Answer:
The closest straight-line distance from Caleb's school to the library is:
1480.92 feetStep-by-step explanation:
Imagine a triangle, where five blocks are a side and two blocks another side, to obtain the closest straight-line distance from Caleb's school to the library you can use the Pythagoras theorem, where the hypotenuse is the closest straight-line:
[tex]perpendicular^{2} +base^{2} =hypotenuse^{2}[/tex]Clearing the hypotenuse is:
[tex]\sqrt{perpendicular^{2}+base^{2}}= hypotenuse[/tex]Now, you only need to identify the distance in each case:
Five blocks = 275 feet * 5 = 1375 feet.
Two blocks = 275 feet * 2 = 550 feet.
At last, you must replace the distances found in the equation cleared:
[tex]\sqrt{1375 feet^{2}+550 feet^{2}}= hypotenuse[/tex]Hypotenuse or closest straight-line = 1480.92 feet.Identifying this, the closest straight-line distance from Caleb's school to the library is 1480.92 feet.
all integers between -14 and 10
Answer:
-13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Step-by-step explanation:
Which choices are in the solution set of the equation below? Check all that
apply.
10x = 30
A. 3.5
B. 1.5
C. 1
D1/3
E. 5
F. 3
A stack of 20 coins contains only nickels and
quarters and has a total value of $4. How many of each
coin are in the stack?
Answer:
16 quarters and 4 nickels
4×25=1.00 × 4 = 4.00 4×4=16-quarters
20-16=4-nickels
Step-by-step explanation:
Hope this helps!
If x+4=5 the x=1 what the hypothesis
Answer:
i think 1+4=5 i have no clue if thats the hypothesis but like thats the correct equation
Step-by-step explanation:
Is X =5 a solution to the equation X -3x+10=5?− 3 x + 10 = 5 ?
Answer:
No; x=1.6
Step-by-step explanation:
Find the distance between the following two points: *
(3,6) and (9,2)
Answer:
Step-by-step explanation:
(3 , 6 ) ;( 9 , 2)
Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]= \sqrt{(9-3)^{2}+(2-6)^{2}}\\\\=\sqrt{6^{2}+(-4)^{2}}\\\\=\sqrt{36+16}\\\\=\sqrt{52}\\\\=\sqrt{2*2*13}\\\\=2\sqrt{13}[/tex]
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs \$3.25$3.25dollar sign, 3, point, 25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most \$30$30dollar sign, 30 before tax. The restaurant only sells pancakes in stacks of 444 pancakes for \$5.50$5.50dollar sign, 5, point, 50.
Complete question:
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs \$3.25$3.25dollar sign, 3, point, 25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most \$30$30dollar sign, 30 before tax. The restaurant only sells pancakes in stacks of 444 pancakes for \$5.50$5.50dollar sign, 5, point, 50. Let SSS represent the number of stacks of pancakes that Benjamin buys. 1) Which inequality describes this scenario?
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Cost of chocolate milk = $3.25
Cost of pancakes = $5.50 (stack of 4)
Number of stacks of pancakes purchased = S
Maximum amount spent ≤ $30
Cost of chocolate + (Cost of pancake stack * number of stacks) ≤ $30
3.25 + 5.50S ≤ 30
5.50S ≤ 30 - 3.25
5.50S ≤ 26.75
S ≤ 26.75 / 5.50
S ≤ 4.86
Hence maximum number of pancake stacks he can purchase without exceeding budget = 4
Hence total number of pancakes = number of stacks * number in a stack
= 4 * 4
= 16
Answer:
Chose option have answer 3.25+5.50S [tex]\leq[/tex] 30
16 pancakes
Step-by-step explanation: If you find answer from Khan please use this answer
The John Jay Theater Dept has tickets at $6 for adults, $4 for teachers, and $2 for students. A total of 280 tickets were sold for one showing with a total revenue of $1010. If the number of adult tickets sold was twice the number of teacher tickets, how many of each type of ticket were sold for the showing?
Answer:
number of adults tickets sold = x = 90
number of teachers tickets = y = 45
number of students tickets = z = 145
Step-by-step explanation:
Cost of tickets
Adults = $6
Teachers = $4
Students = $2
Total tickets sold = 280
Total revenue = $1010
Let
x = number of adults tickets
y = number of teachers tickets
z = number of students tickets
x + y + z = 280
6x + 4y + 2z = 1010
If the number of adult tickets sold was twice the number of teacher tickets
x = 2y
Substitute x=2y into the equations
x + y + z = 280
6x + 4y + 2z = 1010
2y + y + z = 280
6(2y) + 4y + 2z = 1010
3y + z = 280
12y + 4y + 2z = 1010
3y + z = 280 (1)
16y + 2z = 1010 (2)
Multiply (1) by 2
6y + 2z = 560 (3)
16y + 2z = 1010
Subtract (3) from (2)
16y - 6y = 1010 - 560
10y = 450
Divide both sides by 10
y = 450/10
= 45
y = 45
Substitute y=45 into (1)
3y + z = 280
3(45) + z = 280
135 + z = 280
z = 280 - 135
= 145
z = 145
Substitute the values of y and z into
x + y + z = 280
x + 45 + 145 = 280
x + 190 = 280
x = 280 - 190
= 90
x = 90
Therefore,
number of adults tickets sold = x = 90
number of teachers tickets = y = 45
number of students tickets = z = 145
4x3-5x2-17x-8 divided by x+1
Answer:
4x2 - 9x - 8
Step-by-step explanation:
The following points are a minimum and a maximum of a sinusoid. Complete the following steps to
model the curve using the sine function.
(4.5, 2), (1.5, 22)
a) What is the vertical shift, k, of this curve?
b) What is the amplitude, a, of this curve?
c) What is period and frequency factor, b, of this curve?
d) Write an equation using the sine function that models this curve.
Answer: K= 12
A=10
P= 6
B=pi/3
Equation: y=10sin(pi/3(x))+12
Step-by-step explanation: You can find k by finding the midline, or adding the minimum and maximum y values together and then dividing by 2.
You find a by using the midline value (12) and subtracting it from the maximum y value to get the amplitude.
To find the period, find the difference between the min and max x values, which is 3, then double it to get the full period.
To find the b value, plug it into the 2pi/b=p equation, using the period value you found before you should get pi/3.
When assembling the equation use this format: y=asin[b(x-h)]+k.
You can also graph it with a graphing calculator to check to be sure the max and min points line up.
A sine function is represented as: [tex]\mathbf{y = A\sin(Bx) + k}[/tex]
The vertical shift is 12The amplitude is 10The period is 6, and the frequency factor is [tex]\mathbf{\frac{\pi}{3}}[/tex].The sine function is [tex]\mathbf{y = 10\sin(\frac{\pi}{3}x) + 12}[/tex]The given parameters are:
[tex]\mathbf{(x_1,y_1) = (4.5,2)}[/tex]
[tex]\mathbf{(x_2,y_2) = (1.5,22)}[/tex]
(a) The vertical shift (k)
The vertical shift is calculated using:
[tex]\mathbf{k = \frac{y_1 + y_2}{2}}[/tex]
So, we have:
[tex]\mathbf{k = \frac{2 + 22}{2}}[/tex]
[tex]\mathbf{k = \frac{24}{2}}[/tex]
[tex]\mathbf{k = 12}[/tex]
(b) The amplitude (A)
The amplitude is calculated using:
[tex]\mathbf{A = \frac{y_2 - y_1}{2}}[/tex]
So, we have:
[tex]\mathbf{A = \frac{22 - 2}{2}}[/tex]
[tex]\mathbf{A = \frac{20}{2}}[/tex]
[tex]\mathbf{A = 10}[/tex]
(c) The period (p) and the frequency factor (b)
The period is calculated using:
[tex]\mathbf{p = x_1 + x_2}[/tex]
So, we have:
[tex]\mathbf{p = 4.5 + 1.5}[/tex]
[tex]\mathbf{p = 6}[/tex]
The frequency factor (b) is calculated using:
[tex]\mathbf{b = \frac{2\pi}{p}}[/tex]
So, we have:
[tex]\mathbf{b = \frac{2\pi}{6}}[/tex]
[tex]\mathbf{b = \frac{\pi}{3}}[/tex]
(d) The equation of the sine function
A sine function is represented as:
[tex]\mathbf{y = A\sin(Bx) + k}[/tex]
So, we have:
[tex]\mathbf{y = 10\sin(\frac{\pi}{3}x) + 12}[/tex]
Read more about sine functions at:
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s= {(0,5), (-9,3) , (-8 , -8), (3, -9)
whats the domain
Answer:
0,-9,-8,3
Step-by-step explanation:
Domain
0
-9
-8
3
I need help pls!!!
It is really important for my high school assignment!
Answer
Step-by-step explanatio
clause A
Rewrite the expression in the form z n z n z, start superscript, n, end superscript. Z − 1 3 z − 5 6 = z − 6 5 z − 3 1 =start fraction, z, start superscript, start superscript, minus, start fraction, 1, divided by, 3, end fraction, end superscript, end superscript, divided by, z, start superscript, start superscript, minus, start fraction, 5, divided by, 6, end fraction, end superscript, end superscript, end fraction, equals () Stuck
Answer:
[tex]2z^4[/tex]
Step-by-step explanation:
Given the expression [tex]\frac{z^{-1}}{3} \div\frac{z^{-5}}{6}[/tex], we are to write it in the form of [tex]nz^n[/tex]. To do that we will simplify the given indicinal expression as shown;
[tex]\dfrac{z^{-1}}{3} \div\dfrac{z^{-5}}{6}\\= \dfrac{z^{-1}}{3} \times\dfrac{6}{z^{-5}}\\= \dfrac{6z^{-1}}{3z^{-5}}\\ = \dfrac{2z^{-1}}{z^{-5}}\\[/tex]
According to indices [tex]\dfrac{a^m}{a^n} = a^{m-n}[/tex], the resulting equation will become;
[tex]= \dfrac{2z^{-1}}{z^{-5}}\\= 2z^{-1-(-5)}\\= 2z^{-1+5}\\= 2z^{4}[/tex]
Hence expression in the form [tex]nz^n \ is \ 2z^4[/tex].
Answer:
9z
Step-by-step explanation:
Khan Academy
Solve for x (4x-10) 58 degrees
Answer: solving for x is not meant for this type of problem.
Step-by-step explanation:
[tex] \frac{b - 4}{6 } = \frac{b}{2} [/tex]
Can somene explain how to do this please.
Use cross-multiplication
[tex]\frac{b - 4}{6} = \frac{b}{2}\\2(b- 4) = 6b\\2b - 8 = 6b\\2b - 6b = 8\\-4b = 8\\b = -2[/tex]
Solve the system of equations –4x – 4y = -8 and 3x + 7y = –18 by combining
the equations.
Answer:6 im not to sure
Step-by-step explanation:
What is the equation of the line y=4x-6
Answer:
B
Step-by-step explanation:
13 + x - 5 + 4x + 2y
Coefficients:
Constants:
Like terms:
Help
Answer:
coefficients: 1, 4
like terms 13, -5 and 1x, 4x
constant: 13, 5
What is the slope of the line containing the points (-8, 1) and (4,7)?
which value of n will make the rational number -17 over n an integer
Is it A.18 B.102 C.170 or D. None of them
An integer is a whole number.
-17/n
Replace n with the choices:
-17/18 = -0.9444
-17/102 = -0.1666
-17/170 = -0.1
None of those are a whole number so the answer would be d. None of them.
Evaluate the expression below using the properties of operations. Show your steps.−36 ÷ 14 ⋅ (−18) ⋅ (−3) ÷ 6
Answer:
(-162)/7 or -23 1/7 as mixed fraction
Step-by-step explanation:
Simplify the following:
(-36)/14 (-18) (-3)/6
Hint: | Express (-36)/14 (-18) (-3)/6 as a single fraction.
(-36)/14 (-18) (-3)/6 = (-36 (-18) (-3))/(14×6):
(-36 (-18) (-3))/(14×6)
Hint: | In (-36 (-18) (-3))/(14×6), divide -18 in the numerator by 6 in the denominator.
(-18)/6 = (6 (-3))/6 = -3:
(-36-3 (-3))/14
Hint: | In (-36 (-3) (-3))/14, the numbers -36 in the numerator and 14 in the denominator have gcd greater than one.
The gcd of -36 and 14 is 2, so (-36 (-3) (-3))/14 = ((2 (-18)) (-3) (-3))/(2×7) = 2/2×(-18 (-3) (-3))/7 = (-18 (-3) (-3))/7:
(-18 (-3) (-3))/7
Hint: | Multiply -18 and -3 together.
-18 (-3) = 54:
(54 (-3))/7
Hint: | Multiply 54 and -3 together.
54 (-3) = -162:
Answer: (-162)/7
-10b + 5 = 7b + 5 what is b
Answer:
0?
Step-by-step explanation:
Original Equation:
-10b + 5 = 7b + 5
Add 10b to both sides
5 = 17b + 5
Subtract 5 from both sides.
0 = 17b
Divide both sides by 17
b = 0
Hope I helped :)
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Tyler is packing lunches for a local youth program. He has 36 sandwiches, 72 apples, and 108 granola bars. What is the greatest number of lunches he can pack so that each lunch has an equal number of sandwiches, apples, and granola bars? How many of each item will the lunch contain?
Answer:
The greatest number of lunches he can pack so that each lunch has an equal number of sandwiches, apples, and granola bars is 12.
Each lunch will contain 3 sandwiches, 6 apples and 9 granola bars
Step-by-step explanation:
The greatest common divisor (GCD) of two or more numbers is the largest number by which these numbers can be divided, that is, it is the largest number that divides them all exactly.
In other words, the greatest common divisor of two numbers a and b is the largest number that divides a and divides b.
To find the greatest common divisor of two or more numbers, you start by breaking those numbers down into prime factors. In this case:
36=2²*3²
72 = 2³*3²
108 = 2²*3
The greatest common divisor is obtained by choosing only the prime factors common to the numbers, raised to the smallest exponent. That is, you choose only the common factors and those that are repeated must be raised to the minimum exponent.
The 2 appears as a prime factor in the three decompositions, whose minimum exponent is 2.
3 also appears as a common factor, whose minimum exponent is 1.
By doing the multiplication to get the greatest common divisor, you get:
2²*3=12
So the greatest number of lunches he can pack so that each lunch has an equal number of sandwiches, apples, and granola bars is 12.
To calculate how many lunches each item will contain, you simply divide the amount you have of each item by the most lunches Tyler can pack, 12.
Sandwiches: 36÷12= 3
Apples: 72÷12= 6
Granola bars: 108÷12= 9
Each lunch will contain 3 sandwiches, 6 apples and 9 granola bars
Maria cut 3/4 yard of ribbon into pieces that are 1/8 yard long. How many pieces of ribbon did Maria cut? PLEASE HELP MEEEEE!!!
Answer:
6 pieces
Step-by-step explanation:
What is the slope of the line represented by the equation y=-1/2x+1/4 ?
Answer:
-1/2
Step-by-step explanation:
The slope is always the value with the x.
Answer:
Slope = - 1/2x
Step-by-step explanation:
1. Find the value of the polynomial 5 - 3x + 7 at:
(i) x=1
Simplify the expression in part D to find the temperature of the water after Raul added the ice cubes. Show your work
70 + (-30)+2+(-9)+0.3+(-0.1)=[70+(-30)]+[2(-9)]+[0.3+(-0.1)]
Answer:
33.2°F
Step-by-step explanation:
[70 + (-30)] + [2 +(-9)] + [0.3 + (-0.1)]
=
40 + (-7) + 0.2
=
33 + 0.2
=
33.2°F
The temperature of the water dropped to 33.2°F after Raul added the ice cubes.
Hoped this helped!<3
Answer:
[70 + (-30)] + [2 +(-9)] + [0.3 + (-0.1)]
=
40 + (-7) + 0.2
=
33 + 0.2
=
33.2°F
The temperature of the water dropped to 33.2°F after Raul added the ice cubes.
Step-by-step explanation:
If (72)p = 76, what is the value of p?
2
3
4
8
Answer:
it would be +2
Step-by-step explanation:
the equation would be (72)+2= 76
Answer: Positive 2
Step-by-step explanation:
my brain is just cool like that
A set of 4 consecutive even integers has a sum of 380. What is the least of the 4 integers ?
Answer:
92
Step-by-step explanation:
If the 4 consecutive even integers have a sum of 380, then the average value is 380/4.
380/4 = 95
There must be 2 integers less than 95 and 2 grater than 95.
The 4 integers are: 92, 94, 96, 98
Sum: 92 + 94 + 96 + 98 = 380
Answer: 92
The 4 consecutive even integers are 92,94,96 and 98 whose sum is 380.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The 4 consecutive even integers has a sum of 380.
x+2+x+4+x+6+x+8=380
Add the like terms
4x+20=380
Subtract 20 on both sides
4x=380-20
4x=360
Divide both sides by 4
x=90
So the four consecutive integers are
x+2=90+2=92
x+4=90+4=94
x+6=90+6=96
x+8=90+8=98
Hence, the 4 consecutive even integers are 92,94,96 and 98 whose sum is 380.
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which represents the graph plzz help
Answer:
y=2-1x
Step-by-step explanation:
the would be the answer because the way your line is going