N8) solve the system using substitution method and then graph the equations.2x - 4y = -23x + 2y = 3-
Answers
Solution
Given:
2x - 4y = -2
3x + 2y = 3
Substitution method
\(\begin{gathered} From\text{ 3x+2y=3} \\ 3x=3-2y \\ x=\frac{3-2y}{3} \end{gathered}\)\(\begin{gathered} Substitute\text{ }x=\frac{3-2y}{3}\text{ into the first equation} \\ 2x-4y=-2 \\ 2(\frac{3-2y}{3})-4y=-2 \\ \frac{6-4y}{3}-4y=-2 \\ Multiply\text{ }trough\text{ by 3} \\ 6-4y-12y=-6 \\ 6-16y=-6 \\ -16y=-6-6 \\ -16y=-12 \\ y=\frac{-12}{-16} \\ y=\frac{3}{4} \end{gathered}\)\(\begin{gathered} Substitute\text{ y=}\frac{3}{4}\text{ into }x=\frac{3-2y}{3} \\ x=\frac{3-2(\frac{3}{4})}{3}=\frac{3-\frac{3}{2}}{3}=\frac{\frac{6-3}{2}}{3}=\frac{\frac{3}{2}}{3} \\ x=\frac{3}{6} \\ x=\frac{1}{2} \end{gathered}\)\(Thus,\text{ x=}\frac{1}{2},y=\frac{3}{4}\)Graphical method:
Plot the graph of the two equations on the same graph
The point of intersection of the two graphs gives the solution to the system of equations
The point of intersection is (0.5, 0.75)
Which in fraction gives (1/2, 3/4)
Thus. x = 1/2, y= 3/4
Related Questions
Fill in the table 'using this function rule.
y = -5x+2
x
-1
0
1
2
y
0
0
0
X
4
S
Answers
Answer:
7, 2, -3, -8
Step-by-step explanation:
y = -5x + 2 Substitute in -1 for x
y = -5(-1) + 2
y = 5 + 2
y = 7
y = -5x + 2 Substitute in 0 for x
y = -5(0) + 2
y = 0 + 2
y = 2
y = -5 + 2 substitutes in 1 for x
y = -5(1) + 2
y = -5 + 2
y = -3
y = -5x + 2 Substitute in 2 for x
y = -5(2) + 2
y = -10 + 2
y = -8
Helping in the name of Jesus.
A building is 1ft from an 11 ft fence that surrounds the property. A worker wants to wash a window in the building 14ft from the ground. He plans to place a ladder over the fence so it rests against the building. He decided he should place the ladder 11ft from the fence for stability. To the nearest tenth of a foot, how long a ladder will he need?
Answers
Answer:
L = 18,4 ft
Step-by-step explanation:
The building, the ground, and the ladder make up a right triangle, with legs:
The distance (a) between the bottom of the ladder and the building 12 ft
The distance (b) between the gound and the window 14 ft up
The hypothenuse is the length of the ladder (L)
According to Pythagoras theorem
L² = a² + b²
L = √ (12)² + (14)²
L = √ 144 + 196
L = √ 340
L = 18,4 ft
Using the formula developed by Dr's Mosteller, doctors can approximate the Body Surface Area TIW (BSA) of an adult The formula is written as BSA where H is the Height in cm and W is 3800 the Weight in kg: If the BSA of a certian adult is 96 whose height Is 210 cm. About how much does this adult weight? The adult weights (Round t0 decimal place )
Answers
From the body surface area formula, the adult weight is 508.97.
The Mosteller formula takes the square root of the height multiplied by the weight divided by 3600
The Body Surface Area TIW (BSA) of an adult.
The formula is written as BSA
where H is the Height(cm), Weight is 3800(kg)
BSA=96
Height=210cm
BSA=\(\sqrt{\frac{H*W}{3600} }\)
\(96=\sqrt{\frac{210*W}{3600} \\\)
\(96=\frac{\sqrt{210*W}}{\sqrt{3600} } \\96=\frac{14.49*\sqrt{W}\\}{61.64}\\ 96=\frac{\sqrt{W} }{0.235}\\ 96*0.235=\sqrt{W}\\ 22.56=\sqrt{W}\\\)
Squaring on both sides
508.97=W
Therefore, the adult weight is 508.97(kg).
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If (x^2 − 5x + 7)(4x − 5)(2x + 1) = Ax^4 + Bx^3 + Cx^2 + Dx + E,
what is the value of 80A + 28B + 8C + 4D?
Be sure to show your work.
Answers
Answer:
hi
Step-by-step explanation:
I don't know how to do this question
17-3/4 17-3/4 just that
Answers
Answer: 264.0625
Step-by-step explanation:
let me know if im wrong
the corollary to the polygon angle-sum theorem finds the measure of each interior angle of a regular n-gon. *write a formula to find the measure of each interior angle using n
Answers
The Corollary to the polygon is explained below and the formula to find the measure of each interior angle is " (n - 2)×180°/n " .
The Corollary to the polygon Angle Sum Theorem states that : the sum of the interior angles of a regular n gon is written as :
that means , ⇒ Sum of interior angles = (n - 2) × 180° ...equation(1)
In a regular "n-gon" , all the interior angles are said to be congruent.
Let "x" be measure of each interior angle of a regular n-gon.
So , we can write ;
⇒ Sum of interior angles = (n)×(x) ;
Equating the above expressions with equation(1),
⇒ (n)×(x) = (n - 2) × 180° ;
On Solving for x,
⇒ x = (n - 2)×180°/n ;
Therefore, the measure of each interior angle of a regular "n-gon" is x = (n - 2)×180°/n .
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A refrigerator magnet uses five eights of an inch of magnetic tape how many refrigerator magnets can you make with 10 inches of magnetic tape
Answers
ANSWER: You can make 16 refrigerator magnets.
If you divide 10 by 5/8, you multiply by the reciprocal of 5/8 which is 8/5. You have 8/5 x 10. Cross simplify and you have 16.
3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara
Answers
The time Jack left Santa Clara is 1 : 55 pm
What is word problem?A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.
The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.
Therefore, the total time he spent is
25mins + 25 mins = 50 mins
He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;
2:45 pm = 14 :45
= 14:45 - 50mins
= 13:55
= 1 : 55pm
Therefore he left at 1:55 pm
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In a class of 152 students, 100 are taking math (M), 77 are taking science (S), and 55 are taking both math and science. One student is picked at random. Find the probability.
P(taking math or science or both)
Answers
The probability of taking math or science or both is 123/152
The total number of students = 152 students
Number of students who take math = 100 students
Number of student who take science = 77 students
Number of students who take both math and science = 55 students
The probability = Number of favorable outcomes / Total number of outcomes
We have to find each term
The number of favorable outcomes =55+45+23
= 123
Total number of outcomes = 152
Substitute the values in the equation
Probability of taking math or science or both = 123/152
Hence, the probability of taking math or science or both is 123/152
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Find the exact perimeter (in inches) and area (in square inches) of the segment shown, given that m∠O = 60° and OA = 24 in.
Answers
Answer:
A. Perimeter of segment = 49 in.
B. Area of segment = 52 in².
Step-by-step explanation:
Data obtained from the question include:
Radius (r) = 24 in.
Angle at the centre (θ) = 60°
Perimeter of segment =.?
Area of segment =.?
A. Determination of the perimeter of the segment.
Perimeter of segment = length of arc + length of chord
Length of arc = θ/360 x 2πr
Length of chord = 2r x sine (θ/2)
Pi (π) = 3.14
Length of arc = θ/360 x 2πr
Length of arc = 60/360 x 2 x 3.14 x 24
Lenght of arc = 25.12 in
Length of chord = 2r x sine (θ/2)
Length of chord = 2 x 24 x sine (60/2)
Length of chord = 24 in
Perimeter of segment = length of arc + length of chord
Perimeter of segment = 25.12 + 24
Perimeter of segment = 49.12 ≈ 49 in.
B. Determination of the area of the segment.
Area of segment = Area of sector – Area of triangle.
Area of sector = θ/360 x πr²
Area of triangle = r²/2 sine θ
Area of sector = θ/360 x πr²
Area of sector = 60/360 x 3.14 x 24²
Area of sector = 301.44 in²
Area of triangle = r²/2 sine θ
Area of triangle = 24²/2 x sine 60
Area of triangle = 249.42 in².
