Answer:
-262
Step-by-step explanation:
Given sequence is: 33, 28, 23, 18...
First term a = 33
Common Difference d = 28 - 33 = - 5
To find: [tex] t_{60}[/tex]
By nth term of an AP.
[tex]t_n = a + (n - 1)d \\ t_{60} = 33 + (60- 1)( - 5) \\ t_{60} = 33 + 59( - 5) \\ t_{60} = 33 - 295\\ t_{60} = - 262\\ [/tex]
6. Tori and Terry spend the day at the mall. At the end of the ey, se two added up their
purchases and found they spent a total of $107.50, Tori spent $10.00 more fean Tery, Witte
guation that can be used to find how much each girl spent
Answer:
y + (y+10) = 107.50
Step-by-step explanation:
Let y represent Terry's purchases. Then Tori's purchases are (y+10). The sum of their purchases is given by the equation ...
y + (y+10) = 107.50
_____
Then y = 48.75 represents Terry's spending, while y+10 = 58.75 represents Tori's spending.
Please someone help me...
Step-by-step explanation:
First factor out the negative sign from the expression and reorder the terms
That's
[tex] \frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \cot(6A) - \cot(2A) } [/tex]
Using trigonometric identities
That's
[tex] \cot(x) = \frac{1}{ \tan(x) } [/tex]Rewrite the expression
That's
[tex]\frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \frac{1}{ \tan(6A) } } - \frac{1}{ \frac{1}{ \tan(2A) } } [/tex]
We have
[tex] - \frac{1}{ \tan(2A) - \tan(6A) } - \frac{1}{ \frac{ \tan(2A) - \tan(6A) }{ \tan(6A) \tan(2A) } } [/tex]Rewrite the second fraction
That's
[tex] - \frac{1}{ \tan(2A) - \tan(6A) } - \frac{ \tan(6A) \tan(2A) }{ \tan(2A) - \tan(6A) } [/tex]Since they have the same denominator we can write the fraction as
[tex] - \frac{1 + \tan(6A) \tan(2A) }{ \tan(2A) - \tan(6A) } [/tex]
Using the identity
[tex] \frac{x}{y} = \frac{1}{ \frac{y}{x} } [/tex]Rewrite the expression
We have
[tex] - \frac{1}{ \frac{ \tan(2A) - \tan(6A) }{1 + \tan(6A) \tan(2A) } } [/tex]Using the trigonometric identity
[tex] \frac{ \tan(x) - \tan(y) }{1 + \tan(x) \tan(y) } = \tan(x - y) [/tex]Rewrite the expression
That's
[tex] - \frac{1}{ \tan(2A -6A) } [/tex]Which is
[tex] - \frac{1}{ \tan( - 4A) } [/tex]Using the trigonometric identity
[tex] \frac{1}{ \tan(x) } = \cot(x) [/tex]Rewrite the expression
That's
[tex] - \cot( - 4A) [/tex]Simplify the expression using symmetry of trigonometric functions
That's
[tex] - ( - \cot(4A) )[/tex]Remove the parenthesis
We have the final answer as
[tex] \cot(4A) [/tex]As proven
Hope this helps you
Answer: see proof below
Step-by-step explanation:
Use the following identities:
[tex]\cot\alpha=\dfrac{1}{\tan\alpha}\\\\\\\cot(\alpha-\beta)=\dfrac{1+\tan\alpha\cdot \tan\beta}{\tan\alpha-\tan\beta}[/tex]
Proof LHS → RHS
Given: [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\cot 6A-\cot 2A}[/tex]
Cot Identity: [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{1}{\tan 6A}-\dfrac{1}{\tan 2A}}[/tex]
Simplify: [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{1}{\tan 6A}\bigg(\dfrac{\tan 2A}{\tan 2A}\bigg)-\dfrac{1}{\tan 2A}\bigg({\dfrac{\tan 6A}{\tan 6A}\bigg)}}[/tex]
[tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{\tan 2A-\tan 6A}{\tan 6A\cdot \tan 2A}}[/tex]
[tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{\tan6A\cdot \tan 2A}{\tan 2A-\tan 6A}[/tex]
[tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{\tan6A\cdot \tan 2A}{\tan 2A-\tan 6A}\bigg(\dfrac{-1}{-1}\bigg)[/tex]
[tex]= \dfrac{1}{\tan 6A-\tan 2A}+\dfrac{\tan6A\cdot \tan 2A}{\tan 6A-\tan 2A}[/tex]
[tex]= \dfrac{1+\tan6A\cdot \tan 2A}{\tan 6A-\tan 2A}[/tex]
Sum Difference Identity: cot(6A - 2A)
Simplify: cot 4A
cot 4A = cot 4A [tex]\checkmark[/tex]
We run a linear regression and the slope estimate is 0.5 with estimated standard error of 0.2. What is the largest value of b for which we would NOT reject the null hypothesis that β1=b ? (assume normal approximation to t distribution, and that we are using the 5% significance level for a two-sided test; need two significant digits of accuracy)
Answer:
0.9
Step-by-step explanation:
Y = B0 + B1X
B1 is the slope an from the question the slope estimate is 0.5
S.E= standard error at 0.2
At 5percent Level of significance, the z value for the test is equal to 1.96
We are required to find out the largest value of b for which the null hypothesis would be accepted.
0.5 + 1.96 x 0.2
= 0.892
Approximately 0.9
Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <10,0>, V = <0,-9>
Answer:
Orthogonal.
Step-by-step explanation:
Given:
u = <10, 0>
v = <0, -9>
In unit vector notation, the above vectors can be re-written as:
u = 10i + 0j
v = 0i - 9j
Now, note the following:
(i) two vectors, u and v, are parallel to each other if one is a scalar multiple of the other. i.e
u = kv
or
v = ku
for some nonzero value of a scalar k.
(ii) two vectors are orthogonal if their dot product gives zero. i.e
u . v = 0
Let's use the explanations above to determine whether the given vectors are parallel or orthogonal.
(a) If parallel
u = k v
10i + 0j = k (0i - 9j) ?
When k = 1, the above equation becomes
10i + 0j ≠ 0i - 9j
When k = 2,
10i + 0j ≠ 2(0i - 9j)
10i + 0j ≠ 0i - 18j
Since we cannot find any value of k for which u = kv or v = ku, then the two vectors are not parallel to each other.
(b) If Orthogonal
u.v = (10i + 0j) . (0i - 9j)
[multiply the i components together, and add the result to the multiplication of the j components]
u.v = (10i * 0i) + (0j * 9j)
u.v = (0) + (0)
u.v = 0
Since the dot product of the two vectors gave zero, then the two vectors are orthogonal.
What is the measure in degrees of angle EDF?
Answer:
20 degrees.
Step-by-step explanation:
Since these triangles are similar, they will have congruent angles.
Since BAC is corrosponding to EDF, they will have the same angle measurment.
BAC = 20, so EDF = 20
Answer:
EDF = 20
Step-by-step explanation:
If the triangles are similar, the angle measurements have to be equal
<A = <D
<B = <E
<C = <F
Since BAC = 20, <A = 20 that means D = 20
EDF = 20
Find the percentage of: 21% of 18 use a set of fraction operations method to find the percentage.
Answer:
4.8%
Step-by-step explanation:
21% of 18
following the BODMAS rule, OF means multiplication
and also this sign% always means 100
so,it will be 21/100 * 18/1
this a laptop so i cant put it in a fraction way.....okay
this is how it shows...21/100 * 18/1
lets divide....
