We typically write linear equations in slope-intercept form:
[tex]y=mx+b[/tex]
m = slopeb = y-intercept (the value of y when x=0)Solving the QuestionWe're given:
Line passes through (0, -1) and ( -13, -4)1) Determine the slope (m)
To find the slope, we can use the slope equation:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two points through which the line passes
⇒ Plug in the given points:
[tex]m=\dfrac{-1-(-4)}{0-(-13)}\\\\m=\dfrac{-1+4}{0+13}\\\\m=\dfrac{3}{13}[/tex]
Therefore, the slope of the line is [tex]\dfrac{3}{13}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\dfrac{3}{13}x+b[/tex]
1) Determine the y-intercept (b)
In this case, the y-intercept is already given to us.
The y-intercept is the value of y when x=0. Given that the line passes through (0,-1), we know that this is -1.
Plug this into [tex]y=\dfrac{3}{13}x+b[/tex]:
[tex]y=\dfrac{3}{13}x+(-1)\\\\y=\dfrac{3}{13}x-1[/tex]
Answer[tex]y=\dfrac{3}{13}x-1[/tex]
On a plane, 2 men had 135 kilograms of luggage added together. The first paid $1.35 for his excess luggage and the second paid $2.70 for his excess luggage. The charge was at a flat rate. If all of the luggage belonged to one person, the ecess luggage charge would have been $8.10. At most, how many kilograms of luggag is each person permitted to bring onto the plane free of an additional charge?A. 55 kilogramsB. 50 kilogramsC. 45 kilogramsD. 40 kilograms
Let's call the amount of lugagge the first men had as x, and the amount of lugagge the second men had as y.
Since both had to pay for excess of luggage, both had the permitted amount of luggage plus an extra amount. Let's call the permitted amount as a, the extra the first men had as z, and the extra the second man had as w. Then, our total amounts of luggage can be rewritten as
[tex]\begin{gathered} x=a+z \\ y=a+w \end{gathered}[/tex]Since their total amount of luggage added together was 135 kg, this gives to us the following equation
[tex]x+y=135[/tex]The charge for the extra luggage is a flat rate, let's call it r, then, the price you pay for the extra luggage is given by the product between this rate and the amount of extar luggage. The first paid $1.35 for his excess luggage and the second paid $2.70 for his excess luggage, therefore
[tex]\begin{gathered} zr=1.35 \\ wr=2.70 \end{gathered}[/tex]If we divide one equation by the other, we can write the excess of luggage of one as a function of the other.
[tex]\begin{gathered} \frac{zr}{wr}=\frac{1.35}{2.70} \\ \frac{z}{w}=\frac{1}{2} \\ w=2z \end{gathered}[/tex]If all of the luggage belonged to one person, this person would have to pay $8.10 for the excess. If we call the excess of this person as p, the amount of luggage this person had would be
[tex]a+p=135[/tex]Using the "rate formula" we created before, we can also write p as a function of z.
[tex]pr=8.10\Rightarrow\frac{pr}{zr}=\frac{8.10}{1.35}\Rightarrow p=6z[/tex]Rewritting all the total amounts, we have
[tex]\begin{gathered} a+6z=135 \\ a+2z=y \\ a+z=x \end{gathered}[/tex]If we add the equations for x and y together, we have
[tex]\begin{gathered} (a+z)+(a+2z)=(x)+(y) \\ a+z+a+2z=x+y \\ 2a+3z=x+y \end{gathered}[/tex]From the first equation, we know that the sum between both total amounts of luggage is equal to 135.
[tex]\begin{cases}x+y=135 \\ 2a+3z=x+y\end{cases}\Rightarrow2a+3z=135[/tex]Now, we have two equations for our two variables.
[tex]\begin{cases}2a+3z=135 \\ a+6z=135\end{cases}[/tex]If we multiply the first equation by 2, and subtract the second equation, we're going to get a new equation only for a(the amount in kilograms of permitted luggage).
[tex]\begin{gathered} 2\cdot(2a+3z)-(a+6z)=2\cdot(135)-135 \\ 4a+6z-a-6z=270-135 \\ 3a=135 \\ a=45 \end{gathered}[/tex]The amount of luggage permitted to bring onto the plane for free is 45 kilograms.
4(-8x + 5) - (-33x - 26)
Answer:
x+46
Step-by-step explanation:
Distribute
Combine like terms
Samuel buys 3 4K TVs for $1200 each. There is ashipping charge of $90 to have all 3 TVs delivered to hishouse. How much does Gordon pay in total?
Answer:
$3,690
Explanation:
The shipping charge for all 3 TVs =$90
Cost of a TV = $1200
Therefore, the cost of 3 TVs = 3 x $1200 =$3,600
The total amount paid by Gordon will be:
=$3600+90
=$3,690
Question 1 (10 points)
[tex] = 2^{3} \\ = 2 \times 2 \times 2 \\ = (2 \times 2) \times 2 \\ = 4 \times 2 \\ = 8[/tex]
ATTACHED IS THE SOLUTION
LAST OPTION IS THE ANSWER.
6b³ +16b² -15b-40
Factor
Answer:
(2[tex]b^{2}[/tex] - 5) (3b + 8)
Step-by-step explanation:
First factor out 2[tex]b^{2}[/tex] from the first set of parentheses and -5 from the second
2[tex]b^{2}[/tex] ( 3b + 8) - 5 (3b + 8)
Next factor out (3b + 8)
(2[tex]b^{2}[/tex] - 5) (3b + 8)
(9) 0.5= A. 3 B. 4.5 C. 1/81
The expression is 0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]. The evaluated expression is 3a+4.5b+c=40.5
Given that,
The expression is 0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]
We have to evaluate the expression
Evaluating an algebraic expression involves determining its value when a particular integer is substituted for a variable. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.
Take,
0.5=[tex]\frac{a\times3+b\times4.5+c\times1}{81}[/tex]
0.5×81=a×3+b×4.5+c
40.5=3a+4.5b+c
The expression can be written in 4 ways
1st- 3a+4.5b+c=40.5
2nd- a=[tex]\frac{40.4-4.5b-c}{3}[/tex]=13.4-1.5b-c (this is the expression with subject a)
3rd- b= [tex]\frac{40.5-3a-c}{4.5}[/tex]=9-1.6a-c (this is the expression with subject b)
4th- c= 40.5-3a-4.5b (this is the expression with subject c)
Therefore, The evaluated expression is 3a+4.5b+c=40.5
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Find the absolute value of x
4-|x|=1
Answer:
3
Step-by-step explanation:
Absolute value is how far away the value is from 0. The only value of x that would make this equation true is 3.
-(8-²)=
Evaluate the expressions
After evaluating the given expression -(8⁻²), the resultant expression is - 1/64.
What are expressions?An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules. A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.2x + 3 is an illustration of a mathematical expression with a variable. Each and every variable needs to have a coefficient or a value multiplied by the variable. The number 2 is the coefficient of x in the expression 2x + 3, which means 2 times x plus 3.So, -(8⁻²):
Now, evaluate -(8⁻²) as follows:
-(8⁻²)-(1/64)- 1/64Therefore, after evaluating the given expression -(8⁻²), the resultant expression is - 1/64.
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Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the mean of the sample means?.
The value obtained for z-score for the given sample mean is 0.5.
What is described as the z-score?A Z-score is a numerical quantification that describes the relationship of a value to the mean of a set of values. The Z-score is expressed in standard deviations of the mean. A Z-score of 0 signifies that the data point's points tally is the same as the mean score.For the given question;
The formula for finding the z-score is;
z = (x - μ)/σ
x = sample size
μ = population mean
σ = standard deviation population.
The given values are-
μ = 25σ = 20x = 35Put the value in the z-score.
z = (35 - 25)/20
z = 10/20
z = 0.5
Therefore, the value obtained for z-score for the given sample mean is 0.5.
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The correct question is-
Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the z-score for the of the sample means for the sample less than 35?.
Please help!!!
Have school tomorrow
This is due tomorrow!
I have no clue how to do this
Yes , ∠WGR is congruent ∠GHR because both angles are on one line.
What does the word "congruent" mean in math?
If it is possible to impose one geometric figure on the other such that their surface area coincides, that geometric figure is seen to be congruent, or to be in the connection of congruence.Congruent Figures Examples Two butterflies that are the same size and form. Two candy ice creams of equal size and shape. Two equal Lego bricks in respect of size and shape.a) No, ∠PHG is not congruent ∠MGH because both angles are not equal.
b) No, ∠RHG and ∠MGH are not supplementary angle because in supplementary angle is equal to 180° .
c) No, ∠SGW is not congruent ∠PHV.
d) Yes , ∠WGR is congruent ∠GHR because both angles are on one line.
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The table shows information about the
masses of some dogs.
a) Work out the minimum number of
dogs that could have a mass of more than 27 kg.
b) Work out the maximum number of
dogs that could have a mass of more than 27 kg.
a) The minimum number of dogs that could have a mass of more than 27 kg is 4.
b) The maximum number of dogs that could have a mass of more than 27 kg is 17.
The given table shows information about the masses of some dogs.
a) Because we need the minimum number of dogs,
Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the minimum value out of 13 and 4 is 4.
b) Because we need the maximum number of dogs,
Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the maximum of the values present in the interval 20 to 40 is 13 + 4 = 17
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Answer:
Step3
-by-step explanation:
Find the sum of (2.8 × 10−9) and (9.1 × 10−10). Write the final answer in scientific notation.
11.9 × 10−19
1.19 × 10−18
3.71 × 10−10
3.71 × 10−9
Answer: [tex]3.71 \times 10^{-9}[/tex]
Step-by-step explanation:
[tex](2.8 \times 10^{-9})+(9.1 \times 10^{-10})\\\\=10^{-10}(28+9.1)\\\\=10^{-10}(37.1)\\\\=3.71 \times 10^{-9}[/tex]
Answer:
The answer is C: 3.71 × 10−9.
Step-by-step explanation:
Which of the contexts below represents exponential growth?
The amount of a certain medication in a person's bloodstream decreases by
every hour.
Snow was falling at a rate of 1.75 inches per hour.
A population of 200 bacteria quintuples every week.
A car depreciates at a rate of 5.3% per year.
Answer:
I believe it would be "A population of 200 bacteria quintuples every week"
Step-by-step explanation:
If it is quintupling each week then the number is getting larger and larger exponentially.
What is the slope of the ramp from the ground to the landing? Write your answer as a fraction with a whole-number numerator and denominator.
The slope of the ramp is m = h/√(r² - h²).
What is mean by square root of a number?
A square root of a number is a value that multiplied by itself gives the same number.
Let h = height of the landing.
And, r = the length of the ramp.
Then, the length from the ground where the ramp touches it, to the ground directly below the landing is
⇒ √(r² - h²)
And, The slope of the ramp is m = h/√(r² - h²)
For example, if the ramp is 5 meters long and the landing height is 3 meters high, the slope of the ramp is 3/4.
As, Slope of the ramp (m) = 3/√(25-9) = 3/√16 = 3/4
Thus, The slope of the ramp is m = h/√(r² - h²).
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he function y=f(x)y=f(x) is graphed below. What is the average rate of change of the function f(x)f(x) on the interval −1≤x≤0?
The estimate of the average rate of change f is -2
How to estimate the average rate of change f?The possible graph that completes the question is added as an attachment
The interval is given as
-1 ≤ x ≤ 0
This can be rewritten as
x = -1 to x = 0
This can also be represented as
(a, b) = (-1, 0)
From the attached graph, we have
f(-1) = 7
f(0) = 5
The estimate (to one decimal place) of the average rate of change f is
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [f(-1) - f(0)]/[-1 - 0]
So, we have
Rate = [7 - 5]/[-1 - 0]
Evaluate
Rate = -2
Hence, the average rate of change f is -22
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On a coordinate plane, a dashed straight line with negative slope goes through (0, 1) and (2, negative 2). Everything to the left of the line is shaded.
Which inequality is represented by the graph?
y > Negative two-thirdsx + 1
y < Negative two-thirdsx + 1
y < Negative three-halvesx + 1
y > Negative three-halvesx + 1
The inequality which is represented by the dashed line and the description as in the task content is; y < Negative three-halvesx + 1.
Which inequality correctly represents the dashed line as described in the task content?It follows from the task content that the inequality which correctly represents the line is to be determined.
Therefore, first, the slope which is the rate of change of y to x according to the two points given is;
slope, m = (y2 - y1)/(x2 - x1)
m = (-2 - 1)/(2 - 0)
m = -3/2.
Also, since the point, (0, 1) is given, the y-intercept of the line is; 1.
Therefore the equation of the dashed line is;
y = (-3/2)x + 1.
And ultimately, since the line is dashed and everything to the left is shaded, the required inequality is;
y < (-3/2)x + 1.
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The height of square room is Sm and volume is 180m³. Find the length.
Answer:
length = 6m
Step-by-step explanation:
H=5m
V=180m^3
Here
V=l^2 ×H ( being a square)
180=a^2×5
a^2=36
a=6m
What is the percentage of 150 out of 329.5 million?
The number 150 is 0.0000455 % out of 329.5 million
How to determine the percentage?The statement is given as
the percentage of 150 out of 329.5 million
The percentage can be calculated as
Percentage = 150 out of 329.5 million *100%
Express as fraction
So, we have
Percentage = 150/329.5 million *100%
Rewrite as
Percentage = 150 *100/329.5 million %
Evaluate the product
Percentage = 15000/329.5 million %
Evaluate the quotient
Percentage = 0.0000455 %
Hence, the percentage of 150 out of 329.5 million is 0.0000455 %
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Solve the following equation: 2=|3x-3|
Answer:
x = 5/3, 1/3
Or
x=1.6 repeating ,0.3 repeating
A line has a slope of 1/4 and includes the points (-6, -7) and (z, -5) what is the value of z
Michelle has an average score of 70 for three tests.
What must she score on the next test to increase her average to 74?
Answer:
86
Step-by-step explanation:
average is calculated as
average = [tex]\frac{sum}{count}[/tex]
given her average was 70 in 3 tests , then
[tex]\frac{sum}{3}[/tex] = 70 ( multiply both sides by 3 )
sum = 210
let the score she must get in test 4 be x for an average of 74 , then
[tex]\frac{210+x}{4}[/tex] = 74 ( multiply both sides by 4 )
210 + x = 296 ( subtract 210 from both sides )
x = 86
she must score 86 in her next test
Answer:
[tex]\frac{x}{3}[/tex]= 70
x=210
[tex]\frac{210+x}{4}[/tex] = 74
210+x=74x4
210+x=296
x=296-210
x=86
Plss mark as brainliest
- Find the measure of <8.
Find the measures of the remaining numbered angles.
Answer:
<8=66°
Step-by-step explanation:
2 angles on a straight line will add up to 180° so
180-114=66.
<8,<4, <1, <5 all equal 66° since vertical angles are equal
Sum of 8 consecutive numbers is 124. Find the numbers
i will mark you as brainliest for giving breif explanation step by step
Answer:
x = 12
Step-by-step explanation:
Be the 8 consecutive numbers like this:
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) = 124
8x + 28 = 124
8x = 124 - 28
8x = 96
x = 12
Montraie bought snacks for his team's practice. He bought a bag of popcorn for $2.45
and a 18-pack of juice bottles. The total cost before tax was $29.99. How much was
each bottle of juice?
Answer:
$1.53
Step-by-step explanation:
Let x represent each bottle of juice, then the equation will be -->
2.45+18x=29.99
18x=29.99−2.45=27.54
Therefore, x=1.53
Each bottle of juice costs $1.53
By what number should you multiply $3\frac{1}{3}$ to get a product of $4$? Express your answer as a mixed number.
The number you should multiply 3 1/3 to get a product of 4 is 1 1/5
How to determine the number?From the question, the statement is given as
What number should you multiply 3 1/3 to get a product of 4
Let the number be x
So, we have the following representation
3 1/3 * x = 4
Express 3 1/3 as an improper fraction
So, we have the following representation
10/3 * x = 4
Multply both sides by 3
So, we have
10 * x = 12
Divide both sides by 10
This gives
x = 12/10
Express as mixed numbers
x = 1 1/5
Hence, the number is 1 1/5
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help me i need help.
Answer:108 inches
Step-by-step explanation:
to find the area of one of the right triangles you do.
base = 6/2 =3
3x6=18
18/2=9
there are 8 right triangles so you would do
9x8 = 72.
then you would add 72 and the area of the square in the middle
6x6=36
36+72= 108
so Area of SA = 108 inches ^2
The vertex form of the equation of a parabola is y = (x- 5)2 + 16.
What is the standard form of the equation?
Answer: [tex]y=x^2 -10x+41[/tex]
Step-by-step explanation:
[tex]y=(x-5)^2 +16\\\\y=x^2 -10x+25+16\\\\y=x^2 -10x+41[/tex]
9×+1=16
Two step equation
Answer:
[tex]x=5/3[/tex]
Step-by-step explanation:
[tex]9x+1=16 \\ \\ 9x=15 \\ \\ x=5/3[/tex]
Mia is factoring the polynomial
x^2+4x−12. She uses the steps shown.
x^2+4x−12
Step 1
x^2+6x−2x−12
Step 2
(x^2+6x)−(2x+12)
Step 3
x(x+6)−2(x+6)
Step 4
(x+6)(x+2)
In which step did Mia make an error?
Answer:
Step 4
Step-by-step explanation:
Mia made a mistake in step 4.
Step3: x(x + 6) -2(x + 6)
In both terms, (x + 6) is common.
Step 4: When we take (x + 6) out, it will be (x + 6 ) (x - 2)
Help me please with this assignment
Given:
Let the cost of chocolate bar be 'x'.
[tex]\text{Cost of Peanut butter bar=x+0.07}[/tex][tex]\begin{gathered} 5(x+0.07)+6(x)=6.40 \\ 5x+0.35+6x=\text{6}.40 \\ 11x=6.40-0.35 \\ x=\frac{6.05}{11} \\ x=0.55 \end{gathered}[/tex]Cost of chocolate bar is $0.55