Answer:
[tex]\angle B = 60^o[/tex]
[tex]b =17.3[/tex]
[tex]c = 20[/tex]
Step-by-step explanation:
Given
[tex]a= 15[/tex]
[tex]\angle A = 30^o[/tex]
[tex]\angle C = 90^o[/tex]
See attachment for illustration
Required
Solve the triangle
First, we calculate the measure of B
[tex]\angle A + \angle B + \angle C = 180^o[/tex] --- angles in a triangle
[tex]30^o + \angle B + 90^o = 180^o[/tex]
Collect like terms
[tex]\angle B = 180^o-90^o-30^o[/tex]
[tex]\angle B = 60^o[/tex]
Solve for (c) using sine function
[tex]\sin(30) = \frac{a}{c}[/tex]
Make c the subject
[tex]c = \frac{a}{\sin(30)}[/tex]
Substitute known values
[tex]c = \frac{10}{0.5}[/tex]
[tex]c = 20[/tex]
Solve for (b) using Pythagoras
[tex]c^2 = a^2 + b^2[/tex]
This gives:
[tex]20^2 = 10^2 + b^2[/tex]
[tex]400 = 100 + b^2[/tex]
Collect like terms
[tex]b^2 =400 - 100[/tex]
[tex]b^2 =300[/tex]
Take square roots
[tex]b =17.3[/tex]
yannie read 24 pages of a book. one fourth of the book is unread.how many pages are there?
Answer:
32
Step-by-step explanation:
24/3=8, 24+8=32
that's how I think of it
What is the reason for each step in the solution of the equation?
-5(x - 6) = 10x
Drag and drop the reasons into the boxes to correctly complete the table.
–5(x – 6) = 10x
Given
-5x + 30 = 10x
30 = 15x
2 = x
Division Property of Equality
Commutative Property
Addition Property of Equality
Given
Distributive Property
Answer:
Distributive property (-5 is being multiplied to x and - 6)
Addition property of equality (5x is being added in both side of the equation)
Division property of equality (15 is being devided in both side of the equation)
Brainliest please~
The reason for each step will be
Distributive property (-5 is being multiplied to x and - 6)
Addition property of equality (5x is being added in both sides of the equation)
Division property of equality (15 is being divided into both sides of the equation)
What are algebraic properties?
We can solve mathematical equations thanks to algebra's inherent characteristics. The algebraic properties are distributive property, addition property of equality, and division property of equality.
Given expressions are:-
-5x + 30 = 10x
30 = 15x
2 = x
-5x + 30 = 10x ⇒ Distributive property (-5 is being multiplied to x and - 6)
30 = 15x ⇒ Addition property of equality (5x is being added in both sides of the equation)
30 = 15x ⇒ Division property of equality (15 is being divided into both sides of the equation)
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The scores for a particular examination are normally distributed with a mean of 68.5% and a standard deviation of 8.2%. What is the probability that a student who wrote the examination had a mark between 80% and 100%? Give your answer to the nearest hundredth.
Answer:
[tex]P(80/100<x<100/100)=0.08[/tex]
Step-by-step explanation:
We are given that
Mean,[tex]\mu=68.5[/tex]%=68.5/100
Standard deviation, [tex]\sigma=8.2[/tex]%=8.2/100
We have to find the probability that a student who wrote the examination had a mark between 80% and 100%.
[tex]P(80/100<x<100/100)=P(\frac{80/100-68.5/100}{8.2/100}<\frac{x-\mu}{\sigma}<\frac{100/100-68.5/100}{8.2/100})[/tex]
[tex]P(80/100<x<100/100)=P(1.40<Z<3.84)[/tex]
We know that
[tex]P(a<Z<b)=P(Z<b)-P(Z<a)[/tex]
Using the formula
[tex]P(80/100<x<100/100)=P(Z<3.84)-P(Z<1.40)[/tex]
[tex]P(80/100<x<100/100)=0.99994-0.91924[/tex]
[tex]P(80/100<x<100/100)=0.0807\approx 0.08[/tex]
Given that f(x)=x^2 and g(x)=5x+2 , find (f-g)(2), if it exists.
Answer:
(f - g)(2) = -8
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = x²
g(x) = 5x + 2
Step 2: Find
Substitute in functions: (f - g)(x) = x² - (5x + 2)[Distributive Property] Distribute negative: (f - g)(x) = x² - 5x - 2Substitute in x [Function (f - g)(x)]: (f - g)(2) = 2² - 5(2) - 2Evaluate: (f - g)(2) = -8Module 8: Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.
Question: Describe how to eliminate the parameter to change from parametric to rectangular form. How does this ability help us with graphing parametric equations?
Answer:
rectangular equation, or an equation in rectangular form is an equation composed of variables like xx and yy which can be graphed on a regular Cartesian plane. For example y=4x+3y=4x+3 is a rectangular equation.
A curve in the plane is said to be parameterized if the set of coordinates on the curve, (x,y)(x,y) , are represented as functions of a variable tt .
x=f(t)y=g(t)x=f(t)y=g(t)
These equations may or may not be graphed on Cartesian plane.
Step-by-step explanation:
I hope this helps
In 1995 the U.S. federal government debt totaled 5 trillion dollars. In 2008 the total debt reached 10 trillion dollars. Which of the following statements about the doubling time of the U.S. federal debt is true based on this information?
Where are the statements?
3x-2=2(x-5)
find the value of x
Now we have to,
find the required value of x.
Let's begin,
→ 3x-2 = 2(x-5)
→ 3x-2 = 2x-10
→ 3x-2x = -10+2
→ x = -8
Hence, value of x is -8.
Answer:
x = -8
Step-by-step explanation:
3x - 2 = 2 ( x + 5
Solve for x.
Let's solve,
3x - 2 = 2 ( x + 5 )
Step 1:- Distribute 2.
3x - 2 = 2 × x + 2 × 5
3x - 2 = 2x - 10
Step 2 :- Move constant to the right-hand and change their sign.
3x = 2x - 10 + 2
Step 3:- Add -10 and 2.
3x = 2x - 8
Step 4 :- Move variable to the left-hand side and change their sign.
3x - 2x = -8
Step 5 :- Subtract 2x from 2x.
x = -8
Hence, value of x = -8.
Which of the following is true about congruent figures?
Write an expression representing the unknown quantity.
There are 5,682,953 fewer men than women on a particular social media site. If x represents the number of women using that site, write an expression for the number of men using that site.
The expression for the number of men is
.
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Answer:
x - 5,682,953
Step-by-step explanation:
If x is the number of women, and the number of men is 5,682,953 less, then the number of men is x -5,682,953
An object is dropped from 24 feet below the tip of the pinnacle atop a 1468-ft tall building. The height h of the object after t seconds is given by the equatior h= - 16t2 + 1444. Find how many seconds pass before the object reaches the ground. seconds pass before the object reaches the ground. (Type an integer or a decimal.)
Answer:
9.5 seconds pass before the object reaches the ground.
Step-by-step explanation:
Height of the ball:
The height of the ball after t seconds is given by the following equation:
[tex]h(t) = -16t^2 + 1444[/tex]
Find how many seconds pass before the object reaches the ground.
This is t for which h(t) = 0. So
[tex]h(t) = -16t^2 + 1444[/tex]
[tex]-16t^2 + 1444 = 0[/tex]
[tex]16t^2 = 1444[/tex]
[tex]t^2 = \frac{1444}{16}[/tex]
[tex]t^2 = 90.25[/tex]
[tex]t = \pm \sqrt{90.25}[/tex]
Since it is time, we only take the positive value.
[tex]t = 9.5[/tex]
9.5 seconds pass before the object reaches the ground.
Find the sum of the series if possible, if not possible explain why:
1+(−2/5)+(−2/5)^2+(−2/5)^3+⋯
Answer:
Step-by-step explanation:
5/7
Sum of a geometric series is a/(1-r) = 1/(1-(-2/5)) = 5/7
When male workers were asked how many hours they worked in the previous week, the mean was with a standard deviation of . Does this suggest that the population mean work week for men exceeds hours
Answer:
We can conclude that the population mean work week for men exceed 40 hours.
Step-by-step explanation:
Given that :
Mean, xbar = 45.6
Standard deviation, s = 14.6
Sample size, n = 893
x = 40
Hypothesis :
H0 : μ = 40
H1 : μ > 40
Using test statistic for one sample t test :
Test statistic = (xbar - μ) ÷ (s/√(n))
Test statistic = (45.6 - 40) ÷ (14.6/√(893))
T = (5.6 / 0.4885703)
Test statistic = 11.46
Using the Pvalue approach :
Reject H0 : if Pvalue < α
Pvalue for test statistic of 11.46 will be approximately 0 (Extremely low)
Hence, Pvalue < α ; We reject H0 ; and conclude that population mean work week for men exceed 40 hours
Multiply (8 + 3i)(3 + 5i).
39 + 491
9+ 491
24 + 152
24 + 491 + 15/2
(8+3)(3+5)=88
88+(39+491)= 618.
88+(9+491)= 588
88+(24+152)= 264.
sorry could not find the last ansswer..
d = 3.2(t+1)(2t - 3)
An air pump increases the oxygen levels in
an aquarium and reduces the build-up of
waste materials. The equation shown above
gives the depth, d, in inches of an air
bubble beneath the surface of the water t
seconds after it emerges from the air pump.
After how many seconds does the air
bubble reach the surface?
Answer:
3/2=1.5 sec
Step-by-step explanation:
Equate d=0 and solve the expression, t=-1 and 3/2 but t can't be negative.
The air bubble will reach the surface in 1.5 seconds.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The given expression is d = 3.2(t+1)(2t - 3) where d is the height of the aquarium and t is the time taken by the bubbles to come to the surface.
When the bubble will come to the surface height D becomes zero.
d = 3.2(t+1)(2t - 3)
3.2(t+1)(2t - 3) = 0
t + 1 = 0 and 2t - 3 = 0
t = -1 and t = 3 / 2 = 1.5
Therefore, the air bubble will reach the surface in 1.5 seconds.
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surface areas of two similar figures are given. the volume of the larger figure is given. find the volume of the smaller figure
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Answer:
216 in³
Step-by-step explanation:
The ratio of volumes is the 3/2 power of the ratio of areas.
small volume = ((small area)/(large area))^(3/2) × (large volume)
= (212/1325)^(3/2) × 3375 in³ = (4/25)^(3/2) × 3375 in³ = (8/125)×3375 in³
small volume = 216 in³
many ® Black pencils cost N75 each and coloured pencils cost N105 each. If 24 mixed pencils cost #2010, how of them were black? (Hint: Let there be x black pencils. Thus there are 24 - x) coloured pencils.)
Answer:
85
Step-by-step explanation:
I hope my answer help you
(2 + i)-(4 - 6/)(-3 +3/)
Answer:
C
Step-by-step explanation:
(2+i)-(4-6i)(-3+3i)
=(2+i)-(-12+12i+18i-18i^2)
=(2+i)-[-12+30i-18(-1)]
=(2+i)-(-12+30i+18)
=(2+i)-(30i+6)
=2+i-30i-6
=-4-29i
Solve - 2x - 7 > X+ 8.
O A. x<-3
O B. x<-5
O C. x>-5
O D. x>-3
Answer:
x < -5
Step-by-step explanation:
- 2x - 7 > x+ 8
Add 2x to each side
- 2x+2x - 7 > x+2x+ 8
-7 > 3x+8
Subtract 8 from each side
-7-8 > 3x+8-8
-15 > 3x
Divide by 3
-15/3 > 3x/3
-5 >x
x < -5
[tex]\lim_{x \to \4} x^{2} -3x[/tex]
(4)^2-3(4)=4Answer:
Step-by-step explanation:
how many terms are there in the series. 201.208.215......319
Answer:
222
Step-by-step explanation:
add 7 no. to each of like 201+7 = 208, 208+7=215 ,215+7=222
I need help pls help me in geometry homework
Type your answer into the box. X 30° Calculate the size of angle x. angle x =
Answer:
x = 60°Step-by-step explanation:
We know:
All triangles have internal angles that add up to 180°.
And
All right triangles have acute angles that up to 90°.
Therefore
x + 30° + 90° = 180°
x + 120° = 180° |subtract 120° from both sides
x + 120° - 120° = 180° - 120°
x = 60°orx + 30° = 90° |subtract 30° from both sides
x + 30° - 30° = 90° - 30°
x = 60°The size of angle x will be 60°
TriangleIt is a plane figure with three straight sides and three angles.
What are steps to solve this problem?The steps are as follow:
As per rule of triangle, the sum of all three internal angle must be equal to 180°The given triangle is right angle triangle having one angle 30° and other we have to findGiven:z = 90°
y = 30°
x = ?
∴ x + y + z = 180°
∴ x + 30 + 90 = 180
∴ x + 120 = 180
∴ x = 60°
So the size of angle x will be 60°
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Which set of statements explains how to plot a point at the location (Negative 3 and one-half, negative 2)?
A: Start at the origin. Move 3 and one-half units right because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between 3 and 4. Move 2 units down because the y-coordinate is -2.
B: Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units left because the y-coordinate is -2.
C: Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.
D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.
Answer:
D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.
Jarvis invested some money at 6% interest. Jarvis also invested $58 more than 3 times that amount at 9%. How much is invested at each rate if Jarvis receives $1097.19 in interest after one year? (Round to two decimal places if necessary.)
Use the variables x and y to set up a system of equations to solve the given problem.
9514 1404 393
Answer:
$3309 at 6%$9985 at 9%Step-by-step explanation:
Let x and y represent amounts invested at 6% and 9%, respectively.
y = 3x +58 . . . . . . . the amount invested at 9%
0.06x +0.09y = 1097.19 . . . . . . total interest earned
__
Substituting for y, we have ...
0.06x +0.09(3x +58) = 1097.19
0.33x + 5.22 = 1097.19 . . . . . . . . . simplify
0.33x = 1091.97 . . . . . . . . . . . . subtract 5.22
x = 3309 . . . . . . . . . . . . . . . . divide by 0.33
y = 3(3309) +58 = 9985
$3309 is invested at 6%; $9985 is invested at 9%.
The height (in meters) of a shot cannonball follows a trajectory given by h(t) = -4.9t^2 + 14t - 0.4 at time t (in seconds). As an improper fraction, for how long is the cannonball above a height of 6 meters? Please show steps. Thank you!
The radius of a sphere is 6 units.
Which expression represents the volume of the sphere,
in cubic units?
이 (6)
○ (6)
이 (12)
ㅇ (12)
Answer:
B. ⁴/3π(6)³
Step-by-step explanation:
Formula for volume of a sphere = ⁴/3πr³
Where,
radius (r) = 6 units
Plug in the given value into the volume formula
Volume of the sphere = ⁴/3 × π × (6)³
Volume of the sphere = ⁴/3π(6)³
The expression that represents the volume of the given sphere is therefore ⁴/3π(6)³ cubic units.
The expression for the volume of the sphere is:
V = (4/3)*3.14*(6)^3
Which expression represents the volume?
For a sphere of radius R. the volume is given by:
V = (4/3)*pi*R^3
Where pi = 3.14
Here we know that the radius is 6 units, so we can write the volume as:
V = (4/3)*3.14*(6)^3
As you can see, the second option (counting from the top) is the correct one.
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Talerie has a bathtub that she needs to fill with wa-
ter to fill the tub, she first needs to fill a bucket
with water and then dump this into the bathtub. If
the bucket is a cylinder with a radius of 6 in, and a
height of 12 in, how many buckets will it take to
fill the 5 ft. x3 ft. x3 ft. tub?
a 50 buckets
B. 48 buckets
C. 57 buckets
D. 62 buckets
Answer:
áedw
Step-by-step explanation:
đá
Find the missing length Indicated
Answer:
60
Step-by-step explanation:
x² = 144×25
= 3600
x =√3600 =60
Does the point (9, 0) satisfy the equation y = 9x2 + x + 9?
52 POINTS I need help!
Question 1
The vertex form of the equation of a vertical parabola is given by
, where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use the GeoGebra geometry tool to create a vertical parabola and write the vertex form of its equation. Open GeoGebra, and complete each step below. If you need help, follow these instructions for using GeoGebra.
Part A
Mark the focus of the parabola you are going to create at F(6, 4). Draw a horizontal line that is 6 units below the focus. This line will be the directrix of your parabola. What is the equation of the line?
Part B
Construct the line that is perpendicular to the directrix and passes through the focus. This line will be the axis of symmetry of the parabola. What are the coordinates of the point of intersection, A, of the axis of symmetry and the directrix of the parabola?
Part C
Explain how you can locate the vertex, V, of the parabola with the given focus and directrix. Write the coordinates of the vertex.
Part D
Which way will the parabola open? Explain.
Part E
How can you find the value of p? Is the value of p for your parabola positive or negative? Explain.
Part F
What is the value of p for your parabola?
Part G
Based on your responses to parts C and E above, write the equation of the parabola in vertex form. Show your work.
Part H
Construct the parabola using the parabola tool in GeoGebra. Take a screenshot of your work, save it, and insert the image below.
Part I
Once you have constructed the parabola, use GeoGebra to display its equation. In the space below, rearrange the equation of the parabola shown in GeoGebra, and check whether it matches the equation in the vertex form that you wrote in part G. Show your work.
Part J
To practice writing the equations of vertical parabolas, write the equations of these parabolas in vertex form:
focus at (-5, -3), and directrix y = -6
focus at (10, -4), and directrix y = 6.
Answer:
Step-by-step explanation:
A. Directrix: y = 4-6 = -2
:::::
B. Axis of symmetry: x = 6
Axis of symmetry intersects directrix at (6,-2)
:::::
C . Vertex is halfway between focus and directrix, at (6,1)
:::::
D. The focus lies above the directrix, so the parabola opens upwards.
:::::
E. Focal length p = 1/(4×0.5)
:::::
F. p = 0.5
::::
G. y = 0.5(x-6)² + 1
Answer:
the one above is correct
Step-by-step explanation:
h.We start with a circle and a line that goes through the center of the circle (C) and one vertex of the triangle (E).
Using the point on the line opposite the vertex as a center (D), we draw an arc with the same radius the circle has.
The two points of intersection with the circle are the other two vertices of the inscribed triangle (F, G).
