Answer:
x=-1189/36, y=242/9. (-1189/36, 242/9).
Step-by-step explanation:
-8x-16y=-166
8x+7y=-76
----------------
-9y=-242
9y=242
y=242/9
8x+7(242/9)=-76
8x=-76-1694/9
8x=-2378/9
x=(-2378/9)/8
x=-1189/36
Which of the following is true of vertex-edge graphs.
(1)They can model real-world problems.
(2)They can all be solved.
(3)Euler paths are the same as Hamilton paths.
(4)All vertices must be used once in Hamilton circuits.
Final answer:
Vertex-edge graphs can model real-world problems, not all graphs can be solved, Euler paths and Hamilton paths are different, and in a Hamilton circuit, all vertices must be used exactly once.
Explanation:
Vertex-edge graphs, also known as graphs or networks, are mathematical structures that consist of vertices (also called nodes) connected by edges. They are widely used to model real-world problems across various fields such as computer science, transportation planning, and social networks, among others (1). While some vertex-edge graphs can be solved, it is not true that all graphs can be solved. Solvability depends on the specific problem being represented by the graph and the algorithms or methods used to solve it (2). Euler paths and Hamilton paths are not the same. An Euler path is a path in a graph that visits every edge exactly once, while a Hamilton path visits every vertex exactly once (3). In a Hamilton circuit, all vertices must be used exactly once, but not in a Hamilton path. There can be more than one Hamilton path in a graph, depending on its structure (4).
hool.
uch
2. The length of a room is 10 feet. What is the
length of the room in inches?
Answer:
30
Step-by-step explanation:
1 foot=3 in
10*3=30 there,easy
Answer:
Should be 120 inches
Step-by-step explanation:
1 feet = 12 inches
10 feet = 12( inches) × 10 (feet)
Therefore, the formula should be:
12×10
=120 ( inches)
Hope it helps!
How to substitute for -5x+3y=51 and y=10x-8
Answer:
x=3, y=22. (3, 22).
Step-by-step explanation:
-5x+3y=51
y=10x-8
----------------
-5x+3(10x-8)=51
-5x+30x-24=51
25x-24=51
25x=51+24
25x=75
x=75/25
x=3
y=10(3)-8
y=30-8
y=22
The value of x is 3 and y is 22.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
-5x+3y=51 ..........(1)
y=10x-8 .............(2)
Put the value of y from equation (2) in equation (1) we get
-5x+ 3(10x - 8)= 51
-5x + 30x - 24 = 51
25x = 51+ 24
25x = 75
x= 3
and, y= 10(3)- 8= 30 -8 = 22
Hence, the value of x is 3 and y is 22.
Learn more about Equation here:
https://brainly.com/question/29657983
#SPJ2
From end zone to end zone in football field is 120 yards long how long is the football field in feet
Answer:
1,440 feet
Step-by-step explanation:
there are 12 feet in one yard
you have 120 yards so you need to multiply 120*12
you would get 1,440
Answer:
360 feet
Step-by-step explanation:
1 yard = 3 feet
120 yard x 3 = 360 feet
if p^3 is 0.027, what is p's value
Answer:
0.3
Step-by-step explanation:
To find p we require the cube root of 0.027, that is
p³ = 0.027, then
p = [tex]\sqrt[3]{0.027}[/tex] = [tex]\sqrt[3]{\frac{27}{1000} }[/tex] = [tex]\frac{3}{10}[/tex] = 0.3
bob bedroom room weights 62 kilograms how many grams does bob bed weight
Answer:
62,000 grams as there are 1000 grams in a kilogram
In the year 2006, a company made $7 million in profit. For each consecutive year after that, their profit increased by 9%. How much would the company's profit be in the year 2008, to the nearest tenth of a million dollars?
Answer:
The company's profit be in the year 2008 is $8.3 million.
Step-by-step explanation:
Given:
In the year 2006, a company made $7 million in profit, their profit increased by 9%.
So, we need to calculate the company's profit be in the year 2008.
Now, by putting the formula to find the profit(P) after the two year:
Difference between the year = 2008 - 2006 = 2 year.
So, number of years(n) = 2 year
Rate of profit increasing(r) = 9%
Amount company made in 2006 (A) = $7 million.
[tex]P=A(1+\frac{r}{100})^{n}[/tex]
[tex]P=7(1+\frac{9}{100})^{2}[/tex]
[tex]P=7(1+0.09)^{2}[/tex]
[tex]P=7(1.09)^{2}[/tex]
[tex]P=7\times 1.188[/tex]
[tex]P=8.316[/tex]
Profit in the year 2008 would be 8.316 million, and nearest to the tenth of a million dollars is $8.3 as 3 is in the tenth place of the decimal and 1 in the hundredth so rounding will change $8.316 to $8.3.
Therefore, the company's profit be in the year 2008 is $8.3 million.
Final answer:
To find the company's profit in 2008 after a 9% increase each year from 2006, we calculate compound growth over two years. The profit in 2008 would be $8,316,700, which rounds to $8.3 million.
Explanation:
To calculate the company's profit in the year 2008 after it increased by 9% each year following 2006, we can use the formula for compound interest which is similar to calculating compounded profit growth. The formula is:
[tex]P = P_0 \times (1 + r)^t[/tex]
Where:
P is the future profit
P₀ is the initial profit ($7 million)
r is the annual growth rate (9% or 0.09)
t is the number of years since 2006 (2008 - 2006 = 2 years)
Let's calculate the profit for 2008:
P = $7,000,000 × (1 + 0.09)²
First, calculate the growth factor for one year:
1 + 0.09 = 1.09
Now, apply the growth factor for two years:
1.09² = 1.1881
Multiply the initial profit by the growth factor:
P = $7,000,000 × 1.1881 = $8,316,700
To the nearest tenth of a million dollars, the company's profit in 2008 would be $8.3 million.
How to graph x-4y=-4
Answer:
Step-by-step explanation:
Re-write the equation, for convinience, as
y = 1/4(x) + 4
set x = 0 to get y = 1 and set y = 0 to get x = -4.
You have the coordinates of 2 points, (0 , 1) and ( -4 , 0).
Join the two points which obviously cuts the y-axis at y = 1,
Create your own cubic trinomial. You can type exponents like this: x6 as x6.Cubic trinomial:
Answer:
[tex]3x^{3}-2x^{2} +6x[/tex]
Step-by-step explanation:
The cubic trinomial is in this form :
[tex]Ax^{3}+Bx^{2} +Cx[/tex]
So, instead A, B, and C we can use any number.
We use :
A=3
B=2
C=6
[tex]3x^{3}-2x^{2} +6x[/tex]
A cubic polynomial has a degree of 3.
Since 3 is the highest degree, the polynomial could contain terms with degree 2, 1, or 0 (quadratic, linear, or constant).
A trinomial can have only 3 terms.
Including terms with degrees of 3, 2, 1, and 0 would mean the polynomial has 4 terms.
The cubic trinomial could consist of a cubic, quadratic, and linear term, with no constant term.
hey how to do this and what the answer
Answer:
5x + y - 4 = 0
Step-by-step explanation:
When we are given two points and are asked to find the equation of the line we use the two - point form.
Two - point form: [tex]$ \frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1} $[/tex].
where: [tex]$ (x_1,y_1) $[/tex] and [tex]$ (x_2,y_2) $[/tex] are the two points on the line.
Given the two points are: (5,21) and (-5,-29).
Substituting in the two point form:
⇒ [tex]$ \frac{y - 21}{-29 - 21} = \frac{x - 5}{-5 -5} $[/tex]
[tex]$ \implies \frac{y - 21}{-50} = \frac{x - 5}{-10} $[/tex]
[tex]$ \implies y - 21 = 5x - 25 $[/tex]
⇒ 5x + y - 4 = 0
Solve each problem as indicated. Type your answer in the box. Do not use any spaces.
(-33) + (-22) =
Hello.
Answer: -55. When adding two negatives, you add like you would any positive number.
What numbers add up to 3 but multiply -18
Answer:
-3 and 6
Step-by-step explanation:
-3 + 6 = 3
-3 * 6 = -18
Final answer:
The two numbers that add up to 3 and multiply to -18 are 6 and -3. By setting up equations based on these conditions and solving them, we determine these two numbers.
Explanation:
The question asks about two numbers that when added together equal 3, and when multiplied together equal -18. To find these numbers, we need to set up a system of equations based on the given conditions:
Let the two numbers be x and y.
The sum of x and y is 3: x + y = 3.
The product of x and y is -18: xy = -18. Let's use factorization and proceed as follows:
Assume y = 3 - x.
Substitute y into the second equation: x(3 - x) = -18.
This simplifies to x2 - 3x - 18 = 0.
Factor the quadratic: (x - 6)(x + 3) = 0.
So, x = 6 or x = -3.
Using x + y = 3, if x = 6, then y = -3. If x = -3, then y = 6.
The two numbers that satisfy the given conditions are 6 and -3.
62. A roof in the e
escape through it
side BC is 9.8 m, and
in the shape of a rectangular pyramid is going to be filled with insulation so that heat does not
through it. The dimensions of the attic are shown in the following diagram. Side AB is
BC is 9.8 m, and side EC is 12.9 m. Answer the following questions to determine the heign
the attic. Round your answers to one decimal place.
s to determine the height, EF of
12.9 m
9.8 m
14.6 m
a) To find the height of EF using the Pythagorean Theorem, you first have to find the distance
(Hint: start by determining the length of AC, then you can figure out the length of Ch)
CF=
b) Determine the length of EF.
Answer:
9.4m
Step-by-step explanation:
Let the diagram of the rectangular pyramid be as shown in the attached
If a point C' is selected midway between C and B and F' is selected midway between D and C as shown in pyramid 2
FC can then be computed using pythagoras theorem such that
FC^2 = FC'^2 + CC'^2
FC^2 = (14.6/2)^2 + (9.8/2)^2
FC^2 =53.29 + 24.01
FC^2 = 77.3
FC = sqrt(77.3) = 8.8
To determine the height of the attic, we estimate EF, Pythagoras theorem can be used for triangle EFC
such that EC^2 = EF^2 + FC^2
therefore EF^2 = EC^2 - FC^2
EF^2 = 12.9^2 - 8.8^2
EF^2 = 166.41 - 77.44
EF^2 = 88.97
EF = sqrt(88.97)
EF = 9.4
The height of the attic is therefore 9.4m
mckenna had $32 when she got to the carnival . after riding 6 rides , she had $20 left . write an eqaution and solve to find the price for each ride
Answer:
$2 per ride
Step-by-step explanation:
$32-$20=$12
McKenna rode 6 rides so $12 divided by 6 rides is $2 for every ride
Final answer:
The equation to find the price for each ride McKenna paid at the carnival is $32 - 6P = $20. Solving for P gives us P = $2, so each ride costs $2.
Explanation:
To find the price for each ride that McKenna paid at the carnival, we need to set up an equation based on the information given. McKenna started with $32 and ended with $20 after riding 6 rides. The amount spent on rides is the difference between the starting amount and the remaining amount.
The equation will be:
Initial amount - (Price per ride × Number of rides) = Remaining amount
$32 - (Price per ride × 6) = $20
Let's denote the price for each ride as P. So the equation becomes:
$32 - 6P = $20
To solve for P, we rearrange the equation:
6P = $32 - $20
6P = $12
P = $12 / 6
P = $2
Hence, the price for each ride is $2.
Please answer this correctly is the answer
7:33pm
1:33pm
4:33pm
6:57am
Answer:
the answer should be 1:38 pm, but if not, 1:33 pm is correct
Answer:
1:33 PM
Step-by-step explanation
When the plane arrives in Salt Lake City, the time in eastern time period should be 15:33 or 3:33 PM. From eastern time period to the mountains, the time should decrease by 2 hours. 3:33 - 2 hours is 1:33. 1:33 is still in the afternoon so the answer is 1:33 PM.
there were 2 yellow straws and 3 red how many red in 30
Answer:
30 yellow straws and 45 red straws
30:45
Step-by-step explanation:
Make a ratio:
2:3, 2 being the yellow straw and 3 being the red straws
They are now asking how many red if there are 30 yellow straws
2:3 = 30:x
You could either cross multiply or simply do 30 ÷ 2 = 15 then 15 × 3 = 45. Your answer is 45
Cross multiplying
2x = 90
90 ÷ 2 = 45
what is three half squared as a fraction
Final answer:
Three half squared is (3/2)², which equals 9/4 when you square the numerator (3² = 9) and the denominator (2² = 4) separately.
Explanation:
The expression 'three half squared' refers to the quantity (3/2) squared. To square a fraction, you square the numerator and the denominator separately. Therefore, (3/2) squared is (3 squared) over (2 squared), which is 9 over 4. Since there are no further simplifications to make, 9/4 is the final answer as a fraction.
To understand this conceptually, think about the process of squaring as finding the area of a square with side lengths of the original number. So, if the side length of a square is 3/2, the area (which represents the square of the number) will be 9/4 square units.
Final answer:
To determine what three-half squared is as a fraction, you simply square the numerator and denominator separately, arriving at the fraction 9/4.
Explanation:
Calculating Three-Half Squared as a Fraction
To find what three half squared is as a fraction, you square both the numerator and the denominator of the fraction 3/2. When you square the numerator (3), you get 9, and when you square the denominator (2), you get 4. Therefore, the answer to three half squared is 9/4, as we have calculated (3/2)² = (3²)/(2²) = 9/4.
This calculation is similar to understanding that if you start with half of a pie and you multiply this amount by itself, you are essentially getting a fraction of the original whole. In our example, by squaring half, we get a quarter, thereby following the intuitive sense of fractions.
Shirley and her family ate out last night.the bill was $95 including tax. If the tax was 8.25%, what is the total price?
Answer:
$87.76
Step-by-step explanation:
108.25/100 = 95/x
95×100=9500
9500÷108.25=87.76
To find the total price including tax after a meal at a restaurant, convert the tax rate to a decimal, then multiply it by the total cost and add the result to the original total cost.
Explanation:First, find the amount of sales tax. To do this, convert the percent to a decimal by dividing by 100: 8.25% = 0.0825.
Then multiply the total cost by the decimal tax rate to get the tax amount. In this case, $95 * 0.0825 = $7.8375.
Next, add the tax amount to the original total cost to find the total price: $95 (original cost) + $7.8375 (tax) = $102.8375.
Therefore, the total price, including tax, for Shirley and her family's meal last night was $102.84.
Find the value of c that completes the square.
a2 + 12a + c
Answer:
c = 36
Step-by-step explanation:
Given
a² + 12a + c
To complete the square
add ( half the coefficient of the a- term )² to a² + 12a
a² + 2(6)a + 6²
= (a + 6)² + 36
Hence the value of c = 36
If we mix the alcohol solution we have with pure water at the ratio 3:2, we will obtain a solution of 18% alcohol. If we instead mix them at a ratio of 4:1, what will be the alcohol percentage of the solution?
Final answer:
To find the alcohol percentage in the 4:1 ratio, we use the information from the 3:2 ratio. For every 3 parts alcohol, there are 2 parts water. When mixed at a ratio of 4:1, the alcohol percentage is 24%.
Explanation:
To determine the alcohol percentage of the solution when mixed at a ratio of 4:1, we can use the information given in the question. When mixed at a ratio of 3:2, the solution contains 18% alcohol. This means that for every 3 parts alcohol, there are 2 parts water. We can use this information to find the alcohol percentage for the 4:1 ratio.
Let's say we have 4 mL of alcohol and 1 mL of water. The total volume is 4+1 = 5 mL. In the 3:2 ratio, the alcohol percentage is 18%. So, for 3 mL of alcohol, the total volume is 3+2 = 5 mL. Therefore, the alcohol percentage for the 4:1 ratio is (18/3) * 4 = 24%.
Eggs were $2.05 per dozen on January 1 and $2.00 per dozen on February 1. What percent did the price increase during January?
Answer:
2.5%
Step-by-step explanation:
The price increased from 2 to 2.05. So the increase was:
2.05 - 2 = 0.05 dollars
Now, to find percentage increase, we use the formula below:
[tex]\frac{New-Old}{Old}*100[/tex]
Where
New is the latest price (here it is the increased price of 2.05)
Old is the previous price (here it is the less price of 2.00)
Now, we substitute and find:
[tex]\frac{2.05-2.00}{2.00}*100=2.5[/tex]
So the price increase was 2.5%
In order to prepare for your summer bash, you go to the supermarket to buy hamburgers and
chicken. Hamburgers cost $2 per pound and chicken costs $3 per pound. You have no more than
$30 to spend. You expect to purchase at least 3 pounds of hamburgers.
The complete question is:
In order to prepare for your summer bash, you go to the supermarket to buy hamburgers and chicken. Hamburgers cost $2 per pound and chicken costs $3 per pound. You have no more than $30 to spend. You expect to purchase at least 3 pounds of hamburgers.
Write a system of inequalities to represent this situation.Graph the system of inequalities on the grid.Give three possible combinations for buying hamburgers and chicken for your summer bash.Justify your answers
Answer:
A) System of inequalities:
2x + 3y ≤ 30x ≥ 3x ≥ 0y ≥ 0B) Graph: see the picture attached
C) Three possible combinations:
3 pounds of hamburgers and 8 pounds of chicken3 pounds of hamburgers and 0 pounds of chicken15 pounds of hamburgers and 0 pounds of chickenExplanation:
A) Write the system of inequalities to represent this situaction.
1. Variables:
x: number of pound of hamburgersy: number of pound of chicken2. Costs:
x pounds of hamburgers at $2 per pound: 2xy: pounds of chicken at $3 per pound: 3ytotal cost: 2x + 3y3. First constraint:
You have no more than $ 30 to spend: means that the cost of what you buy can be at most (less than or equal to) $ 30.2x + 3y ≤ 304. Second constraint:
You expect to purchase at least 3 pounds of hamburgers: means that the number of pounds of hamburgers may be greater than or equal to 3.x ≥ 35. Additional constraints:
Both, x and y cannot be negative: x, y ≥ 06. System of equations:
2x + 3y ≤ 30x ≥ 3x ≥ 0y ≥ 0B) Graph
You have to graph all the constraints in a x-y coordinate system.
1. To graph 2x + 3y ≤ 30 graph the line 2x + 3y = 30
Choose the y-intercept and x-intercept.x = 0 ⇒ 3y = 30 ⇒ y = 10 ⇒ point (0, 10)y = 0 ⇒ 2x =30 ⇒ x = 15 ⇒ point (15, 0)With two points you can draw the lineClear y: y ≤ 10 - 2x/3. Since, the symbol is ≤ you shade the region below the line, and the line is included, so you draw it as as solid line.2. To graph x ≥ 3 just draw the vertical line x = 3 and shade the region to the right of it. The points of the line are included (solid line).
3. The constraints x ≥ 0 and y ≥ 0 mean that the region is restricted to the first quadrant (including the positive axis).
4. The feasible solutions are the set of points inside the common regions (intersection).
With all that information the graph is the one attached. The feasible solutions is the region defined by the triangle with vertices (3,8), (3,0), and (15,0).
C) Give 3 possible combinations.
You can pick any three points inside the region, as long as the coordinates are integer numbers. For instance the 3 vertices are solutions:
(3, 8) ⇒ 3 pounds of hamburgers and 8 pounds of chicken(3,0) ⇒ 3 pounds of hamburgers and 0 pounds of chicken(15,0) ⇒ 15 pounds of hamburgers and 0 pounds of chickenYou could also prove that (5,4), 5 pounds of hamburgers and 4 pounds of chicken meet, the inequalities.
This is how you prove it:
5 ≥ 05 ≥ 34 ≥ 02(5) + 3(4) = 10 + 12 = 22 ≤ 30And you can do the same for any pairs to verify whether they are solution or not.
Which of the following statements is true about the triangles below
Answer:
Step-by-step explanation:
From the given diagram we notice that
1. Line AB is equal to Line DE.
2. Line AC is equal to line DF.
3. Angle A is equal to angle D
Then, it shows that 2 sides of the triangle are similar and 1 of it's angle is also similar. Then, it is SAS
Where, S- represent sides and A- represents angle
NOTE : we have SSS, ASA, AAS and SAS, we don't have SSA
To write the similar triangle equation
∆ABC ≈ ∆DEF
Since AB is equal to DE, the we replace It with DE and also Angle A is equal to angle D. Also AC is equal to DF, then we replace C with F.
So the answer is C
∆ABC ≈ ∆DEF SAS
1192 people per square mile in New Jersey and a national average of 86.4 Americans per square mile in 2012
Answer:
First number is 1379.63% of the second number.
Step-by-step explanation:
Consider the provided information.
1192 people per square mile in New Jersey.
The national average is 86.4.
We need to 1192 people per square mile in New Jersey is how much % of a national average of 86.4 Americans per square mile in 2012.
Let 1192 is x percent of 86.4.
[tex]1192=\frac{x}{100}\times 86.4[/tex]
[tex]x=\frac{1192\times 100}{86.4}[/tex]
[tex]x=\frac{119200}{86.4}[/tex]
[tex]x\approx 1379.63\%[/tex]
Hence, first number is 1379.63% of the second number.
Tomas was flying from Neww York to visit his brother in paris. From takeoff of landing,it was exactly 12 hours. The map he had showed that he had traveled approximately 6,000 miles. About how fast was the plane traveling
Answer:
500 miles per hour
Step-by-step explanation:
6000 miles/12 hours = 500 miles per hour
In ∆ABC the angle bisectors drawn from vertexes A and B intersect at point D. Find ∠ADB if:
m∠A = α , m∠B = β
Answer:
The measure angle ADB = 180 - (α/2+ β/2)
Step-by-step explanation:
measure angle A is α degrees, this means that, the angle bisector divides the angle into two equal angles each of measure α/2 degrees
measure angle B is β degrees, this means that the angle bisector divides the angle into two equal angles each of measure β/2 degrees
In triangle ADB, we know that the sum of all measure of a triangle is 180 degrees and we have measure angle MAB = α/2 degrees and measure angle MBA = β/2 degrees
Therefore,
measure angle ADB = 180 - (α/2+ β/2)
What is the slope of the line that contains these points?
Each increase of 1 in x decreases y by 7, i.e. increases y by -7. That's a slope of
Answer: -7
Answer:
[tex] -7[/tex]
Step-by-step explanation:
Use the rise over run equation
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
what is.3x^2 +x+2-4x^2(3x-4) equal to
Answer:
-12x^3+17x^2+x+2
Step-by-step explanation:
3x^2+x+2-4x^2(3x-4)
3x^2+x+2-12x^3+14x^2
3x^2+14x^2-12x^3+x+2
17x^2-12x^3+x+2
-12x^3+17x^2+x+2
Blaine buys 2 books and the total cost is $24.18 What is the constant of proportionality that
relates the cost in dollars y, to the number of books X?
I’ll give Brainly answer quick!!
Answer:
$12.09
Step-by-step explanation:
formula; Y= kx
where; y = $24.18
x = 2 books
k = constant of proportionality
Step 1. Do the equation based on the data given
Y = kx
$24.18 = k2
Step 2. Compute the mathematical equation. Divide both sides by 2 to eliminate coefficient in the variable.
24.18 =k2
2
k = $ 12.09 is the constant of proportionality cost in dlooars per book
-2(a + 16) = 2
Do I guys know the answer and work to this
Answer:
a = - 17
Step-by-step explanation:
Given
- 2(a + 16) = 2 ( divide both sides by - 2 )
a + 16 = - 1 ( subtract 16 from both sides )
a = - 17
Answer:
a=-17
Step-by-step explanation:
-2(a+16) =2
-2a-32=2
+32 +32
-2a=34
divided in both sides by -2
a=-17