The easiest way to solve this question is to write out both equations in the form y = mx + c, where m is the gradient and c is the y-intercept.
a) Thus, if we start with 9x - 10y = 21, then we get:
9x - 10y = 21
(9/10)x - y = 21/10 (Divide both sides by 10)
(9/10)x = y + 21/10 (Add y to both sides)
(9/10)x - 21/10 = y (Subtract 21/10 from both sides)
Thus, our first equation may be written as y = (9/10)x - 21/10
b) Now if we take the second equation, (3/2)x - (5/3)y = 7/2, we can follow the same process to get:
(3/2)x - (5/3)y = 7/2
(9/10)x - y = 21/10 (Multiply each side by 3/5)
(9/10)x = y + 21/10 (Add y to each side)
(9/10)x - 21/10 = y (Subtract 21/10 both sides)
Thus, the second equation may be written as y = (9/10)x - 21/10.
Now you might have already realised this but the two equations are actually exactly the same; if they are the same line then they are said to be coincident.
Note that if the two lines are parallel, then their gradients (m) would be the same, but the y-intercepts (c) would be different (eg. y = 2x + 3 and y = 2x + 4 are parallel).
If they just intersect at a point, then the gradients of the lines would be different, but the y-intercepts could be the same or different (eg. y = 4x + 2 and y = 9x + 2 intersect at one point).
For them to be coincident however, both the gradient and y-intercept must be the same as only then would they be the same line.
(7−4n)⋅6 Apply the distributive property to create an equivalent expression.
Answer:
42-24n
Step-by-step explanation:
(7 - 4n) . 6
= (7)(6) - (4n)(6) ...........using distributive property, multiply each term by (6)
= 42 -24n (answer)
Which of the following could be the equation of the graph shown below? A. y=-10 B. 2x- 3y= -9 C. y = 3x-2 D. -4x+ 2y= -6
Answer:
C. y = 3x - 2
Step-by-step explanation:
Since the y intercept is negative, it is seen in this equation that the b value (the y intercept) is also negative. Since the slope is increasing upward, we know that the slope is greater than 1 and is going upward, and it matches with the equation since it matches with both of the requirements.
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Answer: c and d
Step-by-step explanation:
A regular octagon has an apothem measuring 10 in, and a
perimeter of 66.3 in
What is the area of the octagon, rounded to the nearest
square inch?
10 in
88 in 2
175 in 2
332 in2
700 in 2
Answer:
332 square inch
Step-by-step explanation:
Solving for an area of a regular octagon, we can make use of the formula shown below:
Area = 1/2 * apothem*perimeter
In this problem, the following values were given such as:
Apothem = 10 inches
Perimeter = 66.3 inches
Solving for the area:
Area = 1/2*10*66.3
Area = 331.5 inches²
The answer is 332.
Answer:
Option C. 332 in²
Step-by-step explanation:
In the figure attached, a regular octagon has been drawn with all equal sides and apothem OP = 10 in.
Perimeter of the given octagon is given as 66.3 in
We have to calculate the area of the octagon.
As we can see in the figure an octagon is a combination of 8 triangles.
So we will find the area of one triangle first.
Area of ΔBOC = [tex]\frac{1}{2}(BC)(OP)[/tex]
Since perimeter of octagon = 8 × one side = 8×BC
66.3 = 8× BC
BC = [tex]\frac{66.3}{8}[/tex]
BC = 8.288 in
Therefore, area of ΔBOC = [tex]\frac{1}{2}(10)(8.288)[/tex]
= 5×8.288
= 41.44 in²
Now area of octagon ABCDEFGH = 8×41.44 = 331.5 ≈ 332 in²
Therefore, area of the regular octagon will be 332 in²
Option C. is the answer.
What divides a line segment into two congruent segments?
Answer:
segment bisector
Step-by-step explanation:
Too cut in half, think bisect.
So we are talking about a segment, so segment bisector
In which direction does the left side of the graph of this function point?
f(x) = 3x^3– x^2 + 4x - 2
Answer:
Down.
Step-by-step explanation:
ƒ(x) = 3x³ - x² + 4x - 2
"They" are asking you to determine the end behaviour of the function, that is, what happens to the function as x ⟶ -∞.
The important point to remember is that, when x is large enough, the term of highest degree (the x³ term) will be so large that you can ignore all the other terms.
If x is large and negative,
f(x) ≈ 3(-x)³ = 3(-1)³(x)³= -3x³
Thus, the graph is in the third quadrant and the graph points down.
The figure below shows the graph of your function. It points sharply down on the left-hand side.
Is the Histogram uniform, symmetric, or skewed ?
Answer:
Symmetric
Step-by-step explanation:
If you put a line in the middle of the third row and fold it on itself, it would match.
Answer:
i have to say it's symmetric cos technically uniform would kinda mean "with form if u know what i mean, and is kinda like "random" and like, cut the graph in half and it's a perfect fit
What is the first quartile of the data set?
10, 11, 12, 15, 17, 19, 22, 24, 29, 33, 38
A. 12
B. 19
C. 29
D. 10
Answer:
A
Step-by-step explanation:
First find the median of the data set.
The median is the middle value of the data set arranged in ascending order
10, 11, 12, 15, 17, 19, 22, 24, 29, 33, 38
The median = 19
The first quartile ( lower) is the middle value of the data to the left of the median.
10, 11, 12, 15, 17
The first quartile is 12 → A
What is the value of x
We know that the whole angle of the triangle is 73. Since the known angle is 45 degrees, we need to find out what the other is.
Subtract 45 from 73 to find the angle of the unknown triangle.
73-45=28.
Now that we know the value of the unknown triangle, solve for x
Make an equation.
2x+5=28
Subtract 5 on both sides.
2x=23
Divide 23 by 2 to isolate x.
X=11.5
The answer is C. 11.5
Hope this helps!
Your school is organizing a carnival. You are building a ramp for a game the surface of the ramp will be 5 feet long with a total rise of 3 feet. Find the angle of elevation of the ramp
Answer:
Step-by-step explanation:
this angle is related to the ramp surface length (hypotenuse) and the rise in the ramp by the tangent function:
sin Ф = opp / hyp = 3 ft / 5 ft = 0.60
Use the inverse sine function to determine the angle Ф.
arcsin 0.60 = 36.9 degrees
Final answer:
The angle of elevation of the ramp is approximately 36.87 degrees, calculated using the tangent function in trigonometry and the given dimensions of the ramp's rise and length.
Explanation:
To find the angle of elevation of the ramp, we can use trigonometry, specifically the tangent function, which relates the angle of a right triangle to the ratio of the opposite side (rise) to the adjacent side (run). In this case, the ramp surface is the hypotenuse of the right triangle, the rise is the vertical change, and the run is the horizontal distance, which would be the horizontal projection of the ramp if it were flat. Since we know the rise is 3 feet and the ramp length (hypotenuse) is 5 feet, we can calculate the run using the Pythagorean theorem.
Calculate the run (horizontal distance): run = √(hypotenuse^2 - rise^2) = √(5^2 - 3^2) = √(25 - 9) = √16 = 4 feet.Now, calculate the angle of elevation using the definition of tangent: tangent(angle) = opposite/adjacent, which leads to angle = arctan(opposite/adjacent).Plug in the values for the rise and run: angle = arctan(3/4). Use a calculator to find the angle: angle ≈ 36.87°.The angle of elevation of the ramp is approximately 36.87 degrees.
A system of equations is given below. -3x + 6 and y = 6 - 3x
Which of the following statements best describes the two lines?
They have different slopes and different y-intercepts, so they have no solution. They have different slopes and different y-intercepts, so they have one solution. They have the same slope and the same y-intercept, so they have no solution. They have the same slope and the same y-intercept, so they have infinitely many solutions.
Answer:
They have different slopes and different y-intercepts, so they have no solution
Step-by-step explanation:
Answer:
Infinite solutions Answer explained below
Step-by-step explanation:
Let us see the various conditions for intersections of two lines in simplest way.
1. Same slope and same y intercept : Infinite solutions
2. Same slope and different y intercepts : No solution
3. Different slope and same y intercept : unique solution
4. Different slope and different y intercept : Unique solution
Here slope means the tangent of the angle line makes with the positive x axis and y intercept is the y coordinate at which the line intersect the y axis.
In our equations , we our slopes and y intercepts as
y=-3x+6
slope = -3 and y intercept = 6
y=6-3x
slope = -3 and y intercept = 6
Hence same slope and same y intercept , thus have infinite solutions
A line passes through the point (-4,-8) and has a slope of -5/2.
Write an equation in slope-intercept form for this line..
Plz
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = m\implies -\cfrac{5}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=-\cfrac{5}{2}[x-(-4)] \\\\\\ y+8=-\cfrac{5}{2}(x+4)\implies y+8=-\cfrac{5}{2}x-10\implies y=-\cfrac{5}{2}x-18[/tex]
write an equation in slope intercept form for the line that passes through the points (3,2) and(-9,6)
Answer:
y = - [tex]\frac{1}{3}[/tex] x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (- 9, 6)
m = [tex]\frac{6-2}{-9-3}[/tex] = [tex]\frac{4}{-12}[/tex] = - [tex]\frac{1}{3}[/tex], hence
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 9, 6), then
6 = 3 + c ⇒ c = 6 - 3 = 3
y = - [tex]\frac{1}{3}[/tex] x + 3 ← in slope- intercept form
Michael can spend a maximum of $234 on office supplies. Each ream of
paper costs $6. Each ink cartridge costs $18. Which of the following graphs
represents the possible combinations of paper and ink cartridges that he may
buy?
I added the graph below for the verified Apex answer :)
The inequality equation will be 6x + 18y ≤ 234.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Michael can spend a maximum of $234 on office supplies.
Each ream of paper costs $6. Each ink cartridge costs $18.
Then the inequality equation will be
Let x be the number of reams of paper and y be the number of the ink cartridge. Then we have
6x + 18y ≤ 234
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Choices to pick are : y=3x
And y=2x+2 can someone please help out ??
Answer:
y = 2x + 2
Step-by-step explanation:
Start at point (2, 6).
Go up 2 units up (rise = 2) and 1 unit right (run = 1). Now you are at point (3, 8) which is on the graph.
slope = rise/run = 2/1 = 2
The slope of the graph is 2. m = 2
Now look at point (0, 2). The y-intercept is 2. b = 2
The equation is
y = mx + b
y = 2x + 2
Answer:
y = 2x + 2
Step-by-step explanation:
Here we're asked to come up with a linear function relating x and y.
First we find the slope of the line. As we move from (0, 2) to (3, 8), x increases by 3 and y by 6. Thus, the slope is
m = rise / run = 6 / 3 = 2.
Plugging givens into the slope-intercept formula y = mx + b, we find b:
2 = 2(0) + b, so that b = 2.
Then the desired relationship between x and y is y = 2x + 2.
In the figure given l || m , then find the value of X.
Answer:
42
Step-by-step explanation:
Line m and l are parallel so C and where that intersection is on the inside have the parallel lines, the angle there is an same side interior angle with C. Those add up to 180 degrees. So 180-82 is 98. Use vertical angle to find the angle in the triangle (not x yet; the other one). Vertical angles are congruent so that one is 98.
Now angles in a triangle add up to 180 degrees.
So we have 40+98=138.
The difference between 180 and 138 is 180-138=42 (that is x)
Answer:
42
Step-by-step explanation:
The solution is in the image below.
98+82 = 180
If A=1/2h(x+y), what is y in terms of A, h, and x?
Answer:
see explanation
Step-by-step explanation:
Given
A = [tex]\frac{1}{2}[/tex] h(x + y)
Multiply both sides by 2 to eliminate the fraction
2A = h(x + y) ( divide both sides by h )
[tex]\frac{2A}{h}[/tex] = x + y ( subtract x from both sides )
y = [tex]\frac{2A}{h}[/tex] - x
The solution to the equation A=1/2h(x+y) for y in terms of A, h, and x, is y = 2A/h - x, obtained by algebraic rearrangement.
Explanation:To solve the given equation A=1/2h(x+y) for y in terms of A, h, and x, we first perform algebraic rearrangement. We want to get y in terms of A, h, and x. So, the first step is to eliminate the 1/2h from the right side of the equation. We can do this by multiplying both sides of the equation by 2/h, we get: 2A/h = x + y.
Now, to solve for y, we can simply subtract x from both sides: y = 2A/h - x. So now we have y expressed in terms of A, h, and x.
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help answer question 3
Answer:
The answer is the first one. Inside the absolute value symbols it is negative but absolute value answers are always positive. Instead of -30 the answer is 30.
What is the area of the triangle 10 13 12
Answer:
A= 57 sq units
Step-by-step explanation:
To calculate the are area of a triangle we use the Herons formula:
A=√s(s-a)(s-b)(s-c) where a, b and c are the sides of the triangle.
s=(a+b+c)/2
s=(10+13+12)/2
=17.5
A=√[17.5(17.5-10)(17.5-13)(17.5-12)]
A= 57 sq units
Answer:
60 units ^2
Step-by-step explanation:
Deena has 4 pairs of of white socks , 3 pairs of black sock, 1 pair of red socks, and 2 pairs of Navy socks in her drawer each pair of socks is folded together . If she pulls a pair of socks out of her drawer in the morning without looking what is the probability she will choose a pair of white socks
The probability she will choose a pair of white socks is [tex]\frac{2}{5}[/tex]
Probability :Given that,
Deena has 4 pairs of of white socks3 pairs of black sock1 pair of red socks 2 pairs of Navy socksTotal number of outcomes [tex]=4+3+1+2=10[/tex]
We have to find the probability she will choose a pair of white socks.
Number of favourable outcomes[tex]=4[/tex]
the probability she will choose a pair of white socks is,
[tex]P=\frac{4}{10} =\frac{2}{5}[/tex]
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5 1/3 divided by 1 1/6
Answer:
32/7
Step-by-step explanation:
5 1/3=16/3
1 1/6=7/6
----------------
(16/3)/(7/6)
(16/3)(6/7)
(16/1)(2/7)
32/7
How many 3 digit multiples of both 4 and 6 are there?
