The value of k for this line is equal to -6.
How to calculate the gradient of a line?In Mathematics and Geometry, the gradient of any straight line is also referred to as slope and it can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
2 = (-14 - k)/(k + 2)
-14 - k = 2(k + 2)
-14 - k = 2k + 4
-14 - 4= 2k + k
3k = -18
k= -18/3
k = -6
In this context, we can reasonably infer and logically deduce that the value of k is equal to -6.
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Complete Question:
The gradient of the line joining the points (-2,k) and (k, -14) is 2 . Calculate the value of k.
how many tickets are there when it weighs 135 grams
Answer:
about like 4-5
Step-by-step explanation:
its 4 or 5
35,617 minus by 15,624
Answer:
19, 993
Step-by-step explanation:
35, 617
15, 624
19, 993
Answer:
Step-by-step explanation:
20,047 using simple subtraction
Help asap ty !!!!! Thanks
So, we have an equation relating the volume of the prism to the dimensions of the base. However, we still need more information to solve for x. Then x is 2.5 xyxx
What is height?Height generally refers to the distance from the base of an object, such as a person or a building, to the highest point of that object. In the case of a person, height is typically measured in feet and inches or centimeters and is a measurement of how tall someone is from the top of their head to the soles of their feet. In the case of a building or structure, height is typically measured in meters or feet and is a measurement of how tall the structure is from its base to its highest point, such as its roof or antenna. Height can also refer to the vertical distance between two points, such as the height of a mountain or the height of a wave in the ocean.
by the question.
Volume = base area x height
Since the bases of the prism are right triangles, we can calculate their area using the formula:
base area = 1/2 x base x height
where base is the length of the base of the triangle and height is the height of the triangle.
Let's assume that the length of the base of each right triangle is x, and that the height of each right triangle is y. Then we can write:
base area = 1/2 x y
The total volume of the prism is given as So. Therefore, we can write:
So = base area x height
Substituting the expression for base area and the given value for height, we get:
So = 1/2 x y x 5
Simplifying this equation, we get:
So = 2.5 x y x x
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Brainliest for helpers asap
Answer: Please provide further information for help so I can assist you.
I WILL GIVE BRAINLYEST!! ALGEBRA 1 HW
Answer:☠️☠️☠️☠️do ur hw lil bro u actually need to learn this fr fr dont let me catch u slippin on foenem
Step-by-step explanation:
b. 650 because in the directions it says for groups of more than ( > ) 8 people they charge a FIXED fee of 650 so it's not 75 times 9 which would have been 675
Step-by-step explanation:
C(n) = {
75n, if n <= 8
650, if n > 8 and n <= 12
}
This function states that for groups of 8 people or fewer, the total cost is 75n, while for groups of 9 to 12 people, the total cost is a fixed $650.
b. To determine the total cost of a 1-hour private guided tour with 9 people, we can simply plug n = 9 into the equation we derived in part a:
C(9) = {
75*9, if 9 <= 8
650, if 9 > 8 and 9 <= 12
}
Since 9 is greater than 8 but less than or equal to 12, we use the second case:
C(9) = 650
Therefore, the total cost of a 1-hour private guided tour with 9 people is $650.
ChatGPT
The number of years from the start of the Great Depression to the first presidential election of Richard Nixon is six years less than three times Raul’s age. Nixon’s first presidential election happened 39 years after the Great Depression. Using the given information, write an equation to find Raul’s age, r.
Answer:
Raul is 15 years old.
Step-by-step explanation:
The number of years from the start of the Great Depression to Nixon's election is six years less than three times Raul's age: 3r-6
If then Nixon's first election happened 39 years after the Great Depression, then: 3r-6=39
3r-6=39 Add six to both sides so the 6 on the left side gets canceled out (positive and negative cancel each other out) so the equation will now look like this: 3r=45
Then divide 3 on both sides (multiplication and division also cancel each other out), then the equation looks like this: r=15
And so, Raul is 15 years old.
es calculo del %
38% de 1610
solve the following equations by graphical method: 2x+y=7 and x-y=1
Answer:
Step-by-step explanation:
Suppose that the value of a stock varies each day from $10.82 to $33.17 with a uniform distribution. Find the upper quartile; 25% of all days the stock is above what value?
Answer:
The range of the stock prices is from $10.82 to $33.17. To find the upper quartile, we need to find the value of the stock price that is greater than 75% of the data.
