Answer:
The solution of this system of linear equations is [tex](x,y) = (-3,-2)[/tex].
Step-by-step explanation:
Let be the following system of linear equations:
[tex]2\cdot x - 7\cdot y = 8[/tex] (1)
[tex]-3\cdot x + 2\cdot y = 5[/tex] (2)
From (1) we clear [tex]y[/tex]:
[tex]2\cdot x -8 = 7\cdot y[/tex]
[tex]y = \frac{2\cdot x - 8}{7}[/tex]
And we apply this variable in (2):
[tex]-3\cdot x+2\cdot \left(\frac{2\cdot x -8}{7} \right)= 5[/tex]
[tex]-3\cdot x +\frac{4}{7} \cdot x -\frac{16}{7} = 5[/tex]
[tex]-\frac{17}{7}\cdot x = \frac{51}{7}[/tex]
[tex]x = -\frac{51}{17}[/tex]
[tex]x = -3[/tex]
And the value of [tex]y[/tex] is:
[tex]y = \frac{2\cdot (-3)-8}{7}[/tex]
[tex]y = -\frac{14}{7}[/tex]
[tex]y = -2[/tex]
The solution of this system of linear equations is [tex](x,y) = (-3,-2)[/tex].
14. Classify a triangle with the following side lengths: 16 cm, 12 cm, and 16 cm.
Answer:
Isosceles
Step-by-step explanation:
The triangle has two equal sides of 16 cm. Isosceles triangles are classified to have either two of the same sides or two of the same angles.
22. Find the missing terms indicated by variables in the arithmetic sequence shown.
a, 30, b, 42, c, d, e
The complete sequence is 24, 30, 36, 42, 48, 54, 60
The nth term of an arithmetic progressionThe nth term of an arithmetic progression is expressed according to the equation;
Tn = a + (n-1)d
where
a is the first term
n is the number of terms
d is the common difference
Determine the common difference
d = 42-b = b - 30
-b-b = -30-42
-2b = -72
b = 36
d = 36-30
d = 6
For the first term;
d = 30 - a
6 = 30 - a
a = 24
For the value of c
c = 42 + 6
c = 48
For the value of d
d = 48 + 6
d = 54
For the value of e
e = 54 + 6
e = 60
Hence the complete sequence is 24, 30, 36, 42, 48, 54, 60
Learn more on arithmetic sequence here: https://brainly.com/question/24989563
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d) A rectangular vessel can hold 40 litres of milk when it is full. If the area ofthe base of the vessel is 2000 cm, find the height of the vessel.
Answer:
height of the vessel should be 50 cm I guess
Find a number if 7/10 of it is 0.8.
Answer:
8/7
Step-by-step explanation:
0.8/0.7=8/7
Answer:8/7
Step-by-step explanation:
i need this now ....... EXPLAIN YOUR ANSWER!!!
solve the formula Ax + By= C for x.
A. x= c/a+by
B. x= c-by/a
c. x= c-by/a
d. x= c+by/a
Answer:
ax + by = c
<=> ax = c - by
<=> x = [tex]\frac{c-by}{a}[/tex]
Step-by-step explanation:
Algebra 2
S varies inversely as G. If S is 8 when G is 3.5, find S when G is 7.
a) Write the variation.
b) Find S when G is 7.
Answer:
a) S varies inversely as G
[tex]S\propto\frac{1}{G}[/tex]
or [tex]S=\frac{K}{G}[/tex]
b) S=4 when G=7
Step-by-step explanation:
a) Write the variation.
S varies inversely as G
[tex]S\propto\frac{1}{G}[/tex]
So, We can write: [tex]S=\frac{K}{G}[/tex]
Where k is constant of proportionality
b) Find S when G is 7.
Now, if S=8, G = 3.5 we will find K
[tex]S=\frac{K}{G}\\K=SG\\K=8\times 3.5\\K=28[/tex]
So, value of K= 28
Now, find S when G is 7
[tex]S=\frac{K}{G}\\S=\frac{28}{7}\\S=4[/tex]
So, S=4 when G=7
A store pays $81 for a lawn ornament. The store marks up the price by 10%. What is the amount of the mark-up?
Anyone mind helping? This one might be kinda hard idk tho lol BUT PLEASE HELPPPP
Answer:
Ok
Step-by-step explanation:
Mrs. Claus wants to have a nice meal ready when Santa comes home. She wants to make waffles and she knows that he will be hungry. If each recipe requires ¾ cups of butter and she has 4 ½ cups of butter, how many waffle recipes can she make?
Answer:
6
Step-by-step explanation:
Each recipe of waffles requires 3/4 cups of butter
Mrs Claus has 4 1/2 cups of butter
Therefore the number of recipes which she will be able to make can be calculated as follows
= 4 1/2 ÷ 3/4
= 9/2 ÷ 3/4
= 9/2 × 4/3
= 6
Hence Mrs Claus can make 6 recipes
The bag contained only red marbles and white marbles. If the ratio of red marbles to white marbles was 5 to 4, what fraction of the marbles were white? *Complete the statement by providing the correct response in number form, using / as the fraction symbol.
