Complete question is;
Henrique began to solve a system of linear equations using the linear combination method. his work is shown below
1. 3 (4x-7y=28) -> 12x-21y=84
-2 (6x-5y=31) -> -12x 10y =62
2. 12x - 21y = 84
-12x + 10y = -62
-----------------------
-11y = 22
3. y= -2
complete the steps used to solve a system of linear equations by substituting the value of y into one of the original equation s to find the value of x. what is the solution to the system
Answer:
x = 3.5
Step-by-step explanation:
We are given;
1. 3(4x - 7y = 28) -> 12x - 21y = 84
-2(6x - 5y = 31) -> -12x + 10y = 62
2. 12x - 21y = 84
-12x + 10y = -62
-----------------------
-11y = 22
3. y= -2
Since y = - 2, let's put -2 for y into the equation; 12x - 21y = 84
This gives;
12x - 21(-2) = 84
This gives;
12x + 42 = 84
12x = 84 - 42
12x = 42
x = 42/12
x = 3.5
(6−3x
2
−8x
4
−2x
3
)+(6+7x
2
)+(2−7x
3
+3x
2
)
What is the constant?
Answer:
14
Step-by-step explanation:
I tried to put the problem together as best as I could and i got the problem as (6-3x^2-8x^4-2x^3)+(6+7x^2)+(2-7x^3+3x^2)
That means that the constants are 6+6+2.
6+6+2= 14
how many phone numbers are possible in the (404) area code if the seven digit number have the form FGH-XXXX where F is restricted to 3-9 and X,G and H can be any digit 0-9?
Answer:
900 phone numbers possible.
Step-by-step explanation:
Given the seven digit numbers are of the form:
FGH-XXXX
Possibilities for F = 3 - 9 and X i.e. 9 possibilities
Possibilities for G = 0 - 9 i.e. 10 digits
Possibilities for H = 0 - 9 i.e. 10 digits
To find:
How many numbers are possible ?
Solution:
This problem is nothing but a problem in which we have to find out how many numbers are possible where each digit has a few options available.
Number of ways to select F = 8 digits from 3 to 9 and 1 alphabet X = 9
Number of ways to select G = 10 digits from 0 to 9
Number of ways to select H = 10 digits from 0 to 9
XXXX part will be same in all the numbers.
So, total phone numbers possible = [tex]9 \times 10 \times 10 = \bold{900}[/tex]
Hence, the answer is:
900 phone numbers possible.
What is the exact value of cos(-60°)?
Answer: 1/2
Step-by-step explanation:
cosine=adjacent/hypotenuse
Cos (-60)=1/2
This is a special triangle
see below as the ratio of each side
Hope this helps!! :)
Please let me know if you have any question
Which equation is correctly rewritten to solve for x?
x/r - s = t A. x = t+s/r B. x= rt + s C. x= r(t + s) D. x= r(t - s)
Answer:
x=r(t+s)
Step-by-step explanation:
x/r - s = t
x/r=t+s
x=r(t+s)
Answer:
x=r(t+s)
Step-by-step explanation:
hope this helps
Need help with 6 math problems please
Answer:
9) 60
10) 16
11) 12
12) 3
13) 60
14) 4
Step-by-step explanation:
9) (2)(5)(6)
(10)(6)
60
10) 4(5-1)
4(4)
16
11) 3+4+2+6
7+2+6
9+6
12
12) 3- (1-[tex]\frac{6}{6}[/tex])
3- (0)
3
13) 5(6+1+6-1)
5(7+6-1)
5(13-1)
5(12)
60
14) 2-3(1-1)+4
2-3(0)+4
-1(0)+4
0+4
4
Determine the standard form of the equation of the line that passes through (-2,0) and (-8,5)
Answer: 5/6x + 1y = -5/3 or 5x + 6y = -10
Step-by-step explanation:
First you need to write an equation in slope intercept form and convert it to Standard form. To write an equation in slope intercept form using the coordinates we need to find the slope and the y-intercept.
The slope is the change in y over the change in x.
0-5 = -5
-2-(-8) = 6
Slope is -5/6
Now find the y intercept using the formula y =mx + b where m is the slope and b is the y-intercept.
5 = -5/6(-8) + b
5 = 40/6 +b
-40/6 -40/6
b= -5/3
So now the equation is y= -5/6x - 5/3
So now write it in standard form as ax+by = c where x is constant.
y = -5/6x -5/3
+5/6x
5/6x + 1y = -5/3 now you can multiply it by 6 to get rid of the fractions.
5/6x(6) + y(6) = -5/3(6)
5x + 6y = -10
Alice is riding a Ferris wheel, where t is time in seconds. Suppose the Ferris wheel is 22 m tall. Let h(t) = 11cos(12t) represent the height of Alice in m above or below the centre of the Ferris wheel. Relative to the centre of the Ferris wheel, what is the lowest height Alice achieves?
Answer:
Alice reaches 11 metres below the centre as lowest height.
Step-by-step explanation:
Cosine is a bounded function between -1 and 1, so that the lowest height that Alice achieves in Ferris wheel is:
[tex]h(t) = 11\cdot \cos (12\cdot t)[/tex]
Where:
[tex]t[/tex] - Time, measured in seconds.
[tex]h(t)[/tex] - Height with respect to centre, measured in metres.
If [tex]\cos (12\cdot t) = -1[/tex], then:
[tex]h_{min} = 11\cdot (-1)[/tex]
[tex]h_{min} = -11\,m[/tex]
Alice reaches 11 metres below the centre as lowest height.
Answer: 80m got it on edge
if alpha and beta are zeroes of the quadratic polynomial f(x) = x2-x-2 then find a polynomial whose zeroes are 2alpha + 1 and 2beta + 1
Answer:
Step-by-step explanation:
Hello, as alpha and beta are zeroes of
[tex]x^2-x-2[/tex]
it means that their sum is alpha+beta=1 and their product alpha*beta=-2.
The polynomial whose zeroes are 2 alpha + 1 and 2 beta + 1, means that the sum of its zeroes is 2(alpha+beta)+2=2+2=4
and the product is (2alpha+1)(2beta+1)=4 alpha*beta + 2(alpha+beta) + 1 = 4 * (-2) + 2*(1) +1 = -8 + 2 + 1 = -5. so one of these polynomials is
[tex]\Large \boxed{\sf \bf \ \ x^2-4x-5 \ \ }[/tex]
Thank you.
N this conversation the two people speak a total of 42 words in 21 seconds. When we have a comparison of two numbers with different units (like words and seconds), that is called a _______ .
Answer: I believe it would be called a rate.
Riley is saving up to buy a new television. She needs a total of $1,372.35. Riley has saved $200.55 already and earns $78.12 per week at her job. How many weeks does Riley need to work to save enough money to buy the new television? A. 14 B. 16 C. 15
Answer: C. 15
Step-by-step explanation: You take the total amount that she needs: $1,372.35 and you subtract $200.55. Then you are left with $1171.1. This is the amount that she needs still. Then you take $78.12 and multiply it by 15. You get $1171.8. Then when you add $200.55 and $1171.8 you get $1171.1.
what is the pattern between 5,3,9,7,13
Answer it takes away 2 than adds 3 and takes away 2 than instead of adding 3 on the fourth number it adds 6 so maybe it doubles the number it adds every time or it adds three onto the last number it added with and continues like that.
Step-by-step explanation:
need the answer asap!! thank you!!!
Answer: C
Positive and between 0.0 and 0.5
Work out 114 % of 818.07 kg Give your answer rounded to 2 DP.
Answer:
932.60 kg
Step-by-step explanation:
To find a percent of a number, change the percent to a decimal and multiply by the number.
114% of 818.07 kg =
= 114% * 818.07 kg
= 114/100 * 818.07 kg
= 1.14 * 818.07 kg
= 932.60 kg
Answer:932.60
Step-by-step explanation:
i had the same question on hegarty lol
there are (4 to the 9th power) to the 5th power times 4 to the 0 power books at the library. what is the total number of books?