The distance between the minimum value and the maximum value is:
$33.17 - $10.82 = $22.35
To find the upper quartile, we need to find the value that is three-quarters of the distance above the minimum value:
$10.82 + 0.75($22.35) = $26.69
Therefore, the upper quartile of the stock price is $26.69.
To find the value above which the stock price is higher 25% of the time, we need to find the value that is 75% of the distance above the minimum value:
$10.82 + 0.25($22.35) = $15.62
Therefore, 25% of the time, the stock price is above $15.62.
To find the upper quartile, we need to first find the median of the stock prices, which is the value that divides the distribution into two equal parts. The midpoint of the distribution is:
Midpoint = (10.82 + 33.17) / 2 = 22.995
Now, we can find the upper quartile, which is the median of the upper half of the distribution. The upper half of the distribution ranges from the midpoint to the highest value of 33.17. Therefore, we calculate the median of this range as follows:
Upper quartile = (22.995 + 33.17) / 2 = 28.0825
So, the upper quartile of the stock prices is $28.08.
To find the value above which the stock is priced 25% of the time, we need to find the 75th percentile of the distribution. Since the distribution is uniform, we can use the formula for the percentile as follows:
Percentile rank = (percentile / 100) = (value - minimum) / (maximum - minimum)
Solving for the value, we get:
value = minimum + percentile rank x (maximum - minimum)
For the 75th percentile, we have:
value = 10.82 + 0.75 x (33.17 - 10.82) = 28.49
Therefore, the stock is priced above $28.49 on 25% of all days.
can you solve this question?
y=?
(?,?)
Answer:
The tangent line is: y = 8x - 58
The tangent point is at (7, -2)
===================================================
Explanation:
One of the definitions of derivatives is
[tex]\displaystyle f'(a) = \lim_{x\to a} \frac{f(x)-f(a)}{x-a}[/tex]
where f ' (a) represents the derivative evaluated at x = a.
The value of f ' (a) will get us the slope of the tangent at x = a.
The idea is that x is getting closer and closer to 'a'. In doing so, the secant lines slowly approach the tangent line.
Keep in mind that x will never reach 'a' itself (if it did, then we'd have a division by zero error).
---------------
The given limit we have is
[tex]\displaystyle \lim_{x\to 7} \frac{f(x)+2}{x-7} = 8[/tex]
and that is equivalent to
[tex]\displaystyle \lim_{x\to 7} \frac{f(x)-(-2)}{x-7} = 8[/tex]
and also equivalent to
[tex]\displaystyle \lim_{x\to 7} \frac{f(x)-f(7)}{x-7} = 8[/tex]
Compare that to the template I mentioned at the top to see that
a = 7f(a) = f(7) = -2f ' (a) = f ' (7) = 8Therefore, we can say the tangent slope is 8 and the tangent touches the f(x) curve at (x,y) = (a, f(a)) = (7,f(7)) = (7,-2)
---------------
[tex]m = 8 = \text{slope}\\\\(x_1,y_1) = (7,-2) = \text{tangent point}\\\\[/tex]
Let's use that info to determine the equation of the tangent line.
I'll use point-slope form to isolate y.
[tex]y-y_1 = m(x-x_1)\\\\y-(-2) = 8(x-7)\\\\y+2 = 8x-56\\\\y = 8x-56-2\\\\y = 8x-58\\\\[/tex]
That's the equation of the tangent line to the point (7,-2).
Janelle makes fruit punch by mixing the ingredients listed below.
•5 pints of orange juice
•6 cups of grape juice
•8 cups of apple juice
How many quarts of fruit punch does Janelle make?
TIPS:
1 quart is 2 pints
1 pint is 2 cups
1 cup is 8 fluid ounces
Answer:
6 quarts
Step-by-step explanation:
2 pints = 1 quart
4 cups = 1 quart
• 5 pints of orange juice
5 pints = 5/2 =>2.5 quarts
• 6 cups of grape juice
6 cups = 6/4 => 1.5 quarts
• 8 cups of apple juice
8 cups = 2 quarts
2.5 + 1.5 + 2 = 6 quarts
Find the surface area of a rectangular prism with a height of 6 inches, a width of 7 inches, and a length of 13 inches.
Answer:
A fast and easy surface area of a rectangular prism calculator to find just what its name suggests.
Step-by-step explanation:
l=13in
w=7
h=6
A=422in squared
Annie is concerned over a report that "a woman over age 40
40
has a better chance of being killed by a terrorist than of getting married." A study found that the likelihood of marriage for a never-previously-wed, 40
40
-year-old university-educated American woman was 3.4%
3.4
%
. To demonstrate that this percentage is too small, Annie uses her resources at the Baltimore Sun to conduct a simple random sample of 407
407
never-previously-wed, university-educated, American women who were single at the beginning of their 40
40
s and who are now 45
45
. Of these women, 20
20
report now being married. Does this evidence support Annie’s claim, at the 0.01
0.01
level of significance, that the chances of getting married for this group is greater than 3.4%
3.4
%
?
The answer is no. As the p-value is more than 0.01, evidence does not support Annie's claim that the chances of getting married for this group is greater than 3.4%.
What is null hypothesis?It assumes that the observed result is due to chance and there is not any difference between specified populations.
To determine this, we must calculate the p-value.
The number of successes in the sample is 20 and the number of observations is 407.
The sample proportion = 0.049. (20/407)
The hypothesis is that the percentage of women who got married is greater than 3.4%.
The null hypothesis is that the percentage is 3.4%.
We can use the z-test statistic to test this hypothesis.
The z-test statistic is calculated as:
z = (0.049-0.034)/(√(0.034(1-0.034)/407))
= 1.66.
The p-value is calculated as:
p-value = Φ/(1.66)
= 0.97.
This is more than 0.01 ,so we can not reject the null hypothesis.
This evidence does not support Annie's claim that the chances of getting married for this group is greater than 3.4%.
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Hi i need help with this question
The angles of the given Rhombus are:
= 31°= 90°= 59°= 59°= 31°= 59°The above are arrived at using the qualities of a Rhombus and the theorem of alternate angles.
What are the properties of a rhombus?A rhombus is a quadrilateral with certain properties that distinguish it from other types of quadrilaterals. The key properties of a rhombus are:
All sides are congruent (i.e., have the same length).Opposite angles are congruent (i.e., have the same measure).Diagonals bisect each other (i.e., they intersect at their midpoint), creatign 90° angles.The diagonals are perpendicular to each other (i.e., they form a right angle where they intersect).It is a parallelogram (i.e., opposite sides are parallel).So we stated that ∠ = 31° because ∠KNM have been dissected into two equal halves by diagonal, LN.∠2 = 90° because Diagonals bisect each other (i.e., they intersect at their midpoint), creating 90° angles.Since we know ∠2 and ∠LNM = 31° (both of which are angles in ΔN2M), ∠3 = 180 -31-90 = 59° (Sum of Angles in a Triangle)because Diagonals bisect each other (i.e., they intersect at their midpoint), creating 90° angles, ∠4 is also equal to 59°Since ∠L2M = 90°, ∠5 = 180 - 90 - 59° = 31° ∠6 = ∠3 = 59° (Alternate angles)Learn more about Rhombus;
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In a class of 60 students, 40 are Democrats, 10 are business majors, and 4 of the business majors are Democrats. If one student is randomly
selected from the class, find the probability of choosing a Democrat or a business major.
P(Democrat or business major) =
In conclusion, the probability of selecting a Democrat or a business major is 11/15.
How to solve?
To find the probability of selecting a Democrat or a business major, we need to add the probabilities of selecting a Democrat and selecting a business major, and then subtract the probability of selecting a student who is both a Democrat and a business major (since we would be double counting this student).
So, let's calculate each of these probabilities:
Probability of selecting a Democrat: There are 40 Democrats out of 60 students, so the probability of selecting a Democrat is 40/60 = 2/3.
Probability of selecting a business major: There are 10 business majors out of 60 students, so the probability of selecting a business major is 10/60 = 1/6.
Probability of selecting a student who is both a Democrat and a business major: We know that there are 4 business majors who are also Democrats, so the probability of selecting one of these students is 4/60 = 1/15.
Now we can calculate the probability of selecting a Democrat or a business major:
P(Democrat or business major) = P(Democrat) + P(business major) - P(Democrat and business major)
= 2/3 + 1/6 - 1/15
= 11/15
Therefore, the probability of selecting a Democrat or a business major is 11/15.
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Please please help
f ₁(x) = x²
Find f(x)
Answer:√x
Step-by-step explanation:
I am assuming the equation says [tex]f^{-1}(x)=x^{2}[/tex]
What you do is put x instead of [tex]f^{-1}(x)[/tex] and y² instead of x²
So x = y²
Rearrange for y
y = √x
Replace y with f(x)
f(x) = √x
Find the percent of each number What is 59% of 640?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{59\% of 640}}{\left( \cfrac{59}{100} \right)640}\implies 377.6[/tex]
Answer:
377.6
Step-by-step explanation:
640÷10=64 to find 10%
64×5=320 to find 50%
640÷100=6.4 to find 1%
6.4×9=57.6 to find 9%
320+57.6=377.6
answer: 377.6
Given the volume of a sphere formula: V =
³
Find the volume of spheres with the following radii. Rewrite the equations and show your substitutions.
Remember to include units. LEAVE YOUR ANSWER IN TERMS OF TT.
1. r = 12 ft
Answer:
The volume of the sphere is 2304π ft³.
Step-by-step explanation:
The formula for the volume of a sphere is:
[tex]\boxed{V=\dfrac{4}{3}\pi r^3}[/tex]
where r is the radius of the sphere.
Given the radius of the sphere is 12 feet, substitute r = 12 into the formula and solve for V:
[tex]\begin{aligned}\implies V&=\dfrac{4}{3} \cdot \pi \cdot 12^3\\\\&=\dfrac{4}{3} \cdot \pi \cdot 1728\\\\&=\dfrac{6912}{3} \cdot \pi \\\\&=2304\pi\; \sf ft^3 \end{aligned}[/tex]
Therefore, the volume of the sphere in terms of π is 2304π ft³.
A parabola opening up or down has vertex (-1, 2) and passes through (-14, - 153/8)
Write its equation in vertex form.
Simplify any fractions.
The quadratic equation is:
y = (149/1,800)*(x + 1)² + 2
What is the equation of the parabola?Remember that if the parabola has a vertex (h, k) and a leading coefficient a can be written as:
y = a*(x - h)² + k
Here we know that the vertex is (-1, 2), then we will get the following equation:
y = a*(x + 1)² + 2
And we know it passes through (-14, - 153/8), then we will get:
-153/8 = a*(14 + 1)² + 2
-153/8 = a*225 + 2
a = (153/8 - 2)/225 =
a = 149/1,800
The quadratic is:
y = (149/1,800)*(x + 1)² + 2
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Place the slopes in order from steepest to least steep:
(a) m = 4
(b) y = -5x + 3
(c) 2x + 4y = 8
(d) y = 3
Carla buys a bag of 12 apples for $1.44. How much is each apple worth?
Answer:
Each apple is worth $0.12
Step-by-step explanation:
Total of 12 apples ÷ Quantity of Apples = Cost of each apple
1.44 ÷ 12 = 0.12
Area and Square Units
Area is amount of surface covered by a figure.
It is measured in square units.
Model each figure.
The area of the given figures is 1) 4 sq. units; 2) 16 sq units; 3) 6 sq units.
Define area and perimeter.
The distance around a closed figure is its perimeter, while the area is the portion of the surface that it occupies. The size of a plane or the space it encloses is expressed in square meters.
1. In this figure, the longest side has 4 units and the smallest one has 1 unit.
Area of the rectangular figure(A) = 4 * 1 = 4 sq units
Perimeter(P) = 4 + 1 + 4 + 1 = 10 units.
2. In this figure, the longest side has 4 units and the smallest one has 4 units.
Area of the rectangular figure(A) = 4 * 4 = 16 sq units
Perimeter(P) = 4 + 4 + 4 + 4 = 16 units.
3. In this figure, the longest side has 4 units, 3 units, then 2 units the smallest one has 1 unit.
Area of the rectangular figures combinely (A) = 4 * 1 + 2 * 1= 6 sq units
Perimeter(P) = 4 + 3 + 2 + 2 + 1 = 12 units.
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solve the area of bottom of tiffin box is 0.30m(sq) and weight is 60n=?
The pressure exerted (in N/m²) by the box on the shelf given that the bottom of the box has an area of 0.30 m² and weighs 60 N, is 200 N/m²
How do i determine the pressure exerted by the box?Pressure is defined a force per unit area. Mathematically, it is written as
Pressure (P) = force (F) / area (A)
P = F / A
With the above formular, we can obtain the pressure exerted by the box as follow:
Area of box (A) = 0.30 m² Weight of box (W) = 60 NPressure exerted (P) =?Pressure exerted (P) = Weight of box (W) / Area of box (A)
Pressure exerted = 60 / 0.30
Pressure exerted = 200 N/m²
Thus, we can conclude that the pressure exerted is 200 N/m²
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Complete question:
The area of the bottom of a tiffin box is 0.30 sq. m and weight is 60 N, Calculate the pressure exerted by the box on the shelf in N/sq. m *
The image shows a point and a line. Suppose we create a parabola using the point as the focus and the line as the directrix. Decide whether each point on the list is on this parabola.
A (-1.5) True or False
B.(3.3) True or False
C. (5,5) True or false
D. (7,5) True or false
E. (3,9) True or false
The correct answers for the equation of parabola with (3,5) are:
A. True
B. False
C. True
D. True
E. True
EquationsUsing the vertex form equation of the parabola with vertex (h, k) and p = 2,
[tex](y-4)^{2}[/tex] = 8(x - 3)
[tex]y^{2}-10y+25[/tex] = 8x - 24
[tex]y^{2}-10y+49[/tex] = 8x
A. (-1, 5): Substitute x = -1 and y = 5 into the equation:
25 - 10(5) + 49 = 8(-1)
-16 = -16
This is true, so the point (-1, 5) is on the parabola.
B. (3, 3): Substitute x = 3 and y = 3 into the equation:
9 - 10(3) + 49 = 8(3)
-8 = 8
This is false, so the point (3, 3) is not on the parabola.
C. (5, 5): Substitute x = 5 and y = 5 into the equation:
25 - 10(5) + 49 = 8(5)
9 = 9
This is true, so the point (5, 5) is on the parabola.
D. (7, 5): Substitute x = 7 and y = 5 into the equation:
25 - 10(5) + 49 = 8(7)
25 = 25
This is true, so the point (7, 5) is on the parabola.
E. (3, 9): Substitute x = 3 and y = 9 into the equation:
81 - 10(9) + 49 = 8(3)
1 = 1
This is true, so the point (3, 9) is on the parabola.
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What is the value of x?
Answer:
x = 26
Step-by-step explanation:
the 3 angles lie on the straight line DAC and sum to 180° , that is
4x - 8 + 34 + 76 - x = 180
3x + 102 = 180 ( subtract 102 from both sides )
3x = 78 ( divide both sides by 3 )
x = 26
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
Step-by-step explanation: ??? There is no picture
If w=f x d w hitch of the following equations shows work being calculated using correct units
From the given answer choices, the equation that shows work being calculated with the correct unit is C. 113J = (17.4N) x (6.51m)
What is Work Done?In physics, work is defined as the amount of energy transferred by a force when it causes an object to move over a certain distance. Work is a scalar quantity and is expressed in units of joules (J) or foot-pounds (ft-lbs).
Mathematically, work (W) is given by the product of the force (F) applied on an object and the displacement (d) of the object in the direction of the force, as expressed in the formula:
W = F * d * cos(theta)
where theta is the angle between the force vector and the displacement vector.
Thus, the correct units which are Joules, metres and Newton are used.
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What’s the product of 2/8 and3/5
Answer:
3/20
Step-by-step explanation:
To find the product of 2/8 and 3/5, we simply multiply the numerators and the denominators:
(2/8) x (3/5) = (2 x 3) / (8 x 5) = 6/40
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
6/40 = (6 ÷ 2) / (40 ÷ 2) = 3/20
Therefore, the product of 2/8 and 3/5 is 3/20.
twice the difference between two numbers is 44. three times their sum is 96
Answer:
Step-by-step explanation:
Let's say the two numbers are x and y.
From the first statement "twice the difference between two numbers is 44", we can set up the equation:
2(x-y) = 44
Simplifying this equation, we get:
x - y = 22 (dividing both sides by 2)
From the second statement "three times their sum is 96", we can set up the equation:
3(x+y) = 96
Simplifying this equation, we get:
x + y = 32 (dividing both sides by 3)
Now we have two equations:
x - y = 22
x + y = 32
We can solve for x and y by adding the two equations together:
2x = 54
x = 27
Substituting x = 27 in either of the two equations, we get:
y = 5
Therefore, the two numbers are 27 and 5.
x = 27;
y = 5.
Step-by-step explanation:1. Name the number as variables.Say "x" is the first number.
Say "y" is the second number.
