Given a=10 and B=150° in Triangle ABC, determine the values of b for which A has
A) exactly one value
B) two possible values
C) no value
Answers
Answer:
A) b > 10
B) none
C) b ≤ 10
Step-by-step explanation:
For the purpose of this answer, we assume ABC is a triangle if and only if all angles and side lengths have measures greater than 0, and the sum of angles is exactly 180°.
The fact that B = 150° means A+C = 30°. That is, 0 < A < 30°. Taking the sine of A, we have ...
0 < sin(A) < 1/2
A, B)The Law of Sines tells us ...
sin(A)/a = sin(B)/b
sin(A) = a·sin(B)/b = 10·(1/2)/b = 5/b
Substituting this into the inequality for sin(A), we get ...
0 < 5/b < 1/2
0 < 10 < b . . . . . multiply by 2b (which is > 0)
In order to form a triangle, the value of b must be greater than 10. In that case, there will always be only one value for A:
A = arcsin(5/b) . . . . b > 10
__
C)For b = 10, the "triangle" is a straight line, a disallowed condition. That is A will have no allowed value.
For b < 10, A > 30°, which forces C < 0°. This is also a disallowed condition. So we can say ...
b ≤ 10, A has no allowed value
_____
The attached diagram shows triangle ABC. Point A can be anywhere on ray BA. As segment c gets longer, angle C increases from near 0 to near 30°. At the same time, angle A decreases from near 30° to near 0°. When b=10, c=0, and the figure is not a triangle. Nor is it a triangle for b < 10.
Related Questions
A circular plate has circumference 16.3 inches. What is the area of this plate? Use 3.14 for pi.
The area of this plate is about " blank" square inches
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest thousandth as needed.)
Plz answer will give brainiest to the person who answers this plz help!!!!!!!
Answers
Answer:
The area of this plate is about 21 in².
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTerms/Coefficients
Geometry
Circumference Formula: C = 2πr
r is radiusArea of a Circle Formula: A = πr²
r is radiusStep-by-step explanation:
Step 1: Define
Identify given.
C = 16.3 in
Step 2: Find Radius r
[Circumference Formula] Substitute in C:16.3 in = 2(3.14)r[Division Property of Equality] Divide 6.28 on both sides:
r = 2.596 in
Step 3: Find Area
[Area of a Circle Formula] Substitute in r:A = 3.14(2.596 in)²Evaluate:
A = 21.1611 in²Round:
A ≈ 21 in²
∴ we have found the area of the plate.
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Topic: Geometry
Find which term in the geometric sequence 1, 3, 9, 27, ... is the first to exceed 7,000.
hint (use a table)
Answers
Answer:
10th term
Step-by-step explanation:
3ⁿ⁻¹ > 7000
log₃ 7000 = 8.05
n - 1 > 8
n > 9
10th term
check: 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683
In which month was the peak, the largest deposit, made?
A January. B June. July. D August
Answers
Answer: It was made in B June
Step-by-step explanation: The following transactions occurred in June through August 2020. June 1 After much thought, Natalie sells a mixer to Curtis on credit, terms n/30, for $1,150 (cost of mixer $620). 30 Curtis calls Natalie. He is unable to pay the amount outstanding for another month, so he signs a one-month, 8.35% note receivable. July 31 Curtis calls
Answer:
C. July
Step-by-step explanation:
It's the tallest one in the plot.
I hope this helped. B)
what is the y intercept of f(x)=2x^2+8x+6
Answers
Answer:
6 is the y intercept
Step-by-step explanation:
What is the equivalent of 4 meters?
Answers
Mr. Lopez wrote the equation 32 g + 8 g minus 10 g = 150 on the board. Four students explained how to solve for g.
Alyssa: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then subtracted 30 from 150 to find the value of g, which is 120.”
Rahul: “I added 32, 8, and 10 to get 50, and then I subtracted 150 to find the value of g, which is –100.”
Toni: “I subtracted 18 from 32 to get 14, which I then divided into 150 to find the value of g, which is 10 and StartFraction 5 Over 7 EndFraction.”
Wilhem: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then divided both sides by 30 to find the value of g, which is 5.”
Which student’s work is correct?
Alyssa
Rahul
Toni
Wilhem
Answers
Answer:
Option D.
Step-by-step explanation:
The given equation is
[tex]32g+8g-10g=150[/tex]
It can be written as
[tex](32+8-10)g=150[/tex]
To solve this equation, add 32 and 8.
[tex](40-10)g=150[/tex]
Subtract 10 from 40.
[tex]30g=150[/tex]
Divide both sides by 30.
[tex]\dfrac{30g}{30}=\dfrac{150}{30}[/tex]
[tex]g=5[/tex]
The value of g is 5 and wilhem is correct.
Therefore, the correct option is D.
Answer:
The correct answer is d. wilhem
(will give brainlesit if correct )
The map shows the location of the airport and a warehouse in a city. Though not displayed on the map, there is also a factory 96 miles due north of the warehouse.
A truck traveled from the warehouse to the airport and then to the factory. What is the total number of miles the truck traveled?
156
192
216
252
Answers
Answer:
its 176, the warehouse is 88 miles from the airport and the factory
Step-by-step explanation:
a rectangle field has an anrea of 40cm^2. if one side of the field is 3m longer than the other side, find the new area of the field where the length of each side is increased by 10%
Answers
The area of the field where the length of each side is increased by 10% is 48.4 [tex]cm^{2}[/tex].
Step-by-step explanation:
The given is,
A rectangle field has an area of 40 [tex]cm^{2}[/tex]
If one side of the field is 3 cm longer than the other side
The length of new area in each side is increased by 10%
Step:1
Let,
[tex]b[/tex] - One side of rectangle
[tex]l[/tex] - Other side of rectangle
From given.
[tex]l[/tex] - [tex]b[/tex] +3
Formula for area of rectangle,
[tex]Area, a = lb[/tex]
40 = ( b+3) × b
40 = [tex]b^{2}[/tex] + 3b
Solving the above the equation,
b = 5 cm
l = 8 cm
Step:2
If the area of rectangle increased by 10%,
l = 8 + ( 8 × [tex]\frac{10}{100}[/tex] )
= 8.8
b = 5 + ( 5 × [tex]\frac{10}{100}[/tex] )
= 5.5
Area of rectangle is,
a = ( 8.8 × 5.5 )
= 48.4 square centimeters
Result:
The area of the field where the length of each side is increased by 10% is 48.4 [tex]cm^{2}[/tex], if a rectangle field has an area of 40 square centimeters and one side of the field is 3 cm longer than the other side.
You have a package of 20 assorted thank-you cards. You pick the four cards shown. How many of the 20 cards would you expect to have flowers on them?
what is shows in the picture:
2 with thank you's then one with flowers that says thank you than on with a dragon fly that says thank you for you kindness
this is the question: You would expect ___cards to have flowers on them.
Answers
Out of 20 there are 5 cards which have flowers on them.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have total 20 thank-you cards.
Now, we choose four cards.
Out of 4 cards 2 with thank you then one with flowers that says thank you than on with a dragon fly
So, We choose pair of 4 cards 5 times.
Then, we get total cards with flower
= 1 x 5
= 5
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HELPPPppp MEEEEEEeeee
Answers
’ he should also have applied the exponent -3 to 4...’
What is the slope if the line graphed below? Type answer as fraction. Rise divided by run or whole number if can be reduce.
Answers
Answer:
3/5
Step-by-step explanation:
3 up and 5 over from point to point
Answer:
3/5
Rise=3
Run=5
Step-by-step explanation:
For this question it makes it easy because they have provided you with Lines labeled Rise and Run. All you need to do now is Count the rise and run.
For Rise over run if you go up as a rise it's a positive number...But if you go down its a Negative number same with Run.... If it runs to the right its positive and if it runs to the left its negative.
For Rise it goes up...1,2,3 Spaces so Rise is 3
For run it moves to the Right 1,2,3,4,5 spaces so Run is 5
3/5 cant be reduce so it stays as a fraction.
q= r/2 (s +t) for t.
Answers
Answer:
t=2Q-sr/r
Step-by-step explanation:
We are to make t the subject of formula from the given question
Q=r/2 (s+t)
Q=Sr+tr/2
Cross multiply
2Q=Sr+tr
2Q-sr=tr
t=2Q-sr/r
Given that the measure of ∠x is 60°, and the measure of ∠y is 110°, find the measure of ∠z.
Answers
Answer:
∠z = 10°Step-by-step explanation:
A triangle is always 180 degrees.
If ∠x is 60°
and ∠y is 110°,
110 + 60 = 170
∠z = 10 degrees
Answer:
50
Step-by-step explanation:
Which expression represents 22 more than the difference between 95 and 63
A. (22+95)
B. 22+(95+63)
C. (95-63)+22
Answers
Answer:
C
Step-by-step explanation:
Difference: 95 - 63
22 more: (95 - 63) + 22
Answer:
C. (95-63)+22
Step-by-step explanation:
difference means subtraction
95-63
more than means add after
(95-63) +22
A pack of 4 chocolate bars costs £1.20
What is the price per unit?
Answers
Answer:
30 cents
Step-by-step explanation:
Since 4 bars cost 1.20 pounds, divide 1.20 by 4
f(x)=-x^2-9x-4 find f(10)
Answers
The value of the given expression f(x)=-x² - 9x - 4 is -194.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given expression f(x)=-x² - 9x - 4 will be solved as below:-
f(x)= -x² - 9x - 4
f(x)= -( 10 )² - 9x(10) - 4
f(x) = -100 - 90 - 4
f(x) = -194
Therefore, the value of the given expression f(x)=-x² - 9x - 4 is -194.
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Avery received $80 in cash for mowing lawns. She did the following with the $80. Put 20% of the $80 into a bank account. Spent 1/4 of the $80. Kept the rest of the $80 in cash. How much of the $80 did Avery keep as cash?
Answers
Answer:
$48
Step-by-step explanation:
To start off, we know that Avery put 20% of the $80 in her bank account. We can figure out how much 20% of 80 is by multiplying 80 by 20% and then subtracting that number from 80. Remember to switch 20% to its decimal form (20% -> .2).
Step 1) 80 x .2 = 16
Step 2) 80 - 16 = 64
Next, we have to figure out how much 1/4 of the remaining $64 would be. We just simply divide 64 by 4 to figure out how much Avery spent.
Step 3) 64 / 4 = 16
Lastly, since we know Avery spent 16 dollars, we can subtract the 16 from 64 to get our final answer.
Step 4) 64 - 16 = 48
Avery kept $44 of the $80 as cash after putting 20% into a bank account and spending 1/4 of it.
Avery received $80 in cash for mowing lawns. Let's calculate how much she kept after her transactions. First, she put 20% of the $80 into her bank account. Calculating 20% of $80 involves multiplying $80 by 0.20, resulting in $16. Next, Avery spent 1/4 of the $80, which equals $20, as $80 divided by 4 gives $20. To find the amount Avery kept as cash, we subtract the amounts she put in her bank and spent from the original $80.
$80 - $16 - $20 = $44
Therefore, Avery kept $44 of the $80 as cash.
How to write 0.985 in expanded form in decimals
Answers
The expanded form of 0.985 is 0.9 + 0.08 + 0.005.
What is decimal?Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.
Example: 1.2 is the decimal number, where 1 is the whole part and 0.2 is the fractional part.
Given:
The decimal number 0.985.
To find the expanded form of 0.985:
First, convert the number to fractional form.
0.985 = 985/1000
= 900/1000 + 80/1000 + 5/1000
= 0.9 + 0.08 + 0.005
0.985 = 0.9 + 0.08 + 0.005
Therefore, 0.9 + 0.08 + 0.005 is the expanded form of 0.985.
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Can you get this question answered please
Answers
You times all the denominators of the fractions to reach one common multiple
Debra plans to invest $2,250 for 10 years. She can invest in a savings account that pays 4% simple intrest or a savings account that pays 4% intrest compounded annually. How much more money will she have at the end of 10 years if she chooses the account with compound interest?
Answers
Answer:
[tex]\$180.55[/tex]
Step-by-step explanation:
step 1
Simple interest
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=10\ years\\ P=\$2,250\\r=4\%=4/100=0.04[/tex]
substitute in the formula above
[tex]A=2,250(1+0.04*10)[/tex]
[tex]A=2,250(1.4)[/tex]
[tex]A=\$3,150[/tex]
step 2
Interest compounded annually
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ P=\$2,250\\r=4\%=4/100=0.04\\n=1[/tex]
substitute in the formula above
[tex]A=2,250(1+\frac{0.04}{1})^{1*10}[/tex]
[tex]A=2,250(1.04)^{10}[/tex]
[tex]A=\$3,330.55[/tex]
step 3
Find the differences between the two final amounts
[tex]A=\$3,330.55-\$3,150=\$180.55[/tex]
11. Find the next 4 numbers in the pattern. 21, 24, 19, 22, 17, 20,
Answers
Answer:
The answer is 23???....?
Answer:
16,19,15,18
Step-by-step explanation:
rule=+3,-4
5. A 200 pound person weighs 33 pounds on the moon.
a. How much did the person's weight decrease?
Answers
Answer:
Step-by-step explanation:
The answer will be 167
Final answer:
The weight of a 200-pound person decreases by 167 pounds on the moon due to the weaker gravitational force. Weight varies with gravity, but mass remains constant.
Explanation:
If a 200-pound person weighs 33 pounds on the moon, the person's weight has decreased by 167 pounds. The weight decrease can be calculated by subtracting the weight on the moon from the original weight on Earth.
Weight decrease = Original weight on Earth - Weight on moon
Weight decrease = 200 pounds - 33 pounds
Weight decrease = 167 pounds
This calculation shows how weight varies with the acceleration due to gravity, which is weaker on the moon. Therefore, the gravitational force acting on a person on the moon is less, resulting in a lower weight, although the person's mass remains constant.
Pharrell wants to write equations in the form y = mx + b for the lines passing through point P that are parallel and perpendicular to line w. First he finds the slope of line w and line v to be 1/2 and the slope of line n to be -2. Point P is located at (-4, 2). Which step could he use to find the y-intercepts?
A. Multiply the slope, -2, by the x-coordinate, -4, and add the y-coordinate, 2, to the product.
B. Substitute the slope, -2, and the coordinates of point P (-4, 2) in y = mx + b and then solve for b. Repeat using the slope 1/2 for the second equation.
C. Multiply the slope, -2, by the y-coordinate, 2, and subtract the result from the x-coordinate, -4. Repeat for the slope 1/2 for the second equation.
D. Solve the proportion m/b = y/x for b, where m = -2, y = 2, and x = -4. Then solve the proportion m/b = y/x for b, where m = 1/2, y = 2, and x = -4.
Answers
Answer:
B. Substitute the slope, -2, and the coordinates of point P (-4, 2) in y = mx + b and then solve for b. Repeat using the slope 1/2 for the second equation.
Step-by-step explanation:
The graph shows a linear relationship between the
height and years of a plant's growth. Find the rate of
change. Select all that apply.
The rate of change of a linear function is always the
same.
Height (in)
The rate of change of a linear function increases as
the input increases.
The rate of change from 2 years to 4 years on the
graph is 1.5 inches per year.
L! The rate of change from 0 years to 6 years on the
graph is 1.5 inches per year.
8
Time (yrs)
Answers
Answer:
a, c, d
Step-by-step explanation:
Answer:
The rate of change from 2 years to 4 years on the graph is 1.5 inches per year & The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.
Step-by-step explanation:
Ella deposited $2500 into a savings account. The relationship between the time, t, in years, since the account was first opened, and Ella's account balance, B(t), in dollars, is modeled by the following function.
B(t)=2500⋅e^0.025t
What will the balance of Ella's savings account be after 4 years?
Answers
Answer:
She will have $2762.927
Step-by-step explanation:
The modeled function is
B(t) = 2500*e^0.025t
Where t represent the time in years. In four years, her account would be
B(t) = 2500 * e^0.025(4)
B(t) = 2500 * e^0.1
B(t) = 2762.927
In four years, Ella would have $2762.927 in her account
Answer:
2762.927
Step-by-step explanation:
Zak is going to buy some bookcases and some lamps to sell in his shop. Each bookcase costs £16 Each lamp costs £12 Zak has a maximum of £360 to spend. He is going to buy x bookcases. He is going to buy y lamps. Show that 4 x + 3 y ≤ A where A is a constant to be found
Answers
Answer:
He can buy 8 bookcases and 6 lamps
Step-by-step explanation:
4(16) + 3(12)
64 + 36 = 100
360- 100 = 260
260-100=60
4*2=8 3*2=6
Hi, What is 678 divided by -4 times 56xs then added 7h.
Answers
Answer:-9492xs+7h
Step-by-step explanation:if you do 678 divided by -4 it would be -169.5 then multiply that by 56 witch would be -9492 then times s would be -9492xs then that added to 7h would be -9492xs+7h and your final answer
The length of a rectangle is four times the width. The
perimeter of the rectangle is 40 inches. What is the area of
the rectangle (in square inches)?
Answers
Answer:
Step-by-step explanation:
let the width=x
length=4x
P=2(l+w)=2(4x+x)=10x
10x=40
x=40/10=4
width=4 in
length=4×4=16 in
area=16×4=64 square inches.
The required area of the given rectangle is given as 64 inch².
What is a rectangle?The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.
Here,
As mentioned in the question,
The length of a rectangle is four times the width.
l = 4w
Now,
The perimeter of the rectangle is 40 inches.
2 [l + w] = 40
2 [4w + w] = 40
5w = 20
w = 4 inches
Length,
l = 4(4) = 16 inches
Area of rectangle = l × w
= 16 × 4 = 64 inch²
Thus, the required area of the given rectangle is given as 64 inch².
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At a New Car Dealership a particular model comes in 4 trims levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?
Answers
Answer:
60 different versions
Step-by-step explanation:
4 times 5 times 3 is 60.
The number of different versions of this car model that can be created from these options is 60.
Number of different versions:Using this formula
Number of different versions=Trims levels×Different colors×Different Interior
Where:
Trims levels=4
Different colors=5
Different Interior=3
Let plug in the formula
Number of different versions=4×5×3
Number of different versions=60
Inconclusion the number of different versions of this car model that can be created from these options is 60.
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A discount clothing store is selling a $99 sport jacket for $11 off the regular price. What is the discount rate?
Answers
Answer:
jacket is $99 at a discount of $11 off regular price
add the discount back on to get regular price which is $99+$11=$110
$110x.10=$11
therefore the jacket is sold at a 10% discount
Step-by-step explanation: