[tex]\text{Given that,}\\\\\cos \theta = -\dfrac 25 \\\\\implies \cos^2 \theta = \dfrac 4{25}\\\\\\\implies 1- \sin^2 \theta = \dfrac{4}{25}\\\\\\\implies \sin^2 \theta = 1-\dfrac{4}{25}\\\\\\\implies \sin^2 \theta =\dfrac{21}{25}\\\\\\\implies \sin \theta = \pm \sqrt{\dfrac {21}{25}} = \pm \dfrac{\sqrt{21}} 5\\\\\text{Since}~ \tan \theta>0,~ ~\text{the value of} ~\sin \theta ~\text{wii be:} \\\\\sin \theta = -\dfrac{\sqrt{21}}5[/tex]
Write the linear equation into Standard Form. 8+3x=-9y
Hello! :p
Original: 8+3x=-9y
standard form: 3x + 9y = -8
I hope this helps! Have a wonderful day! :)
Work out the area of triangle ABC.
Answer:
A = 4 cm²
Step-by-step explanation:
The area of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
b = AC = 3[tex]\sqrt{2}[/tex] + [tex]\sqrt{2}[/tex] = 4[tex]\sqrt{2}[/tex]
h = BD
Calculate BD using Pythagoras' identity in Δ ABD
BD² = AB² - AD²
= (2[tex]\sqrt{5}[/tex] )² - (3[tex]\sqrt{2}[/tex] )²
= 20 - 18 = 2 ( take square root of both sides )
BD = [tex]\sqrt{2}[/tex]
Then
A = [tex]\frac{1}{2}[/tex] × 4[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 2 × [tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 4 cm²
5 MINUTES to answer pls help.
20 Points
Answer:
-7
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
-3-(-10)/-2+1
-3-5+1
-8+1
-7
Is this a quadratic function? Why or why not?
Answer:
Not a quadratic function.
Step-by-step explanation:
DefinitionsA function is a relation wherein each input or x-value corresponds exactly to an output or y-value. In other words, a relation is a function if there are no repeating x-values.
Vertical Line Test :A way to determine whether a given graph represents a function is to perform the Vertical Line Test. Using the Vertical Line Test, we must draw vertical lines across the graph. If each of the vertical lines drawn intersects the graph at exactly one point, then the relation is a function.
⇒ The attached screenshot shows that the given graph fails the Vertical Line Test, as each vertical line drawn intersects the graph more than once. This means that those x-values correspond to more than one y-value. Specifically, x = 1 corresponds to the following y-values: y = -1 and y = 1. Hence, the given horizontal parabola is not a quadratic function.
Horizontal Parabola: Not a FunctionThe given graph represents a horizontal (or sideways) parabola.
The vertex form of the horizontal parabola is: x = a(y - k)² + h.
where:
a = Determines the direction of the graph's opening.
a > 0, the graph of the parabola opens to the right.a < 0, the graph of the horizontal parabola opens to the lefty = k is the horizontal axis of symmetry
k = determines the vertical translation of the graph
h = determines the horizontal translation of the graph
Equation of the Horizontal Parabola in Vertex Form:The vertex of the given graph occurs at the point of origin, (0, 0).
Let's use one of the given points on the graph, (1, 1), and substitute these values into the vertex form to solve for a :
x = a(y - k)² + h
1 = a(1 - 0)² + 0
1 = a( 1 )²
1 = a
Equation of the given horizontal parabola in vertex form:
⇒ x = (y - 0)² + 0 or x = y²
It is evident that in the vertex form of a horizontal parabola, the variable, y, is squared.
This implies that each x-values on the graph have more than one corresponding y-values:x = 1 has two y-values: y = -1, and y = 1.
x = 4 has two y-values: y = -2, and y = 2.
Thus, by definition of function, the given horizontal parabola is not a quadratic function, as it fails the vertical line test.
[tex] \sf \: If (3x-1) ^{7} = a _{7} x ^{7} + a _{6} x ^{6} + a _{5} x ^{5}+.... \\ \sf + a₁x + a _{0}, then \: \: a_0 + a₁ + a₂ + a_3 + a_4 + a_5 + a_6 + a7 = [/tex]
a)0
b)1
c)128
d)64
Please solve this for me. Need step-by-step explanation. Spam free answer required. Thank you in anticipation.
