The solution of the system of equation can be solved by using substitution method. Therefore, the solutions of the system 7x + 3y = -3 and y = -2x is (-3, 6)
How to find solution to the system of equation
7x + 3y = - 3
y = - 2x
Substitute the value of y in equation(i)
Therefore,
7x + 3(- 2x) = -3
7x - 6x = -3
x = -3
Let's find y by substituting the value of x in equation(ii)
y = -2x
y = -2(-3)
y = 6
Therefore, the solution set of the equation is (-3, 6)
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how to factor 5r^2+10r-240
Answer:
5 ( r+8) (r-6)
Step-by-step explanation:
5r^2+10r-240
First factor out the greatest common factor
5( r^2 +2r - 48)
Now factor what is inside the parentheses
What multiplies to -48 and adds to 2
8*-6 = -48
8-6 = 2
5 ( r+8) (r-6)
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Answer:
exponential growth
Step-by-step explanation:
f(x) = 2 * 2^x
This is in the form
y = a * b^x where a is the initial value and b is the growth rate or decay rate
b > 1 so it is growth
This is the exponential form
y = mx+b is the linear form
Please answer. will mark brainliest.
Answer:
See explanation
Step-by-step explanation:
Line A
gradient = 4
x-intercept = -1
y-intercept = 4
Line B
gradient = -3
x-intercept = -1
y-intercept = -3
y + 8x = - 72
x-intercept = -9
y-intercept = -72
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CDEF is a kite and mFCE =39. Find m1
A.102
B.39
C.78
Answer: 39
Step-by-step explanation:
Its easy! The triangles CEF and CDE are equals because they have three sides respectively equal. So the angles FCE and angle m1 (DCE) are equal.
Then:
m1 = 39
Please help! Correct answer only!
In a carnival game, there is a machine that will shuffle a deck of 50 cards numbered from 1 to 50 and then spit one card out. If the number on the card is odd, you win $15. If the number on the card is even, you win nothing. If you play the game, what is the expected payoff?
$___
Answer:
$7.50
Step-by-step explanation:
Since there is a 50% chance that the card is odd, the expected payoffs would be $15 * 50%=0.5*15=7.5. Hope this helps!
How many square inches are in 60 ft.
Solve x - 3 < -1. Graph the solution.
Answer: x < 2
Explanation: To solve for x in this inequality, our goal is the same as it would be if this were an equation, to get x by itself on one side.
Since 3 is being subtracted from x, we add 3
to both sides of the inequality to get x < 2.
Before we graph, write your answer in set notation.
We can write this as {x: x < 2}.
It's important to understand what this means.
This means that any number less than 2 is a solution to this inequality.
I have graphed the inequality for you below.
Start with an open dot on +2.
We use an open dot because +2 is not included as a solution.
Then draw an arrow going to the left.
What is the gradient of the graph shown?
Answer:
-1/2
Because, for every one square, the line goes down by 1/2.
Answer:
- 0.5
Step-by-step explanation:
To find the gradient of a line,
divide the value of decrease by the value across.
So, count across from the extreme left toll the extreme right = 13
Where you completed in the extreme right, you have to count down till you reach the other end of the line = 6.5
Now, you divide: 6.5 divided by 13 = 0.5
Since we counted down, it is negative = -0.5
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Megan has three candles of the same length to provide light. Candle A burns for exactly 72 minutes. Candle Burns twice as fast as Candle A. Candle C burns 3 times as fast as candle B. What is the greatest total number of minutes of light all three candles can provide?
Answer:
Candle B: 36 minutes
Candle C: 12 minutes
Step-by-step explanation:
Since Candle A burns for 72, and Candle B burns twice as fast, we can divide the 72 by 2 in order to get the time it burns. We will then see that Candle B burns for 36 minutes.
Candle C burns 3 times as fast as candle B so we can divide the 36 minutes it takes for candle B to burn by 3 to get how long it takes Candle C to burn. We then see that it takes 12 minutes for candle C to burn.
Hope this helps!
X^2-11=53 in the simplest form
Answer:
x=±8
Step-by-step explanation:
You add 11 on both sides
x^2=53+11
x^2 = 64 so
x=8 or x=-8
What is an equation in point-slope form of the line that passes through (1, −6) and (4, 6)
Answer:
Step-by-step explanation:
6--6 = 12
4-1 = 3
12/3 = 4
y=4x
-6-4 = -10
y=4x-10
The formula of slope:
Slope = (d - b) / (c - a)
where (a, b) and (c, d) are the two points.
The equation of the line that passes through (1, -6) and (4, 6) is
y = 4x - 10
What is an equation of a line?
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The line passes through (1, -6) and (4, 6).
The formula of slope:
Slope = (d - b) / (c - a)
where (a, b) and (c, d) are the two points.
Now,
(1, -6) = (a, b) and (4, 6) = (c, d)
Slope = (6 + 6) / (4 - 1) = 12 / 3 = 4
m = 4
The equation of a line is given as y = mx + c.
(1, -6) = (x, y)
-6 = 4 x 1 + c
-6 = 4 + c
-6 - 4 = c
c = -10
Now,
The equation of the line that passes through (1, -6) and (4, 6) is
y = 4x - 10
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Can you please help me this is coordinates only and thank you.
Answer: (2,6)
Step-by-step explanation: you go the the left 3 from F then up 2 and you have it.
Please help me it is only 1 question please help me I have no idea about this
Answer:
53
Step-by-step explanation:
Answer:
(540 - π60 cm²) or 350cm³(351.5)
Step-by-step explanation:
You'll have to subtract the volume of the rectangular prism with the cylinder.
We know that the prism's volume is V = s*s*h = 6*6*16 = 540 cm²
We also know the cylinder's volume: V = πr²h = π(4/2)²*15 = π*4*15 = π*60
Now the only step remaining is to subtract the volume of the prism with the cylinder: 540 - π*60 cm³
540 - π*60 cm³ is the full answer
350 is the approximate answer (rounded it down from 351.5 to 350cm³)
what number times there self eqaul to 64
Answer:
8
Step-by-step explanation:
8 times 8 = 64
model -5 + (-6) on the number line
Answer:
-5+(-6 )= -11 so you would pinpoint -11 on the number line
Step-by-step explanation:
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−→− bisects ∠DGF, m∠DGE=53∘. Find m∠DGF.
1. what is the measure of angle DBF? (image included below)
Answer:
Measure of angle DBF = 106°.
Step-by-step explanation:
Given in the question,
m∠DGE = 53°
and line segment GE is the angle bisector of ∠DGF.
Since segment GE is the angle bisector of ∠DGF that means it divides the angle DGF into two equal parts.
Therefore, m∠DGE ≅ m∠FGE
m∠DBF = m∠DGE + m∠FGE
m∠DBF = 2(m∠DGE)
= 2(53)°
= 106°
Therefore, measure of angle DBF = 106°.
Ay is any one down to work together on this? Not just this question but the whole unit of geometry
Select all the numbers that are in the range of the function f(x)=3-0.5x if the domain is {1,3,4}
Answer:
1
Step-by-step explanation:
Answer:
1,1.5,2.5
Step-by-step explanation:
f(x) = 3 - .5x
The domain is 1,3,4 so theses are the only inputs
f(1) = 3 - .5 = 2.5
f(3) = 3 - .5(3) = 3- 1.5 = 1.5
f(4) = 3 - .5(4) = 3-2 =1
The only outputs are 1,1.5,2.5
Which is a true statement about the diagram?
The right answer is of option C.
hope it helps..
good luck on your assignment
Answer:
c
Step-by-step explanation:
multiply the polynomials (4x^2+3x+7(8x-5)
A. 32x^3-44^2-71x-35
B. 32x^3-4x^2-41x+35
C. 32x^3+4x^2+41x-35
D. 32x^3+4x^2+41x+35
Answer:
32x^3 + 4x^2 + 41x - 35
Step-by-step explanation:
Multiply each of the terms in bracket 1 with those in bracket 2.
4x^2 x 8x = 32x^3
4x^2 x -5 = -20x^2
3x x 8x = 24x^2
3x x -5 = - 15x
7 x 8x = 56x
7 x -5 = -35
Now, put them together and simplify:
32x^3 - 20x^2 + 24x^2 - 15x + 56x - 35
After simplifying:
32x^3 + 4x^2 + 41x - 35
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write in algebraic expression to find the number of seconds in n minutes
Simplify
4a x 6a
8a?
Answer:
[tex]=24a^2[/tex]
Step-by-step explanation:
[tex]4a\cdot \:6a=24a^2\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:6=24\\=24aa\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\aa=\:a^{1+1}\\=24a^{1+1}\\=24a^2[/tex]
Answer:
Simply multiply across.
since they both have the same base(a),add the powers ie.(1+1)=2.
Hence 4a×6a=24a²
Is the relation a function? Why or why not?
{(-8, -4).(-2, 0), (1, 3).(-2.6)}
Answer:
No it's not a function. (-2, 0) and (-2, 6) don't pass the vertical line test.
Step-by-step explanation:
– 4 vc2, when v = –7 and c = –2
Answer:
[tex] \boxed{112} [/tex]
Step-by-step explanation:
[tex]Evaluate - 4v {c}^{2} \: where \: v= - 7 \: and \: c= - 2 : \\ = > - 4v {c}^{2} \\ = > - 4( - 7) {( - 2)}^{2} \\ \\ {( - 2)}^{2} = 4: \\ = > - 4( - 7)4 \\ \\ - 4( - 7) = 28: \\ = > 28 \times 4 = 112[/tex]
some teachers travelled to school by car the table shows the number of teachers in the cars a)what was the modal number of teachers in the cars b) what was the median number of teachers in the cars c) what was the mean number of teachers in the cars
Answer:
WE need the numbers
Step-by-step explanation:
a
Answer:
a)3
b)3
c)?
Step-by-step explanation:
One circle has a diameter of 10 inches. A second circle has a diameter that is twice the diameter of the first circle. What is the ratio of the area of the smaller circle to the larger circle?
Answer:
[tex]78.54:314.16[/tex]
Step-by-step explanation:
First circle area with diameter 10 inches =
[tex]\pi r^2[/tex]
[tex]\pi \times 5^2[/tex]
[tex]=78.53981[/tex]
Second circle area with diameter 20 inches =
[tex]\pi r^2[/tex]
[tex]\pi \times 10^2[/tex]
[tex]=314.159265[/tex]
[tex]78.53981:314.159265[/tex]
Answer:
78.5 : 314.2
Step-by-step explanation:
Diameter of the first Circle = 10 inches
Diameter of the second Circle = 2(10) [TWICE] = 20 inches
So,
Area of the first circle:
Radius = 5 inches
Area = πr²
A = (3.14)(5)²
A = 78.5 inches²
Area of the second circle:
Radius = 10 inches
Area = πr²
Area = (3.14)(10)²
Area = 314. 2 inches
Now the ratio of the area of smaller circle to the larger circle is
78.5 : 314.2
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Penelope and Georgia are each saving money to take a vacation. Penelope started with $710 and saved $25 each week. Georgia opened her account with $570 and saved $45 each week. In how many weeks will they have the same amount of money? Group of answer choices 7 weeks 8 weeks 13 weeks 14 weeks
Answer:
8 weeks
Step-by-step explanation:
Here is a pattern made from sticks:
a) How many sticks would be in pattern number 6?
Answer: 32
b) How many sticks would be in pattern n?
Answer: ____
Recursive formula of an arithmetic sequence is given by the expression,
[tex]T_n=a+(n-1)d[/tex]
Where, [tex]T_n=[/tex] nth term
[tex]a=[/tex] First term of the sequence
[tex]n=[/tex] Number of term
[tex]d=[/tex] Common difference
Therefore, number of sticks in the 6th pattern are 32.
And number of sticks in the nth pattern are [tex]T_n=5n+2[/tex]
From the picture attached,
Number of sticks in 1st pattern = 7
Number of sticks in 2nd pattern = 12
Number of sticks in 3rd pattern = 17
Sequence formed is 7, 12, 17..... nth term
This sequence has a common difference of 5 in each successive term so it will be an arithmetic sequence.
Therefore, nth term of the sequence will be,
[tex]T_n=a+(n-1)d[/tex]
[tex]T_n=7+(n-1)5[/tex]
[tex]T_n=5n+2[/tex]
If [tex]n=6,[/tex]
[tex]T_n=7+(6-1)5[/tex]
[tex]T_n=7+25[/tex]
[tex]T_n=32[/tex]
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what is the quotient (2x^2+12x+18) divided by (x+3)
CHOICES:
a. 2x+6
b. 2x-6
c. 2x+4
d. 2x-4, r=1
Answer:
A. 2x+6 is the correct answer
-7 written as a fraction is _____
Please help! Correct answer only!
In a raffle, one ticket will win a $900 prize, and the remaining tickets will win nothing. There are 500 in the raffle. If you have a ticket, what is the expected payoff?
Answer:
" Expected Payoff " ⇒ $ 1.80 ; Type in 1.80
Step-by-step explanation:
Take the probability of winning into consideration;
[tex]Total Number of Tickets - 500,\\Tickets 1 Person Can Enter - 1 Ticket,\\\\Probability of Winning - 1 / 500,\\Money Won - 900 Dollars,\\\\Proportionality - 1 / 500 = x / 900 - where, x = " Expected Payoff "\\1 / 500 = x / 900 - CrossMultiplication,\\\\500 * x = 900,\\x = 900 / 500,\\x = 1.80 Dollars Won!\\\\Conclusion ; x = 1.80 Dollars[/tex]
Solution ; " Expected Payoff " ⇒ $ 1.80