Perimeter = 18 units; Area = 9 sq. units
GH = √(-4-4)²+(1-1)² = 8 units
HI = √(4-0)²+(1+2)² = 5 units
IG = √(0+4)²+(-2-1)² = 5 units
Perimeter of the given triangle = 8+5+5=18 units
Semi-perimeter of triangle = 18÷2=9 units
Using Heron's formula; √[s(s-a)(s-b)(s-c)]=Area of triangle;
A= √(9)(9-8)(9-5)(9-5)
= √(9)(3)(3)
= 9 sq. units
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Your instructor makes 5 cents per minute. How much does he makes in dollars if he works for 40 hours?
Answer: $120
Step-by-step explanation:
5 * 60 (5 cents every minute with 60 minutes in a hour makes 300 cents per hour)
300 * 40 (300 cents per hour multiplied by 40 hours makes 12000 cents)
12000 / 100 (12000 cents divided by 100 since 100 cents in a dollar)
120 is the answer
How many groups of 3/8 are in 1?
Answer:
2 groups of 3/8 are in one
Step-by-step explanation:
making up 6/8 because you can add another 3/8 to it.
3/4 + 7/8 + 3/4 + 1/2 + 7/8
Answer:
=
15/4
(Decimal: 3.75)
Step-by-step explanation:
Find a polynomial function of degree 5 with -2 as a zero of multiplicity 3, 0 as a zero of multiplicity 1, and 2 as a zero of multiplicity 1
(Use 1 for the leading coefficient.)
The polynomial function with degree 5 is formed as:
f (x) = x (x + 2)³ (x - 2).
What are termed as the polynomial functions?Polynomials are algebraic representations that contain indeterminates and constants.A polynomial is an algebraic expression in which all of the variable exponents have become whole numbers.Any polynomial's variable exponents must be non-negative integers.A polynomial's degree is the highest and greatest exponent of a variable in such a polynomial.The degree is used to approximate the optimal number of solutions to a polynomial function using Descartes' Rule of Signs.(-2) is derived from the factor (x + 2); because it has a multiplicity of three, you must account for that zero three times; thus, it is composed as (x + 2)³.
0 is derived from the factor x.
2 is derived from of the factor (x - 2).
The factored polynomial function is:
f (x) = x (x + 2)³ (x - 2)
Thus, the polynomial function with degree 5 is composed.
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Which list shows the numbers in increasing order?
A) -0.5, 1.5, -2, -0.75, √7
C) -2, -0.75, -0.5, 1.5, √7
B) -0.5, -2, -0.75, 1.5, √7
D) √7, 1.5, -0.5, -0.75, -2
Answer:
Step-by-step explanation:
its ''C''
Evaluate the variable expression when a = 2 and c = −3. 2a − (c + a)2
the expression of the variable for a = 2 and c = 3. 2a − (c + a)2
2a+b^2 2a +b2
2(-3) +(-2)^2 2(-3) + (-2)
-6 +4 -6 -4
-2 -10
An expression is a set of terms combined using the operations +, -, x or ÷, for example 4 x − 3 or 5 x 2 − 3 x y + 17 . An equation is a statement with an equals sign, which states that two expressions are equal in value, for example 4 b − 2 = 6 .
Either the options are incorrect, or the problem is poorly written.
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Ch. 1. Problems 6, 7 & 9
6. The only swimmng pool at a motel is outdoors. It is 5.0 m wide and 12.0 m long. If the weekly
evaporation is 2.35 inches how many gallons of water must be added to the pool if it does not rain? If during the next week the pool still loses two. 35 inches of water to evaporation, even with 20 mm of rainfall, how many liters of water must be added?
Answer:
946 gal
629 gal
Step-by-step explanation:
volume that evaporates = LWH
volume = (5.0 m × 100 cm/m × inch / 2.54 cm) × (12.0 m × 100 cm/m × inch / 2.54 cm) × 2.35 inch
volume = 218,550 in.³
volume = 218,550 in.³ × 1 gal / 231 in.³
volume = 946 gallons
You must add 946 gallons.
The loss to evaporation is 2.35 in.
The amount of rain is 20 mm
The net loss is
2.35 in. × 25.4 mm / inch - 20 mm = 39.69 mm
39.69 mm × 1 inch / 25.4 mm = 1.563 in.
The net loss now is 1.563 in. instead of 2.35 in.
We find the fraction of the the previous loss is the loss with rain and multiply by the previous loss.
1.563/2.35 × 946 gal = 629 gal
With rain, then 629 gallons of water must be added.
Allison ran 5 miles in 40 minutes before running an additional 3 miles in 27 minutes is this proportional are not pls help ASAP
Answer:
no it is not proportional...
Step-by-step explanation:
5 miles/40 minutes is 1/8
3 miles/27 minutes is 1/9...
Wilson has a number in mind. If he takes away one-third of the number from it the
result is 10. Find the number.
hi
if he takes 1/3 , then remains 2/3
then 2/3 X = 10
X = 10 / 2/3
X = 10 * 3/2
X = 30/2
X = 15
let's check :
1/3 of 15 = 15/3 = 5
15 -5 = 10
all macth, so answer is correct
My child is struggling with the answer.
Using the relation between velocity, distance and time, the distances are given as follows:
A. d = 13/3 miles.
B. d = 4.25 miles.
C. d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
Hence the distance is:
d = vt.
In item a, considering the time in hours, we have that:
v = 13, t = 20/60 = 1/3.
Hence:
d = 13/3 miles.
In item b, we have different definitions, then:
d = 15 x 5/60(first five minutes) + 12 x 15/60(last 15 minutes).
d = 15/12 + 15/5
d = 4.25 miles.
For item c, we have that:
d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).
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Convert 50°F to degrees Celsius.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=5/9(F-32)
F=9/5C+32
Answer:
10°C
Step-by-step explanation:
F = 50
C = 5/9 * (F - 32) = 5/9 * (50 - 32) = 5/9 * 18 = 5 * 2 = 10
Find an equation of variation in which y varies jointly as x and z, and y= 48 when x = 8 and z=6
Answer:
y = xzStep-by-step explanation:
Joint variation equation:
y = kxz, where k- coefficient of variationGiveny = 48,x = 8,z = 6Find the value of k by plugging in the given values:
48 = 8*6k48 = 48kk = 1The equation is:
y = xzUsing the associative property, rewrite the following expression. You do NOT need to simplify it. -3y - 6y + 10y
Another form of the given expression using associative property is 10y + (-3y -6y)
Associative propertyAssociative property shows that if two or more property are added or multiplied, the result remains the same. For instance;
a +(b + c) = (a+b) + c
Given the expression below;
-3y - 6y + 10y
Group to have
(-3y - 6y) + 10y
10y - 3y - 6y
This can also be grouped as;
(10y - 3y) - 6y = 10y + (-3y -6y)
Hence another form of the given expression using associative property is 10y + (-3y -6y)
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One-seventh of a number, increased by twelve?
Answer:
x/7+12
Step-by-step explanation:
One seventh refers to 1/7.
Since we do not know what "a number" is it, it is written as "x."
Whenever you see the word "increased" think addition.
So in this case,
x / 7 + 12
What is the slope of the line represented by the equation y =4/5x-3?
Answer:
4/5 is the slope of the line
Chef Smith will be serving a breakfast banquet for 300 guests. Each guest will be served a two-egg
omelet. How many dozen eggs should Chef Smith order?
Answer: 50
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
300(2) bcuz 300 guests and each person gets 2
600(12) bcuz 300(2) is 600 and a dozen is 12
=50
what is the answer for 6x + 3(x-2)
Answer:
9x - 6
Hope this helps! <3
(If you need a step by step lmk)
Answer:
6x+3(x-2)
6x+3x-6
9x-6
4. Which is a step when adding or subtracting numbers written in scientific notation?
We need to know about scientific notation to solve the problem. Convert the numbers to same power of ten for addition or subtraction.
When a number is too big or too small we write it with an exponent raised to 10, this makes the number easy to read and understand. Writing a number like this is called scientific notation. Inorder to add or subtract two numbers written in scientific notation we need to first convert the powers of 10 to the same power, so that we can add the decimal numbers with the power of 10 being the common factor. We can convert the power by either multiplying the number to powers of 10 or by dividing it by powers of 10.
Therefore for addition or subtraction of two numbers written in scientific notation we need to have same powers of 10.
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In 2006, the number of federal hazardous waste sites in California was 3 less than twice the number of sites in Washington. How many hazardous waste sites were there in Washington if there were 19 such sites in California?
Answer:
11
Step-by-step explanation:
2x-3=19
2x=22
x=11
help please I don't quite understand the question much.
The profit in 2012 must be 4.5(in hundreds of dollars) to break even.
Profit for a company is defined as the difference between the revenue and cost of a product.
Let us take an example to learn more about profit.
A company sells a product at a price of 'S' dollars and the company spends 'C' dollars to manufacture the product. Here C includes the cost of raw materials, labor cost, transport etc.. Now the net profit for the company for selling one unit of this particular product is given by
Profit=S-C
When S>C the profit is positive.When S<C the profit is negative or loss .When S=C then the company breaks even.In the given chart it is shown the profit of the company is given as
2.5,1.75,-3.3 and -1.4 (in thousands of dollars) over 4 years.
Net profit over four years=[tex]2.5+1.75-3.3 -1.4=-0.45[/tex]
So over the past four years the company incurred a loss of
[tex]=0.45\times 1000\\[/tex]
[tex]=450[/tex] dollars
Now the company needs to break even in 2012.
So net profit must be zero over 5 years.
Therefore Profit in 2012=0-(-450)=450 dollars
Profit=4.5 (hundreds of dollars)
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The 5000 that invested in Fund A returned a 3% profit. The amount that invested in Fund B returned a 10% profit. How much did she invest in Fund B, if both funds together returned a 5% profit?
The investment in Fund B is $2000.
To understand the given question we first have to understand the logic of percentage and how it affect the return on Investment.
If an investment fund returns a profit on an investment then the profit is calculated by multiplying the investment with the profit(in decimal form).
For Example: If the investment is A and profit is x % then the profit is calculated by:
Profit =A×([tex]\frac{x}{100}[/tex])
Now in the given problem, let us consider the amount of investment into the Fund B be x.
Profit in Fund B=10%
Profit in Fund A is 3%.
Investment in Fund A=$5000
Total profit from both investments=3% of 5000+10% of x
[tex]=\frac{3}{100}\times 5000 + \frac{10}{100}\times x\\ =150+0.1x[/tex]
Now the total investment=5000+x
The combined profit for both the Investments is 150+0.1x
But the combined profit is 5% for both investments.
profit=[tex]5\% of(5000+x)[/tex]
[tex]=\frac{5}{100}\times (5000+x)\\=0.05\times5000+0.05x\\=250+0.05x[/tex]
Now the profit is same, so if we equate both the expressions of profit we get a linear equation in x.
[tex]\therefore 250+0.05x=150+0.1x\\or,250-150=0.1x-0.05x\\or,100=0.05x\\or,x=2000[/tex]
Thus we can conclude that she invested $2000 in the Fund B.
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Find the equation of the line that contains the point (6, -2) and is perpendicular to the line y = - 2x + 8.
O y = -x
Oy=2x-14
O y =
x-5
O y = - 2x + 10
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{-2}x+8\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-2\implies \cfrac{-2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-2}\implies \cfrac{1}{2}}}[/tex]
so, we're really looking for the equation of a line whose slope is 1/2 and that it passes through (6 , -2)
[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{6}) \implies y +2= \cfrac{1}{2} (x -6) \\\\\\ y+2=\cfrac{1}{2}x-3\implies \LARGE \begin{array}{llll} y=\cfrac{1}{2}x-5 \end{array}[/tex]
8.2% of what amount is $2.87
Answer:
35Step-by-step explanation:
8.2% of what amount is $2.87
we find unity and multiply by 1002.87 : 8.2 * 100 =
35
You have two strands of decorative lights. Strand A changes color every 8 seconds and Strand B changes color every 12 seconds. Both strands just changed color. After how many seconds will the strands change color at the same time again?
Answer:
24 seconds
Step-by-step explanation:
Strand A: 3 × 8 secons =24 seconds
Strand B: 2 × 12 seconds= 24 seconds
The lateral surface area of cone A is exactly 1/2 the lateral surface area of
cylinder B.
OA. True
OB. False
Answer:
B. False
Step-by-step explanation:
You want to compare the lateral surface areas of a cone and cylinder, where the slant height of the cone is twice the height of the cylinder. Your proposition is that the cone's lateral area is half that of the cylinder.
Cone lateral areaEffectively, the lateral area of a cone is the area of a triangle whose base is the circumference of the cone, and whose height is the cone's slant height. The formula for the lateral area of a cone of radius r and slant-height s is ...
A = πrs
For the given dimensions (s=2h), the lateral area is ...
A = πr(2h) = 2πrh
Cylinder lateral areaThe lateral area of a cylinder is the area of a rectangle whose base is the circumference of the cylinder, and whose height is the cylinder's height. The formula for the lateral area of a cylinder of radius r and height h is ...
A = 2πrh
ComparisonThe lateral areas of the given figures are both 2πrh, so one is not half the other.
The proposition is False.
Form an equation in x and solve
Answer:
x+(90°-0.5x)=3x
Step-by-step explanation:
Each of the two unknown angles in the triangle is 90°-0.5x because the triangle is isosceles.
So, by the exterior angle theorem, x+(90°-0.5x)=3x.
(A) Find the slope of the line that passes through the given points_
(B) Find the point-slope form of the equation of the line.
(C) Find the slope-intercept form of the equation of the line.
(D) Find the standard form of the equation of the line.
(4,2) and (11,8)
a) The slope of the line is 6 / 7.
b) The point-slope form of the equation of the line is y - 2 = (6 / 7) · (x - 4).
c) The slope-intercept form of the equation of the line is y = (6 / 7) · x - 17 / 7.
d) The point-slope form of the equation of the line is - 6 · x + 7 · y + 17 = 0.
How to find the equation of the line in three different forms
There are three different forms of the equation of the line:
Point-slope
y - y' = m · (x - x') (1)
Slope-intercept
y = m · x + k (2)
Standard
a · x + b · x + c = 0 (3)
Where:
m - Slopek - y-Intercepta) The slope that passes through the two given points is found by secant line formula:
m = [8 - 2] / [11 - 4]
m = 6 / 7
b) The point-slope form of the equation of the line is:
y - 2 = (6 / 7) · (x - 4)
c) The slope-intercept form of the equation of the line is:
y - 2 = (6 / 7) · x - 24 / 7
y = (6 / 7) · x - 17 / 7
d) The standard form of the equation of the line is:
7 · y = 6 · x - 17
- 6 · x + 7 · y + 17 = 0
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after a 27% reduction, you purchase a new painting for $146. what was the original price of the painting?
Answer:
$200
Step-by-step explanation:
At 27% reduction, we pay 100%-27%=73% of the original price O.
73% * O = $146
O = $146 / 73%
O = $2 / 1%
O = $2 / (1/100) = $2 * 100 = $200
Answer:
$ 200
Step-by-step explanation:
27 % off means you pay 73% ( or .73 in decimal)
.73 * x = 146 x = original price
x = 146/.73 = $ 200
10.
7
TR
Connect to Everyday Life Compare
the door's height to the desk's height
using multiplication and addition.
8 ft
2 ft
Using proportions and multiplication, it is found that the door's height is 4 times greater than the desk's height.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The ratio between two amounts a and b is the proportion of a to b, that is, the division of a by b.
For this problem, we have that:
The door's height is of 8 ft.The desk's height is of 2 ft.8/2 = 4, hence, the door's height is 4 times greater than the desk's height.
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what is the multiplicative inverse of
3/5 - 4/27 + 5/18 is it okay if i solve the equation and then the final answer i get i write multiplicative inverse of it as the final answer ..
Answer:
[tex]\frac{270}{197}[/tex]
Step-by-step explanation:
First I need a common denominator. That number is 270