21/100 * 18/1
we will use 2 to divide
2 in 100=50
2 in 18=9
so it will be 21/50 * 9/1
nothing can divide so we will multiply
21*9/50*1
189/50=3.78≈4.8%
Enter the mixed number as an improper fraction. 1 5/6 =
Answer:
11/6
Step-by-step explanation:
To find the improper fraction
Take the denominator times the whole number
6*1 = 6
Add the numerator
6+5 =11
Put this over the denominator
11/6
Answer:
[tex]\frac{11}{6}[/tex]
Step-by-step explanation:
What is 1 5/6 as an improper fraction?
If you wanna make 1 5/6 as a improper fraction, you must take the 5 from 1 5/6 and add it 6.
[tex]6+5=11[/tex]
[tex]\frac{11}{}[/tex]
Since the denominator is 6, you will put it down.
[tex]\frac{11}{6}[/tex]
So now you got your answer!
Hope this Helps!
Two friends went fishing on a lake. One friend’s lure went 23 feet below the lake’s surface, while the other friend’s lure sank to a depth of 81 feet below the surface. What was the difference in the depths of the lures?
Answer:
58 feet
Step-by-step explanation:
Find the difference by subtracting 23 from 81.
81 - 23
= 58 feet
f(x) = 7x − 13. Find f−1(x)
Intersecting lines are _____ coplanar. Sometimes Never Always
Answer:
Always
Step-by-step explanation:
Coplanar lines are lines that intersect making intersecting lines always coplanar.
Christine is typing at a rate of 75 words per
minute. Paula is typing at twice Christine's
speed. If together they need to transcribe a 2000
word paper which of the following expressions
would illustrate the time in minutes, x, it would
take for them to do so.
A) 150
2000X
75
150
B)
+
= 2000
C) 150 + 75 =
2000
2000
D) x =
(150+75)
Answer:
X = 2000 / (75 + 150)
Step-by-step explanation:
Given the following :
Christine's typing rate = 75 words per minute
Paula's speed = 2 times Christine's speed
If 2000 words needs to be transcribed. The time taken in minute 'x' will be :
From the relation :
Time = distance / speed
Distance here is the number of words in the document
Christine's speed = 75 words per minute
Paula's speed = 150 words per minute
Combined speed per minute = 150 + 75 = 225 words per minute
Time taken (x) = 2000 / 225
X = 2000 / (75 + 150)
What’s 5x-2=25x+14? (please explain)
Answer:
x = - [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Given
5x - 2 = 25x + 14 ( subtract 25x from both sides )
- 20x - 2 = 14 ( add 2 to both sides )
- 20x = 16 ( divide both sides by - 20 )
x = [tex]\frac{16}{-20}[/tex] = - [tex]\frac{4}{5}[/tex]
The population of a city is 1,880,000 what is the value of each of the two 8s in this number how are the two values related
Answer:
The value of the 8 in the front is 800,000 and the value of the second is 80,000. The front value is ten times as big as the second value.
Step-by-step explanation:
really need help solving this problem
Answer:
y = 8
Step-by-step explanation:
[tex] \frac{y}{4} = \frac{5 + 5}{5} \\ \\ \frac{y}{4} = \frac{10}{5} \\ \frac{y}{4} = 2 \\ y = 4 \times 2 \\ y = 8[/tex]
Evaluate 9/g+2h+5
when g=3 and h=6
Answer:
20
Step-by-step explanation:
[tex] \frac{9}{g} + 2h + 5 \\ = \frac{9}{3} + 2 \times 6 + 5 \\ = 3 + 12 + 5 \\ = 20[/tex]
At present the sum of Geetha's age and her daughter's age is 44 years. After 2 years, Geetha's age will be three times that of her daughter's age. Find their present ages.
Answer:
Geetha is 32.5 years old
her daughter is 11.5 years old
Step-by-step explanation:
sum of their ages is 44 years
G + D = 44
in two years, Geetha's age is 3 times her daughters age. (to find present age, subtract 2)
G = 3D - 2
substitute
(3D - 2) + D = 44
combine like terms
4D - 2 = 46
4D = 46
D = 11.5
plug in D to either equation
G + (11.5) = 44
G = 32.5
G = 3(11.5) - 2
G = 32.5
Find the mistake made in the steps to solve the equation below.
