Answer:
137
Step-by-step explanation:
given AP
t1 = -3 and t2 = 4
using,
d=t1-t2
=4-(-3)
=7
And,
tn=a+(n-1)d
t21=(-3)+(21-1)(7)
t21=137
Answer:
B) -137
Step-by-step explanation:
a=a1=−3,a2=4
∴d=a2−a1=4−(−3)=4+3=7
Solve the equation sin(x - 20°) = cos(42º) for x, where 0
Answer:
[tex]x = 68[/tex]
Step-by-step explanation:
Sine are Cosine are Complementary Angles.
We can use this formula
[tex] \sin(x) = \cos(y) [/tex]
when x+y=90.
Add the expressions in the parentents to 90 and solve for x.
[tex]x - 20 + 42 = 90[/tex]
[tex]x + 22 = 90[/tex]
[tex]x = 68[/tex]
The answer is
[tex]x = 68[/tex]
Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?
(negative 5 minus StartRoot 34 EndRoot comma negative 5 + Startroot 34 EndRoot)
(negative 5 minus StartRoot 29 EndRoot comma negative 5 + StartRoot 29 EndRoot)
{–12, 2}
{–2, 12}
Answer:
(-12,2)
Step-by-step explanation:
x^2 + 10x = 24
x^2 + 10x + (10/2)^2 = 24 + (10/2)^2
10/2 = 5
5^2 = 25
x^2 + 10x + 25 = 24 + 25
x^2 + 10x + 25 = 49
(x + 5)^2 = 49 Take the square root of both sides
(x + 5) = sqrt(49)
x + 5 = +/- 7
x = +/- 7 - 5
x = +7 - 5 = 2
x = -7 - 5 = -12
Answer:
{ -12 , 2}
Step-by-step explanation:
x² + 10x = 24
In order to complete the square, the equation must first be in the form x² + bx =c.
x² + 10x = 24Divide 10, the coefficient of the x term, by 2 to get 5. Then add the square of 5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x² + 10x + 5² = 24 + 5²expand exponents.
x² + 10x + 25 = 24 + 25Add 24 and 25
x² + 10x + 25 = 49Factor x² + 10x + 25. In general, when x² + bx + c is a perfect square, it can always be factored as ( x + b/2)².
( x + 5 )² =49Take the square root of both sides of the equation.
[tex] \small \sf \sqrt{(x + 5) {}^{2} } = \sqrt{49} [/tex]
simplify
x + 5 = 7x + 5 = +/- 7Subtract 5 from both sides.
x + 5 - 5 = 7 - 5
x = 2x + 5 - 5 = +/- 7 -5
x = -7 - 5 = -12Convert the percentage into a fraction,
3%=
100
Answer:
3% = 0.03 = [tex]\frac{3}{100}[/tex]
Answer: 3/100
Step-by-step explanation:
3%=0.03=3/100
Have a great day!!
Find the equation of a line that is perpendicular to y = -3x – 1 and passes through the point
(3,2).
Give your answer in the form y = mx + b.
Solve for x. Thank you
Answer:
x = sqrt(3)
Step-by-step explanation:
Use Thales theorem
x²=3(4-3)x²=3(1)x²=3x=√3I NEED HELP WITH THIS ONE TOO !!
Answer:
40°
100 + 80 = 180
60 + 80 = 140
140+ 40 = 180
Step-by-step explanation:
Answer:
m<C+m<D=100 degrees m<D=40 degrees
Step-by-step explanation:
Determine the value of x.
4.375 units
4.59 units
13.95 units
15 units
Answer:
13.95 units
Step-by-step explanation:
[tex] \sin \: 35 \degree = \frac{8}{x} \\ \\ \therefore \: x \: = \frac{8}{\sin \: 35 \degree} \\ \\ \therefore \: x \: = 13.9475744 \\ \\ \therefore \: x \: = 13.95 \: units[/tex]
What is the square root of -1
Answer:
i.
Step-by-step explanation:
.
Answer:
[tex]\sqrt{-1}=i[/tex]
The square root of -1 (i)
---------------------------------
~HOPE IT HELP
~HAVE A GREAT DAY!!
If copies of all your computer data are stored on four independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? With four hard disk drives, the probability that catastrophe can be avoided is
Answer:
[tex]P(Atleast\ 1) = 0.9999992[/tex]
Step-by-step explanation:
Given
[tex]p = 3\%[/tex] --- rate of hard disk drives failure
[tex]n = 4[/tex] --- number of hard disk drives
See comment for complete question
Required
[tex]P(Atleast\ 1)[/tex]
First, calculate the probability that the none of the 4 selected is working;
[tex]P(none) = p^4[/tex]
[tex]P(none) = (3\%)^4[/tex]
[tex]P(none) = (0.03)^4[/tex]
Using the complement rule, the probability that at least 1 is working is:
[tex]P(Atleast\ 1) = 1 - P(none)[/tex]
This gives:
[tex]P(Atleast\ 1) = 1 - 0.03^4[/tex]
[tex]P(Atleast\ 1) = 0.9999992[/tex]
If AABC~ DEF and the scale factor from ABC to DEF is , what are the lengths of DE, EF, and DF, respectively?
Step-by-step explanation:
we don't see a picture, and you don't not give us any detailed information (all specific numbers like the scale factor are missing in your text). so, it is impossible to calculate anything.
but you can do it yourself very easily.
let's call the same factor "f".
that means you have to multiply the side lengths of every side of ABC by that factor f to get the cushions side lengths is the sides in DEF.
that's it.
that's all that has to be done.
so, assuming that A -> D, B -> E, C -> F
then
AB × f = DE
BC × f = EF
CA × f = FD
as I said - that's it. just use the actual numbers and multiply.
All the lengths of DE, EF, and DF are, 4 , 8 and 12 respectively.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Triangle ABC and DEF are similar.
And, the scale factor from ABC to DEF is 2.
Now, We get;
This means that each side of the triangle ABC were multiplied by the scale factor 2 in order to get the triangle DEF.
Based on the above, you can set up the following equations;
⇒ DE = 2AB
⇒ EF = 2BC
⇒ DF = 2CA
Finally, substituting the corresponding lengths of the triangle ABC into the equations, and then evaluating, you get the following result:
⇒ DE = 2 x 2 = 4
⇒ EF = 2 x 4 = 8
⇒ DF = 2 x 6 = 12
Thus, All the lengths of DE, EF, and DF are, 4 , 8 and 12 respectively.
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ7
You want to buy juices while shopping at ShopRite but are stuck between buying a bottle of apple juice and orange juice. The apple juice is 2 Liters and costs $3.00 while the orange juice is 3 Liters and costs $3.99. Which juice bottle is the better deal?
Answer:
Orange juice
Step-by-step explanation:
The bottle of apple juice costs 3 dollars for 2 liters, and the bottle of orange juice costs 3.99 dollars for 3 liters. To see which bottle has the better deal, we need to make the liters the same so we can compare them.
We can divide the 2 liters for 3 dollars ratio by 2 to get that 1 liter of apple juice costs 1.5 dollars, and we can divide the orange juice ratio by 3 to get that 1 liter of orange juice costs 1.33 dollars. We see that for 1 liter, orange juice is cheaper, so it is the better deal.
1.) What is the domain and range of the function in the graph?
2.) What is the average rate of change over the interval [1, 0]?
Answer:
Domain → (-∞, ∞)
Range → (-2, ∞)
Step-by-step explanation:
1). Domain of a function is defined by the input values (set of x-values) and Range of the function is defined by the output values (set of y-values).
From the graph attached,
Function is defined for all real values of x.
Therefore, domain of the function will be (-∞, ∞).
On y-axis values of the function vary from -2 (excluding 2) to positive infinity.
Therefore, range of the function will be (-2, ∞).
2). Average rate of change of a function in the interval (a, b) is defined by,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
By using this expression we can find the average rate of change in the given interval.
Please give the correct interval for which the average rate of change is to be calculated.
SOMEONE PLEASE HELP ME OUT!!!!
Answer:
40/30
Step-by-step explanation:
Since tan∅= o/a, 40 is opposite, and 30 is adjacent to angle A, 40/30 is the ratio for tanA.
Answer:40/30
Step-by-step explanation:
....
Which of the following is the graph of the quadratic function y= x2 - 4x + 4
A. Graph D
B. Graph B
C. Graph A
D. Graphic
SUBMIT
Answer:
graph c
Step-by-step explanation:
it is the longest one
please write your answer with explanation
Answer:
Step-by-step explanation:
If cost price (CP) is greater than selling price (SP) , then the item is sold for loss.
Loss = CP - SP
Loss% = [tex]\frac{loss}{CP}*100[/tex]
If SP is greater than Cp, then the item is sold for a profit.
Profit =SP -CP
Gain % = [tex]\frac{gain}{CP}*100[/tex]
a) CP = $50 ; SP = $30 ; CP > SP, loss
Loss = 50 - 30 = $ 20
Loss % = [tex]\frac{20}{50}*100=20*2[/tex]
= 40% loss
b) CP = £ 5000 ; SP = £6250 ; SP > CP , Profit
Profit = 6250 - 5000 = £ 1250
Profit % = [tex]\frac{1250}{5000}*100=25[/tex]
25% Profit
The circle below is centered at (4, q) and has a radius of 3. What is the equation.
Answer:
C
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (4, - 1 ) and r = 3 , then
(x - 4)² + (y - (- 1) )² = 3² , that is
(x - 4)² + (y + 1)² = 9 → C
What is the answer for this equation
Answer:
the answer is -5,-7,-10,-14,-19
Please need a help !!
Need explanation
Urgent
A balloon is going vertically upwards at a speed of 10 ms-1 . When it was 30 m above the ground, an object is dropped from it. How long does the object take to reach the ground? (g = 10 ms-1 )
Answer:
t ≈ 3.65 s
Step-by-step explanation:
Let the distance the object travels after leaving the balloon be x.
Using Newton's equation of motion, we have;
s = ut + ½gt²
We are given;
s = 30 m
u = -10 m/s (negative because it is an upward motion)
Thus;
30 = -10t + ½(10)t²
30 = -10t + 5t²
5t² - 10t - 30 = 0
Using quadratic formula, we have;
t ≈ 3.65 s
David is now 4 years more than twice the age of Henry. If Henry will be 18 in 3 years, how old was David 2 years ago?
Answer:
i think its 10.5
Step-by-step explanation:
Answer:
David was 32 two years ago
Step-by-step explanation:
D = 2H + 4
H = 15
D = 30+4
D = 34
David was 32 two years ago
Write an expression for each statement: A truck has a total of a pounds of fruit which were packed in n boxes. How many pounds of fruit are in each box?
Answer:
The answer is "[tex]\text{Total number of boxes} =\frac{a}{n \ boxes}[/tex]"
Step-by-step explanation:
Total pounds carried by the vehicle are "a" pounds.
This will be spread into many boxes, each containing "n" pounds.
It implies that:
[tex]\text{Total pounds = box number} \times \text{amount of pounds from every box} \\\\a = \text{box number} \times n\\\\\text{Box number} = \frac{a}{n \ boxes}[/tex]
[tex]2 ^{2x + 1} - 9.2 ^{x} + 4 = 0[/tex]
pleas I need this answer. I want to submit it now.
[tex]\displaystyle\bf 2^{2x+1}-9\cdot 2^x+4=0 \quad ; \qquad \boxed{ 2^x=t \; ; \; 2^{2x}=t^2} \\\\2t^2-9t+4=0 \\\\D=81-32 =49 \\\\ t_1=\frac{9+7}{4} =4 \\\\ t_2=\frac{9-7}{4} =\frac{1}{2} \\\\1) \ 2^x=4 \Longrightarrow x_1=2 \qquad 2) \ 2^x=2^{-1}\Longrightarrow x_2=-1 \\\\Answer: \boxed{x_1=2 \quad ; \quad x_2=-1}[/tex]
Evaluate the function. f(x)=−x^2 −6x+12 Find f(4)
1. How to find f(4)?
I explained how to find f(5) in your previous question. It is exactly the same. We substitute x = 4 in the equation.2. Substitution and Evaluate
[tex] \large{f(4) = - {(4)}^{2} - 6(4) + 12} [/tex]
Follow BODMAS/PEMDAS rules as well! Exponent first.
[tex] \large{ f(4) = - 16 - 24 + 12} \\ \large{f(4) = - 40 + 12} \\ \large{f(4) = -2 8}[/tex]
3. Final Answer
f(4) = -28.URGENT!!!!!!HELP NOW PLEASE!!!!!!!!!
Answer:
$2.96
Step-by-step explanation:
Here, we want to get the expected value
To get the expected value, we have to multiply each payout by its corresponding probability and add up for all
So what this mean is that the expected value is the summation of the products of each pay out and their probability
We have the expected value calculated as;
0(0.12) + 1(0.2) + 2(0.38) + 5(0.2) + 10(0.1)
= 0 + 0.2 + 0.76 + 1 + 1 = $2.96
Marking brainliest
I’m getting a belly piercing soon and this guy asked this question but I’m not sure what he means? Someone help
Answer:
Say I want a
Step-by-step explanation:
Ask what do you mean
What value of n makes the equation true?
Answer:25
Step-by-step explanation: Subtract 7 from 2, you get -5. then multiply both sides of the equation by -5 ( to make -1/5n to n) and you get n=25
plz help me find the answers
Answer:
Correct answer B 130
Step-by-step explanation:
<FAE=90
<AFE=40
We have a triangle, so <FEA= 180-90+40=50
<FEA+FEB= 18-, so 180-50=130
AB parralel to CD then <ECD=130
Flying against the wind, a jet travels miles in hours. Flying with the wind, the same jet travels miles in hours. What is the rate of the jet in still air and what is the rate of the wind
Answer:
Velocity in still air: 760 mi/ hr
Velocity against the wind: 210 mi/ hr
Step-by-step explanation:
Given
See attachment for complete question
Required
The rate in still air
The rate of the wind
From the question, the velocity (v) against the wind is:
[tex]v =\frac{distance}{time}[/tex]
[tex]v =\frac{3040}{4}[/tex]
[tex]v_1 =760mi/hr[/tex]
The velocity with the wind is:
[tex]v_2 = \frac{8260}{7}[/tex]
[tex]v_2 = 1180mi/hr[/tex]
Let:
[tex]x \to[/tex] velocity in still air
[tex]y \to[/tex] velocity of the wind
So, we have:
[tex]x - y = 760[/tex]
[tex]x + y = 1180[/tex]
Add both equations
[tex]x + x -y + y = 760 + 1180[/tex]
[tex]2x = 1940[/tex]
Divide by 2
[tex]x = 970[/tex]
Substitute [tex]x = 970[/tex] in [tex]x - y = 760[/tex]
[tex]970 - y= 760[/tex]
Make y the subject
[tex]y = 970 - 760[/tex]
[tex]y = 210[/tex]
sketch the graph of y² = -2x + 5
Answer:
[tex] {y}^{2} = - 2x + 5[/tex]
Step-by-step explanation:
vertex = [tex]( \frac{5}{2} \: ,0)[/tex]
Hope it is helpful....Hello pls help
Find the volume of this sphere.
Use 3 for 7T.
2 ft
V~ [?]ft
V = 3
Answer:
volume of the sphere=4/3πr³
=4/3×3×2³
=32 feet³
Answer:
32 ft³
Step-by-step explanation:
Hi there!
[tex]V=\frac{4}{3} \pi r^3[/tex] where r is the radius
Plug in the given radius, 2 ft
[tex]V=\frac{4}{3} \pi (2)^3[/tex]
Plug in the given value of π, 3
[tex]V=\frac{4}{3} (3) (2)^3\\V=\frac{4}{3} (3) (8)\\V=(4)(8)\\V=32[/tex]
Therefore, the volume of the sphere is 32 ft³.
I hope this helps!
