The substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
A system of linear equation is a group of one or more linear equations which can be solved by using a simultaneous equation or elimination method.
From the information given;
3x + y = -2 ----- (1)
y = 2x +3 ----- (2)
By using substitution method, we will replace the value of equation (2) into equation (1), by doing so, we have:
3x + (2x + 3) = -2
3x + 2x + 3 = -2
5x + 3 = -2
5x = -2 - 3
5x = - 5
x = -5/5
x = -1
From equation (2), let's replace the value of x = - 1 into equation (2);
y = 2x + 3
y = 2(-1) + 3
y = -2 + 3
y = 1
Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
Learn more about substitution method here:
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You use a garden hose to fill a wading pool. If the water level rises 16 centimeters every 7 minutes
and you record the data point of (21,y), what is the value of y? Use slope to justify your answer.
The rate of change at which the water level rises is ____ centimeters per minute. So solving the equation ____ for y gives a y-value equal to ____
How would the expression x3 -3 sqrt 3 be rewritten using difference of cubes?
O A. (x- 13 )(x2-3x - 3)
O B. (x+ 3)(x + 13 x + 3)
C. (x - 13 )(x2 + 3x + 3)
O D. (x- vb)(x2 + v3 x+3)
Answer:
x^3 - (√3)^3
I'm not so sure since it's not even an option
Step-by-step explanation:
x^3 - 3√3 = x^3 - 3^1 × 3^(1/2)from the laws of indices: 3^1 × 3^(1/2) = 3^(1 + 1/2)= 3^(3/2) which is the same as (√3)^3so it could be written as x^3 - (√3)^3What is 196.7 16 in simplest form?
Holly and Jimmy went shopping. For every $2
that Holly spent, Jimmy spent $5. If together
they spent $35, how much did Jimmy spend?
if you want it a a whole number, it would be for every 34$ 85 bucks for jimmy .
Among 2165 passenger cars in a particular region, 235 had only rear license plates. Among 330 commercial trucks, 50 had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.10 significance level. Identify the P-value. Let population 1 correspond to the passenger cars and population 2 correspond to the commercial trucks. Let a success be a vehicle that only has a rear license plate Group of answer choices
Using the z-distribution, it is found that the p-value is of 0.0192.
At the null hypothesis, it is tested if commercial trucks owners do not violate laws requiring front license plates at a higher rate than owners of passenger cars, that is, the subtraction is of at most 0, hence:
[tex]H_0: p_2 - p_1 \leq 0[/tex]
At the alternative hypothesis, it is tested if commercial truck owners violate the laws more, that is, the subtraction is positive, hence:
[tex]H_1: p_2 - p_1 > 0[/tex]
For each sample, the size, the proportion and the standard error are given by:
[tex]n_1 = 2165, p_1 = \frac{235}{2165} = 0.1085, s_1 = \sqrt{\frac{0.1085(0.8915)}{2165}} = 0.0067[/tex]
[tex]n_2 = 330, p_1 = \frac{50}{330} = 0.1515, s_1 = \sqrt{\frac{0.1515(0.8485)}{330}} = 0.0197[/tex]
For the distribution of differences, the mean and the standard error are given by:
[tex]\overline{p} = p_2 - p_1 = 0.1515 - 0.1085 = 0.043[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0067^2 + 0.0197^2} = 0.0208[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
In which [tex]p = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
[tex]z = \frac{0.043 - 0}{0.0208}[/tex]
[tex]z = 2.07[/tex]
The p-value is found using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is more than a value, with z = 2.07.
Using the calculator, the p-value is of 0.0192.A similar problem is given at https://brainly.com/question/15545277
What is the value of X?
the assumption here is that both triangles are similar, if that's so, then we can use proportions to get the sides.
[tex]\stackrel{\textit{assuming both triangles are similar}}{\cfrac{x}{10}=\cfrac{15}{6x}\implies \cfrac{x}{10}=\cfrac{5}{2x}}\implies 2x^2=50 \\\\\\ x^2=\cfrac{50}{2}\implies x^2=25\implies x=\sqrt{25}\implies \boxed{x=5}[/tex]
The directions for Clean-All to mix 1 3/8 cups of cleaner with 2 2/5 cups water. Write a COMMON RATIO as
CLEANER to WATER
Answer:
Step-by-step explanation:
The Mega Clean mixture with 3 1/2 per gallon has more cleaner in it. The first mixture has .75 oz per quart. The second mixture has .875 oz per qt.
HOPE THAT HELP YOU
A dump truck is filled with 82.16 pounds of gravel. It drops off 77.29 pounds of gravel at a construction site. How much gravel is left on the truck?
Answer:
4.87lbs
Step-by-step explanation:
82.16-77.29=4.87
Question : Explore criteria of congruency of triangles using a set of triangle cut outs
Answer:
Explore Various Criteria for Congruence TrianglesSASASAAASSSSRHSSomeone help?
Find the problem:
-5x - 16 = 8x - 1
Fix the problem:
?
[tex]-5x -16 = 8x -1\\\\\implies 8x +5x = -16 +1 \\\\\implies 13x = -15\\\\\implies x = -\dfrac{15}{13}[/tex]
Yoni has a ribbon that measures 5/3 yards. She wants to cut it into 3 equal pieces. What is the length of each piece of ribbon? 5\8 yards 5/6 yards 5/9 yards 5/3 yards
Answer:
5/9 yards
Step-by-step explanation:
[tex] \frac{5}{3} \div \frac{3}{1} \\ = \frac{5}{3} \times \frac{1}{3} \\ = \frac{5}{9} [/tex]
Pleasee help with this question
Answer:
(2 x^2 z^13)/(z^8 y^5)
Hope This Helps!!!
Answer:
2xz⁵/y⁴
Step-by-step explanation:
16/8 = 2
x²/x = x
y/y⁵ = y⁻⁴
z¹³/z⁸ = z⁵
The length of the diagonal of quadrilateral is 48m. The lengths of the Perpendiculars drawn on it from the opposite corners are 15m and 19m.Find its area.
after a party 3/4 cake is leftover. Dennis eats 1/2 of the leftover cake. Which fraction model represents the amount of cake Dennis eats?
A researcher at the Centers for Disease Control and Prevention is studying the growth of a certain bacteria. He starts his experiment with 500 bacteria that grow at a rate of 16% per hour. He will check on the bacteria every 8 hours. How many bacteria will he find in 8 hours? Round your answer to the nearest whole number.
The population of the bacteria after 8 hours is 1639 bacteria.
An exponential function is given by:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let y represent the population of bacteria after x hours.
Given that he starts his experiment with 500 bacteria, hence
a = 500
The bacteria grow at a rate of 16% per hour, hence:
b = 100% + 16% = 1.16
The exponential equation becomes:
y = 500(1.16)ˣ
After 8 hours:
y = 500(1.16)⁸ = 1639
The population of the bacteria after 8 hours is 1639 bacteria.
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Factor
3x2- 2x - 5
*(3xpower of 2 -2x-5)**
Answer:
16
Step-by-step explanation:
3×2-2×-5=
6-(-10)=
6+10=
16
put the following unit fractions in order from smallest to largest. 1/16 1/24 1/8 1/10 1/4 1/12 1/3 1/6 1/2
Answer:
1/24, 1/16, 1/12, 1/10, 1/8, 1/6, 1/4, 1/3, 1/2
Step-by-step explanation:
If you have this many fractions and they all have the same numerator, then the smallest number will have the biggest denominator and the biggest number will have the smallest.
So when you have all numbers with the same numerator and you're trying to put them in order from smallest to greatest, it's like putting the denominators in order from largest to smallest. (So, the 1/24 is the SMALLEST and the 1/2 is the BIGGEST.
Find the length of the hypotenuse.Round to the nearest 10th if necessary.(40pts)
Answer:
5 is our hypotenuse
Step-by-step explanation:
[tex]a^{2} + b^{2} = c^{2}[/tex]
c is our hypotenuse
[tex]3^{2} + 4^{2} = c^2[/tex]
[tex]9 + 16 = 25[/tex]
[tex]25 = c^{2}[/tex]
c = 5
5 is our hypotenuse
Answer:
x = 5
Step-by-step explanation:
[tex]c=\sqrt{a^2+b^2} \\a= \sqrt{3^2+4^2} \\c=\sqrt{9+16} \\c= \sqrt{25} \\c= 5[/tex]
please help will brain list if correct no links please
Answer:
C
Step-by-step explanation:
the angle opposite of it is 30
Can someone solve this question ~
[tex]\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}[/tex]
[tex]\boxed{\boxed{Step \: by \: step \: explanation \: required~}}\ [/tex]
[tex]\\ \sf{:}\Rrightarrow {\displaystyle{\lim_{x\to -3}}}\dfrac{x^2-9}{x^2+2x-3}[/tex]
[tex]\\ \sf{:}\Rrightarrow {\displaystyle{\lim_{x\to -3}}}\dfrac{(x+3)(x-3)}{x^2+3x-x-3}[/tex]
[tex]\\ \sf{:}\Rrightarrow {\displaystyle{\lim_{x\to -3}}}\dfrac{\cancel{(x+3)}(x-3)}{\cancel{(x+3)}(x-1)}[/tex]
[tex]\\ \sf{:}\Rrightarrow {\displaystyle{\lim_{x\to -3}}}\dfrac{x-3}{x-1}[/tex]
Apply limits[tex]\\ \sf{:}\Rrightarrow \dfrac{-3-3}{-3-1}[/tex]
[tex]\\ \sf{:}\Rrightarrow \dfrac{-6}{-4}[/tex]
[tex]\\ \sf{:}\Rrightarrow \dfrac{3}{2}[/tex]
Hope you could understand.
If you have any query, feel free to ask.
HELP PLSSSS ILL GIVE 5 STARS JUST ANSWER
Answer:
-1 (color bow red)
Step-by-step explanation:
first plug x=7
-12/2(7) - 2
-12/14-2
-12/12
-1
SOMEONE PLEASE HELP ME!!
Answer:
should be 3
Step-by-step explanation:
hope you get a good grade
how to write into fractional expanded form 65.43
Answer:
6543/100
Step-by-step explanation:
Multiply both numerator and denominator by 10 for every number after the decimal point
65.43 × 100
1 × 100
=
6543
100
Which table of ordered pairs represents a proportional relationship?
Answer:
C)
Step-by-step explanation:
Because Its equivalent
what is 1/4 of 5/6???
you search the LCD then you subtracted the top and left the bottom the same
Step-by-step explanation:
im not sure
Monica says,"if 4 bottles cost $10, then 2 bottles cost $5 + $20." Is Monica correct? Explain
6 grade shiiii, help me out doe, thanks luvs <33.
Answer:
Monica is not correct.
Step-by-step explanation:
First of all, if 4 bottles only cost $4, then how would only 2 cost more? (She said the two bottles would be $25, which doesn’t make sense.)
6x + 3 > 26
How do I solve the math problem above
Answer:
x > 23/6
Step-by-step explanation:
Solve this one the same way you would a 2-step linear equation.
6x +3 > 26 . . . . . given
6x > 23 . . . . . . . . subtract the unwanted constant from both sides (step 1)
x > 23/6 . . . . . . . .divide both sides by the coefficient of x (step 2)
__
Additional comment
If the coefficient of the variable in a 2-step linear inequality is negative, then the inequality symbol must be reversed when dividing by that negative number.
Karen stacks a set of cans as shown. The top can has a diameter of 2 inches, the middle can has a diameter of 5 inches, and the bottom can has a diameter of 6 inches.
Answer:
Unknown
Step-by-step explanation:
What is the question? You have the information listed but you forgot to ask the question.
After a discount of 25%, the sale price of a game system is $149.25. what is the original price?
Answer:111.94
Step-by-step explanation:
'Percent (%)' means 'out of one hundred':
p% = p 'out of one hundred',
p% is read p 'percent',
p% = p/100 = p ÷ 100.
25% = 25/100 = 25 ÷ 100 = 0.25.
100% = 100/100 = 100 ÷ 100 = 1.
New value =
149.25 - Percentage decrease =
149.25 - (25% × 149.25) =
149.25 - 25% × 149.25 =
(1 - 25%) × 149.25 =
(100% - 25%) × 149.25 =
75% × 149.25 =
75 ÷ 100 × 149.25 =
75 × 149.25 ÷ 100 =
11,193.75 ÷ 100 =
111.9375 ≈
111.94
Find an equation for the perpendicular bisector of the line segment whose endpoints
are (5, 4) and (-7,-8).
Answer:
y= -x -3
Step-by-step explanation:
A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).
Let's find the slope of the line segment.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope of line segment
[tex] = \frac{4 - ( - 8)}{5 - ( - 7)} [/tex]
[tex] = \frac{4 + 8}{5 + 7} [/tex]
[tex] = \frac{12}{12} [/tex]
= 1
The product of the slopes of 2 perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
m(1)= -1
m= -1
y= -x +c
To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.
Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.
[tex]\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}[/tex]
Midpoint of line segment
[tex] = ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )[/tex]
[tex] = ( \frac{ - 2}{2} , \frac{ - 4}{2} )[/tex]
= (-1, -2)
y= -x +c
When x= -1, y= -2,
-2= -(-1) +c
-2= 1 +c
c= -2 -1
c= -3
Thus, the equation of the perpendicular bisector is y= -x -3.