Answer:
1310720
Step-by-step explanation:
you multiply (4^9) and get 262144 then multiply (262144)^5 and get 1310720*4^0 and multiply 4*0 and get 0 so 1310720 if that makes sense
19x + 8 - 7x = 48 - 8x
Answer:
x = 2
Step-by-step explanation:
19x - 7x + 8x = 48 - 8
20x = 40
20x/20 = 40/20
x =2
Answer:
x=2
Step-by-step explanation:
[tex]19x + 8 - 7x = 48 - 8x \\ ⟹ 12x + 8 = 48 - 8x \\ ⟹ 12x + 8x = 48 - 8 \\ ⟹20x = 40 \\ ⟹ x = \frac{40}{20} \\ ⟹x = 2[/tex]
Which set of angle measures could be the measures of the interior angles of a triangle? 90°, 42°, and 58° 60°, 60°, and 60° 100°, 48°, and 42° 31°, 75°, and 70°
Answer:
60°, 60°, and 60° is the set of interior angles of triangle.
Step-by-step explanation:
Given:
Set of interior angles
90°, 42°, and 58° 60°, 60°, and 60° 100°, 48°, and 42° 31°, 75°, and 70°Find:
Set of interior angles of triangle
Computation:
We know that, sum of interior angles of triangle is 180°
So,
90° + 42° + 58° = 190°
60° + 60° + 60° = 180°
100° + 48° + 42° = 190°
31° + 75° + 70° = 176°
So,
60°, 60°, and 60° is the set of interior angles of triangle.
Answer:
60°, 60°, and 60°
Step-by-step explanation: I took the quiz
Which of the following statements are true? The coordinates of point p (2,3) lie along the directed segment
Answer:
3
ehebehejhebehsueywbw
Answer:
It was number 2
Step-by-step explanation:
The one where P is located at (3,5)
A bag of chips contains 145 calories per serving. Each bag of chips contain 3 servings. How many calories are in 2 bags of chips?
Answer:
870
Step-by-step explanation:
you take the calories per serving, 145, and multiply it by the number of servings in the bag, 3. this gives you 435, the number of calories in a bag. then you take the number of calories in a bag times the number of bags. you get 870
Answer:
870
Step-by-step explanation:
In the given diagram, if AP = 15 cm, AQ = 24 cm and PB + QC = 26 cm, find QC – PB, given PQ || BC.
Answer:
QC - PB = 6
Step-by-step explanation:
Given PQ is parallel to BC then it divides the sides proportionally, that is
[tex]\frac{AP}{AQ}[/tex] = [tex]\frac{PB}{QC}[/tex] = [tex]\frac{15}{24}[/tex] = [tex]\frac{5}{8}[/tex] , then
[tex]\frac{PB}{QC}[/tex] = [tex]\frac{5}{8}[/tex] ( cross- multiply )
8PB = 5QC → *
Given PB + QC = 26 , then
PB = 26 - QC
Substitute into *
8(26 - QC) = 5QC ← distribute left side
208 - 8QC = 5QC ( subtract 5QC from both sides )
208 - 13QC = 0 ( subtract 208 from both sides )
- 13QC = - 208 ( divide both sides by - 13 )
QC = 16
Thus PB = 26 - QC = 26 - 16 = 10
QC - PB = 16 - 10 = 6
Susan plans to rent a bike in New Orleans to tour the city. The cost of the rental is $20 per day. The cost of a helmet is for as long as Susan needs the bike . Susan has 250 to rent a bike for 15 days. Does Susan have enough moneyExplain .
Susan does not have enough money.
20 times 15 will cost $300. Susan only have $250.
I'm not sure if this is correct.
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after minutes of calls is , and the remaining credit after minutes of calls is . What is the remaining credit after minutes of calls?
Answer and Step-by-step explanation: Suppose remaining credit is y and time in minutes is x. To determine a value of y corresponding to a value of x, first find the equation for the function.
Since the function is linear, the equation is of the form: y = mx + b. To determine it:
1) Find slope, or inclination, of the line:
slope (m) = [tex]\frac{y_{b}-y_{a}}{x_{b}-x_{a}}[/tex]
where x's and y's are points of the function.
2) Determine the y-intercept, or b: Use a point of the function, replace them at the equation, y = mx + b, and find b.
3) The equation will be: y = mx + b
With the equation, replace x for the minutes the question is asking and calculate to find the remaining credit.
Th result will be a pair (x,y)
A product has a production cost function C(x)x and a revenue function R(x)x. Find and analyze the break-even quantity, then find the profit function.
A product has a production cost function C(x) =165x + 3630 and a revenue function R(x)= 220x. Find and analyze the break-even quantity, then find the profit function.
Answer:
the break-even quantity = 66
the profit function = 55x - 3630
Step-by-step explanation:
Given that:
C(x) = 165x + 3630
R(x) = 220 x
The Break-even quantity is C(x) = R(x)
∴
165x + 3630 = 220x
collecting the like terms, we have:
3630 = 220 x - 165 x
3630 = 55 x
[tex]x = \dfrac{3630}{55}[/tex]
x = 66
Thus, the break-even quantity = 66
The profit function = R(x) - C(x)
The profit function = 220x - 3630 - 165x
By rearrangement
The profit function = 220x - 165x - 3630
The profit function = 55x - 3630
what are equations in algebra?
1. Jean spent $37.50 for 500 paperclips. How much did he pay for each paperclip?
Answer:
Step-by-step explanation:
It's simple simply do
3750÷500=7.5
Answer:
0.075
Step-by-step explanation:
0.075x500=37.50
I NEED HELP PLEASE !!!
Answer:
-3
Step-by-step explanation:
Solve each piece then use order of operations to solve.
[tex]4^{\frac{1}{2} }[/tex] = 2
[tex]\sqrt[4]{16}[/tex] = 2 so [tex]\frac{2}{\sqrt[4]{16} }[/tex] = [tex]\frac{2}{2}[/tex] = 1
Use the order of operations to finish solving. Multiplication and division come before addition and subtraction.
2 * 1 - 10 ÷ 2
2 - 5 = -3
-3
Can someone please help?
Answer:
Multiply by 3, 162
Step-by-step explanation:
2 x 3 is 6.
6 x 3 is 18.
18 x 3 is 54.
54 x 3 is.... you get the deal.
54 x 3 is 162.
Simplify the expression. (5+3)×4 8 17 23 32
Answer:
32
Step-by-step explanation:
BIDMAS
(5 + 3) = 8
8 x 4 = 32
solve for x -18+26=-2(x+2)
Answer:
x = -6
Step-by-step explanation:
-18 + 26 = -2(x + 2)
8 = -2x - 4
12 = -2x
x = -6
if you were to describe a translation of triangle ABC what information would you need to include your description
Answer:
In order to describe the translation of the triangle ABC we need to know the rule of translation, i.e. we need to know how many units to the left or to the right the x coordinate will move and how many units up or down the y coordinate will move
Step-by-step explanation:
You need to how many units the y coordinate will move up or down, must be understood in order to describe the translation of the triangle ABC.
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions on the actual figure or object
Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.
For example, If shift up by 1 unit, add 1 to the function
If shift down by 4 units, subtract 4 from the function
The rule of translation, which states how many units the x coordinate will move to the left or right and how many units the y coordinate will move up or down, must be understood in order to describe the translation of the triangle ABC.
Learn more about the Scale images here:
brainly.com/question/13194929
#SPJ2
The figure to the right has its congruent segments marked. Find
the measure of AB.
17 meters
B
5 meters
AB = meters
(Type an integer or a decimal.)
Answer:
AB = 17 meters
Step-by-step explanation:
Given that the triangle, ∆ABC, has 2 congruent sides that are indicated with a single marking on segment AC and segment AB, both segments would be of equal measure.
Therefore, since the measure of segment C is 17 meters, the measure of segment AB = measure of segment AC = 17 meters.
Segment AB = 17 meters. It is congruent to segment AC.
Answer:
13
Step-by-step explanation: