Find the missing terms in the following geometric sequence.
a.48, 162c.96, 192b.116, 220d.36, 108
Answers
Related Questions
0.43 is 10 times as mush as what
Answers
The number that is 10 times less than 0.43 is 0.043, found by dividing 0.43 by 10.
To find the number that 0.43 is 10 times as much as, we need to divide 0.43 by 10. This is the same as multiplying by 10 raised to the power of -1, which is a division by 10.The operation looks like this:
0.43*10^{-1} = 0.043.
Therefore, 0.43 is 10 times as much as 0.043
what is the greatest number of obtuse angles that a right triangle can contain
A) 3
B) 1
C) 0
D) 2
Answers
Answer:0
Step-by-step explanation:
A right triangle can have at most one obtuse angle since it already contains one right angle, and the sum of its angles must be 180 degrees according to geometrical axioms.
The question asks about the maximum number of obtuse angles that can be contained in a right triangle. In a right triangle, one angle is 90 degrees by definition, which is a right angle. According to Theorem 20, the sum of the angles of a triangle is two right angles, which equals 180 degrees. Having an obtuse angle, which is greater than 90 degrees, combined with a 90 degree angle, would exceed 180 degrees when the third angle is added, and this is not possible in a plane geometric figure. Therefore, a right triangle cannot have more than one right angle. As such, the option with the maximum number of obtuse angles a right triangle can contain is:
Answer: B) 1
On a road trip you and your family stop a truck stop to take a break and to let your puppy Fido stretch. You notice that they have a triangular dog park that is fenced in on two sides. The third side of the field is formed by a creek. If the fences measure 150 feet and 98 feet, and the side along the creek is 172 feet, what are the measures of the angles made by the dog park?
Answers
cosα=(150^2+172^2-98^2)/2*150*172
Answer:
Angles are 34.59°, 85.08° and 60.33°
Step-by-step explanation:
Let ABC is a triangle, ( that show the dog park)
In which,
AB = 150 feet
BC = 98 feet
CA = 172 feet,
By the cosine law,
[tex]BC^2=AB^2+AC^2-2(AB)(AC)cos A[/tex]
[tex]2(AB)(AC)cos A=AB^2+AC^2-BC^2[/tex]
[tex]\implies cos A=\frac{AB^2+AC^2-BC^2}{2(AB)(AC)}-----(1)[/tex]
Similarly,
[tex]\implies cos B=\frac{AB^2+BC^2-AC^2}{2(AB)(BC)}-----(2)[/tex]
[tex]\implies cos C=\frac{BC^2+AC^2-AB^2}{2(BC)(AC)}-----(3)[/tex]
By substituting the values in equation (1),
[tex]cos A=\frac{150^2+172^2-98^2}{2\times 150\times 172}[/tex]
[tex]=\frac{22500+29584-9604}{51600}[/tex]
[tex]=\frac{42480}{51600}[/tex]
[tex]\approx 0.8233[/tex]
[tex]\implies m\angle A\approx 34.59^{\circ}[/tex]
Similarly,
From equation (2) and (3),
m∠B ≈ 85.0°, m∠C ≈ 60.33°
Find an exact value. sine of negative eleven pi divided by twelve.
Answers
The sine of negative eleven pi divided by twelve is -0.5.
Explanation:To find the sine of negative eleven pi divided by twelve, we need to determine the exact value of this trigonometric function. The sine function represents the ratio between the length of the side opposite the angle and the hypotenuse in a right triangle. In this case, the angle is negative, which means it lies on the negative y-axis. Remember that the unit circle can help us determine the values of trigonometric functions for any angle. By mapping the angle on the unit circle, we can see that -11π/12 is equivalent to -330 degrees. Since the sine function has a period of 360 degrees, we can find the reference angle by subtracting 360 degrees. So, the reference angle is 30 degrees (360 - 330).The sine of 30 degrees is 0.5. However, the angle is negative, so the sine function is negative. Therefore, the exact value of sine of -11π/12 is -0.5.
Final Answer:
The exact value of [tex]\(\sin\left(-\frac{11\pi}{12}\right)\)[/tex] is:
[tex]\[\frac{\sqrt{2} + \sqrt{6}}{4}\][/tex]
Explanation:
To find the sine of an angle that is not one of the commonly known angles, such as [tex]\(-\frac{11\pi}{12}\)[/tex], we can use sine sum and difference identities. In this case, we know the sine of [tex]\(-\frac{\pi}{12}\)[/tex] is not a standard angle, but we can express it as a sum or difference of angles like [tex]\(-\frac{\pi}{4}\)[/tex] and [tex]\(-\frac{\pi}{3}\)[/tex] whose sines we do know.
The sum identity for sine is:
[tex]\[\sin(a \pm b) = \sin(a)\cos(b) \pm \cos(a)\sin(b)\][/tex]
We can express the angle [tex]\(-\frac{11\pi}{12}\)[/tex] as the sum of two angles for which we do know the sine and cosine values, for example,[tex]\(-\frac{\pi}{4}\)[/tex] and [tex]\(-\frac{2\pi}{3}\)[/tex] because:
[tex]\[-\frac{11\pi}{12} = -\frac{3\pi}{4} - \frac{2\pi}{3}\][/tex]
Using the sum identity for sine, we can find the sine value as follows:
[tex]\[\sin\left(-\frac{11\pi}{12}\right) = \sin\left(-\frac{3\pi}{4}\right)\cos\left(-\frac{2\pi}{3}\right) + \cos\left(-\frac{3\pi}{4}\right)\sin\left(-\frac{2\pi}{3}\right)\][/tex]
Now, let's find the values of sine and cosine for these angles.
[tex]\(\sin\left(-\frac{3\pi}{4}\right) = -\sin\left(\frac{3\pi}{4}\right) = -\sin\left(\frac{\pi}{2} + \frac{\pi}{4}\right) = -\frac{\sqrt{2}}{2}\)[/tex]since sine is an odd function.
[tex]\(\cos\left(-\frac{2\pi}{3}\right) = \cos\left(\frac{2\pi}{3}\right) = -\frac{1}{2}\)[/tex] since cosine is an even function.
[tex]\(\cos\left(-\frac{3\pi}{4}\right) = \cos\left(\frac{3\pi}{4}\right) = -\frac{\sqrt{2}}{2}\)[/tex] since cosine is an even function.
[tex]\(\sin\left(-\frac{2\pi}{3}\right) = -\sin\left(\frac{2\pi}{3}\right) = -\frac{\sqrt{3}}{2}\)[/tex] since sine is an odd function.
Substitute these trigonometric values into the sum identity:
[tex]\[\sin\left(-\frac{11\pi}{12}\right) = \left(-\frac{\sqrt{2}}{2}\right)\left(-\frac{1}{2}\right) + \left(-\frac{\sqrt{2}}{2}\right)\left(-\frac{\sqrt{3}}{2}\right)\][/tex]
Simplify the expression:
[tex]\[\sin\left(-\frac{11\pi}{12}\right) = \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\][/tex]
Combine the terms with a common denominator:
[tex]\[\sin\left(-\frac{11\pi}{12}\right) = \frac{\sqrt{2} + \sqrt{6}}{4}\][/tex]
Therefore, the exact value of [tex]\(\sin\left(-\frac{11\pi}{12}\right)\)[/tex] is:
[tex]\[\frac{\sqrt{2} + \sqrt{6}}{4}\][/tex]
which of the following fractions will convert to repeating decimals?
a. 1/3
b. 1/6
c. 1/4
d. 3/8
e. 1/5
Answers
a. 1/3 = 0.33333333
b. 1/6 = 0.16666666
c. 1/4 = 0.25
d. 3/8 = 0.375
e. 1/5 = 0.2
10-2v=-5-50
+5 +5
10-3v=-50
+3 +3
10=47
Answers
10-2v=-5-50
add : 5
10 - 2v + 5 = 5 - 5 - 50
15 -2v = -50
add : -15
-15 +15 -2v = -15 -50
-2v =-65
v = 65/2
how many integers from 42 to 92, inclusive, have a remainder of 4 when divided by 6
Answers
If they have a remainder of 4 when divided by six the sequence of terms are: 6n+4
42≤6n+4≤92
subtract 4 from both ends
38≤6n≤88
divide both ends by 6
6.3≤n≤14.6
since n must be an integer...
7≤n≤14 so the number of integers is:
14-7+1=8
they are 6n+4 for n=[7,14]...46,52,58,64,70,76,82,88
There are 8 integers between 42 and 92, inclusive, that have a remainder of 4 when divided by 6. These integers can be expressed in the form of 6n + 4 and can be found by incrementally adding 6, starting from the smallest integer greater than 42 that meets this condition.
To find how many integers from 42 to 92, inclusive, have a remainder of 4 when divided by 6, we need to identify the numbers that fit the condition. These numbers are of the form 6n + 4, where n is an integer. Starting with the smallest number greater than 42 that fits the condition, which is 46 (as 6*7 + 4 = 46), we can find the next by adding 6 to get 52, then 58, and so on, up until we reach the largest number less than or equal to 92 that fits the condition, which is 88 (as 6*14 + 4 = 88).
To find the total count, we calculate (88 - 46) / 6 + 1 = 42 / 6 + 1 = 7 + 1 = 8. Therefore, there are 8 numbers between 42 and 92 that have a remainder of 4 when divided by 6.
An ostrich that is 108 inches tall is 20 inches taller than 4 times the height of a kiwi. What is the height of a kiwi in inches?
Answers
'4 times the height of a kiwi' = 4x
'20 inches taller than 4 times the height of a kiwi' = 4x + 20
An ostrich is 108 inches tall and this is EQUAL to 4x + 20
108 = 4x + 20
108 - 20 = 4x
88 = 4x
88 ÷ 4 = x
x = 22
The height of the kiwi is 22 inches
An object is dropped from a height of 1,600 feet. The amount of time, in seconds, the object takes to hit the ground can be found by solving the equation −16t2+1,600=0. How many seconds will it take to hit the ground?
Answers
-16t² + 1600 = 0
Transpose the terms without variable to the other side of the equation,
-16t² = -1600
Divide the equation by -16.
t² = 100
Solve the value of t by getting the square root of the equation.
t = +/- 10
Thus, it will take the object 10 seconds to reach the ground.
To find the time it takes for the object to hit the ground, we can solve the quadratic equation -16t^2 + 1600 = 0 using the quadratic formula. The positive solution to this equation gives us the time in seconds. Therefore, the object will take √102400/32 seconds to hit the ground.
Explanation:To find the time it takes for the object to hit the ground, we need to solve the equation -16t^2 + 1600 = 0. This is a quadratic equation, so we can use the quadratic formula. Plugging in the values, we get t = (-b ± √(b^2 - 4ac))/(2a). In this case, a = -16, b = 0, and c = 1600. Plugging in these values, we get t = (± √(0 - 4(-16)(1600)))/(2(-16)). Simplifying the equation further, we get t = (± √(0 + 102400))/(32). This gives us two possible values for t: t = √102400/32 and t = -√102400/32. Since time cannot be negative in this context, we can discard the negative solution. Therefore, the object will take √102400/32 seconds to hit the ground.
Write the equations in graphing form, then state the vertex of the parabola or the center and radius of the circle.
y=2x^2+16
Answers
It is a positive-slope parabola with vertex of (0,16) "concave up"
Find the midpoint of the segment below
Answers
If we are given 2 points A(a, b) and B(c, d),
the midpoint M, of segment AB has coordinates:
[tex]M_A_B=( \frac{a+c}{2} , \frac{b+d}{2} )[/tex]
2.
We are given the points A(2, 3) and B(10, 3)
the midpoint of AB, is given by the above formula:
[tex]M_A_B=( \frac{2+10}{2} , \frac{3+3}{3} )=(6, 3)[/tex]
3.
Remark, since the segment is horizontal, that is the y-coordinate of both points is 3, the y coordinate of the midpoint will also be 3.
While the x coordinate is still found by [tex]\frac{2+10}{2}[/tex]
Answer: (6, 3)
A card is chosen at random from a standard deck of 52 playing cards. What is the probability that the chosen card is a jack or a queen?
Answers
The perimeter of a triangle is 510 ft and the sides are in the ratio of 11:16:24. Find the area of the triangle. Need help, is there a specific formula for this?
Answers
The side lengths are in the ratio 11:16:24, so let them be
11k, 16k, and 24k for some number k.
11k+16k+24k=510
k(11+16+24)=510
51k=510
k=10
so the actual sides are 110, 160 and 240 feet.
2.
There is a famous formula, called Heron's formula, which calculates the area of a triangle, given its sides a, b and c.
we first calculate the half perimeter, which we usually denote by u:
[tex]u= \frac{a+b+c}{2} [/tex]
then the theorem states that the area A is as follows:
[tex]A= \sqrt{u(u-a)(u-b)(u-c)} [/tex]
3.
In our case:
[tex]u= \frac{a+b+c}{2} =\frac{110+160+240}{2} = \frac{510}{2} [/tex]
[tex]u-a= \frac{510}{2} -110= \frac{510-220}{2} = \frac{290}{2} [/tex]
[tex]u-b= \frac{510}{2} -160= \frac{510-320}{2} = \frac{190}{2} [/tex]
[tex]u-a= \frac{510}{2} -240= \frac{510-480}{2} = \frac{30}{2} [/tex]
[tex]A= \sqrt{\frac{510}{2}*\frac{290}{2}* \frac{190}{2} * \frac{30}{2}} =7,258.745[/tex] feet squared
Answer:D 7,258.745 ft squared
Final answer:
To find the area of a triangle with sides in a given ratio, first find the value of x by setting up and solving an equation using the perimeter. Then, multiply each side by x to find the base and height of the triangle. Finally, substitute the base and height into the formula for the area of a triangle.
Explanation:
To find the area of a triangle, we can use the formula: Area = 1/2 × base × height. In this case, we don't know the base and height directly, but we do know that the sides of the triangle are in the ratio of 11:16:24. Let's assume the sides are 11x, 16x, and 24x. The perimeter of the triangle is 510 ft, which means 11x + 16x + 24x = 510. Simplifying this equation, we get 51x = 510. Therefore, x = 10. Now we can find the base and height of the triangle by multiplying the corresponding sides by 10. The base is 11x * 10 = 110 ft and the height is 16x * 10 = 160 ft.
Now we can substitute these values into the formula to calculate the area of the triangle. Area = 1/2 × base × height = 1/2 × 110 ft × 160 ft = 8800 square feet.
A chocolate bar measures 40 mm wide, 80 mm long, and 5 and 1 over 2 mm high. Will’s Wrapping Company is making a wrapper to cover the chocolate bar. Use the correct net and determine how much paper will be needed to make the wrapper
Answers
The surface area of the rectangular prism is calculated through the equation,
SA = 2LW + 2WH + 2LH
Substituting the known values,
SA = (2)(80 mm)(40 mm) + 2(40 mm)(5.5 mm) + 2(80 mm)(5.5 mm)
SA = 6400 mm² + 440 mm² + 880 mm²
SA = 7720 mm²
Thus, the least area needed to completely cover or wrap the chocolate bar is 7720 mm².
Answer:
Will’s Wrapping Company needs 7,720 mm of paper to wrap the chocolate bar.
Find the value of x in the equation √ x + 5 = √ x + 45.
Answers
Carissa is budgeting for her next semester at college. She spent $50 on gas this month. Economists are predicting gas prices to rise 8% per month for the next 6 months. How much should she budget for gas if classes start next month and are 4 months long?
The answer is D.243.33
(I looked up the question and couldnt find it so i thought i'd post it for anyone who needed it)
Answers
Predicted spent of gas next month = $50 * 1.08
Predicted spent of gases for the four months:
$50 * 1.08
$50 * 1.08^2
$50 * 1.08^3
$50 * 1.08^4
Total spent for the four months: $50 (1.08 + 1.08^2 + 1.08^3 + 1.08^4) = $50 * (4.8666) = $243.33, which is the option D. 243.33
Please help me with my geometry!
Answers
The theorem suggests: multiplying the whole length of one secant by the external part of the secant, it is equal to the other side exterior secant x whole secant.
Knowing that, let's begin!
Let's use the total length of the first secant on a (x and 5).
5 + x * 5 =
and
4 + 6 * 6 =
BOTH of the equations must be equal...keep that in mind!
Let's set them into one full equation, shall we?
5 + x * 5 = 4 + 6 * 6
Simplify:
5 + 5x = 60
Now, we solve for X!
First, subtract 5 from both sides,
5 - 5 + 5x = 60 - 5
5x = 55
Divide 5 from both sides,
5x/5 = 55/5
x = 11!
Now, moving on to B.
5 + 3 * 3
&
x + 4 * 4
Same thing with the problem above, let's set them as one equation since they are equal to each other.
5 + 3 * 3 = x + 4 * 4
Simplify:
(It wouldn't be 4x + 4 because order of operations says to multiply 4 * 4 first! Just thought you should know...just in case.)
24 = 16 + x
Now, we subtract 16 from each side...
24 - 16 = 16 - 16 + x
Simplify:
8 = x
x= 8 for b!
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Have a good one.
God bless!
Find the measure of an angle whose supplement is 9 times the measure of its complement
Answers
180 - x = 9(90-x)
180-x = 810 - 9x
8x = 630
x = 78.75 degrees
The equation is 180 - x = 9 (90 - x).Then the measure of the angle will be 78.75 degrees.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
Let 'x' be the angle. Then the equation is given as,
180 - x = 9 (90 - x)
180 - x = 810 - 9x
8x = 630
x = 78.75 degrees
The measure of the angle will be 78.75 degrees.
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One cell phone plan charges $20 per month plus $.15 per minute used. A second cell phone plan charges $35 per month plus $.10 per minute used. Write and solve an equation to find the number of minutes you must talk to have the same cost for both calling plans.
Answers
20+0.15x = 35+0.10x
0.15x=15+0.10x
0.05x=15
x= 15/0.05
x= 300minutes
check:
300*.015 = 45+20=65
300*0.10 = 30 + 35 = 65
they equal
so number of minutes would be 300
Melissa has scored 83 , 84 , 93 , 77 , and 85 on her previous five tests. what score does she need on her next test so that her average (mean) is 83 ?
Answers
83 x 6 = 498
all six of her scores need to equal at least 498 for an 83 average
83 + 84 + 93 + 77 + 85 = 422
498-422 = 76
she needs a 76
For the function h defined by h(x)=2x2−2, find h(−12)
Answers
To find h(-12), substitute -12 into the function h(x)=2x²-2. The value of h(-12) is 286.
Explanation:To find h(-12), we substitute -12 into the function h(x)=2x²-2:
h(-12) = 2(-12)² - 2
h(-12) = 2(144) - 2
h(-12) = 288 - 2
h(-12) = 286
Therefore, h(-12) is equal to 286.
Which is a stretch of an exponential decay function?
f(x) =4/5(5/4)^x
f(x) =4/5(4/5 )^x
f(x) =5/4(4/5)^x
f(x) =5/4(5/4)^x
Answers
for such a question, it is required to graph each function, the answer is
f(x) =4/5(4/5 )^x
check the attached file for proof
Find the number of permutations of the first 8 letters of the alphabet taking 4 letters at a time.
Answers
8P4
using the calculator this will give us:
8P4=1,680
This tells us that there are more than 1,680 different ways that the leteers will be selected.
Special air bags are used to protect scientific equipment when a rover lands on the surface of Mars. On Earth, the function approximates an object's downward speed in feet per second as the object hits the ground after bouncing x ft in height. The corresponding function for Mars is compressed vertically by a factor of about 2/3. Estimate to the nearest tenth how fast a rover will hit Mars' surface after a bounce of 15 ft in height.
A) 20.7 ft/s
B) 25.3 ft/s
C) 7.3 ft/s
D) 46.5 ft/s
Answers
The answer is
20.7 ft/s
Without the specific function that calculates the object's downward speed on Earth, it is not possible to estimate the impact speed on Mars even with knowing the vertical compression factor.
Explanation:Estimating Impact Speed on Mars
The question asks us to estimate how fast a rover would hit the surface of Mars after bouncing 15 ft in height, with the Mars function being compressed vertically by a factor of about 2/3 compared to the function used on Earth. Although the specific Earth function isn't provided, we can still proceed with a general understanding. To find this, we would normally use the Earth function for speed and multiply the result by 2/3 to adjust for Mars' weaker gravity. However, since we are only given the option to select an answer, no calculation can be performed without the Earth function. Therefore, it's not possible to provide a confident answer to this question.
Someone please answer this
Answers
Combine like terms
-10= 0
Check for equality
-10≠0
Because it is false, this means there is no solution.
Final answer: No solution
what is a transformation that proportionally reduces or enlarges a figure.
Answers
Answer: Dilation is a transformation that proportionally reduces or enlarges a figure.
Step-by-step explanation:
A dilation a transformation that changes the size of the shape by using scale factor in particular ways .It stretches or shrinks the actual figure. It produces similar figures.
Since the corresponding sides of similar figures are in proportion.
⇒ It proportionally reduces or enlarges a figure.
Hence, A dilation is a transformation that proportionally reduces or enlarges a figure.
Final answer:
A scale transformation or dilation is a linear transformation that proportionally enlarges or reduces a figure, maintaining the proportional size relationships within the figure.
Explanation:
A transformation that proportionally reduces or enlarges a figure is known as a scale transformation or dilation. In such a transformation, lines are transformed into lines, and parallel lines remain parallel, consistent with the requirement for a transformation to be linear. This is important because it maintains the proportionality of the figure, meaning the size relationship of the parts of a figure to each other and to the whole figure remains constant, even though the overall size changes. Dilation can be characterized by a scale factor, which dictates how much larger or smaller the figure will become. If the scale factor is greater than 1, the figure enlarges; if it is between 0 and 1, the figure reduces in size.
To make lemonade, you used one gallon of water, four quarts of lemon juice, and 32 ounces of honey. How much lemonade did you make?
Answers
We have 4 quarts of lemon and it is 1 gallon ( and we also have 1 gallon of water ). Also we have 32 ounces of honey, which is 1 quart more.
4 quart + 4 quart + 1 quart = 9 quarts = 2 gallons 1 quart
Answer:
There is 9 quarts or 2 gallons and 1 quart of lemonade.
Which statistical test would be most appropriate for examining the relationship between temperature and the number of ice cream cones sold?
Answers
The most appropriate statistical test for examining the relationship between temperature and the number of ice cream cones sold would be a correlation analysis, specifically a Pearson correlation coefficient.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Correlation coefficient test measures the strength and direction of the linear relationship between two continuous variables, which is suitable for examining the relationship between temperature and the number of ice cream cones sold.
Additionally, a scatterplot could be used to visually assess the relationship between the two variables before conducting the statistical test.
Hence, statistical test for examining the relationship between temperature and the number of ice cream cones sold would be a correlation analysis
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Zeus Industries bought a computer for $2011. It is expected to depreciate at a rate of 24% per year. What will the value of the computer be in 5 years?
Answers
Value after 1 year:
24/100*2011
=$482.64
2011-482.64
=$1528.36
or
76/100*2011
=$1528.26
Value after 2nd year:
76/100*1528.36
=$1,161.55
Value after 3rd year:
76/100*1,161.55
=$882.78
Value after 4th year:
76/100*882.78
=$670.91
Value after 5th year:
76/100*670.91
=$509.89
hence the value after five years will be: $509.90
The length of a rectangle is 6 feet more than twice the width. if the length is 24 feet, what is the width?
Answers
L = 24
24 = 2W + 6
24 - 6 = 2W
18 = 2W
18/2 = W
9 = W <=== width is 9 ft