Answer:
hope it helps have a great day
Answer is option C
How many feet does each student climb after 10 steps?
Pilar climb 6.5 feet and Jake climbed 9.5 feet.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
slope of pilar = 3-2/3-1 = 1/2
After 10 steps let the height covered by x.
then, slope= x-2/10-1
1/2 = x-2/ 9
9 = 2x -4
13 = 2x
x= 6.5 feet
now, slope of Jake= 8-5/7-1 = 3/6 = 1/2
After 10 steps let the height covered by y.
then, slope= x-5/10-1
1/2 = y-5/9
2y- 10 = 9
2y= 19
y= 19/2
y= 9.5 feet
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The product of w and 2 is greater than or equal to 19.
Equation Form:
w x 2 [tex]\geq[/tex] 19
Divide both sides by 2:
w [tex]\geq[/tex] 9.5
So, w must be equal to or greater than 9.5 for this equation to work.
Teresa will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $59 and costs an additional $0.08 per mile driven, The second plan has an initial fee of $48 and costs an additional $0.10 per mile driven. For what amount of driving do the two plans cost the same? Omiles What is the cost when the two plans cost the same? $0
Answer:
1. 550 miles
2. $103
Step-by-step explanation:
y = total rental cost
m = initial fee
x = cost per mile
n = number of miles
Plan 1: y = m + xn = 59 + 0.08n
Plan 2: y = m +xn = 48 + 0.10n
Q1. if total cost is the same : 59 + 0.08n = 48 + 0.10n >>> 0.02n = 11 >>> n = 550
Q2. y = m + xn = 59 + 0.08n = 59 + 0.08(550) = 103
Desperately need help on question 2 & 3 !
13
x=15
because of the other one is the only thing
1/4 divided by 3 I’m behind and I really just want to get this over with :) plus math is my least favorite subject thanks to my teacher so yeah plz help:)
Answer:
XD [tex]\frac{1}{12}[/tex] is the answer.
Step-by-step explanation:
So, to divide a fraction with a whole number you'll have to multiply the denominator with the whole number.
Hopes This Helps
It takes 1 3/4 cups of cherries to make a cherry pie. Emma wants to make 3 cherry pies. How many cups of cherries will Emma need
Answer:
5 1/4 please give brainliest
Step-by-step explanation:
1 x 3 = 3 3/4 x 3 = 2 1/4
Answer:
5 1/4 please give brainliest
Step-by-step explanation:
1 x 3 = 3 3/4 x 3 = 2 1/4
14. Janine has job offers at two companies. The Nabisco company offers her a starting salary of $28,000 plus $2,000 for transportation costs with a raise of $3000 each year. The Keebler company offers a starting salary of $36,000 with a $2000 a year raise, After how many years would her salary at Nabisco be greater than Keebler?
Answer:
eight years
Step-by-step explanation:
at year one: nabisco 30k and keebler: 36k
year two: nabisco: 33k and keebler: 38k
year three: nabisco: 36k and keebler: 40k
year four: nabisco: 39k and keebler: 42k
year five: nabisco: 42k and keeber: 44k
year six: nabisco: 45k and keebler 46k
year seven: nabisco: 48k and keeber 48k
year eight: nabisco: 51k and keebler 50k
please i beg for help !!!!!!!!!!! will mark brainlist
Answer:
[tex]x=-10[/tex]
Step-by-step explanation:
This deals with negative exponents.
[tex]x^{-2}=\frac{1}{x^2}[/tex]
27 and 9 are both powers of 3, so we need to find a way to make both of these into a base 3.
9 is easy, thats just:
[tex]9=3\times3=3^2[/tex]
1/27 is a little more difficult. Start with 27:
[tex]27=9\times3=3\times3\times3=3^3[/tex]
and because its a 1/27, that exponent has to be negative.
[tex]3^3=27\\3^-^3=\frac{1}{27}[/tex]
Now we can get both of them to base 3, so do that in the given equation:
[tex]3^{(-3)\times(4-x)}=3^{(2)\times(2x-1)}[/tex]
Same as last time, the bases can be canceled out as the exponents have to be equal for this equation to be true.
[tex]3^{(-3)\times(4-x)}=3^{(2)\times(2x-1)}\\(-3)\times(4-x)=(2)\times(2x-1)[/tex]
Finally, solve for x:
[tex]-3(4-x)=2(2x-1)\\-12+3x=4x-2\\-10+3x=4x\\x=-10[/tex]
Need help due in 1 min!!
Simplify!!
Answer:
C. 3^9
Step-by-step explanation:
You would simply just add the exponents.
Answer:
3^9
Step-by-step explanation:
5+4=9
60
60
boys at a summer camp were asked to complete a survey about their favorite outdoor activity.
18
18
boys chose biking and 29
29
boys chose fishing.
The remaining boys did not complete the survey.
Which expression gives the percent of survey participants who chose fishing?
Answer:
48.3%
Step-by-step explanation:
When we are using percentages, what we are really saying is that the percentage is a fraction of 100. "Percent" means per hundred, and so 50% is the same as saying 50/100 or 5/10 in fraction form.
So, since our denominator in 29/60 is 60, we could adjust the fraction to make the denominator 100. To do that, we divide 100 by the denominator:
100 ÷ 60 = 1.6666666666667
Once we have that, we can multiple both the numerator and denominator by this multiple:
29 x 1.6666666666667
60 x 1.6666666666667
=
48.333333333333
100
Now we can see that our fraction is 48.333333333333/100, which means that 29/60 as a percentage is 48.3333%.
The sum of 423 and 65 is
Answer:
488
Step-by-step explanation:
In a factory 54,680 parts were made. If 300 parts were found to be defective what is the percent of error?
Find a scale with a unit of 1 and choose the correct answer (for example, 1 cm=7 yards).
Car 18ft moele 5in
Scale: _____
1 in = 3.6 ft
1 ft=18 in
1 in = 10 ft
1 ft=11 in
Answer:
1 ft=18 in or 1ft=11in
Step-by-step explanation:
:D
Solve the following system: y = x 3 4x y = 18 (6, 3) (3, 6) (â’3, 6) (3, â’6).
The solution of the given equation is (3,6). The correct option is B.(3,6)
Given equations,[tex]y=x+3.......(1)\\4x+y=18.....(2)[/tex]
How to solve the equations?putting the value of y from equation (1) in equation (2) , we get
[tex]4x+x+3=18\\[/tex][tex]5x=18-3\\5x=15\\x=3[/tex]
substitute the value of x=3 in equation (1) we get,
[tex]y=3+3\\y=6[/tex]
Hence, the solution of given equation is (3,6).
So, the correct option is B.
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Jason likes to play video games. His parents allow him to play
Answer:
If its for a reasonable time yes, most parents will let their child to play a reasonable time. However, if things get out of control resulting the child being addicted to video games. It is the child's fault and parent's fault
School days: 0 to 60 minutes per day On school days and 2 hours or less on non- school days. There is some advantages in gaming. But in all don't play to much if so, your body will melt. ( not really but melt melt)
Because Bernard has some health issues, he must pay 15% more for life insurance. About how much more annually will a $115,000 10-year term insurance at age 35 cost Bernard than someone of the same age without health issues? A 3-column table with 3 rows. Column 1 is labeled age with entries 35, 40, 45. Column 2 is labeled 10-year term, male, with entries 1. 40, 1. 64, 2. 7. Column 3 is labeled 10-year term, female, with entries 1. 36, 1. 59, 2. 1. A. $161 b. $185 c. $1,073 d. $24 Please select the best answer from the choices provided A B C D.
From the given table, the annual premium rate as a percentage of value insured a person at age 35 has to pay is 0.14%.
The amount more annually a $115,000 10-year term insurance at age 35 cost Bernard than someone of the same age without health issues is option d. $24Reasons:
The data in the table are presented as follows;
[tex]\begin{tabular}{|c|c|c|}Age&Annual Insurance Premiums (per \$1,000 of face value)&\\&10-Year Term &\\&Male&Female\\35&1.40&1.36\\40&1.64&1.59\\45&2.07&2.01\end{array}\right][/tex]
From the above table, we have that the amount a 35 year old without health issues will pay per $1,000 is $1.40
Therefore, the amount to be paid for $115,000 is 115 × $1.4 = $161
The amount Bernard pays = 15% more = 1.15 × $161 = $185.15
Therefore;
The amount more Bernard has to pay = $185.15 - $161 = $24.15 ≈ $24
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Answer:
$24 or D, Hope this helps :D
Step-by-step explanation:
A worm wriggled forward
4
5
of an inch in 3 minutes. At that rate, how far would the worm go in 1 minute?
Answer:
4/15 of an inch
Step-by-step explanation:
=> At that rate, the distance the worm would go in 1 minute is:
D = (4/5)/3 = 4/(5x3) = 4/15 of an inch
Hope this helps
Have a great day
~Zero
Answer:
4/15 of an inch
Step-by-step explanation:
A worm wriggled forward 4/5 of an inch in 3 minutes.
=> At that rate, the distance the worm would go in 1 minute is:
D = (4/5)/3 = 4/(5x3) = 4/15 of an inch
Solve by factoring : x^2-5x-36=0
Part III: The sum of your two factors must be -5. Which of your factor pairs
above could produce this sum? (2 points)
Answer:
-9 and +4 are the factors
Step-by-step explanation:
-9 times +4 is -36 and if you add +4 to -9, you get -5.
After this your function will look like this:
[tex]x^2-9x+4x-36[/tex]
and then:
[tex]x(x-9)+4(x-9)[/tex]
so the answer is:
[tex](x-9)(x+4)[/tex]
what is 850000+21195=
Answer: 871195
Step-by-step explanation:
I NEED BOTH OF THESE
60 POINTS
asap
Answer:
107.5
Step-by-step explanation:
20% of 70 = 14
70 - 14 = 66
10% of 45 = 4.5
45 - 4.5 = 41.5
66 + 41.5 = 107.5
PLEASE HELP ME WITH THIS
Answer:
35/132
Step-by-step explanation:
The probability of selecting a boy for president is 7/12, the ratio of the number of boys to the number of candidates. Then the probability of selecting a girl for vice president is 5/11, the ratio of the number of girls to the remaining number of candidates. The joint probability is ...
(7/12)(5/11) = 35/132 . . . P(b=P&g=VP)
__
We can also look at this another way.
The number of ways two candidates can be selected from 12 is 12P2 = 132. The number of ways that the first can be a boy and the second can be a girl is (7)(5) = 35. Then the probability of a (BG) pair from the 12 candidates is 35/132.
_____
Additional comment
These numbers assume that selection is random and all possibilities are equally-likely. That is unlikely to be the case in an election.
1 A recipe uses 1 - cups of milk to make 10 servings. If the same amount of milk is used each serving, how many servings can be made using 1 gallon of milk? Show your work
Answer:
160 servings
Step-by-step explanation:
Step One:
1 gallon=16 cups
1 cup=10 servings
Step Two:
Multiply 16 by 10
which gives you your answer 160
Please help with this
Answer:
the value of ST is 2 of its x is 2
On an architect’s drawing of a house, 1 inch represents 7 feet. If the bedroom window is 5 inches long on the drawing, how long will it be in the actual house?
Work Shown:
1 inch : 7 feet
5*(1 inch) : 5*(7 feet)
5 inches : 35 feet
5 inches on paper correspond to 35 feet in the actual house.
Julio just bought a $267,900 house. He had a 20 year mortgage with a fixed rate of 5. 875%. Julio’s monthly payments are $1,558. 9. What percent of the purchase price was Julio’s down payment? a. 13% b. 15% c. 18% d. 20%.
Julio's down payment was 22.08% of the purchase price.
Given that Julio just bought a $ 267,900 house, and he had a 20 year mortgage with a fixed rate of 5.875%, and Julio's monthly payments are $ 1,558, to determine what percent of the purchase price was Julio's down payment the following calculation must be performed:
(267,900 x 1.05875) - (1558 x 12 x 20) = X
582,682.50 - 373,920 = X
208,762.50 = X
267,900 = 100
208,762.50 = X
208,762.50 x 100 / 267,900
77.92 = X
100 - 77.92 = 22.08
Therefore, Julio's down payment was 22.08% of the purchase price.
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