61 - 1 = -21 + 9
81 - 1 = 9
80 = 10
1. Addition property of
equality
2. Addition property of equality
3. Division property of equality
to
I
CHA
4. Simplification
OA. The justification for step 2 is incorrect and should be the subtraction property of equality.
OB. Step 3 is incorrect and should be r = 100
OC. Step 2 is incorrect and should be r = 8.
OD. The justification for step 3 is incorrect and should be the multiplication property of equality,
Answer:
A
Step-by-step explanation:
A
The mistake made in the justification for step 2 is incorrect and should be the subtraction property of equality. which is the correct answer would be an option (A).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation is given in the question
6x - 1 = -2x + 9
Addition property of equality
8x - 1 = 9
Subtraction property of equality
8x = 10
Division property of equality
x = 10/8
Simplification
x = 5/4
Thus, the mistake made in the justification for step 2 is incorrect and should be the subtraction property of equality.
Hence, the correct answer would be option (A).
Learn more about the equation here:
brainly.com/question/13947055
#SPJ5
Integrated math ll I need help ASAP PLEASE
Greetings from Brasil...
We have 2 conditions:
1 - angles opposed by the vertex - the angles are equal
2 - supplementary angles - the sum of the two angles results in 180
2:
(4X + 15) and (5X + 30) are supplementary angles, so:
(4X + 15) + (5X + 30) = 180
9X = 180 - 15 - 30
9X = 135
X = 151:
(3Y + 15) and (5X + 30) are angles opposed by the vertex, so they are equal
3Y + 15 = 5X + 30
3Y = 5X + 30 - 15
3Y = 5X + 15 above we have already calculated the value of X
3Y = 5.(15) + 15
3Y = 75 + 15
3Y = 90
Y = 90/3
Y = 30What is the product?
Answer:
10x²+3xy+6x-y²+3y
Step-by-step explanation:
(2x+y)(5x-y+3) steps
2x(5x-y+3)=10x²-2xy+6x
y(5x-y+3)= 5xy-y²+3y
add: 10x²-2xy+6x+5xy-y²+3y
10x²+3xy+6x-y²+3y
solve 3(5y+2)–y=2(y–3)
Answer:
y= -1
Step-by-step Explanation:
3(5y +2)-y=2(y-3)
Distribute- 15y +6-y=2y -6
Combine variables- 15y-2y-y=-6-6
Add everything together- 12y= -12
Divide- y= -1
Answer:
y = -1
Step-by-step explanation:
Step 1. Expand the brackets.
3(5y + 2) - y = 2(y - 3)
(3 x 5y) + (3 x 2) - y = (2 x y) - (2 x 3)
15y + 6 - y = 2y - 6
Step 2. Simplify the expanded brackets (not always necessary but is in this case).
15y + 6 - y = 15y - y + 6 = 14y + 6
So
14y + 6 = 2y - 6
Step 3. Solve the equation.
14y + 6 = 2y - 6
+ 6 to both sides
14y + 12 = 2y
- 14y from both sides
12 = -12y
÷ 12 on both sides
1 = -y
flip the negative
-1 = y
Step 3. Write your answer.
y = -1
Two straight edges of a pizza slice meet at an angle of 30°. If the pizza has a radius of 12
inches, what is the area of the slice and how long is its crust? Show how you got your answer step-by-step.
Answer:
area of the slice: A = 12π in² ≈ 37.7 in² lenght of its crust: L = 24π in ≈ 6.28 inStep-by-step explanation:
R = 12 in
360°:30° = 12
so the area of the slice is ¹/₁₂ of whole pizza
A = ¹/₁₂•πR² = ¹/₁₂•π•12•12 = 12π in² ≈ 37.7 in²
Crust is the perimeter of pizza so crust of the slice is ¹/₁₂ of the perimeter:
L = ¹/₁₂•2πR = ¹/₁₂•2π•12 = 2π in ≈ 6.28 in
gage bought a new car for $29000 to use while he is away at college. The car decreases in value by 11% annually. What would the cars value after 4 years?
