Answer:
[tex]y\approx 11.9[/tex]
Step-by-step explanation:
Here, we have the known angle sandwiched between two known sides.
So, we have SAS.
And we want to find the side opposite to the angle.
Therefore, we can use the Law of Cosines:
[tex]c^2=a^2+b^2-2ab\cos(C)\\[/tex]
Again, it is important what we substitute.
a and b are the two side lengths. So, we will substitute 8 for a and 13 for b.
C is our angle. So, substitute 64 for C.
And c is what we’re trying to solve.
Therefore:
[tex]c^2=(8)^2+(13)^2-2(8)(13)\cos(64)[/tex]
Simplify:
[tex]c^2=64+169-208\cos(64)[/tex]
Add:
[tex]c^2=233-208\cos(64)[/tex]
Take the square root of both sides:
[tex]c=\sqrt{233-\cos(64})[/tex]
Use a calculator. So, c is approximately:
[tex]c\approx11.9[/tex]
The c is our y. So, y is approximately 11.9 units.
Sales Tax
Selling Price Rate of Sales Tax Sales Tax
$60.00
4%
?
The sales tax is $
Answer: $2.40
Step-by-step explanation:
$60.00 x .04 = $2.40
Answer:
2.40
Step-by-step explanation:
4% of 60.00 is 2.40
Your turn
The perimeter of a triangular building is 450 feet. Find
the length of each side,
ILL MARK BRAINLIEST ANSWER HURYYYY PLEASEEE‼️‼️‼️‼️‼️
Answer:
450/3
Step-by-step explanation:
What is the slope of the line?
3(y - 1) = 2r + 2
Answer:
43
Step-by-step explanation:
because
Pauline invested $10,000 at two different
rates, 4% and 6%. If her total interest income
was $470, how much did she invest at each
rate?
Answer:
So for this, I will be doing a system of equations. Let x = money invested at 4% and y = money invested at 6%. We know that x and y will total up to 10k since that's how much he initially invested, so that'll be one of our equations.
Our other equation will represent the total balance he has after investing. We know that x's interest is 4% (since the money is increasing, this would translate to 1.04 in decimal form) and y's interest is 6% (aka 1.06 in decimal form since its increasing) and that the total balance is 10470 (initial balance + interest income).
Step-by-step explanation:
Using all this info, these are our two equations:
X+Y=10000
1.04x+1.06=10470
Next, substitute x in the second equation for (10000 - y) and solve for y as such:
1.04(10000-y) +1.06y =10470
10400 - 1.04y + 1.60y = 10470
10400 + 0.02y = 10470
0.02y =70
y = 3500
Now that we have the value of y, substitute it into either equation to solve for x:
x + 3500 = 10000
x= 6500
1.04x + 1.06(3500)= 10470
1.04x = 6500
Answer
In short:
$6,500 was invested in the 4% rate
$3,500 was invested in the 6% rate
53 students divided into groups of 6 students how many groups of students will there be?
Answer:
9
Step-by-step explanation:
53/6 = 8 R5
One of the groups will have only 5 students because you can only have whole students, not parts of a student.
Answer:
Step-by-step explanation:
53/6= 8 5/6
The first 6 groups will have 8 students with 5 students remaining. They can have 5 groups with 9 students and 1 with 8 students
which mortal kombat character is yalls favorite? Mine is kabal.
Answer:
omg! mine is Kabal tooo
Step-by-step explanation: i love mortal combat lol
Answer:
Scorpion
I am a normie yes I know
Leave me alone
Step-by-step explanation:
A computer programming team has 13 members. a. How many ways can a group of seven be chosen to work on a project? b. Suppose seven team members are women and six are men. (i) How many groups of seven can be chosen that contain four women and three men? (ii) How many groups of seven can be chosen that contain at least one man? (iii) How many groups of seven can be chosen that contain at most three women? c. Suppose two team members refuse to work together on projects. How many groups of seven can be chosen to work on a project? d. Suppose two team members insist on either working together or not at all on projects. How many groups of seven can be chosen to work on a project?
Answer:
1716 ;
700 ;
1715 ;
658 ;
1254 ;
792
Step-by-step explanation:
Given that :
Number of members (n) = 13
a. How many ways can a group of seven be chosen to work on a project?
13C7:
Recall :
nCr = n! ÷ (n-r)! r!
13C7 = 13! ÷ (13 - 7)!7!
= 13! ÷ 6! 7!
(13*12*11*10*9*8*7!) ÷ 7! (6*5*4*3*2*1)
1235520 / 720
= 1716
b. Suppose seven team members are women and six are men.
Men = 6 ; women = 7
(i) How many groups of seven can be chosen that contain four women and three men?
(7C4) * (6C3)
Using calculator :
7C4 = 35
6C3 = 20
(35 * 20) = 700
(ii) How many groups of seven can be chosen that contain at least one man?
13C7 - 7C7
7C7 = only women
13C7 = 1716
7C7 = 1
1716 - 1 = 1715
(iii) How many groups of seven can be chosen that contain at most three women?
(6C4 * 7C3) + (6C5 * 7C2) + (6C6 * 7C1)
Using calculator :
(15 * 35) + (6 * 21) + (1 * 7)
525 + 126 + 7
= 658
c. Suppose two team members refuse to work together on projects. How many groups of seven can be chosen to work on a project?
(First in second out) + (second in first out) + (both out)
13 - 2 = 11
11C6 + 11C6 + 11C7
Using calculator :
462 + 462 + 330
= 1254
d. Suppose two team members insist on either working together or not at all on projects. How many groups of seven can be chosen to work on a project?
Number of ways with both in the group = 11C5
Number of ways with both out of the group = 11C7
11C5 + 11C7
462 + 330
= 792
Solve. 2x - 1 = 7
A) x=2
B) x=3
C) x=4
D) x=5
Answer:
C
Step-by-step explanation:
2x - 1 = 7
2*4=8
8-1=7
Answer:
C
Step-by-step explanation:
2x-1= 7
add 1 one on both sides
2x = 8
divide both sides by 2
x=4
which expression is equivalent to 45-20s
I need to see the other expressions
A line segment AB has the coordinates A (2,3) AND B ( 8,11) answer the following questions (1) What is the slope of AB? (2) What is the length of AB? (3) What are the coordinates of the mid point of AB?(4) What is the slope of a line perpendicular to AB ?
Answer:
1. Slope: [tex]m = \frac{4}{3}[/tex]
2. Distance: [tex]AB = 10[/tex]
3. Midpoint: [tex]M = (5,7)[/tex]
4. Slope of perpendicular line: [tex]m_2 = -\frac{3}{4}[/tex]
Step-by-step explanation:
Given
[tex]A = (2,3)[/tex]
[tex]B = (8,11)[/tex]
Solving (1): Slope of AB
Slope (m) is calculated as follows:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where:
[tex]A = (2,3)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]B = (8,11)[/tex] --- [tex](x_2,y_2)[/tex]
So, we have:
[tex]m = \frac{11 - 3}{8 - 2}[/tex]
[tex]m = \frac{8}{6}[/tex]
[tex]m = \frac{4}{3}[/tex]
Solving (2): Length AB
This is solved by calculating the distance of AB using the following formula.
[tex]AB=\sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}[/tex]
Where:
[tex]A = (2,3)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]B = (8,11)[/tex] --- [tex](x_2,y_2)[/tex]
So:
[tex]AB = \sqrt{(2-8)^2 + (3 - 11)^2}[/tex]
[tex]AB = \sqrt{(-6)^2 + (-8)^2}[/tex]
[tex]AB = \sqrt{36 + 64}[/tex]
[tex]AB = \sqrt{100}[/tex]
[tex]AB = 10[/tex]
Solving (3): Midpoint of AB.
Midpoint, M is calculated as follows:
[tex]M = \frac{1}{2}(x_1+x_2, y_1 + y_2)[/tex]
Where
[tex]A = (2,3)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]B = (8,11)[/tex] --- [tex](x_2,y_2)[/tex]
So:
[tex]M = \frac{1}{2}(2+8,3+11)[/tex]
[tex]M = \frac{1}{2}(10,14)[/tex]
[tex]M = (5,7)[/tex]
Solving (4): Slope of line perpendicular to AB
The relationship between the slopes of two perpendicular lines is:
[tex]m_2 = -\frac{1}{m_1}[/tex]
Where
[tex]m_1[/tex] represents the slope of AB
[tex]m_1 = \frac{4}{3}[/tex]
So:
[tex]m_2 = -1/\frac{4}{3}[/tex]
[tex]m_2 = -1*\frac{3}{4}[/tex]
[tex]m_2 = -\frac{3}{4}[/tex]
Which equation, in point–slope form, passes through (–2, 4) and has a slope of 3?
y – 4 = 3(x – 2)
y – 4 = 3(x + 2)
y + 4 = 3(x – 2)
y + 4 = 3(x + 2)
Answer:
y - 4 = 3(x + 2)
Step-by-step explanation:
y - y₁ = m(x - x₁)
y - 4 = 3(x - (-2))
y - 4 = 3(x + 2)
Mr. Trask wants to fill his four hummingbird feeders with liquid food. Two feeders hold 6 fluid ounces each. One larger feeder holds 1 cup of liquid. The largest feeder holds 1 pint. How many fluid ounces of liquid food does Mr. Trask need to fill the four bird feeders?
A. 14 fl oz
B. 28 fl oz
C. 30 fl oz
D. 36 fl oz
Answer:
Step-by-step explanation:
8 fluid ounces in one cup
16 fluid ounces in a pint
2 feeders of 6 fluid ounces each
8 plus 16 plus 12
36, D
There are a total of 950 boxes of shoes at a store. • Half of the boxes contain athletic shoes. • Another 125 boxes contain dress shoes. • Of the remaining boxes of shoes, 4 out of 5 boxes contain sandals. Based on the expression below, how many boxes at the store contain sandals? 4(950 ÷ 2 − 125) ÷ 5
Answer: 355
Step-by-step explanation:
Hope this helps !
A used-car costs $5,000. You figure you can get 4 years out of it. You drive 10,000 miles per year. Your car insurance costs $1,200 per year. You figure you'll spend $400 per year on maintenance. Gas costs $3 per gallon, and the car gets 25 miles per gallon. What will your average cost (all costs included) per mile be over the 4 years?
Answer:
26,800
Step-by-step explanation:
Im not sure but thats what I got
Answer:
$0.405
I just took the test.
someone please help with my math on my page!!!
I'll try! What's the link?
50 POINTS PLEASE HELP! In order to rewrite log9 (6/5) as log9 (6) - log9 (5) , which of the following is used?
SEE PHOTO FOR ANSWER OPTIONS PLEASE HELP !! WILL MARK BRAINLIEST
Answer:
1
Step-by-step explanation:
A concert ticket costs $23. About how much will tickets costs for a group of 22 people?
Answer:
$506
Step-by-step explanation:
We know that 1 concert ticket is $23
Multiply 23 by 22 to get 506
They spend $506 in total for the tickets.
The total cost for a group of 22 people is $506 if a concert ticket costs $23. , the answer is $506.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A concert ticket costs $23.
Let x be the total cost for the group of 22 people:
The value of x can be found as follows:
The linear equation in one variable:
x = 23×22
x = $506
Thus, the total cost for a group of 22 people is $506 if a concert ticket costs $23. , the answer is $506.
Learn more about the linear equation here:
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2) Fill in an angle measure greater than 100 degrees for the missing angle in yellow below. You will fill
this in at the top of the chart and base all other angles you calculate on this measure. Find all the
missing angle measure.
Answer:
m∠a = 110°
m∠b = 110°
m∠c = 70°
m∠d = 70°
m∠i = 110°
m∠h = 110°
m∠j = 70°
m∠g = 110°
m∠f = 70°
m∠e = 70°
m∠k = 57°
m∠m = 70°
m∠l = 167°
Step-by-step explanation:
Let the measure of the yellow angle = 110°
Therefore;
m∠a = 110° by vertically opposite angles
m∠b = m∠a = 110° by opposite interior angles of a parallelogram
m∠c = 180° - 110° = 70° by same side interior angles
m∠d = m∠c = 70° by opposite interior angles of a parallelogram
m∠i and m∠c are supplementary angles, therefore, m∠i = 110°
m∠h = m∠i = 110° by vertically opposite angles
m∠j = m∠c = 70° by vertically opposite angles
m∠g and m∠d are supplementary angles, therefore, m∠g = 110°
m∠f = m∠d = 70° by alternate interior angles
m∠f = m∠e = 70° by vertically opposite angles
m∠k = 180° - (m∠h + 13°) = 180° - (110° + 13°) = 57°
m∠b and m∠m are supplementary angles, therefore, m∠m = 70°
m∠l and 13° are supplementary angles, therefore, m∠l = 167°
I need help with number 6
Answer:
90 i think if i did the math correct
Step-by-step explanation:
Answer:
90 inches
Step-by-step explanation:
12" in a foot so in order to convert 3' to inches after Walt apply it by 12. once you have that just the formula to find the perimeter.
3 × 12 = 36
the perimeter formula is: 2L + 2W = P
36 × 2 = 72 9 × 2 = 18
72 + 18 = 90
your answer should be 90 inches.
Matt and Molly and selling cheesecakes for a school fundraiser.
Customers can buy French silk cheesecakes and chocolate marble
cheesecakes. Matt sold 7 French silk cheesecakes and 14
chocolate marble cheesecakes for a total of $259. Molly sold 3
French silk cheesecakes and 5 chocolate marble cheesecakes for a
total of $97. What is the cost of one French silk cheesecake (x) and
one chocolate marble cheesecake (y)?
What is the value of y?Exaplain what the coordinates repersent
Answer:
(1, 35) means that $35 is the cost per hour of hiring a face painter.
Step-by-step explanation:
Notice that this is a linear function that goes through the origin and also through the point (5, 175) which according to the data plotted in both axis, means that for 5 hours of service, the cost is $175.
One can calculate the slope of this line as that of the segment that joins (0, 0) with (5, 175) as:
slope = (175 - 0) / (5 - 0) = 175 / 5 = 35 / 1
Notice as well that such slope reads the amount of dollars to hire a face painter for ONE hour (so it is the rate per hour for hiring a face painter).
So the point (1 , y) should be completed as: (1, 35) and means "the rate per hour for hiring a face painter."
A lumber yard offers boards based on wood species, size, and grade. If a customer can choose among 3 species, 3 sizes, and 2 grades, how many different boards could the customer choose?
There are 18 different boards from which the customer can choose.
How many different boards could the customer choose?The total number of different boards is given by the product between the number of options for each of the possible selections.
The selections (and their options) are:
Species (3 options)Sizes (3 options)Grades (2 options).Then the total number of different boards is given by:
N = 3*3*2 = 18
There are 18 different boards from which the customer can choose.
If you want to learn more about combinations:
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Help me find what x is worth please
Answer:
i think is 167
Step-by-step explanation:
Eli wanted to order candy online. Company A is offering 2 1/2 pounds of chocolate for $32.00. How much is Company A charging per pound of chocolate?
Answer:
Therefore, Company B is offering the lowest price/lb at $12.73/lb.
So, Company A's price / lb = ($32.50/2.5lbs) = $13.00/lb
Step-by-step explanation:
To determine price per lb, divide dollar amount by lbs.
- Company A sells 2 1/2lbs (2.5lbs) for $32.50
- Company B sells 2 3/4lbs (2.75lbs) for $35.00
And, Company B's price / lb = ($35.00/2.75lbs) = $12.73/lb
Please help quickly
Answer:
Figure J does not show y as a function of x ⇒ D
Step-by-step explanation:
y is a function of x if and only if every x has only one value of y
Let us check each given figure if it shows a function or not
#Figure F
∵ Every value of x has an arrow is pointed to one value of y
∴ Every x has only one value of y
∴ The figure shows y as a function of x
#Figure G
∵ The ordered pairs have different values of x-coordinates
∴ Every x-coordinate has only one value of y-coordinate
∴ The figure shows y as a function of x
#Figure H
∵ Every x in the table appears once
∴ Every x has only one value of y
∴ The figure shows y as a function of x
#Figure J
∵ The ordered pairs were drawn in the figure are (-3, -2), (-3, -3), (-2, 0),
(-2, -1), (-1, 1), (-1, 2), (0, 3), (0, 4)
∵ x = -3 has two values of y, y = -2 and -3
∵ x = -2 has two values of y, y = 0 and -1
∵ x = -1 has two values of y, y = 1 and 2
∵ x = 0 has two values of y, y = 3 and 4
∴ Every x-coordinate has more than one value of y-coordinate
∴ Figure J does not show y as a function of x
Find the difference between 45,985 and 1,715.
Answer:
44,270
Step-by-step explanation:
Peyton received a graduation gift from his grandparents of $12,700. He
does not need the money for the first year of college. So he decided to
invest the money in a high interest savings account. If he puts all the
money in a high interest savings account paying 8.8% interest
compounded semiannually, how much money will be in the account at the
end of one year to use for college? *
Answer:
Peyton's account will have $13,842.18 after a year.
Step-by-step explanation:
Given that Peyton received $ 12,700 and decided to invest it for a year in an account that grants an interest of 8.8% per year, compounded semiannually, to determine the amount of money that will be in said account after the passage of one year, it is necessary to perform the following calculation:
X = 12,700 (1 + 0.088 / 2) ^ 1x2
X = 13,842.18
Therefore, after a year has passed, Peyton's account will be $ 13,842.18.
Please help emergency
Answer:
1/20÷950
Step-by-step explanation:
hope this helps!
Answer:
the first one
Step-by-step explanation:
How is x to the power of 4 times x to the power of 3 different from x to the power of 4 divided by x to the power of 3?
HELP QUICK PLEASEEE
Answer:
Step-by-step explanation:
x^4(x^3) is x^7 (when multiplying two same variables with exponents you just add the exponents)
(x^4)/(x^3) is x^1 or just x (when dividing two same variables with exponents you just subtract the exponents)
I need help with 2&3
Answer:
2. A 4√3
3. B -5/3
Step-by-step explanation: