \: + \: \dfrac{cos \: \alpha \times cos \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]
[tex] : \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \times sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \: sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \: cos \: \alpha } } [/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha \: + \: cos {}^{2} \alpha}{cos \: \alpha \: sin \alpha} } [/tex]
Now, here we would be using the identity of square relations.
[tex]\red{\boxed{ \sf{sin {}^{2} \alpha \: + \: cos {}^{2} \alpha \: = \: 1}}}[/tex]By using the identity we gets,
[tex] : \: \implies \: \sf{ \dfrac{1}{cos \: \alpha \: sin \alpha} }[/tex]
[tex]: \: \implies \: \sf{ \dfrac{1}{cos \: \alpha } \: + \: \dfrac{1}{sin\: \alpha} }[/tex]
[tex]: \: \implies \: \bf{sec \alpha \: cosec \: \alpha}[/tex]
Hence proved..!!Chang has 2 shirts: a white one and a black one. He also has 2 pairs of pants, one blue and one tan. What is the probability, if Chang gets dressed in the dark, that
he winds up wearing the white shirt and tan pants? Show your work.
Answer:
1/4
Step-by-step explanation:
White = w
Black = B
Blue = b1
Tan = t
Wb1
Wt
Bbi
Bt
The answer will be 1/4, because there are 4 ways it can work and only 1 way it can be white shirt and tan pants.
Answer:
1/4
Step-by-step explanation:
it would be 1/4 because there are 4 different clothing pieces in total and there is only one way it would work the way the problem says.
khai niem hinh cat don gian ?
Answer:
khai niem hinh cat don gian?
The polynomial equation x cubed + x squared = negative 9 x minus 9 has complex roots plus-or-minus 3 i. What is the other root? Use a graphing calculator and a system of equations. –9 –1 0 1
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Answer:
(b) -1
Step-by-step explanation:
The graph shows the difference between the two expressions is zero at x=-1.
__
Additional comment
For finding solutions to polynomial equations, I like to put them in the form f(x)=0. Most graphing calculators find zeros (x-intercepts) easily. Sometimes they don't do so well with points where curves intersect. Also, the function f(x) is easily iterated by most graphing calculators in those situations where the root is irrational or needs to be found to best possible accuracy.
Answer:
The answer is b: -1
Step-by-step explanation:
good luck!
Suppose a sample of 1453 new car buyers is drawn. Of those sampled, 363 preferred foreign over domestic cars. Using the data, estimate the proportion of new car buyers who prefer foreign cars. Enter your answer as a fraction or a decimal number rounded to three decimal places
Answer:
"0.250" is the appropriate answer.
Step-by-step explanation:
Given:
New car sample,
= 1453
Preferred foreign,
= 363
Now,
The amount of new automobile purchasers preferring foreign cars will be approximated as:
= [tex]\frac{363}{1453}[/tex]
= [tex]0.250[/tex]
Pleaseee Help. What is the value of x in this simplified expression?
(-1) =
(-j)*
1
X
What is the value of y in this simplified expression?
1 1
ky
y =
-10
K+m
+
.10
m т
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Answer:
x = 7
y = 5
Step-by-step explanation:
The applicable rule of exponents is ...
a^-b = 1/a^b
__
For a=-j and b=7,
(-j)^-7 = 1/(-j)^7 ⇒ x = 7
For a=k and b=-5,
k^-5 = 1/k^5 ⇒ y = 5
Which statement best compares the two functions?
A) Neither function A nor function B has an x-intercept.
B) Neither function A nor function B has a y-intercept.
C) The domain and range of both functions contain only
positive numbers.
D) The domain and range of both functions contain only
positive numbers and zero
Answer:
A) Neither function A nor function B has an x-intercept.
Step-by-step explanation:
By selling a radio for $8400 a dealer gained 12% .how much money did she gain
Answer:
Amount gained = $900
Step-by-step explanation:
Let the cost price be = x
Given selling price = 8400
And profit% = 12%
Profit = selling price - cost price
= 8400 - x
[tex]Profit \ \% = \frac{profit}{cost \ price} \times 100\\\\12\% = \frac{8400 - x}{x} \times 100\\\\\ 12 \times \frac{1}{100} = \frac{8400 - x}{x}\\\\\frac{12 \ x}{100} = 8400 - x \\\\\frac{12x}{100} + x = 8400\\\\12x + 100x = 8400 \times 100\\\\112x = 8400 \times 100\\\\x = \frac{8400 \times 100}{112} = 7500[/tex]
Therefore , cost price of the radio $7500
The amount she gained = 8400 - 7500 = $ 900
Which side of the polygon is exactly 6 units long?
Answer:
AB is correct as It is the shorter parallel line
as the line measures 6 units.
Step-by-step explanation:
The polygon is a trapezoid / (trapezium Eng/Europe)
We see the given coordinates (2, 6) - (-4, 6) = x-6 y 0 = x = 6units
as x always is shown as x - 6 as x= 6
We can also show workings as y2-y1/x2-x1 = 6-6/-4-2 0/-6
y = 0 x = 6 = 6 units as its horizontal line.
when y is 6-6 = 0 then we know the line is horizontal for y = 0.
The difference of the measures -4 to 2 is 6units so if no workings we just add on from -4 to 2 and find the answer is 6 units long.
When looking at diagonal lines we still group the x's and y's and make the fraction whole.
When looking for solid vertical lines that aren't shown here we use the y values if showing workings and show x =0 to cancel out.
Suppose point (4, −9) is translated according to the rule (, ) → ( + 3, − 2). What are the coordinates of ′? Explain
What is the explicit formula for the sequence ? -1,0,1,2,3
Answer:
B
Step-by-step explanation:
substitute the values in the eq. Ot is also arithmetic progression.
What is the complete factorization of the polynomial below?
x3 + 8x2 + 17x + 10
A. (x + 1)(x + 2)(x + 5)
B. (x + 1)(x-2)(x-5)
C. (x-1)(x+2)(x-5)
O D. (x-1)(x-2)(x + 5)
Answer: A (x+1)(x+2)(x+5)
Step-by-step explanation:
If $6^x = 5,$ find $6^{3x+2}$.
If 6ˣ = 5, then
(6ˣ)³ = 6³ˣ = 5³ = 125,
and
6³ˣ⁺² = 6³ˣ × 6² = 125 × 6² = 125 × 36 = 4500
The administration conducted a survey to determine the proportion of students who ride a bike to campus. Of the 123 students surveyed 5 ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus? Check all that apply.
a. The sample needs to be random but we don’t know if it is.
b. The actual count of bike riders is too small.
c. The actual count of those who do not ride a bike to campus is too small.
d. n*^p is not greater than 10.
e. n*(1−^p)is not greater than 10.
Answer:
b. The actual count of bike riders is too small.
d. n*p is not greater than 10.
Step-by-step explanation:
Confidence interval for a proportion:
To be possible to build a confidence interval for a proportion, the sample needs to have at least 10 successes, that is, [tex]np \geq 10[/tex] and at least 10 failures, that is, [tex]n(1-p) \geq 10[/tex]
Of the 123 students surveyed 5 ride a bike to campus.
Less than 10 successes, that is:
The actual count of bike riders is too small, or [tex]np < 10[/tex], and thus, options b and d are correct.
For -180°<θ<0 , which of the primary trigonometric functions may have positive values?
Answer:
cos theta = adj / hyp is positive (+/+)
Step-by-step explanation:
In this open interval, the hypotenuse (radius) is always positive, whereas the adjacent side is positive and the opposite side negative.
in this interval:
sin theta = opp / hyp is neg (-/+)
cos theta = adj / hyp is positive (+/+)
tan theta = opp / adj = (-/+) : negative
a triangle has sides of 6 m 8 m and 11 m is it a right-angled triangle?
Answer:
No
Step-by-step explanation:
If we use the Pythagorean theorem, we can find if it is a right triangle. To do that, set up an equation.
[tex]6^{2}+8^{2}=c^2[/tex]
If the triangle is a right triangle, c would equal 11
Solve.
[tex]36+64=100[/tex]
Then find the square root of 100.
The square root of 100 is 10, not 11.
So this is not a right triangle.
I hope this helps!
X+34>55
Solve the inequality and enter your solution as an inequality comparing the variable to a number
Answer:
x > 21
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
x + 34 > 55
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 34 on both sides: x > 21Which one goes where?
"RS tangent to circle a..." is first statement Reason: Given
Second Reason: "Radius perpendicular to tangent"
Second Statement: "AR is parrallel to BS" Reason: "2 lines perpendicular..."
An isosceles trapezoid has a consecutive-sides of length: 10,6,10 and 14. Find the measure of each angle if the trapezoid.
Answer:
Angle A = Angle D = 69° 30'
Angle B = Angle C = 110° 30'
Step-by-step explanation:
B ___ C
/ \
/ \
A ________ D
AB and CD are 10
BC is 6
AD is 14
If we divide the trapezoid, we can imagine a line.
B_ F_C
/ | \
/ | \
A ___E____ D
AE = ED = 7 (14/2)
BF = FC = 3
So now, we draw another line from B or C to AE or ED
B_ F_ C
/ | | \
/ | | \
A ___E_ G_ D
EG = GD = 3.5 (7/2)
There is a right triangle now, GCD
GD is 3.5 and CD is 10. To determine angle D, we can apply trigonometric function:
CD is H, and GD is A
cos D = A/H
cos D = 3.5/10 → 0.35
angle D = 69° 30'
By theory, we know that angle D and angle A, are the same so:
Angle D = Angle A = 69° 30'
Angle B = Angle C
We also make a cuadrilateral, which is EFCD.
Angle D is 69° 30', Angle E is 90°, Angle F is also 90°
Sum of angles in cuadrilateral is 360°
360° - 69° 30' - 90° - 90° = Angle C = Angle B
Angle C = Angle B = 110° 30'
Let's confirm the angles in the trapezoid:
69° 30' + 110° 30' + 69° 30' + 110° 30' = 360°
A + B + C + D
Assuming that the sample mean carapace length is greater than 3.39 inches, what is the probability that the sample mean carapace length is more than 4.03 inches
Answer:
The answer is "".
Step-by-step explanation:
Please find the complete question in the attached file.
We select a sample size n from the confidence interval with the mean [tex]\mu[/tex]and default [tex]\sigma[/tex], then the mean take seriously given as the straight line with a z score given by the confidence interval
[tex]\mu=3.87\\\\\sigma=2.01\\\\n=110\\\\[/tex]
Using formula:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The probability that perhaps the mean shells length of the sample is over 4.03 pounds is
[tex]P(X>4.03)=P(z>\frac{4.03-3.87}{\frac{2.01}{\sqrt{110}}})=P(z>0.8349)[/tex]
Now, we utilize z to get the likelihood, and we use the Excel function for a more exact distribution
[tex]=\textup{NORM.S.DIST(0.8349,TRUE)}\\\\P(z<0.8349)=0.7981[/tex]
the required probability: [tex]P(z>0.8349)=1-P(z<0.8349)=1-0.7981=\boldsymbol{0.2019}[/tex]
hope anyone help me please
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Answer:
a) Lahulspiti: -8; Srinigar: -2; Shimla: 5; Ooty: 14; Bengahuru: 22
b) 30
c) 6
d) yes; no
Step-by-step explanation:
a) The values are read from the graph.
__
b) 22 -(-8) = 22 +8 = 30 . . . . difference between highest and lowest
__
c) -2 -(-8) = -2 +8 = 6 . . . positive difference
(Technically, the difference between L and S is L - S = (-8) -(-2) = -6.)
__
d) -2 + 5 < 5 . . . . true
-2 + 5 < -2 . . . . false
As one once said Another one
Answer:
f
Step-by-step explanation:
Answer:
S = 62.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan S = opp side / adj side
tan S = sqrt(42)/ sqrt (11)
tan S = sqrt(42/11)
Taking the inverse tan of each side
tan ^ -1( tan S) = tan ^-1(sqrt(42/11))
S=62.89816
Rounding to the nearest tenth
S = 62.9
Graph the inequality.
7 <= y - 2x < 12
Answer:
X(-12,-7)
Step-by-step explanation:
This is the answer to your problem. I hope it helps. I don't know how to explain it sorry.
what is the discrimination of the polynomial below ?
9x2-18x+9
2/3y = 1/4 what does y equal?
Answer:
Step-by-step explanation:
2/3y=1/4 this means 3y=8 then you divide both sides by 8 you will get the value of y =8/3
PLEASE HELP WILL MARK BRAINLIEST
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Answer:
x = 10/3 = 3 1/3 ≈ 3.33
Step-by-step explanation:
Triangles ABC and ADE are similar, so corresponding sides are proportional.
DE/DA = BC/BA
x/(4+6) = 2/6
x = 10(2/6) = 10/3 = 3 1/3
Describe the transformation of f(x) to g(x). Pleaseee helllp thank youuuu!!!
The transformation set of [tex]y[/tex] values for function [tex]f[/tex] is [tex][-1,1][/tex] this is an interval to which sine function maps.
You can observe that the interval to which [tex]g[/tex] function maps equals to [tex][-2,0][/tex].
So let us take a look at the possible options.
Option A states that shifting [tex]f[/tex] up by [tex]\pi/2[/tex] would result in [tex]g[/tex] having an interval [tex][-1,1]+\frac{\pi}{2}\approx[0.57,2.57][/tex] which is clearly not true that means A is false.
Let's try option B. Shifting [tex]f[/tex] down by [tex]1[/tex] to get [tex]g[/tex] would mean that has a transformation interval of [tex][-1,1]-1=[-2,0][/tex]. This seems to fit our observation and it is correct.
So the answer would be B. If we shift [tex]f[/tex] down by one we get [tex]g[/tex], which means that [tex]f(x)=\sin(x)[/tex] and [tex]g(x)=f(x)-1=\sin(x)-1[/tex].
Hope this helps :)
