The equation of the Line passing through the points (19, -16) and (-7, -15) is: y = (-1/26)x - 397/26
The equation of a line using the point-slope formula or the slope-intercept form, we need either the slope of the line or the y-intercept. Let's calculate the slope of the line using the given points (19, -16) and (-7, -15).
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (19, -16) as (x1, y1) and (-7, -15) as (x2, y2), we can substitute these values into the slope formula:
m = (-15 - (-16)) / (-7 - 19)
m = (-15 + 16) / (-7 - 19)
m = 1 / (-26)
m = -1/26
Now that we have the slope of the line, we can use either the point-slope formula or the slope-intercept form to find the equation.
Using the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the slope (-1/26) and one of the given points (19, -16) into the equation:
-16 = (-1/26) * 19 + b
To solve for b, we can simplify the equation:
-16 = -19/26 + b
To isolate b, we can add 19/26 to both sides of the equation:
-16 + 19/26 = b
Now, we can find the common denominator of 26 and add the fractions:
(-416 + 19) / 26 = b
-397/26 = b
Therefore, the equation of the line passing through the points (19, -16) and (-7, -15) is: y = (-1/26)x - 397/26
This equation represents the line with a slope of -1/26 and a y-intercept of -397/26.
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A rectangular room is tiled with tiles 1
2
inches long and 1
2
inches wide. If the room is L tiles long and W tiles
wide, find the room’s area, in square inches.
The room’s area, in square inches is,
⇒ A = 144LW square inches.
We have to given that,
A rectangular room is tiled with tiles 12 inches long and 12 inches wide.
And, The room is L tiles long and W tiles wide.
Hence, Lenght of L tiles,
= 12L
And, Length of W tiles,
= 12W
Since, We know that,
Area of rectangle is,
⇒ A = Length x width
Substitute given values, we get;
⇒ A = 12L x 12W
⇒ A = 144LW square inches.
Therefore, The room’s area, in square inches is,
⇒ A = 144LW square inches.
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An artist makes a hanging sculpture out of rhombus-shaped pieces. Each rhombus shape has diagonals of 3.5 centimeters and 5 centimeters. What is the area of each rhombus? 4.25 cm2 8.5 cm2 8.75 cm2 17.5 cm2
The area of each rhombus is 8.75 [tex]cm^2[/tex]. The correct option is 8.75 [tex]cm^2.[/tex]
To find the area of each rhombus, we can use the formula for the area of a rhombus:
Area = (diagonal1 × diagonal2) / 2
Given that the diagonals of the rhombus-shaped pieces are 3.5 centimeters and 5 centimeters, we can substitute these values into the formula:
Area = (3.5 cm × 5 cm) / 2
Area = 17.5 [tex]cm^2[/tex] / 2
Area = 8.75 [tex]cm^2[/tex]
Therefore, the area of each rhombus is 8.75 [tex]cm^2[/tex]. The correct option is 8.75 [tex]cm^2.[/tex]
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In quantitative literacy
In quantitative literacy, the solution involves finding the LCM of the numbers and then squaring it to obtain the smallest square number that satisfies the given conditions.
In quantitative literacy, finding the smallest square number that is divisible by 8, 12, 15, and 20.
To solve the problem, we need to determine the least common multiple (LCM) of these four numbers.
Let's list the multiples of each number until we find a common multiple:
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
Multiples of 20: 20, 40, 60, 80, 100, 120, ...
From the lists above, we can see that 120 is the smallest common multiple of all the numbers. To find the smallest square number, we need to square 120:
120^2 = 14,400
The smallest square number that is divisible by 8, 12, 15, and 20 is 14,400.
In quantitative literacy, the solution involves finding the LCM of the numbers and then squaring it to obtain the smallest square number that satisfies the given conditions.
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What is the rate of change for f(x) = 7 sin x-1 on the interval from x = 0 to x = pi/2
A)14/pi
B)pi/14
C)pi/4
D)4/pi
Answer:
a]14/pi
Step-by-step explanation:
Steve is going shopping. This matrix shows his shopping list:
How much will Steve spend if he shops at S2?
Round to the nearest cent
$27.71 is the amount Steve spend if he shops at S2.
Given that Steve is going shopping
The shopping list of steve has 2 cereal, 4 soups , 2 soda, 1 milk and 4 candy.
We have to find the cost spend by Steve when he purchase in shop 2, S2.
In S2, the cereal cost 2.15, soup cost 2.75, soda cost is 3.00, Milk cost 3.25 and candy costs 0.79.
Total cost = 2×2.15 + 4×2.75+2×3+1×3.25+4×0.79
=4.3+11+6+3.25+3.16
=27.71
Hence, $27.71 is the amount Steve spend if he shops at S2.
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i need the whole problem done and i don’t understand, i need a step by step to show my work. its at 12. PLS HELP
The surface area of given triangular prism = 24 ft².
For the given triangular prism
Base = 2 ft
height = 3 ft
side = 3ft
We know that,
Surface area of triangular prism
= side x base + 3x base x height
= 3 x 2 + 3x2x3
= 6 + 18
= 24 ft²
Thus,
Surface area = 24 ft²
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I need help graphing this!! I cent do my table right please help ASAP!
y= 2(1/3^x)-2
Answer: Your line should start at (-1,6) then it should cross (0,0) so, straight down and a small curve. Then you should be at (0 -2), continue the small curve you made. DO not make it a parabola. it is basically just a straight line down, then a really long curve. Make sure you make the curve go across the entire graph.
Vertex for y=2(x-3)^2 +1
The vertex of the equation of the parabola y = 2( x - 3 )² + 1 is (3,1).
What is the vertex of the parabola?Given the equation of the parabola in the question:
y = 2( x - 3 )² + 1
To determine the vertex of the parabola, we use the vertex form of a parabola which is expressed as:
Vertex form: y = a(x - h)² + k
Where (h, k) represents the vertex of the parabola.
The given equation is already in the vertex form:
y = 2( x - 3 )² + 1
Hence, comparing the given equation, y = 2(x - 3)² + 1, with the vertex form, we can see that:
h = 3 and k = 1
Therefore, the vertex is (3,1).
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Change these fractions into decimals. Do not round your answers:
a. 3 8
b. 1 9
Step-by-step explanation:
3/8 = 0.375
1/9 = 0.1111111111
Answer:
Step-by-step explanation:
1. A research poll was conducted to investigate opinions about global warming. The respondents (1 point)
who answered yes when asked if there is solid evidence that the Earth is getting warmer were
then asked to select a cause of global warming. The results were arranged between male and
female responses. Using a 0.05 significance level, a test statistic of 0.792 and a critical value of
5.991 are found. Test the claim that the gender of the respondent is independent of the choice
for the cause of global warming. State the initial and final conclusion
OReject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that the
gender of the respondent is independent of the choice for the cause of global warming.
OReject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that the gender
of the respondent is independent of the choice for the cause of global warming.
Fail to reject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that
the gender of the respondent is independent of the choice for the cause of global warming.
OFail to reject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that the
gender of the respondent is independent of the choice for the cause of global warming.
The initial and final conclusion would be Fail to reject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that the gender of the respondent is independent of the choice for the cause of global warming. Option C
Why does it fail to reject the null hypothesis?The initial hypothesis is that the gender of the respondent is independent of the choice for the cause of global warming.
The alternative hypothesis is that the gender of the respondent is dependent on the choice for the cause of global warming.
The test statistic of 0.792 is less than the critical value of 5.991. Therefore, we do not reject the null hypothesis.
Looking at the statistic that has been provided, we do not have enough evidence to conclude that the gender of the respondent is related to the choice of the cause of global warming at the 0.05 significance level.
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Find the area of the following regular hexagon.
10
Round your answer to the nearest tenth.
Answer:
Step-by-step explanation: