For problems 1–4, solve the given system of equations using either substitution or elimination.
Answers
Answer:
1. -3, -2
2. 2, -7
3. 1, 2.5
4. infinitely many solutions
Answer:
1. (-3,-2)
2. (1, -7)
3. (1, 2.5)
4. No solution
Step-by-step explanation:
Number 1: Substitution
Plug y in to substitute and get
2x + (2x + 4) = -8
4x + 4 = -8
4x = -12
x = -3
Then plug into the y equation
y = 2(-3) + 4
y = -6 + 4
y = -2
(-3, -2)
Number 2: Elimination
Begin eliminating by crossing out same values
40x + 12y = -44
-2y = 14
Solve for y
-2y = 14
y = -7
Solve for x
40x + 12(-7) = -44
40x - 84 = -44
40x = 40
x = 1
(1, -7)
Number 3: Elimination
Add the two and get:
-3x + 2y = 2
6y = 15
Solve for y:
6y = 15
y = 5/2
Solve for x:
3x + 4(5/2) = 13
3x + 10 = 13
3x = 3
x = 1
(1, 2.5)
Number 4: Substitution
Solving for y to begin with:
4x - y = -3
-y = -3 - 4x
y = 3 + 4x
Then solve for y in the second system
-8x + 2y = 6
2y = 6 + 8x
y = 3 + 4x
Set equal to each other
3 + 4x = 4 + 4x
3 = 4
No solution
Related Questions
Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).
Answers
Considering the definition of a line, the linear function that represents the total cost when x tickets are ordered is c= 20.5x + 5.50.
What is a linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Total cost in this caseIn this case, you know:
Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. This is, as service fee is a single fee applied to the total, no matter the number of tickets purchased, the value of "b" is 5.50.The total cost in dollars for ordering 5 tickets is $108.00Being Total cost= set price per ticket× amount of tickets + 5.50, then:
108=set price per ticket× 5 + 5.50
108 - 5.50= set price per ticket× 5
102.5= set price per ticket× 5
102.5÷5= set price per ticket
20.5= set price per ticket
Finally, the total cost is Total cost= 20.5× amount of tickets + 5.50.
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Answer:
Its letter A
Step-by-step explanation:
For a science experiment, each student needs 5 grams of salt. If there are 26 students in the class how many milligrams of salt will they need?
Answers
Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = -2?
Answers
Answer:
C
Step-by-step explanation:
Edge 2021
Answer:
c. (y-1)^2=-20(x-3)
Step-by-step explanation:
edge 2021
(07.01 LC)
Which of the following values in the set below will make the equation 2x + 1 = 3 true? (Only input the number.)
{0, 1, 2, 3,4} (5 points)
Answers
Answer:
1
Step-by-step explanation:
Because 2 times 1 is 2 plus 1 is equal to 3
40mph in feet per secend
Answers
Answer:
58.8 feet per second
CONVERTING MPH TO FPS
If you are moving at the rate of 40MPH, how many feet do you travel in a second? At 40 miles per hour, you are traveling 58.8 feet per second. To convert miles per hour to feet per second, multiply the miles per hour figure by 1.47. There are 5280 Feet in a mile and 3600 Seconds in an hour.
0 0 1 0
0 0 0 1
Let A = 1 0 0 0
0 1 0 0
-0 0 0 1
0
0
0. Find All
0
Answers
Answer:
0
Step-by-step explanation:
Answer:
zero
Step-by-step explanation:
1) The Cuyahoga River is 306 miles long, but boats can only travel on 134
miles of the total length. Write the ratio of the Cuyahoga's navigable length
to its total length as a fraction in simplest form.
Answers
Answer:
67/153
Step-by-step explanation:
Can you please help me
Answers
9514 1404 393
Answer:
x = 30°y = 20°Step-by-step explanation:
The relevant relations are ...
the sum of the arcs of a circle is 360°an inscribed angle subtends an arc twice its measureThese give rise to two equations. (x and y are in degrees)
6y +6y +4x = 360
6y = 2(2x)
Substituting the latter into the former gives ...
6y +6y +6y = 360
y = 20 . . . . . . . . . . . . divide by 18
Then using this in the second equation, we have ...
6(20) = 4x
30 = x . . . . . . . . divide by 4
The measures of x and y are 30° and 20°, respectively.
Twelve out of Sixty students are trying out for the spring musical. What is the percentage of students trying out for the musical?
Answers
If Twelve out of Sixty students are trying out for the spring musical, the percentage of students trying out for the musical is , 20%.
What are percentages?In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Why are percentage representations important?The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
In above question, if Twelve out of Sixty students are trying out for the spring musical, we have,
Number of students trying out for the musical = 12
Total number of students = 60
Percentage of students trying out for the musical is , [tex]\frac{12}{60} *100[/tex] = 20%
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14570.7 to 3 significant figures
Answers
Answer:
14600
Step-by-step explanation:
Move the point to left and round up to 3 significant figures
7. {MCC.7.G.2} *
Which set of numbers cannot
represent the lengths of the sides
of a triangle?
A) 7, 9, 12
B) 8, 6, 7
C) 8, 20, 12
D) 10, 13, 20
O A
B
O D
Answers
If
f
(
x
)
=
2
x
4
−
9999999kwwkqkkaosos
what is the length of JL
Answers
166.8 in (4,237 mm) (2-door) 188.4 in (4,785 mm) (4-door)
Describe the function
Answers
Answer:
linear and increasing
Step-by-step explanation:
since the line still is on (0,0) it's linear. plus it's going up, which is increasing
hope i helped, tell me if you got it right! :)
4.75% as a fraction in simplest form
Answers
Answer: 19/400
Step-by-step explanation:
4.75% = 4.75/100 (in fractions)
= 475/10000 (multiply by 100 for both the numerator and denominator)
= 19 / 400 (divide by 25 for both the numerator and denominator)
How do I know it is 25 for the last step?
Obtain the highest common factor of 475 and 10000. The highest common factor of these two numbers is 25.
Which inequality represents the situation written below?
The temperature outside today should be at least 40 degrees.
Answers
Answer:
at least 40 means minimum 40.
option G
What is the range of the function with the graph given below ?
Answers
The graph in the question is a parabola that opens downwards.
What is function?A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, Python gives you many built-in functions like print(), etc. but you can also create your own functions. These functions are called user-defined functions.
This means that the range of the function is all real numbers less than or equal to the y-intercept of the parabola, which is 0 in this case. Therefore, the range of the function is all real numbers less than or equal to 0.
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Pls help! Step by step
Answers
Answer:
x = 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the cosine ratio in the right triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = 6[tex]\sqrt{2}[/tex]
This is the exact value for x. It may be rounded if you wish
Answer:
[tex]x=6\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
From inspection of the given right triangle:
θ = 45°A = 6H = xSubstitute the given values into the cosine trigonometric ratio and solve for x:
[tex]\implies \cos(45^{\circ})=\dfrac{6}{x}[/tex]
[tex]\implies \dfrac{\sqrt{2}}{2}=\dfrac{6}{x}[/tex]
[tex]\implies x\sqrt{2}=6 \cdot 2[/tex]
[tex]\implies x\sqrt{2}=12[/tex]
[tex]\implies x=\dfrac{12}{\sqrt{2}}[/tex]
[tex]\implies x=\dfrac{12}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]\implies x=\dfrac{12\sqrt{2}}{2}[/tex]
[tex]\implies x=6\sqrt{2}[/tex]
4 less than three sevenths as an algebraic expression
Answers
To write "4 less than three sevenths" as an algebraic expression, we can use the variable x to represent the number we are trying to find, and then use subtraction and division to represent the parts of the phrase "4 less than three sevenths".
3/7x - 4 = an algebraic expression
or
x = 3/7y - 4
where x is the unknown value and y is any given value
Both expressions are algebraic representation of the statement "4 less than three sevenths"
Find the value of the lesser root of x squared -7x +12 =0
Answers
Answer:
3
Step-by-step explanation:
x² -7x + 12 =0
by factoring:
(x-4)(x-3) = 0
x = 4
x = 3
3<4
The triangle flap of an envelope has two sides that are 6 centimeters long and meet at a right angle. How long is the envelope? Round to the 10ths if needed.
Answers
Answer:
Step-by-step explanation:
This is a right triangle that has two equal sides - so it is also isosceles.
It can be solved using Pythagoren Theorem.
a² + b² = c²
In this case a = b
so:
6² + 6² = c²
36 + 36 = c²
72 = c²
[tex]\sqrt{72[/tex] = [tex]\sqrt{c^{2} }[/tex]
8.49 = c
round to 8.5
This is the length of the flap.
Determine the value of x.
A) 2√3 B) 6√3 C) 12 D) 12√3
Answers
Sin60=6/hyperbola
•hyperbola=6/sin60
•hyperbola=4 √3
Now,
We know,
Hyperbola^2= Base ^2 +Perpendicular ^2
•Base(x)= √(Hyperbola^2-Perpendicular ^2)
•Base(x)=2√3
So Value of X is 2√3 (Ans.)
Correct Option: A) 2√3
Question
Translate the phrase into an algebraic expression, the ratio of 4p and 7y,
Provide your answer below:
Answers
9514 1404 393
Answer:
(4p)/(7y)
Step-by-step explanation:
The ratio of 4p to 7y is another way of saying the quotient of (4p) and (7y).
[tex]\boxed{\dfrac{4p}{7y}}[/tex]
Find the total surface area of this cone.
Leave your answer in terms of .
24in
+10in
SA = [ ? ]in2
Answers
The total surface area of the cone in terms of pi is 360π square inches
Total surface area of a cone is expressed as
TSA = πr(r+l)
Given that
radius = 10in
Height = 24in
Get the slant height 'l'.
l² = h²+r²
l² = 24²+10²
l² = 576+100
l² = 676
l = 26in
Substitute the given values into the formula
TSA = pi(10)(10+26)
TSA = pi(36)(10)
TSA = 360π in²
Hence the total surface area of the cone in terms of pi is 360π square inches
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Avery works approximately 2080 hours per year if she earns between $7.50 and $8.25 per hour which is the closest to her annual salary
Answers
Answer:
16,000$ is the answer
hope it helped
Use the data from the table to create a scatter plot Plot all the data points from the table. I really need help its due at 11:59 HELPPP
Answers
Show that 20 subtracted by O is 20, using at least four daily life examples
Answers
Answer:
true
Step-by-step explanation:
20 away from nothing is 20
Answer:
Step-by-step explanation:
20-0=20
Example 1: Suppose you have 20 friends and they are given the choice of choosing a sport from cricket or basketball. All of them decide to play cricket and 0 chooses basketball. So, the total number of students who decided cricket is 20 students(20-0=20).
Example 2: Suppose you have 20 chocolates and you give 0 chocolates to your sister then you have a total of 20 chocolates(20-0=20).
Example 3: Suppose there are 20 students in a class and 0 were absent out of them. So, the total number of students that were present are 20 students(20-0=20).
Example 4: Suppose you have 20 clothes in your wardrobe and you gave 0 clothes for washing. So, the total number of clothes in the wardrobe is 20 clothes(20-0=20).
Find the solution set for this equation -n 2 + 8n=0
Answers
Answer:
0 and 8.
Step-by-step explanation:
n^2+8n=0
n(-n+8)=0
-n=-8 or n=8 and n=0.
The length of a rectangle is 10 cm what is the width if the area is 60 cm
Answers
the width of a rectangle is measured at 6 cm, its length at 10 cm, and its area at 60 cm2.
what is rectangle ?An example of a quadrilateral is a rectangle, which has four vertices that are all 90 degrees apart and parallel sides that are equal to one another. As a result, it is sometimes referred to as an equiangular quadrilateral. The rectangle is a 2D shape with 4 sides, 4 corners, and 4 right angles. The length of each pair of the diagonal sides of a rectangle is equal, with one pair being longer than the other. If all the sides of a rectangle were the same size, the shape would be referred to as a square.
given
Consequently, the rectangle has a length of 10 cm and an area of 60 cm2.
Since,
Area of a rectangle equals length times width
=60=10*breadth
width is 60/10.
= 6 cm in breadth.
the width of a rectangle is measured at 6 cm, its length at 10 cm, and its area at 60 cm2.
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On her to her grandmothers house, Jackie traveled three times as many miles by train as by bus. She traveled four times as many miles by bus as by foot. If Jackie traveled 34 miles in all, how many miles did she travel by train?
Answers
She traveled 6.375 miles by train.
What is the speed of an object?Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time
Given here as per question the formula is x × (4+3×4)=34
∴ x×16=34
x= 6.375
Hence, She traveled 6.375 miles by train.
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3. An empty bag has a weight of 400g. When 6 footballs are packed into it the total weight is
3070g. What is the weight of one football?
Answers
Answer:
Step-by-step explanation:
Weight of empty bag = 400g
Total Weight of bag = 3070g
Weight of 6 footballs packed = 3070g -400 = 2670
Weight of 1 football = 2670 ÷ 6 = 445g