Solve the following system of equations with the substitution method:`{(10 x + 5 y,=,-20),(y, =, -2 x -4):}`
Answers
We will assume that we have the next system of equations:
\(\begin{cases}10x+5y={-20} \\ y={-2x-4}\end{cases}\)Now, since we have to use the substitution method, we need to write the equivalent expression of one of the unknown variables in one of the given equations.
We can see that the unknown variable, y, is given explicitly in the form:
\(y=-2x-4\)Then, we can substitute this equation in the first one as follows:
\(\begin{gathered} y=-2x-4\Rightarrow \\ \\ 10x+5(-2x-4)=-20 \end{gathered}\)And now, we have to solve the resulting expression by using the distributive property, and then simplifying the result as follows:
\(\begin{gathered} 10x+5(-2x-4)=-20 \\ \\ 10x+5(-2x)+5(-4)=-20 \\ \\ 10x-10x-20=-20 \\ \\ -20=-20 \end{gathered}\)Since we ended with this result, we can say that we have an infinite number of solutions, and if we need to express the solutions in terms of x, we can write that the solutions are given, then, by:
\(\begin{gathered} y=-2x-4 \\ \\ \text{ And finally, we can rewrite the solutions as:} \\ \\ (x,-2x-4) \end{gathered}\)In summary, the solution for this system can be written - in terms of x - as follows: (x, -2x-4).
Related Questions
I WILL GIVE BRAINLYIST!!
For every 4 apples, there are
_____oranges
Answers
Answer:
12
Step-by-step explanation:
so here, the ratio of apples to oranges is 1:3. this can also be represented as the fraction 1/3. now, we are trying to find the number of oranges when there are 4 apples using this ratio. this means 1/3=4/x, where x is the number of oranges. we can multiply 1 by 4 (the numerator) to get 4, so we can multiply the denominator of the first fraction by 4 as well 3*4=12, so there are 12 oranges for every 4 apples. (4/12 can also be written as 4:12.)
Answer:
12
Step-by-step explanation:
nos of oranges for 4 apples = 4x 3
= 12
therefore, the ratio is 4:12 i.e. 1:3
pls mark as brainliest!
6(x + 8) = 5(x-4) What is the answer
Answers
Answer:
x = −68
Step-by-step explanation:
make me brainliest please !! <3
Answer:
x = -68
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation: 6*(x+8)-(5*(x-4))=0
(6 • (x + 8)) - 5 • (x - 4) = 0
6 • (x + 8) - 5 • (x - 4) = 0
x + 68 = 0
Solve: x+68 = 0
Subtract 68 from both sides of the equation: x = -68
I hope this helps! Please mark this as braiinlest.
Thanks!
If y(x)=-4x - 5 and x(t)=t^2+ 2t , find y(x(t)).
Answers
9514 1404 393
Answer:
y(x(t)) = -4t^2 -8t -5
Step-by-step explanation:
Fill in the argument value and simplify.
y(x(t)) = y(t^2 +2t) = -4(t^2 +2t) -5
y(x(t)) = -4t^2 -8t -5
Calculate the value 4-2(-5) =
Answers
answer is 14.
4-(2*-5)
4-(-10)
=4+10
=14.
Answer:
\(\bf 14\)Step-by-step explanation:
\(\tt 4-2(-5)\)
Follow the PEMDAS order of operations:-
P: Parentheses
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
1) Multiply and/ or divide:-
\(\tt 2\left(-5\right)\)\(\tt -10\)\(\tt 4 -\left(-10\right)\)
2) Addition/Subtraction:-
\(\tt 4-\left(-10\right)\)\(\tt 4+10\)\(\tt 14\)_____________________
Hope this helps! :)
What is the equation of the line that is perpendicular to y = 3x + 3 and passes through the point (-6, 9)?
y=-1/3x+3
y=-1/3x+7
y=3x-33
y = 3x + 27
Answers
Answer:
y = - \(\frac{1}{3}\) x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 3 ← is in slope- intercept form
with slope m = 3
given a line with slope m then the slope of a line perpendicular to it is
\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{3}\) , then
y = - \(\frac{1}{3}\) x + c ← is the partial equation
to find c substitute (- 6, 9 ) into the partial equation
9 = - \(\frac{1}{3}\) (-6) + c = 2 + c ( subtract 2 from both sides )
7 = c
y = - \(\frac{1}{3}\) x + 7 ← equation of perpendicular line
I don't know the answer please tell me the correct one
Answers
Answer:
See below
Step-by-step explanation:
Radius (r) = 8 inches
Chord = 8 inches
Since, length of radii and chord are equal. Thus the Triangle so formed by radii and chord will be an equilateral triangle.
\(\implies \) angle subtended at the centre of the circle \((\theta)=60\degree \)
Formula for area of segment of a circle is given as:
\(A = \frac{ {r}^{2} \theta }{36 0 \degree} \pi - \frac{1}{2} {r}^{2} \sin \theta \\ \\ \implies \: A = \frac{ {(8)}^{2} ( \cancel{60 \degree)}}{ \cancel{360 \degree}} \pi - \frac{1}{2} {(8)}^{2} \sin 60\degree \\ \\ \implies \: A = \frac {64 }{6} \pi - \frac{1}{2} \times 64 \times \frac{ \sqrt{3} }{2} \\ \\ \implies \: \huge \purple{ \boxed{A = \bigg( \frac {32 }{3} \pi - 16 \sqrt{3}\bigg) }\: sq\:in}\)
If F(x) and G(X) are inverse functions, which statement must be true?
O A. F(G(x)) = x
B. F(x) = -G(x)
C. F(X) 1/G(X)
D. F(G(x)) = 1
Answers
so the answer is option b. so please mark me as brainliest because I only answered
help!! geometry
jjjjjjjjjjjjj
Answers
Answer:
107
Step-by-step explanation:
Since they are congruent triangles angle B is the same as angle D.
To find D, all angles add to 180 degrees, so:
41+32+x=180
73+x=180
X=107
So angle B is 107 degrees
The U.S. Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxide levels
since 1959. At that time, there were 313 parts per million of carbon dioxide in the atmosphere. In 2005,
the figure was 374 parts per million. Find the increase in carbon dioxide levels and the percent of increase.
Round to the nearest tenth of a percent.
Increase carbon dioxide levels:
Percent increase:
196
Submit Question
parts per million
Question Help: Video Message instructor
Answers
Answer: The U.S. Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxide levels since 1959. At that time, there were 313 parts per million of carbon dioxide in the atmosphere. In 2005, the figure was 383 parts per million.
Step-by-step explanation:
What is the answer....................................................
Answers
Answer:A school bus provides a safe way of transportation for your child. Learn resources to talk to your child about school bus and bus stop safety.
Step-by-step explanation:
Solve the equation. 3+ |t+ 4| = 10
Answers
Answer:
t=3 or t=−11
Step-by-step explanation:
trust me and make me brainliest please!
t+4=10-3
t+4=7
t=7-4=3
A rectangle has a length of √3 and a width of √2. What is the perimeter of the rectangle? A. √6 B. √10 C. √6 + √2 D. 2√3 + 2√2
Answers
Answer:
D. 2√3 + 2√2
Step-by-step explanation:
The perimeter is calculated by adding length to width and that multiplied by 2
2×(√3 + √2) = 2√3 + 2√2
Answer:
D
Step-by-step explanation:
To find the perimeter just add the length and the width and multiply by 2
Which relation is not a function?
1) {(2,4), (1,2), (0, 0), (-1,2), (-2,4)}
2) {(2,4), (1, 1), (0, 0), (-1, 1), (-2,4)}
3) {(2,2), (1, 1), (0, 0), (-1, 1), (-2,2)}
4) {(2,2), (1, 1), (0, 0), (1,-1), (2,-2)}
Answers
Answer: D
Step-by-step explanation:
We have the two points (2,2) and (2,-2) which have a repeated x coordinate. This is not allowed if we wanted a function. A function must have any x input lead to exactly one and only one output (assuming the input is in the domain).
Suppose a supplier estimate that a new products will generate the following revenue stream. period. revenue year 0= 0 year 1=$62500 year 2 =$89 400 year 3=$ 136 200 year4 =$ 128300 year5=$ 112000 If the required rate of return is 11%, determine the value of all these cash flows at year 2.
Answers
Answer:
9834
Step-by-step explanation:
11*100*89400.
There are 40 sixth graders and 24 seventh graders in an after school pr
Answers
The percentage of sixth graders at the after party is 62.5%.
How to calculate the percentage?Number of sixth graders = 40
Number of seven graders = 24
Total number = 40 + 24 = 64
Percentage of sixth graders:
= Number or sixth graders / Total number × 100
= 40/64 × 100
= 0.625 × 100
= 62.5%
The percentage is 62.5%.
Learn more about percentages on:
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There are 40 sixth graders and 24 seventh graders in an after school party. What is the percentage of sixth graders?
Please answer the question I need this today
Answers
Answer:
C
Step-by-step explanation:
8 x 10^4 = 80,000
3 x 10^3 = 3,000
1 x 10 ^2 = 100
2 x 10^1 = 20
add it up
83,120
C is correct
What’s 9/3 - 6/10 need it in a reduced fraction
Answers
Answer:
9/3 - 6/10
= (90-18)/30
= 72/30
= 24/10
= 2.4 or = 12/5
Hope u understood..........
Glen's monthly gross pay is $4,500. The deductions from his monthly pay include $764.25 for federal income tax,
$344.25 for FICA taxes, $180 for his retirement plan, and $275 for health insurance. Find the percentage of his gross
wages that Glen takes home, to the nearest percent.
A) 3.5%
B)34%
C) 3.4%
D)65%
Answers
Answer:
It would be 34%
Step-by-step explanation:
The difference between $4500 and $2936.50 (the total after subtracting his monthly payments) is 34.74%
Answer:
Step-by-step explanation:
65%
Perform the followingmathematical operation, andreport the answer to thecorrect number of significantfigures.0.0030 × 8.65 = [?]
Answers
0.0030 has 2 sig figures
Leading zeros are not significant. Trailing zeros are significant
8.65 has 3 sig figures
multiply
.0030*8.65=.02595
We need 2 sig figures
Rounding to 2 sig figures
.026
An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of the residents of a state if you want to be 95% confident that the sample mean is within 4 IQ points of the true mean.
What is the required sample size?
Answers
Answer:
55
Step-by-step explanation:
\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)
Make sure to always round up the required sample size to the nearest integer!
La medida de cada ángulo interno de un polígono regular es 162º. Hallar el número de lados.
Número de lados=
Answers
Answer:
n = 20
Step-by-step explanation:
[ 180° ( n - 2 ) ] / n = 162°
180 ( n - 2 ) = 162 n
180n - 360 = 162n
18n = 360
n = 20
If a quadrilateral has these known angle degrees: 35, 35 and 145, what are the degrees of the fourth angle?
Answers
Answer:
145
Step-by-step explanation:
The total sum of all the angles is 360 degrees. If we add up 35, 35, and 145 we get 215. 360-215=145.
Matthew examines the relation shown in the below.
{(4,-11), (3,1), (0,1), (2,6), (3, -1)}
Is the relation a function? Why or why not?
No. There are x values which map to more than 1 y-value.
Yes. Every y-value maps to exactly 1 x-value.
No. There are y-values which map to more than 1 x-value.
Yes. Every x-value maps to exactly 1 y-value.
Answers
No, there are x values which map to more than 1 y-value.
Given that Matthew examines the relation as shown in the below.
{(4, -11), (3,1), (0,1), (2,6), (3, -1)}
We need to check whether the relation is a function or not,
So, we know that,
A relation can map inputs to multiple outputs. It is a function when it maps each input to exactly one output. The set of all functions is a subset of the set of all relations.
If any x values are repeated, and the corresponding y values are different, then we have a relation and not a function.
Here we can see that the y values are repeated, so it is not a function.
Learn more about functions click;
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The vertices of triangle ABC are given: A (0;-1) B(12; -10) C(10;4)
Find:
a) the equation of the median and bisector drawn from vertex A;
b) the equation of the altitude from vertex B;
c) the point of intersection of the median and height;
d) the coordinates of the center of mass (the point of intersection of the medians).
Answers
verified
Verified by Toppr
Median bisects the line.
D≡(
2
−3+5
,
2
−9−8
)≡(1,
2
−17
)
E≡(−
2
1+5
,
2
6−8
)≡(2,−1)
F≡(−
2
1−3
,
2
6−9
)≡(−2,
2
−3
)
∴ equation of AD:(y−y
1
)=(
x
2
−x
1
y
2
−y
1
)
AD
(x−x
1
)
⇒(y−6)=
⎝
⎜
⎜
⎛
1+1
2
−17
−6
⎠
⎟
⎟
⎞
(x+1)⇒(y−6)=−
4
29
(x+1)
⇒
4
29
x+y−6+
4
29
=0
AD⇒29x+4y+5=0
equation of BE:(y+9)=(−
2+3
1+9
)
BE
(x+3)
⇒(y+9)=
5
8
(x+3)⇒5y+45=8x+24
BE⇒8x−5y−21=0
Equation of CF:(y+8)=
⎝
⎜
⎜
⎛
−2−5
−
2
3
+8
⎠
⎟
⎟
⎞
CF
(x−5)
⇒(y+8)=−
14
13
(x−5)⇒14y+112=−13x+65
CF:13x+14y+47=0
Given the exponential function f (x) and the logarithmic function g(x), which of the following statements is true?
a. As x→∞, f (x)→∞ and g(x)→∞.
b. As x→∞, f (x)→∞ and g(x)→1.
c. As x→∞, f (x)→3 and g(x)→1.
d. As x→∞, f (x)→3 and g(x)→∞.
HELP!!! ASAP!!! PRE-CALCULUS!!!
Answers
Answer:
a
Step-by-step explanation:
Both the exponential and logarithmic functions tend to infinity.
cindy had 12 black shoes and 4 red shoes in her closet. what is the ratio of red shoes to black shoes?
Answers
Answer:
the answer is B because 3x4 is 12
Part 2: Solve the following word problem. Show all work to receive full credit..
4.
Lucy monitors the position of a large fish in the ocean with a depth finder. The device records the
depth of the fish. Initially, the fish swims at a depth of 13.52 feet below sea level. Suddenly the fish
rises 7.8 feet.
a. (2pts) What numerical expression represents the position of the fish relative to sea level after
it rises 7.8 feet?
b. (3pts) What is the position of the fish after it rises 7.8 feet relative to sea level? Show your
work.
Answers
The numerical representation and final elevation of the fish relative to sea level are :
Final position = -13.52 + 7.8 Final position = - 5.72Given the Parameters :
Initial depth of fish = - 13.52
Change in elevation of fish = 7.8 feets
Positions below sea level are represented as negative values (-) ;
Hence, initial position of fish = - 13.52
Change in position = Rise in depth of 7.8 feets
The numerical representation of the final position of the fish can be written thus :
Final position = Initial position + change in position Final position = - 13.52 + 7.8Hence, the final position of the fish will be :
Final position of fish = -13.52 + 7.8 = - 5.72Learn more : https://brainly.com/question/18109354
Answer:
5.72
Step-by-step explanation:
k12
~Happy Helper~
Find the probability of the event.If a single die is tossed once, find the probability of the following event. Rolling a 6
Answers
ANSWER
1/6
EXPLANATION
If we have a fair die and we toss it only once, then the probability of getting any of the numbers is the same,
\(P(one.number)=\frac{\#favorable.outcomes}{\#total.outcomes}\)The die has 6 faces, so the total number of outcomes is 6 and the number of favorable outcomes is always 1, since the numbers on the die don't repeat,
\(P(six)=\frac{1}{6}\)Hence, the probability of rolling a 6 is 1/6.
What is the value of y? y = Find the following angle measures. mAngleJKM = ° mAngleMKL = °
And are we all struggling in geometry and super stressed out and behind or is it just me
Answers
Answer:
What is the value of y?
y = ✔ 10
mAngleJKM = ✔ 106°
mAngleMKL = ✔ 74°
Step-by-step explanation:
Answer:
1: 10 2: 106 3: 74
Step-by-step explanation:
please help me with these problems that are blank.
NO LINKS!!
Answers
Answer:
1. 14.9 cm
2. 16.9 cm
4. 18.7 in
6. 50 m
Step-by-step explanation:
The Pythagorean theorem relates the legs (a, b) and the hypotenuse (c) of a right triangle:
c² = a² +b²
If you want to know the hypotenuse, take the square root:
c = √(a² +b²)
__
1.In the given rectangular prism, length AC is the hypotenuse of right triangle ABC, which has legs AB=14 and BC=5 in units of centimeters. Then ...
AC = √(14² +5²) = √(196 +25) = √221 ≈ 14.9 . . . cm
__
2.Length AD is the hypotenuse of the right triangle with legs AC=√221 and CD=8 in units of cm. Then ...
AD = √((√221)² +8²) = √(221 +64) = √285 ≈ 16.9 . . . cm
__
4.The slant height (s) of the cone is the hypotenuse of the right triangle with legs r=5 and h=18 in units of inches. Then ...
s = √(5² +18²) = √(25 +324) = √349 ≈ 18.7 . . . inches
__
6.The slant height of the pyramid is the altitude of any of the triangular faces. As such, it is the hypotenuse of the right triangle whose legs are half the base dimension, 40 m, and the given height, 30 m. We recognize these numbers as multiples of the sides of a {3, 4, 5} triangle, so we know immediately the slant height is 50 meters.
s = √(40² +30²) = √2500 = 50 . . . meters