Area of segment = Area of sector – Area of triangle.
Area of segment = 301.44 – 249.42
Area of segment = 52.02 ≈ 52 in²
i have a problem on statistics
5. Data on household vehicle miles of travel (VMT) are compiled annually by the Federal Highway Administration and are published in National Household Travel Survey, Summary of Travel Trends. Independent random samples of 15 midwestern households and 14 southern households provided the following data on last year’s VMT, in thousands of miles. At the 5% significance level, does there appear to be a difference in last year’s mean VMT for midwestern and southern households? Use both p-value and critical value approach. Assume population variance to be equal
Midwest
16.2 , 14.6 , 11.2 , 24.4 , 9.4 12.9 , 18.6 , 16.6 , 20.3 ,15.1 , 17.3 , 10.8 , 16.6 , 20.9 , 18.3
South
22.2, 19.2 , 9.3 , 24.6 ,20.2 , 15.8, 18.0 , 12.2 , 20.1 , 16.0 , 17.5 , 18.2 , 22.8 , 11.5
Answers
Answer:
Step-by-step explanation:
Hello!
The objective is to compare the VMT of mid western households and southwestern households. For this two independent random samples of households from both areas and their VMT were recorded:
Be
X₁: VMT of a mid western household
Midwest
16.2 , 14.6 , 11.2 , 24.4 , 9.4 12.9 , 18.6 , 16.6 , 20.3 ,15.1 , 17.3 , 10.8 , 16.6 , 20.9 , 18.3
n₁= 15
∑X₁= 243.20
∑X₁²= 4175.98
X[bar]₁= 16.21
S₁²= 16.64
S₁= 4.08
X₂: VMT of a southwestern household
22.2, 19.2 , 9.3 , 24.6 ,20.2 , 15.8, 18.0 , 12.2 , 20.1 , 16.0 , 17.5 , 18.2 , 22.8 , 11.5
n₂= 14
∑X₂= 247.60
∑X₂²= 4633.24
X[bar]₂= 17.69
S₂²= 19.56
S₂= 4.42
The parameters of study are the population means, if the claim is that the VMT of households is different in both areas, then you'd expect the population means to be different too.
The hypotheses are:
H₀: μ₁ = μ₂
H₁: μ₁ ≠ μ₂
α: 0.05
Assuming both populations are normal and since both population variances are equal the test to apply is an independent samples t test pooled variance:
\(t= \frac{(X[bar]_1-X[bar]2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}\)
\(Sa^2= \frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} = \frac{14*16.67+13*19.56}{15+14-2}= \frac{487.66}{27} = 18.06\)
Sa= 4.249= 4.25
\(t_{H_0}= \frac{(16.21-17.69)-0}{4.25*\sqrt{\frac{1}{15} +\frac{1}{14} } }= -0.937= -0.94\)
Critical value approach:
This test is two-tailed, this means that the rejection region is divided in two tails:
\(t_{n_1+n_2-2; \alpha /2}= t_{27; 0.025}= -2.052\)
\(t_{n_1+n_2-2; 1-\alpha /2}= t_{27; 0.975}= 2.052\)
The decision rule is:
If \(t_{H_0}\) ≤ -2.052 or if \(t_{H_0}\) ≥ 2.052, reject the null hypothesis.
If -2.052 < \(t_{H_0}\) < 2.052, do not reject the null hypothesis.
The calculated value is within the "no rejection region" so the decision is to not reject the null hypothesis.
Using the p-value approach:
The p-value is the probability of obtaining a value as extreme as the calculated value of the statistic under the null hypothesis (\(t_{H_0}\)). Just as the significance level, the p-value is two tailed, you can calculate it as:
P(t₂₇ ≤ -0.93) + P(t₂₇ ≥ 0.93)= P(t₂₇ ≤ -0.93) + (1 - P(t₂₇ < 0.93)= 0.1796 + ( 1 - 0.8204)= 0.1796*2= 0.3592
p-value= 0.3592
The p-value is always compared to the significance level, the decision rule for this approach is:
If the p-value ≤ α, reject the null hypothesis.
If the p-value > α, do not reject the null hypothesis.
The p-value is greater than α, so the decision is to not reject the null hypothesis.
At a 5% significance level, there is no significant evidence to reject the null hypothesis. You can conclude that the population means of the VMT for households of the Midwest South ers households.
I hope this mhelps!
4x^2=x+3
Solve by factoring
Show your work please!
Answers
Answer:
x = - \(\frac{3}{4}\) , x = 1
Step-by-step explanation:
4x² = x + 3 ← subtract x + 3 from both sides
4x² - x - 3 = 0 ← in standard form
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 4 × - 3 = - 12 and sum = - 1
the factors are - 4 and + 3
use these factors to split the x- term
4x² - 4x + 3x - 3 = 0 ( factor the first/second and third/fourth terms )
4x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term
(x - 1)(4x + 3) = 0 ← in factored form
equate each factor to zero and solve for x
4x + 3 = 0 ( subtract 3 from each side )
4x = - 3 ( divide both sides by 4 )
x = - \(\frac{3}{4}\)
x - 1 = 0 ( add 1 to both sides )
x = 1
solutions are x = - \(\frac{3}{4}\) , x = 1
Given that f(x) = |x|, graph the function g(x) = -f(x + 4).
Answers
Conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.
To graph the function g( x) = - f( x 4), we need to start with the graph of the function f( x) = | x| and also apply the given metamorphoses. The function f( x) = | x| represents the absolute value function, which is a V- shaped graph symmetric with respect to the y- axis.
First, we shift the graph of f( x) = | x| horizontally by 4 units to the left by replacing x with( x 4). This results in f( x 4). Next, we multiply the entire function by-1, which reflects the graph vertically. This gives us- f( x 4). Combining these metamorphoses, we've the function g( x) = - f( x 4). To graph g( x), we can compass a many points and also draw the graph by connecting them.
Let's start with the original graph of f( x) = | x| and apply the metamorphoses
For f( x) x = -3,-2,-1, 0, 1, 2, 3
f( x) = 3, 2, 1, 0, 1, 2, 3 For
g( x) = - f( x 4) x = -7,-6,-5,-4,-3,-2,-1
g( x) = -3,-2,-1, 0,-1,-2,-3
conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.
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Solve:|x-3|=7 pls answer
Answers
Answer:
x=10 and x=-4
Step-by-step explanation:
When the absolute value is all by itself on one side of the equation, the next step is to remove the absolute value bars. This will create TWO separate equations.
| x - 3 | = 7
x-3 = 7 This is one of the equations. Just straight up copied the equation but without the bars.
Here is the second equation:
x - 3 = -7
It is the left side copied, without the bars, but the right side has the opposite sign.
Solve these both separately to find the answers.
x-3=7 and x-3=-7
x=10 and x=-4
help please show work
Answers
1/2 • 4.7 x 8 = 18.8
8.) 40.96 square miles
6.4^2 = 40.96
9.) 7 square meters
1/2 • 4 • 3.5 = 7
10.) 36.4 square centimeters
(2.6 + 7.8) ÷ 2 x 7
11.) 22.8 square yards
6 • 3.8 = 22.8
12.) 30.6 square centimeters
5.1 • 6 = 30.6
Explanation:
FORMULAS FOR AREAS OF:
Triangle: 1/2 • base • height
Square: side^2
Parallelogram: base • height
Rectangle: Length • width
Trapezoid: (a + b) ÷ 2 x height
(a & b are the two bases)
hope this helps!
Uhm does anyone know what 8x is as an coefficient?
Answers
Answer:
yes 8x is a coefficient
Step-by-step explanation:
because I know but if I'm wrong than sry
Given that the polynomial f(x) has degree 8, which of the following most accurately describes the number of turning points of f(x)?
Answers
The x intercepts are the roots of the polynomial f(x) = 0.
The fundamental theorem of algebra says that the number of roots of this equation is 9, but not necessarily all of them are real; therefore the MAXIMUM number of x intercepts is 9.
However, since f(x) is of odd degree it must have at least one real root; therefore, the MINIMUM number of x intercepts is 1.
Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial f(x) that has a degree of 8 will have 7 turning points.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
For any polynomial equation, the number of turning points is always less than or equal to the degree of the polynomial.
Generally, the number of turns is one less than the degree of the polynomial.
Hence, the polynomial f(x) that has a degree of 8 will have 7 turning points.
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Need the answer to this pls
Answers
Answer:
0
Step-by-step explanation:
1. First, we should know the slope-intercept form of any equation: y = mx + b.
y = y-coordinatem = slopex = x-coordinateb = y-intercept2. In the equation y = -2/3(x), it appears that the variables we can see are y, m, and x. However, the y-intercept, b, is still there with the value of 0.
Additionally, this is a proportional relationship because it follows the format y = kx. Proportional relationships always have a y-intercept of 0.Therefore, the y-intercept is 0.
Which expression is equivalent to 2(8n) exponent 4 ?
A. (2• 8n) (2 • 8n)(2•8n) (2•8n)
B. 2• 3 •4
C. 2• 8• n •n •n •n
D. 2 •8n -8n • 8n • 8n • 8n
Quickly!
Answers
Answer:
2*8n*8n*8n*8n
Step-by-step explanation:
2(8n)^4
2(8n)(8n)(8n)(8n)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer: G is the answer
Please answer quick just super small explanation pls hurry quick for brainlessly answerr
Answers
Answer:
A
Step-by-step explanation:
2x/√2
2x/√2 x √2/√2 = 2x√2/2
x√2
D A rectangular house has a perimeter of 108 yards and an area of 665 square yards.
What are the dimensions of the house?
Answers
I need help with math ngl
Answers
Answer:
Oldest to newest:
10^-35, 10 ^-10, 0
Step-by-step explanation:
Scientific notation
To figure out the power of 10 think "how many places do I move the decimal point?"
When the number is 10 or greater the decimal point moves to the left, and the power of 10 is positive.
When the number is smaller than 1 the decimal point moves to the right, so the power of 10 is negative.
3х — 7y = 21
6x = 14y + 42
Solve each system of equations using elimination (⚠️ I will give you brainliest if you answer correctly!‼️⚠️)
Answers
Explanation:
3x - 7y = 21
6x = 14y + 42
Or 6x - 14y = 42
3x - 7y = 21 (1)
6x - 14y = 42 (2)
———————
-2(3x - 7y = 21)
6x - 14y = 42
———————
-6x + 14y = -42
6x - 14y = 42
———————
0x + 0y = 0
So I think in this case x and y has infinitely many solution
Aiden leans a 30-foot ladder against a wall so that it forms an angle of 78^{\circ} ∘ with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest hundredth of a foot if necessary.
Answers
Answer:
6.2 approx i believe
Step-by-step explanation:
Rhonda has a USB drive that can hold
8
,
000
,
000
,
000
B
8,000,000,000 B8, comma, 000, comma, 000, comma, 000, start text, space, B, end text.
Choose the best approximation of the number of bytes that Rhonda's USB drive can hold.
Answers
The best approximation of the number of bytes that Rhonda's USB drive can hold is 8 x \(10^9\) B.
What is Scientific Notation?Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.
Given:
We have Rhonda has a USB drive that can hold 8, 000, 000, 000 B.
In Scientific Notation the decimal point should be placed just after one number and the number of extra zeroes raised to power.
Here we have 9 zeroes after 8 then the Scientific Notation is
= 8, 000, 000, 000 B.
= 8 x \(10^9\) B
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What is the total area of the figure shown?
8.3 cm
9.5 cm
14.4 cm
12.3 cm
Answers
Answer:
44.5
Step-by-step explanation:
you add up all of the numbers.
NEED HELP ASAP! 20 POINTS!
use the rules of exponents to evaluate or simplify. write without negative exponents.
(-243)^3/5
Answers
Answer:
-27
Step-by-step explanation:
(-243)^3/5
We know that a^b^c = a^ (b*c)
(-243) ^ 1/5 ^3
We know (-243) ^ 1/5 = -3
(-3) ^3 = -27
HELP ME raaaaaaaa NOWWWWWWWWWW
Answers
Answer:
C: EAF Is the correct answer
Plz help I need help
Answers
Answer:
37 1/2
Step-by-step explanation:
times three fourths by fiffty and the awsewr would be 37.5
.5 is the same as one half