Answer:
x = 30 degrees
y = 67 degrees
z = 83 degrees
Step-by-step explanation:
Since x, y , and z are the angle measure for the first, second and third angle respectively, we can write the following equations following the statements given:
The sum of the measures of the angles of a triangle is 180:
(1) x + y + z = 180
The sum of the measure of the second and third angle is five times the measure of the first angle:
(2) y + z = 5 x
The third angle is 16 more than the second:
(3) z = y + 16
Now we solve the system of three equations. We use the third equation to replace z in the second one:
y + (y + 16) = 5 x
then : 2 y = 5 x - 16; then y = 2.5 x - 8
So , now we can replace this expression for y in the third equation:
z = (2.5 x - 8) +16 = 2.5 x + 8
and finally we made the replacements of y and z shown above in bold, in the first equation:
x + (2.5 x - 8) + (2.5 x + 8) = 180
x + 5 x = 180
6 x = 180
then x = 180/6 = 30 degrees
From this, we get the value of the other angles:
y = 2.5 (30) - 8 = 67 degrees
z = 2.5 (30) +8 = 83 degrees
The expression 1/x+y is equal to which quantities
Step-by-step explanation:
exponents is the awnser
coeffecient of x in -7xyz2
☽------------❀-------------☾
Hi there!
~
The coefficient of x in -7xyz2 is -7.
❀Hope this helped you!❀
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6. Identify the recursive formula for the sequence 3, –15, 75, –375, . . .
Answer:
first option
Step-by-step explanation:
There is a common ratio r between consecutive terms in the sequence, that is
r = - 15 ÷ 3 = 75 ÷ - 15 = - 375 ÷ 75 = - 5
The recursive formula allows a term in the sequence to be found by multiplying the previous term by r , thus
f(n) = - 5f(n - 1) if n > 1
with f(1) = 3 ← first term
Answer:
D . f(n)=f(1)=3
f(n)= -5f(n-1)if n >1
Step-by-step explanation:
i hope this help got it right on test
what two numbers would 39 fall between on a number line
Answer:
38 and 40
Step-by-step explanation:
Hope this helps you :)
Answer:
39 would fall between 38 and 40
Step-by-step explanation:
13/15 × 1 1/39 multiplying/dividing fractions help me
Before multiplying two fractions together, always try to cross-cancel.
So in this problem, the 13 and 39 cross-cancel to 1 and 3.
So we have 1/15 × 11/3 which is 11/45.
Remember, multiply across the numerators and denominators.
Question 8
Solve the equation.
1/3x + 205
Your answer:
A.-9
B.13
C.9
Answer: none of thoses
Step-by-step explanation:
A manufacturing company plans to progressively increase its production capacity over the next few quarters. (A quarter is a period of three months.) The increase in production can be modeled by the equation y = x6 − 25x4 + 199x2, where x is the number of quarters. What is the minimum duration required for the company to reach a production capacity of 4,975 units?
Answer:
5 months
Step-by-step explanation:
We assume that y represents production capacity, rather than increase in production capacity. Then we want to solve the 6th-degree equation ...
x^6 -25x^4 +199x^2 -4975 = 0
This can be factored in groups as ...
x^4(x^2 -25) + 199(x^2 -25) = 0
(x^4 +199)(x^2 -25) = 0
This has 4 complex solutions and 2 real solutions.
x^2 = 25
x = ±5
The duration required for capacity to reach 4975 units is 5 months.
A rocket leaves the surface of Earth at time t=0 and travels straight up from the surface. The height, in feet, of the rocket above the surface of Earth is given by y(t), where t is measured in seconds for 0≤t≤600. Values of y(t) for selected values of t are given in the table above. Of the following values of t, at which value would the speed of the rocket most likely be greatest based on the data in the table?
(1) t=100
(2) t=200
(3)t=300
(4) t=400
Answer:
Remember that:
Speed = distance/time.
Then we can calculate the average speed in any segment,
Let's make a model where the average speed at t = t0 can be calculated as:
AS(t0) = (y(b) - y(a))/(b - a)
Where b is the next value of t0, and a is the previous value of t0. This is because t0 is the middle point in this segment.
Then:
if t0 = 100s
AS(100s) = (400ft - 0ft)/(200s - 0s) = 2ft/s
if t0 = 200s
AS(200s) = (1360ft - 50ft)/(300s - 100s) = 6.55 ft/s
if t0 = 300s
AS(300s) = (3200ft - 400ft)/(400s - 200s) = 14ft/s
if t0 = 400s
AS(400s) = (6250s - 1360s)/(500s - 300s) = 24.45 ft/s
So for the given options, t = 400s is the one where the velocity seems to be the biggest.
And this has a lot of sense, because while the distance between the values of time is constant (is always 100 seconds) we can see that the difference between consecutive values of y(t) is increasing.
Then we can conclude that the rocket is accelerating upwards, then as larger is the value of t, bigger will be the average velocity at that point.
Speed is simply the rate of change of distance over time.
The greatest speed is at [tex]t = 400[/tex]
To calculate the time of the greatest speed, we simply calculate the slope between each interval.
The slope (m) of a line is:
[tex]m = \frac{y_2 - y_1}{t_2 - t_1}[/tex]
When [tex]t = 100[/tex]
[tex](t_1,y_1) = (0,0)[/tex]
[tex](t_2,y_2) = (200,400)[/tex]
So, we have:
[tex]m = \frac{400-0}{200 -0}[/tex]
[tex]m= \frac{400}{200}[/tex]
[tex]m = 2[/tex]
When [tex]t = 200[/tex]
[tex](t_1,y_1) = (100,50)[/tex]
[tex](t_2,y_2) = (300,1360)[/tex]
So, we have:
[tex]m = \frac{1360-50}{300 -100}[/tex]
[tex]m = \frac{1310}{200}[/tex]
[tex]m = 6.55[/tex]
When [tex]t = 300[/tex]
[tex](t_1,y_1) = (200,400)[/tex]
[tex](t_2,y_2) = (400,3200)[/tex]
So, we have:
[tex]m = \frac{3200-400}{400 -200}[/tex]
[tex]m = \frac{2800}{200}[/tex]
[tex]m = 14[/tex]
When [tex]t = 400[/tex]
[tex](t_1,y_1) = (300,1360)[/tex]
[tex](t_2,y_2) = (500,6250)[/tex]
So, we have:
[tex]m = \frac{6250-1360}{500-300}[/tex]
[tex]m = \frac{4890}{200}[/tex]
[tex]m = 24.45[/tex]
From the above computation, the greatest speed (i.e. slope) is
[tex]m = 24.45[/tex]
The corresponding time at [tex]m = 24.45[/tex] is [tex]t = 400[/tex]
Hence, the greatest speed is at [tex]t = 400[/tex]
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what point on a number line repersent sae level
0 because anything below sea level will be in the negatives and anything above will be and positive number higher than 0 :D
Hope this helped
P(n)=4n+1 ; find p(3)
Answer:
13
Step-by-step explanation:
you plug in 3 for n
4n+1
4(3)+1
12+1
13
What is 15 x minus 3 y = 0 written in slope-intercept form? y = 5x y = negative 5 x x = one-fifth y x = 5 y
Answer:
y=5x
Step-by-step explanation:
Answer:
y=5x
Step-by-step explanation:
I just need the Inequality plz
You want to adopt a new puppy. The adoption fee is $250, and you have $105.50 saved up so far. If your after school job pays $7.50 per hour.
Answer:
Hi there!
An inequality to demonstrate this is:
105.5 + 7.5x >= 250
Hope this helps
Please help ive lost my ability for simple patterns. Its due by end of day. Pt. 3
Step-by-step explanation:
On the right side, 3 + 4 + 7 = 14, so the other two numbers must add up to 22. Therefore, they must be 10 and 12.
Let's assume 12 is the top number and 10 is the bottom number.
The left side adds up to 12 + 9 + 2 = 23, so the other two numbers add up to 13. Therefore, they must be 5 and 8.
The bottom side adds up to 10 + 1 + 11 = 22, so the other two numbers add up to 14. Therefore, they must be 6 and 8.
So the bottom left number is 8.
5 plus 5 times 10 minus 5
Answer:
95
Step-by-step explanation:
5+5 = 10 x 10 = 100 - 5 = 95
Have a good day!!
x-2 =3 (x-4) two column proof but i can figure out the reasons on my own.
Answer:
5
Step-by-step explanation:
Step 1:
x - 2 = 3x - 12
Step 2:
- 2 = 2x - 12
Step 3:
10 = 2x
Step 4:
5 = x
Hope This Helps :)
Vertical; through (0,2). Write an equation
Answer:
The line is x =0
Step-by-step explanation:
Vertical lines are of the form
x =
The value of x in the point ( 0,2) is x =0
The line is x =0
Since we are working with a vertical line, we use the equation "x =" and use the x value in the point.
x = 0
Best of Luck!
Classify the equation as a conditional equation, an identity, or a contradiction. 6x−10−8=9+4x−4x
Step-by-step explanation:
this is your answer.........
Answer:
conditional equation
Step-by-step explanation:
Collecting terms on both sides, we get
6x−10−86x−18=9+4x−4x=9
Adding 18 to both sides of the equation, we get
6x=27
This can be solved by dividing by 6 on both sides of the equation, which gives a unique solution of 92. So, this is a conditional equation.
Hi okay no question hello
Answer:
Hello
Step-by-step explanation:
yUh GeT iNtO iT
3x + 2(4x - 4) = 3
What’s the answer?
Drag the tiles to the correct boxes to complete the pairs. Match the angle measurements in radians with equivalent measurements less than or equal to 360°.
Answer:
60° =19π/3
288°=22π/9
315°=23π/4
80°=18π/5
Step-by-step explanation:
The question is incomplete. Find the completed question in the attachment.
We are to convert the radian values to the corresponding degrees that are less than 360°
Since π rad = 180°
For 23π/4:
If π rad = 180°
23π/4 = x
Cross multiply:
πx = 23π/4 × 180
x = 23π/4π × 180
x = (23×180)/4
x = 1035°
Next is to scale down 1035° to a degree less than 360 and to do this we will be subtracting multiples of 360° from the value gotten.
x = 1035 - (360×2)
x = 1035 - 720
x = 315°
Hence 23π/4 = 315°
For 18π/5:
If π rad = 180°
18π/5 = y
Cross multiply:
πy = 18π/5 × 180
y = 18π/5π × 180
y = (18×180)/5
y = 648°
In scaling down:
y = 648°-360°
y = 288°
Hence 18π/5 = 288°
For 22π/9:
If π rad = 180°
22π/9 = t
Cross multiply:
πt = 22π/9 × 180
t = 22π/9π × 180
t = (22×180)/9
t = 440°
In scaling down:
t = 440-360°
t = 80°
Hence 22π/9 = 80°
For 19π/3:
If π rad = 180°
19π/3 = y
Cross multiply:
πy = 19π/3 × 180
y = 19π/3π × 180
y = (19×180)/3
y = 3420/3
y = 1140°
In scaling down:
y = 1140°-(3×360)°
y = 1140-1080
y = 60°
Hence 19π/3 = 60°
Answer:
the other person was almost right except they mixed up 2 of them. this is the right answer, i hope this helps :)
60° =19π/3
288°=18π/5
315°=23π/4
80°=22π/9
have a great day :))
Solve and graph -4<-1-4x<-1
Answer:
x<3/4 and x>0
for graphs, refer to the images attached.
Step-by-step explanation:
-1-4x > -4 AND -1-4x <-1
-1-4x >-4-4x > -3x < 3/4-1-4x<-1-4x<0x>0In 1970, a farmer using a two-row combine with a corn head could easily harvest 0.75 ha (1.85 acres) per hour and a typical corn yield was 5000 kg/ha (80 bu/acre). Before 1940, most corn was harvested by hand and a skilled person could harvest 250 kg/h (10 bu/h). Calculate the productivity ratio.
Answer:
The value is [tex]w = 6.7 \%[/tex]
Step-by-step explanation:
Generally the productivity rate is mathematically represented as
[tex]P_r = K * Z[/tex]
Here K is the ha the farmer could harvest in an hour and Z is a typical yield of corn in kg/ha
Now considering 1970
The productivity rate is
[tex]P_r = 0.75 *5000[/tex]
=> [tex]P_r = 3750 \ kg/h [/tex]
Now considering 1940
The productivity rate is given as [tex]P_R = 250 \ kg/h [/tex]
Generally the productivity ratio is mathematically ration is mathematically represented as
[tex]w = \frac{P_R}{P_r} * 100[/tex]
=> [tex]w = \frac{250}{3750} * 100[/tex]
=> [tex]w = 6.7 \%[/tex]
Kathy read 296 pages of her 590−page novel in 10 days. How many pages per day must she now read in order to complete the book and return it within the library's 17−day deadline?
Answer:
The answer is 42 pages per day.
Step-by-step explanation:
The answer is 42 because 590 minus 296 equals 294 and since the deadline is 17 days and he has done 10 already then 294 divided by 7 equals 42.
Is 7.0001 is terminating or repeating decimals
Answer:
it is terminating
Step-by-step explanation:
The expression that represents the area of this rectangle is . When b = 10, the area of the rectangle is square units.
Answer: 8b and 80
Step-by-step explanation: H3h3
The Area of Rectangle is 80 unit².
What is Area of rectangle?The Area of rectangle is the product of its length to its width.
Area of rectangle = length x width
Given:
Expression that represents the area of this rectangle is 8b.
Now, b = 10
As, area of rectangle = l x w
area of rectangle = 8b
area of rectangle = 8 x 10
area of rectangle = 80 unit².
Hence, the area is 80 unit².
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make doubles. add 5+6
Answer:11
Step-by-step explanation:
What is 180 times 280
Answer: 50,400
Step-by-step explanation: 180 times 280 is like multiplying 180 by 280 times.
We can write 180 times 280 like this; 180 x 280.
180 x 280 = 50,400
Answer:
50,400
Step-by-step explanation:
180×280=50,400
Can someone help pls the question in the pic (geometry)
Answer:
Reflection over y axis, and translate right 1
Step-by-step explanation:
NEED HELP ASAP WILL GIVE BRAINLY AWARD
To find the area of the larger figure, let's multiply the length by the width.
9 ft * 4 ft = 36ft^2
Let's do the same thing with the smaller figure.
3 ft * 4 ft = 12ft^2
Let's add the area of both figures together.
36ft^2 + 12ft^2 = 48ft^2
HELP ASAP !! Suppose line segment AB has one endpoint at A(0, 0). If (5, 3) is the midpoint of AB, what
are the coordinates of point B?
Answer:
(9,3)
Step-by-step explanation:
did the calculations
The co-ordinates of point B is ( 10, 6 ).
What is a line segment ?A line segment is a subset of a line which has two endpoints.
According to the given question a line segment AB has one endpoint at A(0, 0) which is (x₁,y₁)
Given midpoint is at (5,3).
Let B is (x₂,y₂).
We know midpoint of x is (x₁ + x₂)/2 and midpoint of y is (y₁ + y₂)/2.
∴ 5 = ( 0 + x₂ )/2
5 = x₂/2
x₂ = 10.
AND
3 = ( 0 + y₂ )/2
3 = y₂/2
y₂ = 6.
( x₂,y₂ ) = (10,6)
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