The value of b is 5.4
Explanation:
Given that ABC is a triangle.
It is also given that [tex]a=12[/tex] , [tex]\angle B=25^{\circ}[/tex] and [tex]\angle C=45^{\circ[/tex]
We need to find the value of b.
The value of b can be determined using the law of sine formula, which is given by
[tex]\frac{a}{sin A} =\frac{b}{sin B} =\frac{c}{sin C}[/tex]
First, we shall find the angle of A.
Since, ABC is a triangle and all the angles in a triangle add up to 180°
Thus, we have,
[tex]\angle A+\angle B+\angle C=180[/tex]
[tex]\angle A+25+45=180[/tex]
[tex]\angle A+70=180[/tex]
[tex]\angle A=110^{\circ}[/tex]
Thus, the value of angle A is 110°
Let us substitute these values in the law of sine formula.
Hence, we get,
[tex]\frac{12}{sin \ 110^{\circ}} =\frac{b}{sin \ 25^{\circ}}[/tex]
Simplifying, we get,
[tex]\frac{12}{0.9397} =\frac{b}{0.423}[/tex]
Multiplying both sides of the equation by 0.423, we get,
[tex]\frac{12\times 0.423}{0.9397} =b[/tex]
Simplifying, we get,
[tex]\frac{0.5076}{0.9397} =b[/tex]
Dividing, we have,
[tex]5.4=b[/tex]
Thus, the value of b is 5.4
How many solutions does the system of equations have?
The system has infinitely many solutions.
The system has no solution.
The system has exactly one solution.
Answer:
This system has infinitely many solutions because they right on top of each other.
If the lines were perpendicular, then there would be exactly one solution.
If the lines were parallel, there would be no solutions.
Multiply.
38⋅45
Express your answer in simplest form.
A. 3/10
B. 7/40
C. 7/13
D. 12/13
Find the sum of a 10-term geometric sequence when the first term is 3 and the last term is 59049
A. 177147
B. 88572
C. 88575
D. 177144
Find the height of the lamppost to the nearest inch.
Collection: Private
DRAG DROP VALUES
109 in.
108 in.
110 in.
107 in.
Height of the lamppost =
Solution:
We have to find the height of lamppost
From the figure in question,
Given is a right angled triangle
Where,
base = 40 inches
height = ?
By definition of tan,
[tex]tan\ 70 = \frac{opposite}{base}\\\\tan\ 70 = \frac{height}{40}\\\\height = tan\ 70 \times 40\\\\height = 2.7474 \times 40\\\\height = 109.89 \approx 110[/tex]
Thus height of lamp post to nearest inch is 110 inches
: The You Move It Company (YMI) advertises that the cost to rent a moving truck for one day is $40 plus $1.99 for each mile the truck is driven. The Drive and Move Company (DM) advertises that the cost to rent a moving truck for one day is $60 plus $1.79 for each mile the truck is driven. Alex wants to rent a single truck to use on both Saturday and Sunday on a weekend. Part A For what driving distance does it not matter from which company Alex rents the truck? miles. If Alex only plans of driving 150 miles over the weekend, which company should he use? Part B Give a mathematical explanation as to how you arrived at your answer.
Part A: For 100 miles, the cost will be same for both companies.
Part B: Alex should use Drive and Move company as it will cost him less money.
Step-by-step explanation:
Given,
Starting amount of YMI= $40
Per mile charges = $1.99
Let,
x be the number of miles.
y be the total charges.
y = 1.99x+40 Eqn 1
Starting amount of DM = $60
Per mile charges = $1.79
y=1.79x+60 Eqn 2
Part A:
For same charges;
Eqn 1 = Eqn 2
[tex]1.99x+40=1.79x+60\\1.99x-1.79x=60-40\\0.20x=20[/tex]
Dividing both sides by 0.20
[tex]\frac{0.20x}{0.20}=\frac{20}{0.20}\\x=100[/tex]
For 100 miles, the cost will be same for both companies.
Part B:
Total miles = x = 150
Putting x=150 in Eqn 1
y=1.99(150)+40
y=298.5+40
y=$338.50
Putting x=150 in Eqn 2
y=1.79(150)+60
y=268.5+60
y=$328.50
Alex should use Drive and Move company as it will cost him less money.
∠A and \angle B∠B are supplementary angles. If m\angle A=(3x-17)^{\circ}∠A=(3x−17)
∘
and m\angle B=(2x-23)^{\circ}∠B=(2x−23)
∘
, then find the measure of \angle B∠B.
The measure of angle B is 65°
Explanation:
Given that ∠A and ∠B are supplementary angles.
The measures are ∠A = (3x - 17)° and ∠B = (2x-23)°
The value of x:
Since, supplementary angles add up to 180°, then we have,
[tex]\angle A+ \angle B=180^{\circ}[/tex]
Substituting the values, we have,
[tex]3x-17+2x-23=180[/tex]
[tex]5x-40=180[/tex]
[tex]5x=220[/tex]
[tex]x=44[/tex]
Thus, the value of x is 44
Measure of angle B:
Let us determine the measure of angle B by substituting the value of x in ∠B = (2x-23)°
Thus, we have,
[tex]\angle B=(2(44)-23)^{\circ}[/tex]
[tex]\angle B=(88-23)^{\circ}[/tex]
[tex]\angle B=65^{\circ}[/tex]
Thus, the measure of angle B is 65°
A company plans to ship 2,000 packages of chocolate. The company randomly selects 100 packages and finds that five packages have an incorrect weight.
Based on this data, how many packages out of the 2,000 should be predicted to have an incorrect weight?
Answer:
100
Step-by-step explanation:
1. 100 divided by 5 = 20
2. 20 x 100 = 2000
3. Final Answer = 100
A company plans to ship 2,000 packages of chocolate, the number of packages is X=100. This is further explained below.
How many packages out of the 2,000 should be predicted to have an incorrect weight?Generally, the number of packages is given as
X=(No Packages* incorrect weight)/ random selections
Therefore
X=2000*5/100
X=100
In conclusion, the number of packages predicted to have an incorrect weight is
X=100
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What number does x stand for 18*x=54
A. 3
B.1
C. 91
D. 85
Answer:
3
Step-by-step explanation:
18*x=54 (divide both sides by 18)
x = 54 ÷ 18
x = 3
Hello!
The answer to your problem is A) 3
Move all terms to the left
[tex]18x-(54)=0[/tex]
Move all terms containing x to the left, all other terms to the right
[tex]18x=54[/tex]
[tex]x=54/18[/tex]
Get your answer
[tex]x=3[/tex]
Hope This Helps!
Does anyone have any useful tips for the ACT? They would be much appreciated!
great someone deleted all my answers again
Rodrigo added 2/3 and 4/9 using these steps. What is the sum in simplest terms?
1. Check for common denominators.
2/3 and 4/9
2. Write the sum 2/9 + 4/9
3.
Add the numerators. 2+4/9 = 6/9
There was a minor mistake in the second step. The sum should be 2/3 + 4/9, not 2/9 + 4/9. After finding the common denominator and converting the fractions, we add the numerators to get 10/9, which simplifies to 1 1/9.
Explanation:The process Rodrigo followed is correct, but there was a small mistake in the second step. Here, the problem should be 2/3 + 4/9, not 2/9 + 4/9. To add fractions like this, it's critical to ensure they have common denominators. The lowest common denominator (LCD) of 3 and 9 is 9.
So, the fraction 2/3 should be converted to its equivalent fraction with 9 as the denominator. Multiplying both the numerator and the denominator of 2/3 by 3, we get 6/9. So now our problem becomes 6/9 + 4/9.
Now, we can add them by combining their numerators: 6+4 = 10. So, the answer would be 10/9. But in simplest form, we would write this as 1 1/9. Hence, the sum of 2/3 and 4/9 in simplest terms is 1 1/9.
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On a sunny day around noon , a tree casts a shadow that is 12 feet long . At the same time , a person who is 6 feet tall standing beside the tree casts a shadow that is 2 feet long . How tall is the tree?
Answer:
36 ft. tall
Step-by-step explanation:
We can easily solve this problem with a simple proportion:
12 feet / height = 2 feet / 6 feet
6 * 12 = 2h
72 = 2h
h = 36 ft.
It's found that the tree is 36 feet tall.
To find the height of the tree using the lengths of the shadows and the person's height, we can use a proportion based on similar triangles. Since the sun's rays hit both the tree and the person at the same angle, the ratio of the height of the tree to the length of its shadow is the same as the ratio of the person's height to the length of their shadow.
Let's let 'h' represent the height of the tree. We can set up the proportion as follows:
Person's height / Person's shadow length = Tree's height / Tree's shadow length
6 feet / 2 feet = h / 12 feet
Now we solve for 'h' by cross-multiplying:
6 feet * 12 feet = 2 feet * h
72 feet2 = 2 feet * h
Divide both sides by 2 feet to get:
h = 36 feet
Therefore, the tree is 36 feet tall.
