===========================================
Explanation:
x = amount (in inches) the spring is stretched
y = force applied (in pounds)
y = kx for some constant k, since x and y vary directly
---------------
Plug in the given info that x = 5 and y = 150 pair up together
Solve for k
150 = k*5
150/5 = k
k = 30
The equation goes from y = kx to y = 30x. Whatever the stretching distance (x) is, you multiply by 30 to get the force needed (y) to pull the spring.
---------------
Plug in y = 180 to solve for x
y = 30x
180 = 30x
30x = 180
x = 180/30
x = 6
The spring will be stretched 6 inches if you apply a force of 180 pounds.
15. Apply Mathematics (1)(A) Suppose you have a box with a 4 X 4-in.
square base and variable height h. The surface area of this box is a
function of its height. Write a function to represent the surface area.
Evaluate the function for h=6.5 in.
Answer:
Step-by-step explanation:
Formula for calculating the surface area of the box S = 2(LW+LH+WH) where
L is the length of the box
W is the width of the box
H is the height of the box
If the box is square based with dimension 4 * 4in, then L = W = 4in. substituting this values given into the formula we will have;
S = 2(4(4)+4H + 4H)
S = 2(16+8H)
S = 32+16H
Hence, The function that represents the surface area of this box as a
function of its height is S = 32+16H where H is the height of the box
Given H = 6.5in, to evaluate the function, we will substitute h = 6.5in into the modeled equation;
S = 32+16H
S = 32+16(6.5)
S = 32+106
S = 138in²
Hence the total surface area of the box is 138in²
Your hotel sells four types of rooms: double queen beds for $140/night; king bed for $160/night; junior suite for $220, and full business suites for $285. If there are 200, 150, 100, and 50 of each, respectively, what is your average price per room?
Answer:
$176.50
Step-by-step explanation:
Take each room type and multiply the number of rooms by the price of the room. Add the total for prices and add the total for the number of rooms. Divide the total prices by the total number of rooms.
Type of room Number Cost Total
Double queen 140 $200.00 $28,000.00
King 160 $150.00 $24,000.00
Junior Suite 220 $100.00 $22,000.00
Full business 285 $50.00 $14,250.00
$500.00 $88,250.00
Average cos per room $176.50
Need help with this question. I tried simplifying the radical, but apparently it’s not the answer
Answer:
-1/5+(√3)/20i or -0.2+0.05√3i
Step-by-step explanation:
[tex]\dfrac{-8+\sqrt{-12}}{40}=-\dfrac{8}{40}+\dfrac{2\sqrt{3}i}{40}=\boxed{-\dfrac{1}{5}+\dfrac{1}{20}\sqrt{3}\,i=-0.2+0.05\sqrt{3}\,i}[/tex]
_____
Comment on answer form
Satisfying the input format requirements of a computer is always problematic. One never knows if fractions or decimals are preferred, whether radicals must be simplified, and so on. If no clues are offered by general instructions, other questions, or previous experience, then it might be useful to consult your instructor.
6(n - 2) - 8 = 22 + 4(2-n)
Answer:
5
Step-by-step explanation:
6n -12 -8=22+8-4n
6n-20=30-4n
6n=50 -4n
10n = 50
5
Simplify. 1/2−3(12+1)2 Enter your answer, as a simplified fraction, in the box.
Answer: -506.5 or -253.25
Step-by-step explanation:
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\frac{1}{2}-3\ \left(12\ +\ 1\right)^2[/tex]
[tex]= \frac{1}{2}-3 (13^2)[/tex]
[tex]= \frac{1}{2} - (3) (169)[/tex]
[tex]= \frac{1}{2} - 507[/tex]
[tex]= \frac{-1013}{2}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
2/3x+15=17 please and thank you
Answer:
x=3
Step-by-step explanation:
2/3x+15=17
first subtract 15 from both sides
2/3x=2
multiply by 3 to eliminate the fraction
2x=6
divide by 3
x=3
Answer:
x=3
Step-by-step explanation:
2/3x +15 = 17
2/3x = 17-15
2/3x = 2
x = 2 / 2/3
x = 2/1 * 3/2
x = 6/2
x = 3
f(x) = 5x + 12. Find f−1(x)
Answer:
(x-12)/5
Step-by-step explanation:
Compute $(1 + i)(2 + i)(3 + i).$
Answer:
10i
Step-by-step explanation:
Step 1: Expand first 2
(1 + i)(2 + i)
2 + i + 2i + i²
2 + 3i + (-1)
1 + 3i
Step 2: Expand again
(1 + 3i)(3 + i)
3 + i + 9i + 3i²
3 + 10i + 3(-1)
3 + 10i - 3
10i
3+g=a/3h
what does a equal
Answer:
a = 3gh+9hStep-by-step explanation:
[tex]3+g = \frac{a}{3h} \\\\Cross\:Multiply\\\\3h(3+g) = a\\9h +3gh = a\\\\a = 3gh+9h[/tex]
4x + 6 - 11 help needed
Answer:
4x-5Step-by-step explanation:
[tex]4x+6-11\\\\\mathrm{Add/Subtract\:the\:numbers:}\:6-11=-5\\=4x-5[/tex]
The Venn diagram represents different categories of real numbers. Which category on the Venn diagram is represented by 4π? A) Irrational Numbers B) Integers C) Natural Numbers D) Rational Numbers
Answer:
Irrational Number
Step-by-step explanation:
The Venn diagram is not attached; However, the question can still be answered
Given
[tex]Number = 4\pi[/tex]
Required
What category of number is the given number
[tex]Number = 4\pi[/tex]
Substitute [tex]\frac{22}{7}[/tex] for [tex]\pi[/tex]
[tex]Number = 4 * \frac{22}{7}[/tex]
[tex]Number = \frac{4 *22}{7}[/tex]
[tex]Number = \frac{88}{7}[/tex]
[tex]Number = 12.5714285714......[/tex]
Notice that there's .... at the end of the number;
This implies that, the decimal number still extends
Numbers like 12.5714285714...... are categorized as irrational numbers because it can't be changed back to a fraction
Answer:
A. irrational number
Step-by-step explanation:
I took the test
Round off to three significant digits: 4.53619
Answer:
4.54
Step-by-step explanation:
The 4th digit (6) is greater than 4, so the 3rd digit (3) is increased by 1 before you drop the remaining digits:
4.54
12d^2 + 3dx + x
- (-4d^2 + 2dx - 8x)
Answer:
dx+9x+16d^2 dont know it it helps any but i tried
Step-by-step explanation:
I need help again help me pllsssssss
Answer: you end up at (2,2)
Step-by-step explanation:
Answer:
2,2
Step-by-step explanation:
go down to the bottom right corner (5,-5)
move over left 3 boxes
and then up 7 boxes
hope this helps :P
Is x^4+3x^3-x+7 in standard form
Answer:
yes
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
The standard form of a polynomial has the exponents decreasing left to right. Here, the exponents are 4, 3, 1, 0, so are decreasing left to right. The expression is in standard form.
I'm genuinely lost in any problems like this and my teachers are no help, I need help doing exponents in general, everything to do with them. I genuinely need help
Answer:
See below.
Step-by-step explanation:
4)
So we have the expression:
[tex](-6n^{-3})^2[/tex]
We can use the power of a product property, where:
[tex](ab)^n=a^n\cdot b^n[/tex]
So:
[tex]=(-6)^2\cdot(n^{-3})^2[/tex]
For the left, -6 squared is the same as -6 times -6. This equals positive 36.
For the right, we can use the power of a power property. The property says that:
[tex](a^n)^k=a^{nk}[/tex]
So:
[tex](n^{-3})^2=n^{(-3)(2)}\\=n^{-6}[/tex]
So, all together, we have:
[tex]=(-6)^2\cdot(n^{-3})^2\\=36n^{-6}[/tex]
6)
We have the expression:
[tex]-\frac{3x^0}{x^4}[/tex]
First, note that anything to the zeroth power (except for 0) is 1, thus, x^0 is also 1. Simplify:
[tex]=-\frac{3}{x^4}[/tex]
And that's the simplest we can do :)
Notes for 6)
We can put the x^4 to the numerator. Recall that when you put an exponent to opposite side, you put a negative. In other words:
[tex]x^n=\frac{1}{x^{-n}}[/tex]
And vice versa:
[tex]\frac{1}{x^{-n}}=x^n[/tex]
So, we can write the above as:
[tex]=-\frac{3}{x^4}\\=-\frac{3}{x^{-(-4)}}\\=-3x^{-4}[/tex]
However, traditionally, we want only positive exponents, so this wouldn't be correct.
Answer:
Step-by-step explanation:
x^m×x^n=x^{m+n}
x^m÷x^n=x^{m-n}
[tex]\frac{1}{x^m} =x^{-m}\\x^{-n}=\frac{1}{x^n} \\(xyz)^m=x^m\times y^m \times z^m \\(x^m)^n=x^{mn}[/tex]
[tex]x^0=1[/tex]
Help ASAP, Brainliest to whoever answers!
Answer:
these are the ten numbers :
0 8 2 6 9 2 0 8 0 0
Evaluate 1/3m−1−1/2n when m=21 and n=12
Answer:
[tex]0[/tex]
Step-by-step explanation:
[tex] \frac{1}{3}m - 1 - \frac{1}{2}n = \frac{1}{3}(21) - 1 - \frac{1}{2}(12) = 7 - 1 - 6 = 6 - 6 = 0[/tex]
Answer:
0
Step-by-step explanation:
1/3m - 1 - 1/2n
= 1/3(21) -1 1/2(12)
= 7 - 1 - 6
= 0
The 14 digits of a credit card are written in the boxes shown.If the sum of any three consecutive digits is 20, what is the
value of A?
