Solve the system below by substitution
6x-y=-23
2x+5y=-13
Answer:
x= -4 y= -1
6x - y = - 23
-y=-23-6x
y=6x+23, use this to plug in for y in the second equation.
2x + 5y = -13
2x + 5(6x+23) = -13
2x+30x+115=-13
x= -4, use this to plug in for x in the first equation.
6x - y = - 23
6(-4)-y=-23
-24-y=-23
-y=-23+24
-y=1
y= -1
Step-by-step explanation: not doing this to steal points
Answer:
here is your solution.
Step-by-step explanation:
x=4 & y=1
I need help with my math homework
Answer:
1. 2
2. 7
3. 15
4. 80
5. 70
Step-by-step explanation:
Answer:
1st question's answer is 2 x 90 = 180
2nd question's answer is 70 x 7 =490
3rd question's answer is 240 = 4 x 60
4th question's answer is 9 x 80 = 720
5th question's answer is 70 x 8 =560
Would greatly appreciate if any of you can answer the question in the attached image with full explanation including a strategy for solving it. Thanks in advance!
Answer:
B) a = - 3------------------
Multiply both sides by ax - 2 to clear fractions:
24x² + 25x - 47 = (ax - 2)(- 8x - 3) - 5324x² + 25x - 47 = - 8ax² - 3ax + 16x + 6 - 5324x² + 25x - 47 = - 8ax² - (3a - 16)x - 47Comparing both sides we can guess that -8a = 24 ⇒ a = - 3, then:
- (3*(-3) - 16) = - (- 9 - 16) = - (-25) = 25.We see both coefficients match, hence a = - 3 is a right choice.
Give the equation of each quadratic in the form, picture of formula and graphs attached.
The equation of each quadratic in the picture of formula and graphs attached is y=-1(x+8)^2 +9 and y=1/4*(x-6)^2 +3
What is Graph Transformation?
When a graph is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply pushing the graph of the function g(x) = x2 up by 3 units, the graph of the function f(x) = x2 + 3 is generated. graph transformations are highly useful for graphing functions without having to start from scratch since they allow you to move, extend, compress, or reflect the curve. The graph of the parent function is either "moved," "resized," or "reflected" by a graph transformation. The three primary categories of graph transformations are as follows:
Translation DilationReflectionA)
first of all we need to find which type of parabolic graph is it
from the picture give we can clearly see it is a x^2=-4ay type of graph
and using graph transformation formula
i.e. y= a(x-h)^2 + k
where h = -8
k=9
we get y=a(x+8)^2+9
as we know (-5,0) lie on this graph
so,
0=a(-5+8)^2+9
a=-1
so the equation is y=-1(x+8)^2 +9
B)
first of all we need to find which type of parabolic graph is it
from the picture give we can clearly see it is a x^2=-4ay type of graph
and using graph transformation formula
i.e. y= a(x-h)^2 + k
where h = 6
k=3
we get y=a(x-6)^2+3
as we know (0,12) lie on this graph
so,
12=a(0-6)^2+3
a=1/4
so the equation is y=1/4*(x-6)^2 +3
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Is it ever possible to have a graph of a function that is
symmetric about the y-axis AND the origin? Explain your
thinking.
We know that,
By definition, no function is symmetrical about the x-axis (or any other horizontal line). Because the one flipped with respect to the horizontal violates the vertical line test.
On the other hand, functions can be symmetric about a vertical line or a point. In particular, functions symmetric about the y-axis are also "even" functions, and functions symmetric about the origin are also "odd" functions. Because of this correspondence between graph symmetry and function equality or oddness, "symmetry" in algebra is usually applied to the y-axis and the origin.
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Answer:
yes: f(x) = 0
Step-by-step explanation:
You want to know if a function exists that is symmetrical about the y-axis and the origin.
SymmetryA graph is symmetrical about the y-axis if and only if ...
f(-x) = f(x)
A graph is symmetrical about the origin if and only if ...
f(-x) = -f(x)
For both conditions to be met, we must have ...
f(x) = -f(x)
2f(x) = 0 . . . . . add f(x)
f(x) = 0 . . . . . . . divide by 2
The graph of f(x) = 0 will be symmetrical about the y-axis and the origin. (It is the x-axis.)
Need help solving this. Please help
Answer:
Step-by-step explanation:
Reason 2: The box in the corner of the angle indicates that the angle is a right angle, which is 90 degrees.
Statement 3:
m<abd +m<dbc=m<abc
How many degrees do the angles of a triangle contain?
Answer: 180
Step-by-step explanation:
all 3 angles equal 180 degrees if you divide by 3 each angle will be 60 degrees
Use the product property to rewrite log2 256b
The solution for the given logarithmic expression would be x = 8.
What are the logarithms?
In mathematics, the logarithm is the inverse function of exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
Given:
[tex]log_2(256)[/tex]
Let
[tex]x=log_2(256)[/tex]
By using the property of logarithms we can write
[tex]2^x=256\\\\2^x=2^8\\[/tex]
Since the bases are the same, the two expressions are only equal if the exponents are also equal.
x = 8.
Hence, the solution for the given logarithmic expression would be x = 8.
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Wyatt is deciding between two different movie streaming sites to subscribe to. Plan A costs $ 19 per month plus $0.50 per movie watched. Plan B costs $ 13 per month plus $1.50 per movie watched. Let A represent the monthly cost of Plan A if Wyatt watches x per month, and let B represent the monthly cost of Plan B if Wyatt watches x movies per month. Write an equation for each situation, in terms of x, and determine the number of monthly movies watched, x, that would make the two plans have an equal monthly cost.
A=
B=
Answer=
Equations representing the total costs for plan A and B are A = 19 + 0.50x and B = 13 + 1.5x, respectively, where x is the number of movies watches.
Cost of both the plans will be equal for 6 movies.
What is a linear equation?
A linear function is defined as a function that has either one or two variables without exponents.Given that, Wyatt is deciding between two different film streaming sites to subscribe to, plan A costs $19 per month plus $0.50 per film watched, plan B costs $13 per month plus $1.50 per film watched.
According to question,
A = 19 + 0.50x and
B = 13 + 1.5x
For costs being equal, we have,
A = B
19 + 0.50x = 13 + 1.5x
x = 6
Hence, for 6 films the costs of both the plans will be equal and equation for both the plans are A = 19 + 0.50x and B = 13 + 1.5x
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A data set includes data from student evaluations of courses. The summary statistics are n=85, x=3.42, s=0.56. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternativehypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative hypotheses? A.) H0: μ=3.50 H1: μ>3.50 B.) H0: μ≠3.50 H1: μ=3.50 C.) H0: μ=3.50 H1: μ≠3.50 D.) H0: μ=3.50 H1: μ<3.50
Determine the test statistic= ____ (Round to two decimal places as needed.)
Determine the P-value = ____ (Round to three decimal places as needed.)
State the final conclusion that addresses the original claim. ▼ Fail to reject OR Reject H0. There is ▼ sufficient OR not sufficient evidence to conclude that the mean of the population of student course evaluations is equal to 3.50 ▼ is OR not is correct.
- The null hypothesis Is: [tex]$H_0: \mu=4.5$[/tex]
- The alternative hypothesis Is: [tex]$H_1: \mu \neq 4.50$[/tex]
- The test statistic is: t=-0.43
- The p-value of the test is of 0.6684.
What is p-value?
The p-value Is of 0.6684>0.05, which means that we can conclude that the population of student course evaluations has a mean equal to [tex]\mathbf{4 . 5 0}$.[/tex]
We are going to test If the mean Is equals to 4.50, thus, the null hypothesis Is:
[tex]H_0: \mu=4.5[/tex]
At the alternative hypothesis, we test If the mean Is different to 4.50, that is:
[tex]H_1: \mu \neq 4.50[/tex]
Since we have the standard devlation for the sample, the t-distribution is used. The value of the test statistic Is:
[tex]t=\frac{\pi-\mu}{\frac{\sqrt{n}}{\sqrt{n}}}$$[/tex]
For this problem:
[tex]$$\begin{aligned}& t=\frac{4.30-1.5}{\frac{2.21}{\sqrt[3]{80}}} \\& t=-0.43\end{aligned}$$[/tex]
We are testing If the mean is dlfferent from a value, thus, the p-value of test is found using a two-talled test, wlth t=-0.43 and [tex]$80-1=79 \mathrm{df}$[/tex].
Using a t-distribution calculator, the [tex]$\mathrm{p}$[/tex]-value is of [tex]$\mathbf{0 . 6 6 8 4}$[/tex].
The p-value is of 0.6684 > 0.05, which means that we can conclude that the population of student course evaluations has a mean equal to 4.50.
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Using the methods provided in the text for computing confidence intervals for population proportions, a marketing analyst takes a survey of 1000 randomly selected consumers. She asks if they prefer low-sodium soup products. Using the results, she provides a 95% confidence interval for the population proportion of consumers who prefer low-sodium soup products. The interval has a margin of error of 03. Which of the following is an appropriate interpretation of these results? (a) The sample proportion from the survey differs from the population proportion by at most 03. (b) 95% of all possible values of the population proportion are contained in the interval provided. (c) The analyst is 95% confident that all possible values for the sample proportion from a sample of 1000 consumers are in the interval provided. (d) Using these methods, 95% of all possible confidence intervals from a sample of 1000 consumers will contain the population proportion. (e) The reported confidence interval will contain the population proportion 95% of the time.
The reported confidence interval will contain the population proportion of consumers 95% of the time.
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.
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Whats the simplified version of √(√21-2√3)^2
The required simplified solution of the given expression is given as √3(√7 - 2).
Given that,
To determine the simplified solution of the √(√21-2√3)²
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
= √(√21-2√3)²
=√21-2√3 (√a² = a)
= √3(√7 - 2)
Thus, the required simplified solution of the given expression is given as √3(√7 - 2).
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4.4 times 2.727 km Answer with explanation
Answer:
12 km
Step-by-step explanation:
4.4 * 2.727 km = 11.9988 ( using a calculator)
since the smallest factor (4.4) has only 2 significant digits , your answer should be rounded to only 2 S.D. so = 12 km
Help i need help with this question.
Based on the SAS, SSS, and the transitive property of congruence, the reason why ΔABC ≅ ΔGHJ is because of option B.
What is SAS and SSS?The SAS is a triangle theorem that states that two triangles are congruent if they both have two pairs of congruent sides and a pair of included congruent angles.
On the other hand, the SSS states that two triangles that have three pairs of congruent sides are equal.
What is the Transitive Property of Congruence?The transitive property of congruence states that if two triangles are congruent to a third triangle, then all three triangles are congruent to each other.
Based on the SSS, triangle ABC is congruent to triangle DEF.
Based on the SAS, triangle DEF is congruent to GHJ.
Therefore, based on the transitive property of congruence, triangle ABC is congruent to triangle GHJ.
Therefore, the reason why ΔABC ≅ ΔGHJ is because of the reason given in option B.
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Rewrite the expression in terms of the given function. (sec x - csc x) / (1 - tan x) in terms of sin x (sec x - csc x) / (1-tan x) =
The trigonometric expression (sec x - csc x) / (1 - tan x) is equivalent by trigonometric formulas and algebra properties to - sin x.
How to rewrite a trigonometric expression in terms of sine function
Herein we find a trigonometric expression that must be rewritten in terms of sin x by means of trigonometric formulas and algebra properties. The original expression is shown below:
(sec x - csc x) / (1 - tan x)
First, the original expression is written:
(sec x - csc x) / (1 - tan x)
Second, use the definitions of secant, cosecant and tangent:
[(1 / cos x) - (1 / sin x)] / [1 - (sin x / cos x)]
Third, use algebraic properties to simplify the expression:
[(sin x - cos x) / (sin x · cos x)] / [(cos x - sin x) / cos x]
[(sin x - cos x) · cos x] / [sin x · cos x · (cos x - sin x)]
- sin x
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The median weekly gross income for someone with a bachelor's degree was $2,117.00. If they continued their education and training and earned a master's degree, they had an increase in their median weekly income of about 46.1%. Determine the median weekly income for someone with a master's degree.
$2,856.12
$3,092.94
$3,153.76
$2,908.45
A master's degree earner's typical weekly salary is $3,092.94.
What is the meaning of percentage?
A percentage in mathematics is a number or ratio that may be stated as a fraction of 100.In determining a percentage of a number, we should first divide it by 100 before multiply the outcome by 100. As a result, the proportion refers to a part per 100. The word "percent" refers to a fraction of one hundred. The letter "%" stands for it.
Considering that the median gross weekly wage for a bachelor's degree holder was $2,117.00.
If any one had mater degree, then an increase in the median weekly income of about 46.1%.
To find the increment multiply $2,117.00 with increase rate:
The increment is $2,117.00 × 46.1% = 2,117.00 × 46.1/100= $975.937
The total the median weekly income is
$975.937 + $2,117.00
= $3,092.937
≈ $3,092.94
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Simplify by reducing. Begin by determining the domain restrictions. Show all work.
x2 + 6x + 9 over x2 - 9
x2+6x+9/x2-9
3x2 - 9x over x2 - x - 6
3x2-9x/x2-x-6
Using simplification by factorisation and division
(x² + 6x + 9)/(x² - 9) = (x + 3)/(x - 3) and (3x² - 9)/(x² - x - 6) = 3x/(x + 2)
How to simplify the equations by factorizationTo simplify the equations, we shall factorize both the numerator and the denominator, and divide through by a common factor.
for the equation (x² + 6x + 9)/(x² - 9);
the numerator:
x² + 6x + 9 = x² + 3x + 3x + 9
x² + 6x + 9 = x(x + 3) +3(x + 3)
x² + 6x + 9 = (x + 3)(x + 3)
the denominator:
x² - 9 = x² - 3²
x² - 9 = (x + 3)(x - 3) {difference of two squares}
(x² + 6x + 9)/(x² - 9) = (x + 3)(x + 3)/(x + 3)(x - 3)
divide through by the common factor (x + 3)
(x² + 6x + 9)/(x² - 9) = (x + 3)/(x - 3)
For the equation; (3x² - 9)/(x² - x - 6)
the numerator:
3x² - 9 = 3x(x -3)
the denominator:
x² - x - 6 = x² -3x + 2x - 6
x² - x - 6 = x(x - 3) + 2(x - 3)
x² - x - 6 = (x + 2)(x - 3)
divide through by the common factor (x - 3)
(3x² - 9)/(x² - x - 6) = 3x/(x + 2)
Thus, (x + 3)/(x - 3) and 3x/(x + 2) are the results for simplifying (x² + 6x + 9)/(x² - 9) and (3x² - 9)/(x² - x - 6) respectively using factorization.
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What is the correct to this answer ??? ( answers only)
Answer:
k is greater or equal to -5
Step-by-step explanation:
[tex] - 5 \leqslant k[/tex]
here, -5 is on the left side of the inequality sign which means it is less than or equal to k.
In a food cocktail,the ratio of orange juice to apple juice to coconut milk is 3:2:4, respectively. How much of each do I need to take if I have 5 more oz of orange juice than apple juice
By ratios ,orange = 15 , apple = 10 , coconut = 20 are needed to make 45 liters of this cocktail.
What does the math ratio mean?
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A proportion is an equation that sets two ratios at the same value.
As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)
orange = 3
apple = 2
coconut = 4
total = 9
orange = 3/9 * 45 = 15
apple = 2/9 * 45 = 10
coconut = 4/9 * 45 = 20
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The complete question is -
In a fruit cocktail, the ratio of orange juice to apple juice to coconut milk is 3:2:4, respectively. How much of each type is needed to make 45 liters of this cocktail?
plase help me out tanks
Answer: x = 4
Step-by-step explanation:
5x - 3 ≥ 13
Substitute x with 4
5(4) - 3 ≥ 13
20 - 3 ≥ 13
17 ≥ 13
17 is greater than or equal to 13
What is the domain of the function g(x)=3log2(x-1)+4
Answer: x : x e R and R >
Step-by-step explanation:
Please can anyone answer this percentage question cor grade 7
well, we know it was 480, then we reduce it by 50.
a)if we take 480 to be the 100%, what's 50 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 480 & 100\\ 50& x \end{array} \implies \cfrac{480}{50}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 48 }{ 5 } ~~=~~ \cfrac{ 100 }{ x }\implies 48x=500\implies x=\cfrac{500}{48}\implies x=\cfrac{125}{12}\implies \boxed{x\approx 10.4}[/tex]
now, the TV is only 480 - 50 = 430, then it gets reduced another 50.
if we take 430 to be the 100%, what's 50 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 430 & 100\\ 50& y \end{array} \implies \cfrac{430}{50}~~=~~\cfrac{100}{y} \\\\\\ \cfrac{ 43 }{ 5 } ~~=~~ \cfrac{ 100 }{ y }\implies 43y=500\implies y=\cfrac{500}{43}\implies \boxed{y\approx 11.6}[/tex]
b)hmmm the absolute change of the reductions? that sounds like 480 - 50 - 50 = 380.
c)well, the overall percentage hmmm well, that's the $100 reduction total.
if we take $480 as the 100%, what's $100 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 480 & 100\\ 100& z \end{array} \implies \cfrac{480}{100}~~=~~\cfrac{100}{z} \\\\\\ \cfrac{ 24 }{ 5 } ~~=~~ \cfrac{ 100 }{ z }\implies 24z=500\implies z=\cfrac{500}{24}\implies z=\cfrac{125}{6}\implies \boxed{z\approx 20.8}[/tex]
The equation c = 13.99p represents the proportional relationship between the total cost (c) and the number of pounds (p) of shrimp at a grocery store. Which description is true, based on the equation of the proportional relationship?
each pound of shimp costs $13.99
100 points. Which is the graph of f (x) x - 1/ x2 - x 6
Answer:
A – see below
Step-by-step explanation:
You want to identify the graph of f(x) = (x -1)/(x² -x -6).
Factored formThe function can be factored as ...
[tex]f(x) = \dfrac{x-1}{(x-3)(x+2)}[/tex]
The numerator is zero when x=1, so that is where the x-intercept lies.
The denominator is zero for x=-2 and x=3, so those are the locations of the vertical asymptotes.
The graph that has vertical asymptotes at x=-2 and x=3, and an x-intercept of x=1 is Graph A.
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JK is a midsegment of FGH. Find the values of x and y.
JK is a midsegment of triangle FGH. Hence, the values of x and y are 18 and 14 respectively.
What is a midsegment of a triangle?A triangle's midsegment is a line segment that connects the midpoints or centers of two of its opposite or adjacent sides.
Given that, JK is a midsegment of triangle FGH.
Also the values of:
FG = 28
FJ = x
JH = 10
JK = y
As, JK is midsegment of FG, we have:
JK = FG / 2
y = 28 / 2
y = 14
So, the value of y could be 14.
Also, FG = 28
FJ + JH = FG
10+x = 28
x = 28 - 10
x = 18
So, the value of x could be 18.
Hence, the values of x and y are 18 and 14 respectively.
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Answer:
x=10
Y=14
Step-by-step explanation:
big ideas
the number k if 3/11 (fraction) of k is 12
Answer:
k = 44
Step-by-step explanation:
[tex]\frac{3}{4}[/tex]k = 12 Multiple both sides by [tex]\frac{4}{3}[/tex]
k = 44
Answer:
k = 44
Explanation:
You can write this into an equation, where k x 3/11 = 12. If you multiply both sides of the equation by 11 and divide by 3, you get k by itself.
k x 3/11 = 12
3k/11 = 12
3k = 132
k = 44
Exactly 10% of the students in a school are left-handed. Select 15 students at random from the school and define W = the number who are left-handed.
a. yes
b. no
c. unsure
The statement is true , that the given sample follows binomial distribution.
If a random variable has two alternative outcomes (success or failure), it has a binomial distribution.
Each draw must be separate from the ones that came before it.
There is a set number of drawn components.
We randomly select 15 students, and since the sample size of 15 is less than 10% of the total population, we can assume that each draw is independent.
Because X has a binomial distribution, success is determined by whether the student is left-handed (failure is determined by whether the student is not left-handed).
The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for success or failure as the possible outcomes of an experiment.
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Which expression is equivalent to 225/625m⁴n⁶
A. 1/20m²|n³|
B. 1/20m²n⁴
C. 3/5m²|n³|
D. 3/5m²n⁴
The equivalent expression of 225/625m⁴n⁶ is 3/5m²n³.
What is the square root?
A number y such that y = x², or a number y whose square is x, is referred to as the square root of a number x in mathematics. For instance, since 4² = 2 = 16, 4 and -4 are the square roots of 16.
We have,
225/625m⁴n⁶
So, simplifying the given equation,
= 225/625m⁴n⁶
dividing the numerator and denominator by 25 we get,
= 9/25m⁴n⁶
again by taking the square root of the numerator and denominator we get,
= 3/5m²n³.
Hence, the equivalent expression of 225/625m⁴n⁶ is 3/5m²n³.
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Dos cuadrados de lado 10 cm se sobreponen formando un rectángulo de 17 cm de largo, como se muestra en la figura. ¿Cuál es el área de la franja amarilla en centímetros cuadrados?
The area of the rectangular yellow region is of:
30 cm².
How to obtain the area of a rectangle?The area of a rectangle of base b and height h is obtained as the multiplication of these dimensions, as follows:
Area = base x height.
From the image given at the end of the answer, these dimensions are given as follows:
Height = 10 cm, which is the side length of the square.Base = 3 cm, as the two squares would combine for a side length of 20 cm, but they combine for 17 cm, hence 20 - 17 = 3 cm.Then the area of the yellow region is calculated as follows:
Area = 10 x 3 = 30 cm².
TranslationThe problem asks to obtain the area of the rectangular region, considering that:
The squares have side length of 10.The combined squared combine for a side length of 17.Missing InformationThe region is given by the image shown at the end of the answer.
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The sum of two mixed fractions is 12 3/35
If one mixed fractions is 5 31/35 find the other mixed fraction.
let's convert the mixed fractions to improper fractions and then let's proceed.
[tex]\stackrel{mixed}{12\frac{3}{35}}\implies \cfrac{12\cdot 35+3}{35}\implies \stackrel{improper}{\cfrac{423}{35}} ~\hfill \stackrel{mixed}{5\frac{31}{35}}\implies \cfrac{5\cdot 35+31}{35}\implies \stackrel{improper}{\cfrac{206}{35}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]12\frac{3}{35}~~ + ~~x~~ = ~~5\frac{31}{35}\implies \cfrac{423}{35}+x=\cfrac{206}{35}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{423}{35}+x \right)=35\left( \cfrac{206}{35} \right)} \\\\\\ 423+35x=206\implies 35x=-217 \\\\\\ x=\cfrac{-217}{35}\implies x=\cfrac{-31}{5}\implies {\Large \begin{array}{llll} x=- 6\frac{1}{5} \end{array}}[/tex]
to convert an improper fraction like -31/5 to a mixed fraction, well, first off, we nevermind the sign, so we only use 31/5 and then we divide 31 ÷ 5.
hmm 31 ÷ 5 gives us a quotient of 6, and a remainder of 1, we put the quotient upfront and the remainder as the numerator, with the old denominator and sign back in.