You buy a car for $8000 that depreciates (loses value) at a rate of 11% a year. How much is the care
worth after 5 years?
Answer:
$3600
Step-by-step explanation:
Cost of the car = $8000
The car loses value at 11% each year .
That’s
11% /100% x $8000
0.11 x 8000
$880
11% decrease each year means that the cost of the car is reduced by $880 per year.
Therefore,
Worth of the car in 5 years
= $8000 - ($880 x 5)
= $8000 - $4400
= $3600
The car will be worth $3600 in five years
Grace earns $7 for each car she washes. She always saves $22 of her weekly earnings. This week, she wants to have at least $63 in spending money. How many cars must she wash? Enter and solve an inequality to represent this situation. Enter your value as a simplified mixed number, if necessary.
Answer:
12 1/7 cars
Step-by-step explanation:
Let the number of cars she'd wash to earn $63 in spending money be A.
Given she saves $22 of her weekly earnings and wants to have at least $63 for spending money.
That means she’d have to make $63 + $22 = $85
The expression is thus
$85 = A x $7
Where A is the number of cars and $7 is the amount she earns for washing one car and $85 is the total amount she has to make .
Therefore,
85 = A x 7
Divide both sides by 7
85/7 = A x 7/7
12 1/7 = A
A = 12 1/7 cars
She must wash 12 1/7 cars to have at least $63 spending money and also have her weekly Savings of $22
What is the equation for 15+d>10
Answer:
d > -5
Step-by-step explanation:
Step 1: Subtract 15 from both sides
15 + d > 10
15 + d - 15 > 10 - 15
d > -5
Answer: d > -5
What is the mean of: 9.6, 2, 4.1, 8, 5.9, 2, 3.7, 6, 7.6?
Answer:
5.43333 recurring
Step-by-step explanation:
Mean is the average of a set of numbers. That is, the sum of the digits in the set, divided by the number of the digits.
In the question above, we have 9 digits. So we find the sum of the digits divided by 9.
(9.6+2+4.1+8+5.9+2+3.7+6+7.6)/9
48.9/9
5.4333recurring
Jim worked for three different employers. They each paid him $15 000. How much income tax should he have paid?
Jim's income tax liability for the $45,000 he earned from his three employers would be $9,500.
To calculate Jim's income tax, we first need to find his total income. Since he worked for three different employers, his total income would be the sum of his earnings from each employer, which is $15,000 * 3 = $45,000.
Next, we need to know the tax rates that apply to Jim's income. Income tax rates are usually progressive, meaning different portions of income are taxed at different rates.
Using the hypothetical tax rates mentioned above, we can calculate Jim's income tax liability:
First $10,000 at 10%: $10,000 * 0.10 = $1,000
Next $20,000 at 20%: $20,000 * 0.20 = $4,000
Remaining $15,000 at 30%: $15,000 * 0.30 = $4,500
Now, summing up the tax amounts from each tax bracket: $1,000 + $4,000 + $4,500 = $9,500.
Therefore, Jim's income tax liability should have been $9,500.
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Final answer:
Jim earned a total of $45,000 from three employers. Using a simplified marginal tax rate example, his total income tax comes to approximately $7,106.25. This calculation method demonstrates how the marginal tax rate system works in a basic form.
Explanation:
To determine how much income tax Jim should have paid on his earnings from three different employers, where each paid him $15,000, we first need to calculate his total income. Jim's total income is $15,000 from each job, multiplied by 3, because he worked for three different employers, resulting in a total income of $45,000.
Assuming a simple tax rate example (for illustrative purposes), let's use the marginal tax rates provided in the reference:
Income from $0 to $9,075 is taxed at 10%
Income from $9,075 to $36,900 is taxed at 15%
Income from $36,900 and beyond is taxed at 25%
Since Jim earns $45,000, here is how his taxes would be calculated:
The first $9,075 is taxed at 10%, amounting to $907.50.
The next $27,825 ($36,900 - $9,075) is taxed at 15%, amounting to $4,173.75
The remaining $8,100 ($45,000 - $36,900) is taxed at 25%, amounting to $2,025.
Add up these amounts to get the total tax:
$907.50 + $4,173.75 + $2,025 = $7,106.25
Therefore, applying this simplified tax calculation, Jim should have paid a total of roughly $7,106.25 in income tax on his total earnings of $45,000 from three different employers.
If two fractions are between 0 and 1 can their sum be more than 1 ? Explain your thought process.
Answer:
YES
Step-by-step explanation:
If both the fractions are greater than .5, then yes.
Ex. 3/4 and 4/5
Yes if two fractions are between 0 and 1 can their sum be more than 1. Examples are 3 / 4 and 4 / 5.
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.
Given that:-
If two fractions are between 0 and 1 can their sum be more than 1If both the fractions are greater than .5, then yes. examples are 3/4 and 4/5.
Sum = 3 / 4 + 4 / 5
Sum = 31 / 20
We can see that the sum is greater than one.
Therefore if two fractions are between 0 and 1 can their sum be more than 1. Examples are 3 / 4 and 4 / 5.
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What is 9 to the power of zero simplified
2x−5 = 3 (1−x)+22?
is x=6?
Answer:
x=6
Step-by-step explanation:
You are correct. x does equal 6
Answer:
Yes
x = 6
Step-by-step explanation:
Given
2x - 5 = 3(1 - x) + 22
First distribute 3 into (1 - x)
We have
2x - 5 = 3 x 1 -3 x X + 22
2x - 5 = 3 - 3x + 22
The expression can be rearranged as
2x - 5 = 3 + 22 - 3x
2x - 5 = 25 - 3x
Add 3x to both sides
3x + 2x - 5 = 25 - 3x + 3x
5x - 5 = 25
Add five to both sides
5x - 5 + 5 = 25 + 5
5x = 30
Divide both sides by 5
5x/5 = 30/5
x = 6
Which equation, in point-slope form, passes through (-2, 4) and has a slope of 3?
a. y - 4= 3(x - 2)
b. y - 4= 3(x + 2)
c. y + 4 = 3(x - 2)
d. y + 4 = 3(x + 2)
Answer:
B
Step-by-step explanation:
The formula is Y-Y1= M(X-X1)
So y-4=3(x+2)
Addyson's goal is to spend less than $415 on a trip. So far, she has spent $25 on gas for her car. She will spend $100 each day on other expenses. Addyson's trip must last fewer than how many days?
Answer:
4 days
Step-by-step explanation:
$25 on gas
$415-$25=$390 she still can spend $390
390/100=3.9 days
that means she can go for 3.9 days
so she must go for less than 4 days
If point E is translated 2 units right and 4 units up, what are the coordinates of E'?
Answer:
6
Step-by-step explanation:
Answer:
Answer is (2,6) B.
Step-by-step explanation:
Help me with this pls!!! You need to fill in the blanks with the words given above 99 Points!
A simulation is a mathematical model used to represent a situation.
A simulation can be a program or a physical test to "simulate" a situation to predict the outcomes.When we combine two or more simple events we have a compound event
"Compound" means to combine, like a compound word would be a combination of two wordsA Tree Diagram is a diagram that shows all the possible outcomes of an event
In a tree diagram, each possible outcome "branches" off the main stem, making the final diagram look like a tree with many separating branches.All the possible outcomes or results is called the sample space
The outcomes are each different samples, and a sample space is a space that collects each of these samplesWhen an event is not affected by a previous outcome we have an independent event
This event is "independent", not affected by other factors, making it an independent eventLet me know if you need any clarifications, thanks!
~ Padoru
The midpoint of segment AB is (4, 2). The coordinates of point A are (2, 7). Find the coordinates of point B.
A) (5, 3)
B) (6, -3)
C) (2, -5)
D) (6, -5)
Answer:
The option B) is correctTherefore the coordinate of B[tex](x_2,y_2)[/tex] is (6,-3)Step-by-step explanation:
Given that the midpoint of segment AB is (4, 2). The coordinates of point A is (2, 7).
To Find the coordinates of point B:Let the coordinate of A be [tex](x_1,y_1)[/tex] is (2,7) respectivelyLet the coordinate of B be [tex](x_2,y_2)[/tex]And Let M(x,y) be the mid point of line segment AB is (4,2) respectivelyThe mid-point formula is [tex]M(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Now substitute the coordinates int he above formula we get[tex](4,2)=(\frac{2+x_2}{2},\frac{7+y_2}{2})[/tex]Now equating we get[tex]4=\frac{2+x_2}{2}[/tex] [tex]2=\frac{7+y_2}{2}[/tex]
Multiply by 2 we get Multiply by 2 we get
[tex]4(2)=2+x_2[/tex] [tex]2(2)=7+y_2[/tex]
[tex]8=2+x_2[/tex] [tex]4=7+y_2[/tex]
Subtracting 2 on both
the sides Subtracting 7 on both the sides
[tex]8-2=2+x_2-2[/tex] [tex]4-7=7+y_2-7[/tex]
[tex]6=x_2[/tex] [tex]-3=y_2[/tex]
Rewritting the above equation Rewritting the equation
[tex]x_2=6[/tex] [tex]y_2=-3[/tex]
Therefore the coordinate of B[tex](x_2,y_2)[/tex] is (6,-3)Therefore the option B) is correct.there are 6 girls in a music class. this represents 3/7 of the entire class. solve 3/7s=6 to find the number of students,s, in the class.
The number of students in the class is [tex]s=14[/tex]
Explanation:
It is given that there are 6 girls in a music class.
This represents [tex]\frac{3}{7}[/tex] of the entire class.
To determine the number of students in the class, we need to solve the equation [tex]\frac{3}{7}s=6[/tex]
Let us solve the expression for s.
Multiplying both sides of the equation by [tex]\frac{7}{3}[/tex], we have,
[tex](\frac{7}{3} )\frac{3}{7}s=6(\frac{7}{3} )[/tex]
Simplifying the expression, we have,
[tex]s=\frac{42}{3}[/tex]
Dividing by 3, we have,
[tex]s=14[/tex]
Thus, the number of students in the class are 14.
Convert: 100 kilograms to pounds.
22.05
220.5
O 2205
22,050
Answer:
220.5
Step-by-step explanation:
:3
Answer:
220.5 lb
Step-by-step explanation:
1 kg = 2.20462262185 lb
100 kg = 100×2.20462262185 lb
100 kg = 220.462 lb
100 kg = 220.5 lb
Kyle is traveling to Destin over spring break. The total drive is 617 miles. If he travels at a speed of 70 miles per hour, which of the
following functions represents the number of remaining miles, M(x), he has to travel to reach his destination after x hours?
A. M(x)=70-617x
B. M(x)=547x
C. M(x)=617-70x
D. M(x)=70x
Answer:
D)M(x)=70x
Step-by-step explanation:
The function that represents the remaining distance after x hours is M(x) = 617 - 70x (option C).
The question asks about the function that represents the number of remaining miles, M(x), Kyle has to travel after x hours at a speed of 70 miles per hour. To calculate the remaining distance, we subtract the distance traveled (70 miles per hour times x hours) from the total distance of the trip, which is 617 miles. Therefore, the correct function is M(x) = 617 - 70x, which corresponds to option C.
To further illustrate this with an example, if Kyle drives for 1 hour at 70 miles per hour, he would have traveled 70 miles, so the remaining distance would be M(1) = 617 - 70(1) = 547 miles.
What is
3x-y=9
2x-y=7
Answer:
x=2 and y= -3
Step-by-step explanation:
This is a simultaneous equation. To solve this type of equation, there are three methods; substitution, Elimination and Graphical.
But here, we would be using the substitution method.
3x-y=9 Equation 1
2x-y=7. Equation 2
Getting y from equation 2, we have
-y= 7-2x
Multiply both sides by -
y= 2x-7 Equation 3
Substituting y for 2x-7 in equation 1, we have
3x- (2x-7)=9
3x-2x+7=9
x+7=9
x=9-7
x=2
Substituting x as 2 in equation 3
y=2x-7
y= 2(2)-7
y= 4-7
y= -3
Find the equation of the line that is perpendicular to y = – 1 4 x – 8 and passes though the point (2, –4).
The equation of the line is [tex]y=\frac{1}{4}x-\frac{29}{7}[/tex]
Explanation:
The equation of the line is perpendicular to [tex]y=-14 x-8[/tex]
The equation is of the form [tex]y=mx+b[/tex] where m=-14
Slope:
The slope of the perpendicular line can be determined using the formula,
[tex]m_1 \cdot m_2=-1[/tex]
[tex]-14 \cdot m_2=-1[/tex]
[tex]m_2=\frac{1}{14}[/tex]
Thus, the slope of the line is [tex]m=\frac{1}{14}[/tex]
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Substituting the slope [tex]m=\frac{1}{14}[/tex] and the point (2,-4), we get,
[tex]y+4=\frac{1}{14}(x-2)[/tex]
Simplifying, we get,
[tex]y+4=\frac{1}{14}x-\frac{1}{7}[/tex]
[tex]y=\frac{1}{14}x-\frac{1}{7}-4[/tex]
[tex]y=\frac{1}{4}x-\frac{29}{7}[/tex]
Thus, the equation of the line is [tex]y=\frac{1}{4}x-\frac{29}{7}[/tex]
8) At a carnival it costs $54.72 for 36 tickets. Write an equation that can be used to
express the relationship between the total cost (t) and the number of tickets(n) you
buy.