Answer:
9
Step-by-step explanation:
Working backwards, the blank box between the 7 and 4 at the end must be 9 in order for the three digits to equal 20. Then we see the pattern of 947 repeated. The whole number would be 94794794794794. That way, any three consecutive numbers would be 20. The number in the box marked a would be 9.
5 pizzes are shared equally between 10 people. What fraction of a pizza does each person receive?
Answer:
1/2
Step-by-step explanation:
To combine integers with different signs find their _ _ then _ the smaller absolute value from the larger one give the sum the sign of the number with the _ absolute
Answer:
absolute valuessubtractlargestStep-by-step explanation:
To combine integers with different signs find their absolute values then subtract the smaller absolute value from the larger one. Give the sum the sign of the number with the largest absolute value.
K - 8 = -7 What is K?
Answer:
1
Step-by-step explanation:
To find the answer of a negative and a positive, you subtract and then keep the symbol of the bigger number. So in the equation 1-8 you subtract 1 from 8, then keep the symbol of the 8 (which is a negative) since it is the bigger number. 1 minus 8 is 7, and the symbol is negative, so the answer is -7. This makes K=1.
an object is dropped from the top of a cliff 675 meters high. its height above the ground t seconds after it is dropped is 675-4.9t^2. determine its speed 7 seconds after it is dropped, the speed if the object 7 seconds after it's dropped in m/sec
Answer:
V= 68.6 m/s
Step-by-step explanation:
height above the ground t seconds after it is dropped is 675-4.9t^2
For seven seconds
Height above ground= 675-4.9(7)²
height above ground= 675-240.1
Height above ground= 434.9 m
But it's dropped from a cliff and we need to find the distance traveled from the too of the cliff
Distance= 675-434.9.
Distance= 240.1
To determine it's speed
V²= U² +2gs
V= velocity we are looking for
U= initial velocity= 0
G= acceleration due to gravity= 9.8 m/s²
s= distance covered
V²= U² +2gs
V²= 0+2(9.8)(240.1)
V²= 4705.96
V= 68.6 m/s
5+11n=13n help with this one too..
Answer:
n = 2.5
Step-by-step explanation:
We need to isolate n by first moving it to one side.
11n = 13n - 5
11n - 13n = -5
-2n = -5
n = -5/-2
n = 2.5
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Answer:
n = 5/2
Step-by-step explanation:
5 + 11n = 13n
5 = 13n - 11n
5 = 2n
n = 5/2
Check:
5 + 11*5/2 = 13*5/2
10/2 + 55/2 = 65/2
If someone could plz help. p÷5=3.
Answer:
p=2
Step-by-step explanation:
so how to find this u take the five and three and u subtract them both and whatever is left over that is your answer
Mrs. Taylor is making new football uniforms for Fridays nights homecoming game. The trim fro the sleeves of one uniform requires 26 inches of fabric. Mrs Taylor needs to make 63 uniforms total. How many yards of fabric should she buy?
Answer:
Mrs Taylor should buy 45.5 yards of fabric ( 45.5364 actually but rounded to the nearest tenth)
Step-by-step explanation:
Here in this question, we are interested in calculating the total yards of fabric that Mrs Taylor should buy.
From the question, we are made to know that one uniform requires 26 inch of fabrics and she wants to make a total of 63 uniforms
The total inches of fabric needed is thus; 26 * 63 = 1,638 inches of Fabrics
But we want our answer in yards.
Mathematically;
1 inch = 0.0278 yard
1638 inches = x yard
x = 1638 * 0.0278 = 45.5364 yards which is approximately 45.5yards
Order the following expressions by their values from least to greatest.
Answer:
-2, b, a+c
Step-by-step explanation:
Answer:
All you have to do is switch A + C and B around. (basically if you wrote it out, it would look like this: -2, B, A + C.)
can someone help me graph this.
Answer:
Use a graphing calc.
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
For the third equation, m = 2
y = 2x + b
3 = 3(2) + b
3 = 6 + b
b = -3
y = 2x - 3
Fatima has 2 gallons of milk she wants to pour all milk into glasses which each hold 1 cup (1/16 gallon). how many cups can she fill
Answer:
32 cups
Step-by-step explanation:
1 cup= 1/16 gallon
? cup= 2 gallon ( crisscross)
⇒[tex]\frac{2*1}{\frac{1}{16} }\\ \frac{2}{\frac{1}{16}} \\2*16=32 cups[/tex]
Brett and Max are diving. Brett is 34 feet below the surface and Max is 25 feet below the surface. How many feet above Brett isMax?
Answer:
Max is 9 ft above Brett
Step-by-step explanation:
Brett is 34 feet below the surface = -34
Max is 25 feet below the surface = -25
Subtract the heights
-25 - -34
-25 +34
9
Max is 9 ft above Brett