Answer:
-6
Step-by-step explanation:
10x1 + 4y = -14
10+4y=-14
4y=-14-10
4y = -24
y = -24/4
y = -6
How many terms are in the following geometric sequence? Type your numerical answer only. Do not type any additional characters.
0.0625, 0,25, 1, 4194304
Given:
The given geometric sequence is:
0.0625, 0.25, 1, ..., 4194304
To find:
The number of terms in the given geometric sequence.
Solution:
We have,
0.0625, 0.25, 1, ..., 4194304
Here, the first term is 0.0625 and the common ratio is:
[tex]r=\dfrac{0.25}{0.0625}[/tex]
[tex]r=4[/tex]
The nth term of a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting [tex]a_n=4194304, a=0.0625, r=4[/tex] in the above formula, we get
[tex]4194304=0.0625(4)^{n-1}[/tex]
[tex]\dfrac{4194304}{0.0625}=(4)^{n-1}[/tex]
[tex]67108864=(4)^{n-1}[/tex]
[tex]4^{13}=(4)^{n-1}[/tex]
On comparing both sides, we get
[tex]13=n-1[/tex]
[tex]13+1=n[/tex]
[tex]14=n[/tex]
Therefore, the number of terms in the given geometric sequence is 14.
is (x-2) a factor of f(x) = x^3 − 2x^2 + 2x + 3, use either remainder theorem or factor theorem to explain your reasoning
Answer:
Step-by-step explanation:
x-2=0
x=2
f(2)=2³-2(2)²+2(2)+3=8-8+4+3=7≠0
so x-2 is not a factor of f(x).
While you’re at the top of the tower(50 meters), you see an ant walking along the edge of the building. If the ant were to walk straight down the side of the tower until it reached the ground, how far would the ant travel? Which trigonometric ratio would you use to find this distance? Use the ratio to find the measurement.
Answer:
50.4 meters
Step-by-step explanation:
Given
[tex]h = 50[/tex] -- height of the tower
[tex]\theta = 7.1^o[/tex] --- angle with the wall (missing from the question)
Required
The distance walked by the ant (d)
I've added an attachment to illustrate the given parameters.
Where
[tex]h \to[/tex] height of the tower
[tex]d \to[/tex] distance walked
To calculate d, we make use of cosine trigonometric ratio:
[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
So, we have:
[tex]\cos(7.1^o) = \frac{50}{d}[/tex]
Make d the subject
[tex]d = \frac{50}{\cos(7.1^o)}[/tex]
[tex]d = \frac{50}{0.9923}[/tex]
[tex]d = 50.4[/tex]
Simplify (Asap️ )
please answer this if you know
(full steps required )
(please no spam answers)
see the attachment hope this helps you
What is y if the ordered pair (25, y) is a solution of the equation shown?
Answer:
4
Step-by-step explanation:
y = 1/5x -1
Let x = 25
y = 1/5(25) -1
= 5-1
= 4
y =4
Answer:
I think that it is 4
Step-by-step explanation:
Pythagorean Theron can someone help me solve this
josh is standing on the top of a building that is 425 feet tall. He throws a penny up into the air with an initial of 32 ft/sec. How long does it take for the penny to hit the ground?
Y = -4.9x^2 + 32x + 425
A. 10 seconds
B. 6.25
C. 400
D. 0 seconds
Answer:
A
Step-by-step explanation:
cause it will be more faster just because it is in a solid phase or it is solid
The time taken to hit the ground is 6.25 sec.(Option B)
How to calculate time?
It is given that penny follows the trajectory:
[tex]y = -4.9x^2 + 32x + 425[/tex]
Differentiating it we get:
[tex]\dfrac{dy}{dx} =-9.8x+32[/tex]
At y=425, it is obvious that x=0
So dy/dx at x=0 is 32.
Now the vertical component of the velocity is 32sinФ (where Ф is the angle at which penny is thrown).
Ф[tex]=\tan^{-1}(32)[/tex]
Vertical component=[tex]32*\sin(\tan^{-1}(32))[/tex]=31.98 ft/sec
Now applying the equation of motion: acceleration=-32ft/sec^(2)
u=31.98ft/sec s=-425 t=?
[tex]s=ut+\frac{1}{2} at^{2}[/tex]
[tex]-425=31.98t-16t^2[/tex]
[tex]16t^2-31.98t-425=0[/tex]
Solving the quadratic equation we get:
t=6.249 sec≅6.25 sec
Therefore, the time taken is 6.25 sec.
To know more about equation of motion refer:https://brainly.com/question/24966506
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A soccer field has a perimeter of 326 metres. Its area is 6370 square metres. What are the dimensions of the field?
Answer:
Step-by-step explanation:
chiều dài:x,x>0
chiều rộ:y
[tex]\left \{ {({x+y)*2=326} \atop {xy=6370}} \right.[/tex]
[tex]\left \{ {{x+y=163} \atop {xy=6370}} \right.[/tex]
[tex]\left \{ {{y=163-x} \atop {xy=6370}} \right.[/tex]
[tex]\left \{ {{y=163-x} \atop {x*(163-x)=6370}} \right.[/tex]
[tex]\left \{ {{y=163-x} \atop {163x-x^{2} =6370}} \right. \\[/tex]
[tex]\left \{ {{y=163-x} \atop {x_{1} =98; x_{2} =65}} \right.[/tex]
[tex]\left \{ {{y=65} \atop {x=98}} \right.[/tex]
Write the equation of the graph shown below in factored form.
f(x) = (x − 2)2(x + 1)(x − 4)
f(x) = (x + 2)2(x − 1)(x + 4)
f(x) = (x + 2)2(x + 1)(x + 4)
f(x) = (x − 2)2(x − 1)(x − 4)
Answer:
(x+2)2(x+1)(x+4)
Because
x=-4. x=2. x=-1
(x+4). (x+2). (x+1)
Through (-1,2) parallel to the line x=5. Find an equation of a line that satisfies the given conditions.
Answer:
x= -1
Step-by-step explanation:
Since x= 5 is a vertical line, the unknown line would also be a vertical line with an equation of x=___ as they are parallel to each other.
Given that the line passes through (-1, 2), the equation of the line is x= -1.
Parallel lines have the same slope and will never meet.
Answer the following questions using 125 words or more:
Write about the similarity of the original comic to the enlargement. How similar are they and how can you tell? What would cause differences in the two pictures? If you drew another comic using a grid, is there anything you would do differently?
What would happen if you reduced the comic's size rather than enlarged it? Would the process be the same? What would you do differently?
Link to video 2min https://media-release.glynlyon.com/g_mat08_ccss_2016/4/media/html5/anm_scale_drawing_comic_project/media/video.mp4
Answer:
given in a triangle rst and another triangle ratOn a coordinate plane, triangle R S T has points (0, 0), (negative 2, 3), (negative 3, 1). Triangle R prime S prime T prime has points (2, ...
9 votes
The population of a city has increased by 27% since it was last measured. If the current population is 38,100, what was the previous population?
=___
Answer:
the previous population was 62,000.
Step-by-step explanation:
The current population of a city = 83,700
The population of a city has increased by 35% since it was last measured.
We have to calculate the previous population before increasing 35%.
Let the previous population be p
p +(35% × p) = 83,700
p + 0.35p = 83,700
1.35p = 83,700
p =
p = 62,000
Therefore, the previous population was 62,000.
The population of a city has increased by 27% since it was last measured and the previous population was 62,000.
The current population of a city = 83,700
The population of a city has increased by 35% since it was last measured.
We have to calculate the previous population before increasing 35%.
What is the meaning of population?
A population is a distinct group of individuals, whether that group comprises a nation or a group of people with a common characteristic.
Let the previous population be p
p +(35% × p) = 83,700
p + 0.35p = 83,700
p = 83,700
p = [tex]\frac{ 83,700}{1.35}[/tex]
p = 62,000
Therefore, the previous population was 62,000.
To learn more about the population visit:
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The weight of oranges growing in an orchard is normally distributed with a mean weight of 7 oz. and a standard deviation of 1 oz. Using the empirical rule, what percentage of the oranges from the orchard weigh between 4 oz. and 10 oz.?
Answer:
Step-by-step explanation:
Set this up under the "mound" curve with 7 in the dead center. One standard deviation to the right is 8, another one is 9, another one is 10. Do the same going to the left, but go down from 7 to 6 to 5 to 4. Between the 6 and the 8 you will find 68% of the weights; between the 5 and the 9 you will find 95 % of the weights; and between 4 and 10 you will find 99.7% of the weights.
The percentage of the oranges from the orchard weighing between 4 oz and 10 oz is 99.7%
Find the volume of this sphere please help
Answer:
Volume = 108 ft³
Step-by-step explanation:
Volume of a sphere is given by the expression,
V = [tex]\frac{4}{3}\pi r^{3}[/tex]
Here, r = Radius of the sphere
From the picture attached,
Radius of the sphere = 3 ft
By substituting the value of r in the expression,
Volume = [tex]\frac{4}{3}\pi (3)^{3}[/tex]
= 36π
= 36×3
= 108 ft³
help mePsychologists striving to understand the human mind may study the nervous system. Learning how the cells and organs (like the brain) function, help us understand the biological basis behind human psychology. The nervous system is composed of two basic cell types: glial cells (also known as glia) and neurons. Glial cells, which outnumber neurons ten to one, are traditionally thought to play a supportive role to neurons, both physically and metabolically. Glial cells provide scaffolding on which the nervous system is built, help neurons line up closely with each other to allow neuronal communication, provide insulation to neurons, transport nutrients and waste products, and mediate immune responses. Neurons, on the other hand, serve as interconnected information processors that are essential for all of the tasks of the nervous system. This section briefly describes the structure and function of neurons.
Answer:
Hope this helps!
Step-by-step explanation:
Which statement best evaluates the effectiveness of the conclusion
paragraph?
Thesis Statement: My future job must include human interaction, a
nontraditional workspace, and teamwork.
Main Points:
1. Work with people
2. Work in a nontraditional workspace
3. Work in a place where coworkers share ideas
Conclusion: In the end, my future job will be one that allows me to
collaborate with my coworkers in dynamic and nontraditional
workspaces. If I am forced to sit behind a desk I will be extremely bored. Furthermore, I will be less productive if I am forced to work alone without the chance to discuss ideas with my coworkers. So the next time an adult asks me what I want to do when
I grow up, I will tell them a job without a desk, in an office full of
people. That's my dream job!
A. The conclusion is effective because it presents interesting information not addressed in the body paragraphs.
B. The conclusion is ineffective because it does not restate the thesis in a new way.
C. The conclusion is effective because it restates the thesis, summarizes the main points, and includes a satisfying close.
D. The conclusion is ineffective because it fails to leave the reader with a thought-provoking question.Which statement best evaluates the effectiveness of the conclusion paragraph?
Thesis Statement: My future job must include human interaction, a
nontraditional workspace, and teamwork.
Main Points:
1. Work with people
2. Work in a nontraditional workspace
Answer:
Were is the question?
Step-by-step explanation:
Find the missing value in each figure below. What does “y” equal?
Answer:
Step-by-step explanation:
The perpendicular is equal to 6. That's because the left triangle's missing angle is 180 - 45 -90 = 45
The angle in the right triangle is given as 52.
The cos(52) = adjacent side (which we just found to be 6) / y
Multiply both sides by y
y cos(52) = 6
cos(52) = 0.6157
Divide by sides by cos(52)
y = 6 / cos(52)
y = 6 / 0.6157
y = 9.76
Deandre can run 5 miles in 30 minutes.
How many minutes per mile is that?
6 minutes per mile.
As in, 30/5= 6
Answer:
Deandre can run 1 mile in 6 min
Step-by-step explanation:
What is the missing reason in the proof? Given: ∠ABC is a right angle, ∠D B C is a straight angle Prove: ∠ABC ≅ ∠A B D A horizontal line has points D, B, C. A line extends vertically from point B to point A. Angle A B C is a right angle. definition of angle bisector segment addition property definition of congruent angles transitive property
Answer:
Definition of Congruent angles.
Step-by-step explanation:
Given
See attachment
Required
Complete the proof at step 8
At step 8, we have:
[tex]\angle ABC \cong \angle ABD[/tex]
When the sign [tex]\cong[/tex] is used, it means congruence
In other words;
ABC and ABD are congruent
Hence, the missing statement at step 8 is: Definition of Congruent angles.
Answer:
ABC and ABD are congruent
Step-by-step explanation:
Sally collected 22 pounds of cans to recycle
and plans to collect 1.8 more pounds each
week. In this situation, what is the value of
the y-intercept?
Step-by-step explanation:
this is an example u can see and write it yourself...
Which exponential function has an x-intercept?
Answer:
y = a^x is an exponential function with an x intercept.
Step-by-step explanation:
y = a^x is the standard form of an exponential function.
–8, –4, 0, 4, 8, 12 What do these terms represent? an arithmetic series an arithmetic sequence a geometric series a geometric sequence
Answer:
Arithmetic sequence
Step-by-step explanation:
An list of numbers whereby the difference between each consecutive number is constant is called an arithmetic sequence. Given thelistvif numbers:
–8, –4, 0, 4, 8, 12 ;
We can see that each consecutive number in the list has a constant difference of 4. Hence x this is called an arithmetic sequence.
Helppppp meeeeeeeeeeeeeeeee
Answer:
A. 8/10
Step-by-step explanation:
(0.8 × 10) / (1 × 10) = 8/10 (since, multiplying 10 shifts the decimal point towards the right by one place)
Further, we can reduce fractions 8/10 by dividing the numerator and denominator by 2.
(8 ÷ 2) / (10 ÷ 2) = 4/5
Thus, 0.8 as a fraction is 8/10 or 4/5
Answer:
C
Step-by-step explanation:
https://socratic.org/questions/how-do-you-convert-0-8-8-repeating-to-a-fraction
Figure ABCD is a parallelogram.
What is the perimeter of ABCD?
A
4y - 2
B
14 units
VX
0 38 units
3x - 1
44 units
2x + 2
49 units
D
2y + 6
С
Answer:
3rd option, 44 units
Step-by-step explanation:
3x-1 = 2x+2
or, x = 3
so each side, 3×3-1 = 8
4y-2 = 2y+6
or, y = 4
so each side, 4×4-2 = 14
so perimeter
= 2(8+14)
= 44 units
Answered by GAUTHMATH
if two similar rectangles have a scale factor of 5:2 and the area of the smaller rectangle is 45 cm^2, what will be the area of the larger rectangle?
Answer:
281.25 cm^2
Step-by-step explanation:
Given that,
The scale factor of Two similar triangles = 5:2
Area of the smaller rectangle = 45 cm^2
To find,
The Area of the larger rectangle = ?
Procedure:
As we know, similar triangles have similar ratios of sides. Thus, this can be written in proportion with the sides' ratio to the left while ratio of areas on the right.
(5)^2/(2)^2 = a/45
∵ The area of the larger rectangle = 25/4 * 45
= 281.25 cm^2
If 5k = -25, then 5k - 1 = -25 - 1
Segment proof
WHATS YOUR TIKTOKKK OMG I WANT MUTUALS
Which of the following are interior angles in the figure below?
O
A. 21, 22, and 26
B. 25 and 26
C. 23 only
D. 21, 22, and 23
Answer:
(A), 21, 22,and 26
Step-by-step explanation:
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WILL MARK BRAINLIST!!
Please help!!!
Answer:
the sum of total angles of triangle is 180°.
Select point B, and drag it. As you drag B, circle AB changes. Verify that you can make circle AB coincide with AC. Return B to its approximate initial position. When circle AB coincides with circle AC, what do you notice about the regions CAD and EAF? In terms of similarity, what does your observation imply about the relationships among the lengths of the radii of AB and AC and the lengths of arc EF and arc CD? Write the relationship in the form of a proportion, and explain how it follows from your observation.
Answer:
When AB coincides with AC, the boundary of EAF maps exactly onto the boundary of CAD, implying that EAF dilates into CAD. So, the boundaries of EAF and CAD are similar.
The proportional relationship may be stated in different forms, but should be equivalent to this equation:
radius of Ab/ radius of Ac= length of arc EF/ length of arc CD
Explanations will vary, but should be based on the similarity of EAF and CAD. The proportional relationship follows from the fact that corresponding pairs of lengths in two similar figures have the same ratio.
Step-by-step explanation:
This is the exact answer so make sure you change it up a little.
Answer:
When AB coincides with AC, the boundary of EAF maps exactly onto the boundary of CAD, implying that EAF dilates into CAD. So, the boundaries of EAF and CAD are similar.
The proportional relationship may be stated in different forms, but should be equivalent to this equation:
the radius of AB /radius of AC= length of arc EF/length of arc CD
The proportional relationship follows from the fact that corresponding pairs of lengths in two similar figures have the same ratio.
Step-by-step explanation:
In a parallelogram ABCD, prove that (AC)2 + (BD)2= 2[(AB)? +(BC)?].
Answer:
AC² + BD² = 2[AB² + BC²]
Step-by-step explanation:
Let the parallelogram be ABCD with sides AB, BC, CD and AD. It also has diagonals AC and BD.
Since the diagonals are perpendicular and bisect each other at their mid-point, and P is the point of intersection of the diagonals, we have that AP = AC/2, PC = AC/2, PB = BD/2 and PD = BD/2.
Since APB forms a right angled triangles with length of sides AP, PB and AB where AB is the hypotenuse side, using Pythagoras' theorem, we have
AB² = AP² + PB²
Since AP = AC/2 and PB = BD/2, we have
AB² = (AC/2)² + (BD/2)²
AB² = AC²/4 + BD²/4 (1)
Also, BPC forms a right angled triangles with length of sides BP, PC and BC where BC is the hypotenuse side, using Pythagoras' theorem, we have
BC² = BP² + PC²
Since PC = AC/2 and PB = BD/2, we have
BC² = (AC/2)² + (BD/2)²
BC² = AC²/4 + BD²/4 (2)
Adding equations (1) and (2), we have
AB² = AC²/4 + BD²/4 (1)
+
BC² = AC²/4 + BD²/4 (2)
AB² + BC² = AC²/4 + BD²/4 + AC²/4 + BD²/4
AB² + BC² = AC²/2 + BD²/2
Multiplying through by 2, we have
2[AB² + BC²] = AC² + BD²
So, AC² + BD² = 2[AB² + BC²] which proves our expression.