The value of the gauge car after 4 years will be $18195.25.
What is compound interest?Compound interest is applicable when there will be a change in principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
Given,
Principle amount (P) = $29000
Rate of decrement (R) = 11%
Time period(T) = 4 years
Percentage decrement over T time period is given by
Final amount = P[tex][1 - R/100]^{T}[/tex]
Final amount = 29000[tex][1 - 11/100]^{4}[/tex]
Final amount = 29000(0.89)⁴
Final amount = $18195.25.
Hence, The value of the gauge car after 4 years will be $18195.25.
For more information about compound interest,
brainly.com/question/26457073
#SPJ5
The value of the car after 4 years is $18195.24989.
Given,
Gage bought a new car for $29000 to use while he is away at college.
The car decreases in value by 11% annually.
We need to find what would the cars value after 4 years.
we have,
Cost of the car = $29000
The car decreases annually by = 11%
1st-year decrease.
$29000 x 11/100 = $3190
The cost of the car after 1st year = $29000 - $3190 = $25810
2nd-year decrease.
$25810 x 11/100 = $2839.1
The cost of the car after 2nd year = $25810 - $2839.1 = $22970.9
3rd-year decrease.
$22970.9 x 11/100 = $2526.799
The cost of the car after 3rd year = $22970.9 - $2526.799 = $20444.101
4th-year decrease.
$20444.101 x 11/100 = $2248.85111
The cost of the car after 4th year = $20444.101 - $2248.85111 = $18195.24
Thus the value of the car after 4 years is $18195.24989.
Learn more about the value of a product after an annual decrease here:
https://brainly.com/question/28231393
#SPJ2
help me plsssssssssssssssssssssssssssssssssssssss
Answer:
[tex] \frac{1}{5} ( - m - 4)[/tex]
Step-by-step explanation:
But method 1 best suits the question
Answer:
[tex] - \frac{1}{5} m - \frac{4}{5} [/tex]
Answer:
-1/5m -4/5
Step-by-step explanation:
2/5 m -4/5 - 3/5 m
Combine like terms
2/5m - 3/5m -4/5
-1/5m -4/5
Please help as soon as possible Will mark BRAINLIEST!!!!!
Answer:
Width = 40ft
Step-by-step explanation:
Area of a rectangle = Length x Width
=> 1600 = 40 x W
=> 1600 = 40W
=> 1600/40 = 40W/40
=> 40 = W
So, the width is 40 ft
Answer:
40 ft is the correct answer
help :/ ill give brainly :>
Answer:
A. Trapezoid
B. Isoclese triangle
c. Equilateral triangle
d. Kite
Answer:
A, Parallelogram (more specifically a trapezoid)
B. Isosceles Triangle
C. Equilateral Triangle
D. Kite
HELP ME!!! Why is it possible to isolate the variable, x, in the equation 2x = 20 by using either the division property of equality or the multiplication property of equality?
Answer: Because division is the inverse of multiplication.
Step-by-step explanation:
By multiplying the equation 2x=20 by 1/2 you will be able to eliminate the x variable,
For example,
1/2 * 2x = 20*1/2
x= 10
The same way if you divide both sides of the equation 2x=20 by 2 you will be able to to eliminate the x variable.
For example
2x = 20 Divide both sides by 2
x= 10
As you can see 2 is the division inverse of 1/2.
PLZ HELP Find the value of x that makes ΔXYZ~PQR
Answer:
x = 8
Step-by-step explanation:
[tex] \triangle XYZ \sim\triangle PQR... (GIVEN) \\
\therefore \frac{XY}{PQ} = \frac{YZ}{QR}.. (csst) \\
\therefore \frac{20}{30}= \frac{x+6}{21}\\
\therefore \frac{2}{3}= \frac{x+6}{21}\\
\therefore \frac{2\times 21}{3}= {x+6}\\
\therefore 14= {x+6}\\
\therefore 14-6= {x}\\
\therefore 8= {x}\\
\huge \orange{\boxed {\therefore x = 8}} [/tex]
On her first quiz in social studies,Meg answered 92% of the questions correctly.On her second quiz,she answered 27 out of 30 questions correctly. On which quiz did Meg have the better score?
Answer:
on her first quiz
Step-by-step explanation:
27/30=
27÷30=
0.9=
09×100/100=
0.9×100%=
(0.9×100)% =
90%
Answer:
first quiz
Step-by-step explanation:
100 divided by 30 times 27<92%
What is the equation of the line that passes through the points (−2, 1) and (1, 10)?
Answer:
Slope-Intercept form: y=3x+7
Standard form: 3x-y=-7
Point-slope form: y-1=3(x+2)
Step-by-step explanation:
Slope-Intercept form:
First, find the slope, using the formula: [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Our x₁ and y₁ will be the point (-2,1) and our x₂ and y₂ wwill be the point (1,10).
So let's write those in our equation to find slope:
[tex]m=\frac{10-1}{1-(-2)}=\frac{9}{3}=3[/tex]
Therefore, our slope is 3.
Now let's write our linear equation with what we have already in slope-intercept form:
y=3x+b
Well, we still need to find the y-intercept, or "b".
Plug in one of your points for the x and y values of the equation. We'll use the point (-2,1)
[tex]y=3x+b\\1=3(-2)+b\\1=-6+b\\1+6=-6+6+b\\7=b[/tex]
This means our y-intercept is 7. Now we can write our equation in slope-intercept form completely:
y=3x+7
Standard form:
Now, let's find this equation is standard form.
Take your equation in slope-intercept form and write it out again:
[tex]y=3x+7[/tex]
Now, standard form of a linear equation is ax+by=c, so subtract 3x from both sides:
[tex]y-3x=3x-3x+7\\-3x+y=7[/tex]
The "a" coefficient in standard form cannot be negative, so divide the entire equation by -1:
[tex]\frac{-3x+y}{-1}=\frac{7}{-1}\\3x-y=-7[/tex]
Therefore, your equation in standad form is:
3x-y=-7
Point-Slope form:
The formula for point-slope form is y-y₁=m(x-x₁). We already know that our x₁ and y₁ is the point (-2,1) and we know that our slope, m, is 3, so we just have to plug then in where the fit in the equation.
x₁ is -2 and y₁ is 1 and m is 3, so:
y-1=3(x-(-2)) or y-1=3(x+2)
That means our equation in point-slope form is:
y-1=3(x+2)
Which expression is equivalent to (StartFraction 125 squared Over 125 Superscript four-thirds Baseline EndFraction? StartFraction 1 Over 25 EndFraction One-tenth 10 25
Answer:
[tex]\frac{125^2}{125^\frac{4}{3}} = 25[/tex]
Step-by-step explanation:
Given
[tex]\frac{125^2}{125^\frac{4}{3}}[/tex]
Required
Find an equivalent expression
[tex]\frac{125^2}{125^\frac{4}{3}}[/tex]
Apply the following law of indices;
[tex]\frac{a^m}{a^n} a^{m-n}[/tex]
The expression becomes
[tex]125^{2-\frac{4}{3}}[/tex]
Solve the exponents
[tex]125^{\frac{6-4}{3}}[/tex]
[tex]125^{\frac{2}{3}}[/tex]
Express 125 as 5³
[tex]5^{3^*\frac{2}{3}}[/tex]
Solve the exponents
[tex]5^2[/tex]
[tex]25[/tex]
Hence;
[tex]\frac{125^2}{125^\frac{4}{3}} = 25[/tex]
Answer:
d
Step-by-step explanation:
i just took it! edgen