The fraction of white marbles is
Answer:1 1/4
Step-by-step explanation: If it is 5/4 it makes one whole leaving an extra
Helpppp:)
A tank full of water is leaking at a constant rate for 25 minutes. The equation
y = -4x + 220
describes the amount of water in the tank, where yis the number of liters and
x is the number of minutes that has elapsed since the tank started to leak.
Which statement is true?
A. There were 4 liters in the tank when the leak started, and it is
increasing by 220 liters per minute.
B. There were 220 liters in the tank when the leak started, and it is
decreasing by 4 liters per minute,
C. There were 4 liters in the tank when the leak started, and it is
decreasing by 220 liters per minute.
D. There were 220 liters in the tank after 25 minutes, and it
decreasing by 4 liters per minute.
Answer:
Is it B
Step-by-step explanation:
Answer:
Step-by-step explanation:
B test!
Yesterday, grace drove 33 1/2 miles. She used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallon?
Answer:
30 4/5 or 30.8
Step-by-step explanation:
What is the slope of a line on a standard xy-plane that passes through the point (1, 3) and (4,-3)?
A.) -1
B.) 2
C.) -2
D.) 1/2
E.) - 1/2
Therefore, the slope of a line on a standard XY-plane that passes through points (1, 3) and (4,-3) is -2.
So, option (c) is correct.
Given two points are (1, 3) and (4, -3)
We need to find the slope of a line
The slope of a line (m) :
m = y₂ - y₁ / x₂ - x₁
Given (x₁, y₁) = (1, 3) and (x₂, y₂) = (4, -3)
Slope (m) = y₂ - y₁ / x₂ - x₁
= -3 - 3 / 4 - 1
= -6 / 3
= -2
Therefore, the slope of a line on a standard XY-plane that passes through points (1, 3) and (4,-3) is -2.
So, option (c) is correct.
To learn more about slope refer below
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Simplify: (15-13i)-(-1+17i)
Answer:
c
Step-by-step explanation:
16-30i
Can someone help me on this
Answer:
A:90
B:120
Step-by-step explanation:
all you have to do is divide 360 by 4 and then divide 360 by 3
1. Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated with
the origin as the center of dilation using the rule (x, y) - (x, y) to create pentagon
M'N'P'Q'R'. Which statement is true?
Answer:
B
Step-by-step explanation:
if its less than 1 it shrinks
The correct statement is; Pentagon M’N’P’Q’R is smaller than pentagon MNPQR because the scale factor is smaller than 1.
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
If a polygon is dilated by a scale factor = k
Rule to be followed as;
(x, y) → (kx, ky)
Here, k = Scale factor
If 0 < k < 1, size of the image will be reduced.
Similarly, k > 1, size of the image will be enlarged.
We are given that Pentagon MNPQR is dilated with the origin as the center of dilation to form an image M'N'P'Q'R'.
Rule used for the transformation,
(x, y) → (1/4x, 1/4y)
Here, the scale factor through which MNPQR has been dilated is 1/4.
Since, scale factor is between zero and 1/4, size of M'N'P'Q'R' will be reduced.
Therefore, the size of pentagon M'N'P'Q'R' will be 1/4 smaller than pentagon MNPQR.
Option (2) is the answer.
Learn more about scale factors here :
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Answer in an hour!!!! No linkssss
answer:
The correct answers are choices B, C, and D. Here is an explanation for each choice: B. All congruent figures are exactly the same size and shape. This is what makes one figure congruent to another. C. If the figures are the same size and shape, then the corresponding sides will also be congruent. D.If the figures are the same size and shape, then the corresponding angles will also be congruent.
Identify the slope and y-intercept of the line.
y = 3x - 5
Answer:
Slope = 3/1 or 3
Y intercept = (0, -5) or 5
Step-by-step explanation:
The slope intercept form : y = mx+b shows that the m represents the place of the slope and the b represents the place of the y intercept.
I wrote the answer using this app
hope it helps :D
Can someone help me please
Answer:
The first one!
Step-by-step explanation:
The sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side.
Answer:
The answer is C.
Step-by-step explanation:
Hope this helped have an amazing day!
HELP I HAVE TO FINISH IN 2 HOURS
shannon and sarah are mowing a field. shannon can finish mowing by herself in 2 hours. sarah can finish in 4 hours. how long will it take them to mow the field together?
Answer:
1h 20m
Step-by-step explanation:
Let the total amount of work be x.
Shannon:
2h = x
1h = [tex]\frac{1}{2}[/tex]x
So basically Shannon does [tex]\frac{1}{2}[/tex]x work per hour.
Sarah:
4h = x
1h = [tex]\frac{1}{4}[/tex]x
So basically Sarah does [tex]\frac{1}{4}[/tex]x work per hour.
Together:
1h = [tex]\frac{1}{2}[/tex]x + [tex]\frac{1}{4}[/tex]x
= [tex]\frac{2}{4}[/tex]x + [tex]\frac{1}{4}[/tex]x
= [tex]\frac{3}{4}[/tex]x
Amount of time spent = [tex]\frac{4}{4}[/tex]x ÷ [tex]\frac{3}{4}[/tex]x
= [tex]\frac{4}{4}[/tex]x × [tex]\frac{4}{3}[/tex]x
= [tex]\frac{16}{12}[/tex]h
= 1[tex]\frac{4}{12}[/tex]h
= 1h 20m
Answer:
4/3 hours
Step-by-step explanation:
For every hour that Sarah mows, Shannon mows twice as much. Because of this, Sarah is going to mow two times as much of the field as Shannon. You can set up an equation where x is the fraction of lawn mowed. This equation should be:
2x + x = 1 -> 3x = 1
The reason the equation is set up like this is because there is 1 whole lawn that the fraction of the lawn that Shannon mows (2x) plus the fraction of the lawn that Sarah mows (x) adds up to. You can use this equation to solve for x, which will be 1/3.
Since you know x, you can find what fraction of the lawn Shannon and Sarah mow. Since Shannon mows a fraction of 2x of the lawn, the fraction she mows will be 2*1/3 = 2/3. The fraction that Sarah mows will be x = 1/3.
Now that you know the fraction of the whole lawn that both Saran and Shannon mow, you can multiply their respective fraction by the amount of time it takes for them to mow a whole lawn. To do this for Shannon, you multiply 2/3 of the lawn by 2 hours, which gives you 4/3 hours. To do this for Sarah, you multiply 1/3 of the lawn by 4 hours, which also gives you 4/3 hours.
PLEASE HELP FAST ILL GIVE BRIANLIST AND EXTRA POINTS!
What expression is equivalent to
Answer:
A
Step-by-step explanation:
Okay.
A negative exponent means we want to "flip" the term.
so we get
(1/-c^2)^1/3
When we get a fraction exponent, we want to "root" the term by that
so we get
[tex]\sqrt[3]{\frac{1}{-c^2} }[/tex]
Which simplifies to
[tex]\frac{\sqrt[3]{1} }{\sqrt[3]{-c^2} }[/tex]
Which becomes[tex]1/\sqrt[3]{-c^2}[/tex]
Please help me out :(
Answer:
True
True
False
Step-by-step explanation:
Rate of Change is slope. There is no change in slope as the line is straight.
Using the slope formula:
[tex]m=\frac{x_{2}-x_{1} }{y_{2}-y_{1}} \\m=\frac{4-0}{1-0}\\m=4[/tex]
Where m is slope
Since gold beads are on the x-axis, that means there are 4 black beads per gold bead
A delivery truck drove 42 miles per hour. It took 4 hours to travel between two towns. What is the distance between the two towns? Use the equation d=rt, where d is distance, r is rate, and t is time.
Answer:
168 miles
Step-by-step explanation:
d = rt
d = 42 × 4
d = 168
Answer:
d = rt
d = 42×4
d = 168
Step-by-step explanation:
That is the distance between the towns.
You have to multiply the amount of miles by the time it took.
Please help due by 9:30
If you get it right +20 points
Answer:
ad=DC is your answer.....
Match each representation with the correct x- and y-intercept.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse
(-4, 0) (0, -12)
(6, 0) (0, 4)
(3, 0) (0, -9)
(-2, 0) (0, -4)
(10, 0) (0, 10)
Take intercepts from the graph:
(10, 0) and (0, 10)2. The function3x - y = 9Calculate the intercepts
x = 0 ⇒ -y = 9 ⇒ y = - 9y = 0 ⇒ 3x = 9 ⇒ x = 3Points are: (3, 0) and (0, - 9)
3. The tableOrdered pairs given:
(0, 4) and (6, 0)4. The graphTake intercepts from the graph:
(-4, 0) and (0, - 12)5. The function6x + 3y = - 12Calculate the intercepts:
x = 0 ⇒ 3y = - 12 ⇒ y = - 4y = 0 ⇒ 6x = - 12 ⇒ x = - 2Points are: (- 2, 0) and (0, - 4)
Write an equation that can be used to calculate d,the distance traveled by Anthony in m minutes.use your equation to determine how far Anthony will have run after 7 minutes.
Answer:
C I think. Sorry if it's incorrect but I pretty sure it isn't.
19) It will cost $12.50 per person to make dinner. Write an
inequality that represents the number of people you can make dinner
for if you only have $200 to spend
Answer:
12.50x less than or equal to $200
Step-by-step explanation:
Multiply 39.341 × 0.72 = (1 point)
PLease
Answer:
28.32552
Step-by-step explanation:
multiply
Answer:
28.32552
Step-by-step explanation:
39.331 × 0.72= 28.32552
1/2x7 giving your answer as a mixed number