2. Form the first equation from the statements.First statement: "twice the difference between two numbers is 44".
Difference of the numbers:[tex]x-y[/tex]
Twice the difference: [tex]2(x-y)[/tex]
Twice the difference between two numbers is 44: [tex]2(x-y)=44[/tex]
3. Form the second equation from the statements.Second statement: "three times their sum is 96".
Sum of the numbers: [tex](x+y)[/tex]
3 times the sum: [tex]3(x+y)[/tex]
3 times the sum is 96: [tex]3(x+y)=96[/tex]
4. Simplify the equations.Use the distributive property of multiplication to simplify each equation as follows (check this property in the attached image).
[tex]2(x-y)=44\\ \\2x-2y=44[/tex]
[tex]3(x+y)=96\\ \\3x+3y=96[/tex]
5. Solve one of the equations for one of the variables.Let's solve the second equation for "x".
[tex]3x+3y-3y=96-3y\\ \\3x=96-3y\\ \\x=\frac{96-3y}{3} \\ \\x=\frac{96}{3} -\frac{3y}{3} \\ \\x=32-y[/tex]
7. Use the calculated value of "x", plug it in the other equation and calculate.[tex]2((32-y)-y)=44\\ \\2(32-y-y)=44\\ \\2(32-2y)=44\\ \\(2)(32)+(2)(-2y)=44\\ \\64+(-4y)=44\\ \\64-4y=44\\ \\-4y=44-64\\ \\-4y=-20\\ \\y=\frac{-20}{-4} \\ \\y=5[/tex]
8. Find the value of "x".Use any equation to find a value for "x" by substituting "y" by "5" and solving for "x".
[tex]3(x+(5))=96\\ \\3(x+5)=96\\ \\3x+15=96\\ \\3x=96-15\\ \\3x=81\\ \\x=\frac{81}{3} \\ \\x=27[/tex]
9. Verify the answers.To see if the answers are correct, plug in the values of "x" and "y" on each formula and see if they return the correct values (44 and 96).
[tex]2(x-y)=44\\ \\2((27)-(5))=44\\ \\2(22)=44\\ \\44=44[/tex]
Correct.
[tex]3((27)+(5))=96\\ \\3(32)=96\\ \\96=96[/tex]
Correct.
The numbers returned the correct values when evaluated in both opf the equation. Therefore, they are the correct answers.
x = 27;
y = 5.
See the graphic solution to this problem in the second attached image.
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4. A PMV bus left Mt. Hagen at 07 arrived in Lae at 1850. It covered a distance 840 km. a) How long is this journey? (1 mark) b) What was the average speed of the bus? (1 mark) litre. per c) Diesel fuel was sold for K5.74 Calculate the cost of fuel for the journey if the fuel consumption rate was 1 litre per 20km. (2 marks) a) the total surfac 5. An empty cylinder weighing 0.7 kg has a diameter of 10 cm and a height of 30 cm. It is then filled with water and closed. Find correct to 1 decimal place:
a) the journey took 11 hours and 50 minutes.
b)the average speed of the bus was 70.95 km/hour.
c) the cost of fuel for the journey was K240.08.
Define distanceDistance is the measure of how far apart two objects or points are from each other. It is a scalar quantity, which means it only has magnitude and no direction. Distance is usually measured in units such as meters (m), kilometers (km), feet (ft), miles (mi), or any other appropriate unit of length.
a) convert the times to a 24-hour format to perform the calculation.
07:00 in 24-hour format is 07:00, and 18:50 in 24-hour format is 18:50.
The journey duration is:
18:50 - 07:00 = 11 hours and 50 minutes
Therefore, the journey took 11 hours and 50 minutes.
b) The average speed of the bus can be found by dividing the distance traveled by the time taken:
Average speed = Distance ÷ Time
= 840 km ÷ 11.83 hours (converted from 11 hours and 50 minutes)
= 70.95 km/hour
Therefore, the average speed of the bus was 70.95 km/hour.
c) The fuel consumption rate is 1 liter per 20 km. Therefore, the bus consumed 840 km / 20 = 42 liters of diesel fuel for the journey.
The cost of fuel can be calculated by multiplying the fuel quantity by the cost per liter:
Cost of fuel = Fuel quantity x Cost per liter
= 42 liters x K5.74/liter
= K240.08 (rounded to two decimal places)
Therefore, the cost of fuel for the journey was K240.08.
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