Answer:
[tex] \cos L = \dfrac{4}{5} [/tex]
Step-by-step explanation:
The right angle is angle K. KL and JK are legs. JL is the hypotenuse.
For angle L, KL is the adjacent leg.
In general, for acute angle A of a right triangle,
[tex] \cos A = \dfrac{adjacent~leg}{hypotenuse} [/tex]
In this case,
[tex] \cos L = \dfrac{adj~leg}{hyp} [/tex]
[tex] \cos L = \dfrac{KL}{JL} [/tex]
[tex] \cos L = \dfrac{8}{10} [/tex]
[tex] \cos L = \dfrac{4}{5} [/tex]
If NS = 2x + 7 and SQ = 5x - 23, find NQ
Incomplete Question Consider here NS = SQ then we may solve for NQ
Answer:
Therefore,
[tex]NQ=54\ units[/tex]
Step-by-step explanation:
Consider N -S -Q as a Straight line as shown in the figure below such that,
[tex]NS = 2x + 7[/tex]
[tex]SQ = 5x -23[/tex]
[tex]NS =SQ[/tex] ..............Consideration
To Find:
NQ = ?
Solution:
[tex]NS =SQ[/tex] .....Given Consideration
Substituting the values we get
[tex]2x+7=5x-23\\\\3x=30\\\\x=\dfrac{30}{3}=10[/tex]
Therefore,
[tex]NS = 2\times 10 + 7 = 27[/tex]
[tex]SQ = 5\times 10 -23=27[/tex]
N -S-Q is a Straight Line,
Then BY Line Addition Postulate,
[tex]NQ=NS+SQ[/tex] ...............N-S-Q
Substituting the values we get
[tex]NQ=27+27=54\ units[/tex]
Therefore,
[tex]NQ=54\ units[/tex]
If f(x) = 3x + 2 and g(x) = x^2– X, find each value.
A. g(36)
B. f(2) + 1
A) g(36) = 1260
B) f(2) + 1 = 9
Solution:
Given that,
[tex]f(x) = 3x + 2\\\\g(x) = x^2-x[/tex]
Find each value
A) g(36)Substitute x = 36 in g(x)
[tex]g(36) = (36)^2 - 36\\\\g(36) = 1296-36\\\\g(36) = 1260[/tex]
B) f(2) + 1Substitute x = 2 in f(x)
[tex]f(2) + 1 = 3(2) + 2 + 1\\\\f(2) + 1 = 6 + 2 + 1\\\\f(2) + 1 = 9[/tex]
Thus the values are found
Final answer:
To solve the functions, substitute the given values into the relevant function. After performing calculations, g(36) is found to be 1260, and f(2) + 1 is calculated to be 9.
Explanation:
To find the values for given functions, we need to substitute the relevant inputs into each function and then perform the necessary calculations.
A. g(36)
Given g(x) = x² \\- x, we substitute x with 36:
g(36) = 36² \\- 36 = 1296 \\- 36 = 1260.
B. f(2) + 1
Given f(x) = 3x + 2, we first find f(2):
f(2) = 3(2) + 2 = 6 + 2 = 8.
Now, we add 1 to f(2):
f(2) + 1 = 8 + 1 = 9.
Terry Wade's variable costs for his car
totaled $1,876.88 last year and his fixed
costs totaled $1,685. If he drove 10,846
miles last year, what was his cost per
mile? Round to the nearest cent.
A $0.45
B $0.33
C $0.64
D $0.35
To find Terry Wade's cost per mile, his variable and fixed costs are summed and then divided by the total miles driven, yielding a cost per mile of approximately $0.33.
Explanation:To calculate Terry Wade's cost per mile for using his car, we first need to add together his variable and fixed costs, and then divide this total by the number of miles he drove last year.
This gives us the cost per mile.
Step 1: Add variable and fixed costs.
Variable costs = $1,876.88
Fixed costs = $1,685
Total costs = Variable costs + Fixed costs = $1,876.88 + $1,685 = $3,561.88
Step 2: Divide the total costs by the number of miles driven.
Number of miles driven = 10,846 miles
Cost per mile = Total costs ÷ Number of miles driven = $3,561.88 ÷ 10,846 miles
Cost per mile ≈ $0.328 or rounded to the nearest cent, $0.33.
Therefore, the cost per mile for Terry Wade last year was $0.33, making the correct answer B $0.33.
What is distance formula?
Answer:
d = distance
(x_1, y_1) = coordinates of the first point
(x_2, y_2) = coordinates of the second point
Step-by-step explanation:
Answer:
The distance formula itself is actually derived from the Pythagorean Theorem which is a 2 + b 2 = c 2 {a^2} + {b^2} = {c^2} a2+b2=c2
Step-by-step explanation:
11. What must be true about p and q if the equation shows equivalent fractions
Answer:
p and q are both equal to 20.
Step-by-step explanation:
40 / 2 = p, so p = 20
100 / 5 = q, so q = 20
12) The school that Danielle goes to is selling tickets to a choral performance. On the first day of
ticket sales the school sold 5 senior citizen tickets and 9 student tickets for a total of $144. The
school took in $192 on the second day by selling 14 senior citizen tickets and 6 student tickets.
What is the price each of one senior citizen ticket and one student ticket?
Answer:
Senior citizen tickets = $9
Student tickets = $11
Step-by-step explanation:
We begin by converting these into simultaneous linear equation;
Senior citizen tickets = a
Student tickets = b
5a + 9b = 144
14a + 6b = 192
5a = 144 - 9b
a = 144/5 - 9b/5
a = 28.8 - 1.8b
We now substitute this into the first equation
14(28.8 - 1.8b) + 6b = 192
403.2 - 25.2b +6b = 192
-19.2b = 192 - 403.2
b = -211.2/-19.2
b = 11
Put the value of b into either equation
5a + 9b = 144
5a + 9(11) = 144
5a +99 = 144
5a = 144-99
5a = 45
a = 9
1 1/6 • 20 13/24 =? What is the answer to this?
Be sure to explain your reasoning.
Sally makes a fruit drink using ⅔ of a cup of orange juice for every ¼ of a cup of pineapple juice. How many cups of orange juice will Sally need if she uses 2 cups of pineapple juice?
Answer:
Sally need [tex]5\frac{1}{3}[/tex] cups of orange juice.
Step-by-step explanation:
Given:
Sally makes a fruit drink using ⅔ of a cup of orange juice for every ¼ of a cup of pineapple juice.
If she uses 2 cups of pineapple juice.
Now, to find the cups of orange juice.
So, to solve by using unitary method:
As, ¼ of a cup of pineapple juice is needed for orange juice of = ⅔ cup.
So, 1 cup of pineapple juice is needed for orange juice of = [tex]\frac{2}{3}\div \frac{1}{4}[/tex]
[tex]=\frac{2}{3}\times \frac{4}{1}[/tex]
[tex]=\frac{8}{3}[/tex] cups.
Thus, 2 cups of pineapple juice is needed for orange juice of = [tex]\frac{8}{3} \times 2[/tex]
= [tex]\frac{16}{3}[/tex]
= [tex]5\frac{1}{3}[/tex] cups.
Therefore, Sally need [tex]5\frac{1}{3}[/tex] cups of orange juice.
A line has a slope of -1/7 and passes through (4, -2) and (p, -1) what is the value of p
Answer:
Therefore the value of p is -3.
Step-by-step explanation:
Given a line has a slope of [tex]-\frac{1}{7}[/tex] and passes through (4,-2)and (p,-1)
The slope of a line which passes through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex]=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here [tex]x_1= 4,y_1=-2, x_2=p[/tex] and [tex]y_2= -1[/tex]
Therefore the slope of the line which passes through the given points is
[tex]=\frac{-1+2}{p-4}[/tex]
According to the problem,
[tex]\frac{-1+2}{p-4}= -\frac{1}{7}[/tex]
[tex]\Leftrightarrow \frac{1}{p-4} =-\frac{1}{7}[/tex]
[tex]\Leftrightarrow p-4=-7[/tex]
[tex]\Leftrightarrow p = -7+4[/tex]
[tex]\Leftrightarrow p = -3[/tex]
Therefore the value of p is -3.
13-9-x/11=3x/22+121/2
Answer:
x=-248 3/5
Step-by-step explanation:
13-9-x/11=3x/22+121/2
4-x/11=3x/22+121/2
4-121/2=3x/22+x/11
8/2-121/2=3x/22+2x/22
-113/2=5x/22
5x/22=-113/2
5x=(-113/2)*22
5x=-113*22/2
5x=-113*11
x=-1243/5
x=-248 3/5
A cube has side lengths of 4 in.
What is the volume of the cube?
Enter your answer in the box.
Answer:
This would equal 64
Step-by-step explanation:
To find the volume of a cube you multiply the length x width x height.
So in this case this would be 4 x 4 x 4 = 64
This is the easiest shape to find the volume.
If you have any questions feel free to ask in the comments - Mark
Also when you have the chance please mark me brainliest.
John paid $34 for 2 books and 3 pencils. He paid $36 for 3 books and 2 pencils. How much was each?
Cost of each book is $ 8 and cost of each pencil is $ 6
Solution:
Let "a" be the cost of 1 book
Let "b" be the cost of 1 pencil
John paid $34 for 2 books and 3 pencils
Therefore,
2 books x cost of 1 book + 3 pencil x cost of 1 pencil = 34
[tex]2 \times a + 3 \times b = 34[/tex]
2a + 3b = 34 ----------- eqn 1
He paid $36 for 3 books and 2 pencils
3 books x cost of 1 book + 2 pencil x cost of 1 pencil = 36
[tex]3 \times a + 2 \times b = 36[/tex]
3a + 2b = 36 -------- eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 1 by 2
4a + 6b = 68 ---------- eqn 3
Multiply eqn 2 by 3
9a + 6b = 108 --------- eqn 4
Subtract eqn 3 from eqn 4
9a + 6b = 108
4a + 6b = 68
( - ) -------------
5a = 40
a = 8
Substitute a = 8 in eqn 1
2(8) + 3b = 34
16 + 3b = 34
3b = 34 - 16
3b = 18
b = 6
Thus cost of each book is $ 8 and cost of each pencil is $ 6
Western North Carolina Woods have a deer population density of 3.5 deer per acre. If there are a total of 435 deer, how many acres are in this parcel of woods?
There are about 124.29 acres in this parcel woods
Step-by-step explanation:
The given is:
Western North Carolina Woods have a deer population density of 3.5 deer per acreThere are a total of 435 deerWe need to find how many acres are in this parcel of woods
∵ The population density = 3.5 deer per acre
- That means 1 acre for every 3 dears
∵ There are a total of 435 deer
∴ [tex]\frac{3.5}{1}=\frac{435}{x}[/tex] , where x is the number of acres
- By using cross multiplication
∴ 3.5 × x = 1 × 435
∴ 3.5 x = 435
- Divide both sides by 3.5
∴ x = 124.29
There are about 124.29 acres in this parcel woods
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Which expression correctly represents "nine less than the quotient of a number and four, increased by three"?
Answer:9-x/4+3
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Find the greatest common factor (GCF) of both terms 30 and 60
Answer:
30
Step-by-step explanation:
If there is a 61% chance that carol gets accepted to Andover university, what is the chance, or probability, that carol does not get accepted
Answer: if I am correct it is 39%
Step-by-step explanation:
A scale diagram of a garden shows the length as 14.5 cm. If the scale is 1:150, what is the actual length? The garden is m in length
The actual length of the garden is 2175 cm.
Explanation:To find the actual length of the garden, we can use the scale. The scale indicates that 1 cm on the diagram represents 150 cm in real life. Since the length on the diagram is 14.5 cm, we can multiply this length by the scale factor to find the actual length.
Actual Length = Length on Diagram × Scale Factor = 14.5 cm × 150 = 2175 cm
Therefore, the actual length of the garden is 2175 cm.
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What is the volume of this figure? Show your calculations.
Answer:
The volume of the figure given is [tex]4000[/tex] cubic units
Step-by-step explanation:
The given figure is in the shape of a Right Square Pyramid.
The volume of a right square pyramid can be calculate by:
Volume of a right square pyramid =
[tex]a^3\frac{h}{3}[/tex]
where 'a' is the length of the base of the pyramid which is equal for all the four side of the base and 'h' is the height of the pyramid which is perpendicular to the base of it.
Given: [tex]a=10[/tex] units
[tex]h=12[/tex] units
Putting the values in the volume of the right square pyramid.
[tex]=10^3\frac{12}{3}\\\\ =10^3*4\\\\=4000[/tex]
The volume of the figure given is [tex]4000[/tex] cubic units
Add
(-1 - i) + (-10 + 3i)
Answer:
the sum of the 2 expressions is -11+2i.
Step-by-step explanation:
-1-10=-11
-i+3i=2i
-11+2i
Immediately after jumping out of a plane, a 65kg skydiver starts to fall towards the
Earth with an acceleration of 9 8ms? Calculate the downwards force on the
skydiver at the instant he leaves the plane (show working):
it's physics not maths don't know how to change it
Answer:637kgms-2
Step-by-step explanation:the force acting on him will be Made X acceleration due to gravity. Then since the mass is 65, multiply it with 9.8, then you will get the force which is 637kgms-2
What is 199000/10000 as a decimal?
Answer:
19.9
Step-by-step explanation:
divide 199000 by 10000
=19.9
Answer:
19.9
Step-by-step explanation:
Which expression shows a way to find 20% of 950?
950
20
20
What is it
To find 20% of 950, first convert the percentage to a decimal (20% becomes 0.20) and then multiply that value by 950. The mathematical expression representing this calculation is 0.20 x 950, which yields the result: 190.
Explanation:The question is asking about how to find 20% of 950 in mathematics. Here's how you do that:
First, turn the percentage into a decimal. 20% becomes 0.20 in decimal form because percent means 'per hundred'. Thus 20 per hundred is 0.20 as a decimal.Next, to find 20% of 950, you multiply the decimal form of the percentage (0.20) by 950. The mathematical expression that represents this operation is: 0.20 x 950.Therefore, 20% of 950 equals 190. Learn more about Percentage Calculation here:https://brainly.com/question/329987
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To find 20% of 950, convert 20% to decimal form as 0.20 and multiply it by 950. The result of this calculation is 190, which represents 20% of 950.
Explanation:The expression to find 20% of 950 is obtained by multiplying 950 by the percentage in decimal form. Since 20% as a decimal is 0.20, you multiply 950 by 0.20 to find the answer. The calculation is as follows:
Convert the percentage to a decimal: 20% = 0.20Multiply the value by the decimal percentage: 950 × 0.20Calculate the result: 950 × 0.20 = 190So, 20% of 950 is 190.
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What is the quotient? Negative StartFraction 4 over 5 EndFraction divided by 2 Negative 1 and three-fifths Negative two-fifths One-half 1 and three-fifths
Answer:
a
Step-by-step explanation:
The quotient of the given expression is -2/5.
What is quotient?The number we obtain when we divide one number by another is the quotient
Given is the expression as -
- (4/5) ÷ 2
The given expression is -
- (4/5) ÷ 2
- (4/5) x 1/2
- 2/5
Therefore, the quotient of the given expression is -2/5.
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Can you please help me just need the answer pls.please need help
Answer:
20
Step-by-step explanation:
How do you solve it
Answer:
Step-by-step explanation:
400-65=335
The round wading pool at the Greenville Community Center has a diameter of 8 feet. What is the pool's circumference? use 3.14 for pi
Answer:
25.12 feet
Step-by-step explanation:
To find the circumference of the round wading pool with an 8-foot diameter using 3.14 for pi, the formula C = πd is used, resulting in a circumference of 25.12 feet.
The question is asking to find the circumference of a round wading pool with a diameter of 8 feet using 3.14 for pi. The formula for the circumference of a circle is C = πd, where C represents the circumference, π (pi) is approximately 3.14, and d is the diameter of the circle. Given that the diameter (d) of the pool is 8 feet, we substitute the values into the formula to get:
C = 3.14 × 8 feet = 25.12 feet
Therefore, the circumference of the wading pool is 25.12 feet.
11,647 rounded to the nearest hundred
Answer:
11,600
Step-by-step exp
the 4 in the tens place means the 6 stays the same
Answer:
11,600
Step-by-step explanation:
think of 100... that 1 is in the hundred place. when rounding you look to the number to the right of that place. if that number is less than 5 you dont round up. if the number is 5 or greater you round up. in this case 11,647 the number 6 is in the hundred place. look to the right of it. in this case it is 4. 4 is less than five so you don't round up. your number 11,647 rounded to the hundred place is 11,600.
If the equation of a function is y = x2 - 5, what is the output when the input is -1?
Answer:
y = - 4
Step-by-step explanation:
The output is the value of y for a given input x
For an input of - 1, substitute x = - 1 into the equation.
y = (- 1)² - 5 = 1 - 5 = - 4 ← output
please i need help
Answer:
P = (0,4) Q = (2,0)
Step-by-step explanation:
On a map with a scale of 2 cm = 1 km, the
distance from Beau's house to the beach is
4.6 centimeters. What is the actual distance?
A 2.3 km
B 4.6 km
© 6.5 km
D 9.2 km
Answer:
A. 2.3km
Step-by-step explanation:
Since 2cm = 1km
4.6cm = xkm
xkm = 4.6 x 1 / 2
= 2.3km
Answer:
I would believe that the answer is A. 2.3 km
Step-by-step explanation:
If 2cm=1km
then 4cm=2km
not to mention the km is 1/2 or the cm
so i would believe that .6cm would be .3km
therefore the answer must be 2.3km