Answer:
Smallest: 29, Middle: 53, Largest: 58
Step-by-step explanation:
We can represent the angles in this problem using an equation.
We'll use x to represent the smallest angle, and work out other ways to represent the others.
As the largest angle is twice that of the smaller angle, we can represent the largest angle as 2x as 2x is two times x.
The middle angle is 24 more than the smallest, so we can represent that one as x + 24, since it is 24 more than the smallest.
Now we have our angles all represented with x:
Smallest angle = x
Middle = x+24
Largest = 2x
We know that they all add together to 140 so our equation is:
x+2x+(x+24) = 140
Now we can solve for x!
We can remove the brackets (addition does not change the terms) and combine the terms:
x+2x+x+24=140
4x+24=140
Next we move the 24 to the other side so we can solve for x:
4x + 24 - 24 = 140 - 24
4x = 116
Finally we divide both sides by 4:
x=29
The smallest angle is 29!
Now we can use our representations to find the other angles:
Middle angle = x+24, therefore it is 29+24 = 53
Largest angle = 2x therefore it is 2*29 = 58
58+53+29=140 so we have successfully worked out our angles!
Hope this helped!
4. Consider the figure below.
(5x - 14) ft
(2x) - 5x2 - 12x + 14) ft
What is the total area, in square feet, of the figure
Answer:
(10x⁴ - 52x³ + 5x² + 246x - 196) ft²
Step-by-step explanation:
The figure can be divided into two rectangles: the small rectangle and the large rectangle.
Dimensions of the small rectangle:
Length (l) = (x) ft
Width (w) = (x² - 6) - (5x - 14) = x² - 6 - 5x + 14 = (x² - 5x + 8) ft
Area of small rectangle = l*w = (x)(x² - 5x + 8)
Area = x(x²) - x(5x) + x(8) (using distributive property)
Area of small rectangle = (x³ - 5x² + 8x) ft²
Dimensions of large rectangle:
Length (l) = (2x³ - 5x² - 12x + 14) ft
Width (w) = (5x - 14) ft
Area of large rectangle = l*w = (2x³ - 5x² - 12x + 14)(5x - 14)
2x³(5x - 14) - 5x²(5x - 14) - 12x(5x - 14) + 14(5x - 14) (distributive property)
10x⁴ - 28x³ - 25x³ + 70x² - 60x² + 168x + 70x - 196
Combine like terms
Area of large rectangle = (10x⁴ - 53x³ + 10x² + 238x - 196) ft²
Area of figure = area of small rectangle + area of large rectangle
= (x³ - 5x² + 8x) + (10x⁴ - 53x³ + 10x² + 238x - 196)
Open parentheses
= x³ - 5x² + 8x + 10x⁴ - 53x³ + 10x² + 238x - 196
Combine like terms and arrange in standard form (from the greatest degree to the least)
= 10x⁴ + x³ - 53x³ - 5x² + 10x² + 8x + 238x - 196
= 10x⁴ - 52x³ + 5x² + 246x - 196
Area of the figure = (10x⁴ - 52x³ + 5x² + 246x - 196) ft²
Which one of these is not an integer?
a 0.75
b-9
со
d 16
Check it
Answer:
A
Step-by-step explanation:
HURRY HELP!
The formula B = 100 + 75m gives the balance (B) of a bank account after (m) months of saving. Solve for m and then use your solution to find the number of months you would need to save to have a balance of $700.
Answer:
8 Months
Step-by-step explanation:
The formula in the problem (B = 100 + 75m) can be written as this:
(B-100)/75 = M
The problem gives us the balance (B=700), which we can plug into our new formula to find the number of months (m).
(700-100)/75 = M
M = 8
I hope this helps!
-TheBusinessMan
If your car travels 300 miles and uses 10.2 gallons, how many miles per gallon did you get? (Round your answer to three decimal places.)
Square root !!!!!!!!
Answer:
hope this helped
Step-by-step explanation:
Step 1: Calculate. We calculate the square root of 50 to be: √50 = 7.07106781186548.
Step 2: Reduce. 7.07.
Step 3: Round. Round 7.07 so you only have one digit after the decimal point to get the answer: 7.1.
Write the equation of the line that goes through the point
(7, 10) and is parallel to the line y = 2x + 5
Use point slope equation.
Since parallel, the slope is the same. Then jsut plug in the numbers to the formula (u can google this)
y - 10 = 2 (x - 7)
^^this is point slope form
for slope intercept:
y = 2x - 4
Answer:
[tex]y=2x-4[/tex]
Step-by-step explanation:
So we want to write an equation of a line that goes through the point (7,10) and is parallel the the line y=2x+5.
First, we can determine the slope of our new line. Parallel lines always have the same slope. In other words, the slope of our new line must also be 2.
Now, we can use the point-slope form to find our equation:
[tex]y-y_1=m(x-x_1)[/tex]
Let's let (7,10) be x₁ and y₁. Let's also substitute 2 for m. Thus:
[tex]y-10=2(x-7)[/tex]
Distribute:
[tex]y-10=2x-14[/tex]
Add 10 to both sides:
[tex]y=2x-4[/tex]
And we're done!
What is the slope of the line passing through the given points.
(-3,2), (6,-1)
Answer:
-1/3
Step-by-step explanation:
Since we are given two points, we can find the slope using
m = ( y2-y1)/(x2-x1)
= ( -1-2)/( 6- -3)
= ( -1-2) /( 6+3)
= -3/9
= -1/3
Answer:
Slope (m) = [tex]\frac{-1}{3}[/tex] = -0.33333333...
Step-by-step explanation:
Slope (m) = ΔY -1
ΔX 3
(m)= -1/3
You are the manager of a fast-food store. Part of your job is to report to the boss at the end of each day which special is selling best. Use your vast knowledge of descriptive statistics to write one paragraph letting the boss know what happened today. Here are the data. Do this exercise by hand. Be sure to include a copy of your work.SPECIAL NUMBER SOLD COSTHuge Burger 20 $2.95Baby Burger 18 $1.49Chicken Littles 25 $3.50Porker Burger 19 $2.95Yummy Burger 17 $1.99Coney Dog 20 $1.99Total Specials Sold 119
Answer:
A total of 119 Specials were sold today. Chicken Littles had the highest number sold, which represents about 21% (25/119 * 100) of the total sales and a cost of 24% of the total costs. This was followed by Huge Burger and Coney Dog which were sold 20 each or about 17% of the number sold. Poker Burger, Baby Burger, and Yummy trailed behind with total sales of 19, 18, and 17 respectively.
Step-by-step explanation:
a) Data and Calculations:
SPECIAL NUMBER SOLD Percentage COST Percentage
Huge Burger 20 17% $2.95 20%
Baby Burger 18 15% $1.49 10%
Chicken Littles 25 21% $3.50 24%
Porker Burger 19 16% $2.95 20%
Yummy Burger 17 14% $1.99 13%
Coney Dog 20 17% $1.99 13%
Total Specials Sold 119 100% $14.87 100%
raji collected numerical data. which question could raji ask for categorical data?
A. what kind of pet do you have?
B. how long have you had a pet?
C. how much does your pet weigh?
D. how tall is your pet?
Suppose your SAT score is 1180. You look up the average SAT scores for
students admitted to your preferred colleges and find the list of scores below.
Based on your SAT score of 1180, which average score below represents the
college that would be your best option?
A. 1030
B. 1470
C. 1190
D. 900
Answer:
1190
Step-by-step explanation:
Mylie went by the gas station to get 2.4 gallons of gas. She paid with a $10 bill and a $5 bill and received $4.68 as change. What was the cost for one gallon of gas before taxes? $4.30 $8.20 $10.32 $24.77
We don't know what tax percentage or amount is so we have to keep this part out.
Add to find how much she paid with.
10 + 5 = $15
Subtract to find how much she paid.
15 - 4.68 = $10.32
Divide to find the unit price.
10.32 / 2.4 = $4.30 per gallon
Best of Luck!
An atom that becomes positively charged due to the loss of one or more electrons is referred to as a/an proton. cation. . base, ( anion.
Answer:
cation.
right on the test, Mark brainlieste
Step-by-step explanation:
Answer: cation
Step-by-step explanation: an ion formed by the loss of one or more electrons becomes positively charged and is a positive ion, or cation
Find ( f - g ) (x) f (x) = 2x^2 - 2 and g (x) = 4x + 1
Answer:
( f - g ) (x) f (x) = 2x^2 - 2
g (x) = 4x + 1
answers in pics
How many meters are in 3.5 kilometers
Answer:
Hey there!
1000 meters are in one kilometer, so 3500 meters are in 3.5 kilometers.
Hope this helps :)
Answer:
3,500 meters
Step-by-step explanation:
So this is conversation rates. So how I like to remember conversion rates in the metric system is King Henry Doesn't Usually Drink Chocolate Milk.
K=Kilo, H=Hecto, D=Deca, U=Unit (meters, liter, grams), D=Deci, C=Centi, M=Milli.
SO between meters (which is the U) and kilometers (which is the K), there's 3 letters so kilometers is 1000 times greater than meters. SO 3.5*1000=3500.
Hope this helped
Solve for the function X(s) in the Laplace domain by taking the Laplace transform of the following differential equations with given initial conditions. dx +9x = 161, where x(0) = 0 and (0) = 5
Answer:
X(s) = 2/[s³(s + 9)]
Step-by-step explanation:
Here is the complete question
Solve for the function X(s) in the Laplace domain by taking the Laplace transform of the following differential equations with given initial conditions.
dx/dt + 9x = 16t² x(0) = 0 and dx(0)/dt = 5
Solution
dx/dt + 9x = 16t²
Taking the Laplace transform of the differential equation, we have
L{dx/dt + 9x} = L{16t²}
L{dx/dt} + L{9x} = L{16t²}
L{dx/dt} + 9L{x} = 16L{t²}
sL{x} - x(0) + 9L{x} = 16L{t²}
L{x} = X(s)
L{t²} = 2!/s³
Substituting X(s) and L{t²} into the equation above, we have
sX(s) - x(0) + 9X(s) = 2!/s³
Substituting x(0) = 0 into the equation above, we have
sX(s) - x(0) + 9X(s) = 2!/s³
sX(s) - 0 + 9X(s) = 2!/s³
sX(s) + 9X(s) = 2!/s³
Factorizing X(s), we have
(s + 9)X(s) = 2!/s³
X(s) = 2/[s³(s + 9)]
So X(s) in the Laplace domain is
X(s) = 2/[s³(s + 9)]
Write the recurrence relation for the nth term which is defined by multiplying the prior term by 3 and subtracting 12.
Answer: Aₙ = 3*Aₙ₋₁ - 12
Step-by-step explanation:
Here our terms will be denoted as:
Aₙ
Where this is the n-th term of the sequence.
Now we have that the recurrence relation is defined by:
"by multiplying the prior term by 3 and subtracting 12."
Then we will have that:
Aₙ = 3*Aₙ₋₁ - 12
That is the equation to find all the terms in our sequence (remember that we need to know the initial term, A₀ in order to find all the other ones)
Find all x-intercepts and y-intercepts of the graph of the function . f(x) = - x ^ 3 + x ^ 2 + 12x If there is more than one answer, separate them with commas. Click on "None" if applicable.
Answer:
The y-intercept is (0,0)
The x-intercepts are (-3,0), (0,0), and (4,0)
Step-by-step explanation:
So we have the function:
[tex]f(x)=-x^3+x^2+12x[/tex]
And we want to solve for the x- and y-intercepts.
Y)
To solve for the y-intercept, recall that the y-intercept is when the graph touches the y-axis. At that point, the x values is 0. Thus, to find the x-intercept, substitute 0 for x:
[tex]f(x)=-(0)^3+(0)^2+12(0)[/tex]
Simplify:
[tex]f(x)=0[/tex]
So, the y-intercept is (0,0)
X)
To solve for the x-intercept(s), set the function equal to 0 and solve for x:
[tex]0=-x^3+x^2+12x[/tex]
First, factor out a negative x:
[tex]0=-x(x^2-x-12)[/tex]
Factor within the parentheses:
[tex]0=-x(x-4)(x+3)[/tex]
Zero Product Property:
[tex]-x=0\text{ or } x-4=0\text{ or } x+3=0[/tex]
Divide by -1 on the first one. Add 4 on the second one. And subtract 3 on the right:
[tex]x=0\text{ or } x=4\text{ or } x=-3[/tex]
So, our x-intercepts are:
[tex](-3,0), (0,0), (4,0)[/tex]
And we're done :)
PLEASE HURRY
which expression is equivalent to -3 + (7x+13)
Answer: [tex]7x+10[/tex]
Step-by-step explanation:
Combine the terms;
[tex]-3+7x+13\\(7x)+(-3+13)\\7x+10[/tex]
Darren drives to school in rush hour traffic and averages 30 mph. He returns home in mid-afternoon when there is less traffic and averages 40 mph. What is the distance between his home and school if the total traveling time is 1 hr 45 min?
Answer:
Distance problems are word problems that involve the distance an object will travel at a certain average rate for a given period of time.
The formula for distance problems is: distance = rate × time or d = r × t.
Things to watch out for:
Make sure that you change the units when necessary. For example, if the rate is given in miles per hour and the time is given in minutes then change the units appropriately.
It would be helpful to use a table to organize the information for distance problems. A table helps you to think about one number at a time instead being confused by the question.
Step-by-step explanation:
33 points!! The line contains the point (4,-2) and is perpendicular to 4x+3y=-6 The equation of the line is:
Answer:
y = 3/4 x - 5
Step-by-step explanation:
The slopes of perpendicular lines are negative reciprocals. We find the slope of the given line. Then we can find the slope of the reciprocal.
4x + 3y = -6
Solve for y.
3y = -4x - 6
y = -4/3 x - 2
The slope of the original line is -4/3.
The slope of the perpendicular is 3/4.
Now we need to find the equation of line with slope 3/4 that contains point (4, -2).
y = mx + b
-2 = (3/4)(4) + b
-2 = 3 + b
-5 = b
b = -5
The equation is
y = 3/4 x - 5
The highest point in Louisiana is Driskill Mountain at 585 feet. The lowest points -8 feet in New Orleans. What is the difference in feet between the highest and lowest elevation points? PLEASE SHOW THIS ON A VERTICLE NUMBER LINE!!!!!
The answer is a 577 foot difference
How are integers and rational numbers the same ?
Answer:
Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.
Step-by-step explanation:
Answer:
an integer is a rational number
Step-by-step explanation:
I need help by figuring this out, this is geometry.
Joseph stated that 5/4 is a whole number because it does not repeat as a decimal. Is he correct? Why or Why Not?
Answer:
It is not a whole number.
Step-by-step explanation:
5/4 is equals to 1.25
Therefore it is still a decimal and a fraction, NOT a whole number
You have $437 in a savings account. After a deposit, the balance is $1087. What was the amount of the deposit?
what is the density of an object with 17 g and a volume of 3cm^3
Answer:
5.6666666666667 grams/cubic centimeters
Step-by-step explanation:
teps:
ρ = m / v
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
17 gram s / 3 cubic centimeter
= 5.6666666666667 grams/cubic centimeter
I believe this is correct unless you need to round it up
I hope I helped
Answer:
5.67g/cm³
Step-by-step explanation:
Density =mass ÷ volume
17÷3=5.67
Solve the following system of equations using substitution:
2x - 2y + z = 8
-y+z=4
2z=4
Answer:
Step-by-step explanation:
2z = 4
z = 2
-y + 2 = 4
-y = 2
y = -2
2x + 4 + 2 = 8
2x + 6 = 8
2x = 2
x = 1
(1, -2, 2)
E is the midpoint of DF. If DE = 15x and DF = 31x -11, what is DF?
Step-by-step explanation:
(31x-11)-15x=DF
DF= 16x-11
Answer:
(31x-11)-15x=DF
DF= 16x-11
Step-by-step explanation:
It should be right
simplify the expresion: 8(x^4 y^3)2/3
Answer:
Answer is this or not
Step-by-step explanation:
16x^4y^3/3
If f(x) = x+2 and g(x) = radical x-9, find g(f(x)).
Answer:
second option
Step-by-step explanation:
Substitute x = f(x) into g(x) , that is
g(f(x))
= g(x + 2)
= [tex]\sqrt{x+2-9}[/tex]
= [tex]\sqrt{x-7}[/tex]