Find t12 term in an arithmetic progression having t3 = 10 and t10 = −4 .
Answer:
t12= -8
Step-by-step explanation:
t3
a+2d=10 (1)
t10
a+9d=-4. (2)
From (1)
a=10-2d. (3)
Sub into (3) into equ (2)
a+9d=-4
10-2d+9d=-4
10+7d=-4
7d=-4-10
7d=-14
Divide both sides by 7
d=-14/7
d= -2
10=a+2d
10=a+2(-2)
10=a-4
10+4=a
14=a
a=14
t12=a+11d
= 14+11(-2)
=14-22
= -8
t12= -8
Convert y = 8x^2-80x-32 to vertex form by completing the square.
Answer:
y = 8(x-5)^2 -232
Step-by-step explanation:
Factor out the 8 to get
y = 8(x^2-10x-4)
y = 8(x-5)^2 -232
Answer:
y = 8 (x - 5)^2 - 232
Step-by-step explanation:
Dividing the whole equation by 8, we get:
y = 8 (x^2 - 10x - 4)
y = 8 (x - 5)^2 - 232
Hope this helps!
the graph below describes the journey of a train between two cities
Answer:
Step-by-step explanation:
To find : Acceleration in first 15 min . Distance between two cities Average speed of journey
Solution:
Each horizontal block is 1/8 hr = 7.5 min
Each vertical block is 10 km/hr
Time Velocity km/hr
0 Min ( 0 hr) 0
15 Min (1/4 hr) 50
45 Min (3/4 hr) 50
60 MIn ( 1 hr) 100
90 Min ( 3/2 hr) 100
120 Min ( 2hr) 0
Acceleration in first 15 min (1/4 hr) = (50 - 0)/(1/4 - 0) = 50/(1/4)
= 200 km/h²
Distance between two cities
= (1/2)(0 + 50)(1/4 - 0) + 50 * (3/4 - 1/4) + (1/2)(50 + 100)(1 - 3/4) + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)
= 25/4 + 25 + 75/4 + 50 + 25
= 125
Distance between two cities = 125 km
Average Speed of journey = 125/2 = 62.5 km/hr
Acceleration in first 15 min = 200 km/h²
Distance between two cities = 125 km
Average Speed of journey = 62.5 km/hr
Hope this helps..
Answer:
200km/h^2, 125km, 62.5km/h
Step-by-step explanation:
For part a) just use the acceleration formula (change in velocity/time). For part b), remember that distance traveled is the area under the graph. This is because displacement is the integral of velocity, meaning that you integrate to find the area (i.e. displacement). Lastly, for part c), just apply speed = distance/time because in this case, acceleration is constant.
HELPP PLEASE What is the value of x in the diagram below?
48
18
O A. 4
B. 6
C. 5
O D. 3
SUBMIT
Answer:
x = 3
Step-by-step explanation:
The triangles are similar, using ratios
x 8
------ = -----------
18 48
We can use cross products to solve
48x = 8*18
48x = 144
Divide each side by 48
48x/48 = 144/48
x =3
What is the slope of the line shown below?
A. - 1/2
B. 1
C. -1
D. 1/2
Answer:
C. -1
Step-by-step explanation:
Slope is: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given the points (1,7) and (3,5).
[tex]m=\frac{5-7}{3-1} =\frac{-2}{2} =-1[/tex]
The slope is -1, and therefore, Option C should be the correct answer.
What must be added each term to a ratio2:3 so that it may became 4:7
Step-by-step explanation:
HOPE THE ANSWER IS CORRECT AND USEFUL
Can I get help with this?
Answer:
Around 13.7
Step-by-step explanation:
The cosine of an angle in a right triangle is equivalent to the length of the adjacent side divided by the length of the hypotenuse. In this case, this means:
[tex]\cos 70= \dfrac{x}{40} \\\\x=40\cdot \cos 70\approx 13.7[/tex]
Hope this helps!
Which number is an integer?
-3/4 1/5 2 42/3
The Answer:
2 is an integer.
Answer:
c
Step-by-step explanation:
edgeinuity
PLEASE HELP ME PLEASE AND THANK U
Answer:
3/4
Step-by-step explanation:
There is 2 Os and 8 in total.
So the probability of selecting O is 1/4
As the question asks everything but O, you subtract that answer from 1. 1-1/4=3/4
Stetson rents
studio space for
$600 a month for
music lessons. He
charges his
students $40 per
hour and earned a
profit of $2400
this month.
is it (600+40)x=2400
or
40x-600=2400
Answer:
It will be the first option.
Step-by-step explanation:
Why? because you are trying to get the total amount so you need to cancel everything and have the final answer.
and it will be like this:
(600+40)x=2400
x=2400÷ 640
x=3.75
and if you round it; x=4
Would someone help me with this?
Answer:
A,E
Step-by-step explanation:
A The minimum number of pages read was 24. The smallest number is the dot on the left side which is at 24
E The mean is the middle line in the box, this is at 48
Most dietitians recommend that adults consume 20 to 30 percent of their daily caloric intake in protein. Based on this recommendation, what is the minimum amount of calories from protein an adult should consume from an 1,800 calorie diet?
Answer:
360-540 calories
x + 2 4/5 = 3 1/6
someone please help me i don’t get the problem
-11/10
Step-by-step explanation:
so first get the x on one side of the equal sign and the numbers on the other.
x+2 4/5 = 3 1/6
- 2 4/5 - 2 4/5
x= -11/10
is the function in the graph non-linear?
4
3
-32
2
5
O Yes, because it has a constant rate of change.
O Yes, because it does not have a constant rate of change.
No, because it has a constant rate of change.
No, because it does not have a constant rate of change.
Answer:
B. Yes, because it does not have a constant rate of change.
Step-by-step explanation:
For a function to be a function (or linear), the rate of change MUST be proportional. In this data set, the numbers do not seem proportional, which makes it non-linear.
please can you guy help for this questiong
please
Answer:
Step-by-step explanation:
From the figure attached,
Given: ∠P ≅ ∠S
TQ ≅ RQ
To Prove : ΔQRS ≅ ΔQTP
Statements Reasons
1). ∠P ≅ ∠S, TQ ≅ RQ Given
2). ∠RQS ≅ ∠TQP Reflexive property
3). ΔQRS ≅ ΔQTP AAS
Find the third side in simplest radical form
=========================================================
Work Shown:
We see that one of the legs is unknown. We'll call this 'a'.
The other leg is b = 2, which becomes b^2 = 4
The hypotenuse (always opposite the 90 degree angle) is c = sqrt(58). This turns into c^2 = 58 when you square both sides.
---------
Use the pythagorean theorem to get
a^2+b^2 = c^2
a^2+4 = 58
a^2 = 58-4
a^2 = 54
a = sqrt(54)
a = sqrt(9*6)
a = sqrt(9)*sqrt(6)
a = 3*sqrt(6)
The third side in simplest radical form is x=3[tex]\sqrt{6}[/tex]
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios, metric relationships, or the Pythagorean Theorem.
For solving this question, you need to apply the Pythagorean Theorem that says: (hypotenuse)²= (leg1)²+(leg2)².
The question gives:
Hypotenuse= [tex]\sqrt{58}[/tex]Leg1= 2Leg2= third side = unknowApplying the Pythagorean Theorem, you have:
([tex]\sqrt{58}[/tex])² = 2²+ x²
58=4+x²
x²=58-4
x²=54
x=[tex]\sqrt{54}[/tex]
x=[tex]\sqrt{2*3^3}[/tex]
x=[tex]\sqrt{2*3^2*3}[/tex]
x=3[tex]\sqrt{2*3}[/tex]
x=3[tex]\sqrt{6}[/tex]
Learn more about the Pythagorean theorem here:
brainly.com/question/11528638
#SPJ6
9(2a – b)2 – 4(2a – b) – 13
Can some one help me plz trying to figure out? Need help ASAP
Answer:
[tex] a. = -35 \\ b. = 9a + 1 \\ c. = -35 [/tex]
Step-by-step explanation:
[tex]a. \\ = > \: 7a - 1 + 2a + 2 \\ \\ = > 7( - 4) - 1 + 2( - 4) + 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (a = - 4) \\ \\ = > - 28 - 1 - 8 + 2 \\ \\ = > - 37 + 2 \\ \\ = > - 35 \\ \\ \\ b. \\ = > 7a - 1 + 2a + 2 \\ \\ = > 7a + 2a - 1 + 2 \\ \\ = > 9a + 1 \\ \\ \\ c. \\ = > 9a + 1 \\ \\ = > 9( - 4) + 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (a = - 4) \\ \\ = > - 36 + 1 \\ \\ = > - 35[/tex]
G(x)=-2x-9 what is g(-7)
Answer:
g(-7)=5
Step-by-step explanation:
-2(-7)-9
14-9=5
Answer:
5
Step-by-step explanation:
G(x)=-2x-9
Let x = -7
g(-7) = -2(-7) -9
= 14 - 9
= 5
Find the volume of the specified cone. Use 3.14 for Pi, and round your answer to the nearest whole number. Diameter = 5 cm, Height = 9 cm a. 59 cu. cm b. 25 cu. cm c. 38 cu. cm d. 19 cu. cm
Answer:
a
Step-by-step explanation:
r = 2.5 cm
V= 3.14[tex](2.5 cm)^{2}[/tex](9 cm)/3 = [tex]59 cm^{3}[/tex]
Answer:
a
Step-by-step explanation:
A designer wants to create a whisper chamber in the shape of an ellipse. He has a warehouse space with a longest length of 50 yards, which he decides will be the major axis of his elliptical chamber. He determines the best spots for his guests to stand to experience his whisper chamber will be 10 yards from the center of the warehouse space, which will act as the foci. How far out from the center, along the minor axis should he build out his whisper chamber?
53.9 yd
45.8 yd
26.9 yd
22.9 yd
Answer:
22.9 yards
Step-by-step explanation:
Since b² = a² - c² where a = vertex of major axis, 2a = 50 yards the length of the major axis. So , a = 50/2 = 25 yards. c = focus of chamber = 10 yards from center and b = vertex of minor axis.
So, b = ±√(a² - c²)
= ±√(25² - 10²)
= ±√(625 - 100)
= ±√525
= ±22.91 yards
≅ ± 22.9 yards
Since b = length of minor axis from center of chamber = 22.91 yards. So, he should build the whisper chamber 22.9 yards out from the center of the chamber.
David wants to find the solutions of this system of equations: –4x – 7 = y x2 – 2x – 6 = y Which statement is true? Plz its urgent!!
Answer:
(-1, -3)
Step-by-step explanation:
The given equations are:
[tex]-4x-7=y ...... (1)[/tex]
and
[tex]x^2 - 2x - 6 = y ....... (2)[/tex]
Equating (1) and (2):
[tex]-4x -7 =x^{2}-2x-6\\\Rightarrow x^{2}-2x-6+4x+7=0\\\Rightarrow x^{2}+2x+1=0\\\Rightarrow (x+1)^2=0\\\Rightarrow x = -1[/tex]
The two values of x are repeating in nature i.e. x = -1
So, value of [tex]x[/tex] is -1.
Putting value of [tex]x[/tex] in equation (1):
[tex]-4 \times (-1)-7=y \\\Rightarrow y=-3[/tex]
The solution is represented as ([tex]x,y[/tex])
So, the solutions are :
(-1, -3)
Answer:
2
Step-by-step explanation:
give brainliest
Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side BC at point
M.
What is the length of MC?
16 mm
0 24 mm
O 32 mm
O 48 mm
Answer:
Correct option: First one -> 16 mm
Step-by-step explanation:
The equilateral triangle has its three sides with the same length.
So if the perimeter is 96 mm, we have:
[tex]Perimeter = 3*side[/tex]
[tex]3*side = 96[/tex]
[tex]side = 32 mm[/tex]
The segment MA is the height of the equilateral triangle, and its length can be calculated with the equation:
[tex]height = \frac{side * \sqrt{3}}{2}[/tex]
[tex]height = 16\sqrt{3}[/tex]
Using the Pythagoras' theorem in the triangle ACM, we have:
[tex]side^2 = MC^2 + height^2[/tex]
[tex]1024 = MC^2 + 768[/tex]
[tex]MC^2 = 256[/tex]
[tex]MC = 16\ mm[/tex]
Correct option: First one
Answer:
(A) 16mm
Step-by-step explanation:
Would somebody help with this?
Answer:
Both A and D
Step-by-step explanation:
Not absolutely 100%, but I think it's the answer.
George deposit is $750 into an account that earns 7% interest which is compounded two times per year how much money was George have in his account in five years
Answer:
$1475.40
Step-by-step explanation:
Since the interest is two times per year for 5 years, do this 10 times:
1) 750*0.07=52.5
750+52.5=802.5
2) 802.5*0.07=56.18
802.5+56.18=858.69
3) 858.69*0.07=60.11
858.69+60.11=918.79
4) 918.79*0.07=64.32
918.79+64.32=983.11
5) 983.11*0.07=68.82
983.11+68.82=1051.93
6) 1051.93*0.07=73.64
1051.93+73.64=1125.57
7) 1125.57*0.07=78.79
1125.57+78.79=1204.36
8) 1204.36*0.07=84.31
1204.36+84.31=1288.67
9) 1288.67*0.07=90.21
1288.67+90.21=1378.88
10) 1378.88*0.07=96.52
1378.88+96.52=1475.40
if a man walks for 6 miles at a steady speed of 3 mph how long will it take him
Answer:
It will take 2 hours
Step-by-step explanation:
6/3 = 2
Answer:
2 hours
Step-by-step explanation:
3 miles + 3 miles = 6 miles
1 hour + 1 hour = 2 hours
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, 1)B(5, 1),C(5, 6), and D(2, 6). Given these coordinates, what is the length of side AB of this rectangle?
Answer:
The legnth of side AB would be 3 units
Step-by-step explanation:
First, you would determine that both point A and point B would have the same y-coordinate of 1. Then you would determine the difference between the x values of points A and B. Since 5 (the x-value for B) minus 2 (the x-value for A) is 3, the legnth of side AB would be 3 units.
Step-by-step explanation:
I recommend using Desmos to quickly graph things (it's much faster than doing it yourself, I use it often. You can graph points and everything).
The picture ends up looking like the attachment I have below.
This is now a simple subtraction.
A is at 2 on the x-axis and B is at 5.
5-2=3
Answer:
3 units
What is the measure of c?
1489
42°
С
90°
422
489
O 42°
O 48°
O 90°
0 180°
Please help me with this question
For each set of probabilities, determine whether the events A and B are independent or dependent.
Answer:
[tex]\fbox{\begin{minipage}{15em}a, d: A and B are not independent\\b, c: A and B are independent\end{minipage}}[/tex]
Step-by-step explanation:
Step 1: Apply the correct formula to check whether two events are independent or not
If the events A and B are independent, then:
P(A) x P(B) = P(A⋂B)
The formula of conditional probability:
P(A⋂B) = P(A|B) x P(B) = P(B|A) x P(A)
Step 2: Perform the calculation
a)
P(A) x P(B) = (1/6) x (1/4) = 1/24
P(A⋂B) = P(A|B) x P(B) = (1/5) x (1/6) = 1/30
=> P(A) x P(B) is not equal to P(A⋂B)
=> A and B are not independent.
b)
P(A) x P(B) = (1/2) x (1/4) = 1/8
P(A⋂B) = 1/8
=> P(A) x P(B) is equal to P(A⋂B)
=> A and B are independent.
c)
P(A) x P(B) = (1/2) x (1/6) = 1/12
P(A⋂B) = P(A|B) x P(B) = (1/2) x (1/6) = 1/12
=> P(A) x P(B) is equal to P(A⋂B)
=> A and B are independent.
d)
P(A) x P(B) = (1/3) x (1/6) = 1/18
P(A⋂B) = P(B|A) x P(A) = (1/2) x (1/3) = 1/6
=> P(A) x P(B) is not equal to P(A⋂B)
=> A and B are not independent.
Hope this helps!
:)
Find the value of x.
Please help
Answer:
x=5
Step-by-step explanation:
7/5=(2x-3)/x
5(2x-3)=7x
3x=15, x=5