To find the number of 3-digit multiples of both 4 and 6, we find the least common multiple (LCM) of 4 and 6, which is 12. Then, we count the number of 3-digit multiples of 12.
Explanation:To find the number of 3-digit multiples of both 4 and 6, we need to find the least common multiple (LCM) of 4 and 6. The LCM of 4 and 6 is 12. Since 12 is a multiple of both 4 and 6, any multiple of 12 will be a multiple of both 4 and 6.
Now, we need to find the number of 3-digit multiples of 12. The smallest 3-digit multiple of 12 is 108, and the largest is 996. So, we need to find how many numbers from 108 to 996 are divisible by 12.
We can divide 996 by 12 to find that the quotient is 83 and the remainder is 0. So, there are 83 3-digit multiples of 12. Therefore, there are 83 3-digit multiples of both 4 and 6.
What does Pythagoras’ famous theorem involve? A. pentagons B. polygons C. triangles D. rectangles
Answer:
C. triangles
Step-by-step explanation:
Pythagoras Theorem is a theorem which states you can work out a side of a right - angled triangle using the other 2 sides. Pythagoras will not work on shapes except from a right - angled triangle and square
What is the answer of a ?
Answer:
2.2Step-by-step explanation:
Use the cosine law (look at the picture).
We have:
[tex]a=a\\b=4\\c=3\\\gamma=32^o[/tex]
[tex]a^2=4^2+3^2-2(4)(3)\cos32^o[/tex]
[tex]\cos32^o\approx0.848[/tex] → look at the second picture
[tex]a^2=16+9-24(0.848)\\\\a^2=25-20.352\\\\a^2=4.648\to a=\sqrt{4.648}\\\\a\approx2.2[/tex]
1 3/8 divided by 1/6. Please help me
For this case we have to:
[tex]1 \frac {3} {8} = \frac {8 + 3} {8} = \frac {11} {8}[/tex]
We must divide:
[tex]\frac {\frac {11} {8}} {\frac {1} {6}} =[/tex]
Applying double C we have:
[tex]\frac {11 * 6} {8 * 1} = \frac {66} {8} = \frac {33} {4}[/tex]
Converting to a mixed number we have:
[tex]8 \frac {1} {4}[/tex]
Answer:
[tex]8 \frac {1} {4}[/tex]
if y=5 when x=-3 find x when y=-1
Answer:
3/5
Step-by-step explanation:
5 / -1 = -5
so
-3 / -5 = 3/5
To find x when y=-1, substitute y=-1 into the equation y = -173.5 + 4.83x and solve for x.
Explanation:To find x when y=-1, you can use the equation of the line where y = 5 when x = -3. Based on the given information, the line of best fit is y = -173.5 + 4.83x. By substituting y = -1 into the equation, we can solve for x:
-1 = -173.5 + 4.83x
Adding 173.5 to both sides of the equation:
172.5 = 4.83x
Dividing both sides by 4.83:
x = 35.69
Therefore, when y = -1, x is approximately 35.69.
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What is the ordered pair of X′ after point X (3, 4) is rotated 180°?
Answer with explanation:
Pre image= Coordinates of point X= (3,4)
When point ,(x,y) is rotated by an angle of 180°, then coordinates of image that is point (x,y) after rotation = (-x, -y)
⇒≡Coordinates of point X(3,4) after rotation by an angle of 180°=X'(-3,-4)
The coordinates after a rotation of 180 degrees about the origin is: X'(-3, -4)
How to find the transformation?There are different types of transformation such as:
Translation
Rotation
Reflection
Dilation
The transformation rule for the rotation about 180 degrees (180°) about the origin is (x,y)→(−x,−y) .
Thus:
X(3, 4) → X'(-3, -4)
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Under normal conditions, 1.5 feet of snow will melt into 2 inches of water. During a winter season high in the mountains, 301 feet of snow fell. How many inches of water will there be when the snow melts?
Answer: 401.33 inches
Match each quadratic equation with the best way to solve it.
1. 5x2 + 12x - 3 = 0
solve by square root method
2. x2 - 4x = 8
solve by factoring
3. 4x2 - 25 = 0
solve by quadratic formula
4. x2 - 5x + 6 = 0
solve by completing the square
Answer:
5x^2 + 12x -3 =0 ---------> solve by quadratic formula
x^2 -4x = 8 ----------> solve by completing the square
4x^2 -25 = 0 ----------> solve by square root method
x^2-5x+ 6 = 0 -----------> solve by factoring
Step-by-step explanation:
1. 5x^2 + 12x -3 =0
The best way to solve this equation is quadratic formula as all the terms in the equation have coefficients it will be convenient to solve it through quadratic formula.
2. x^2 -4x = 8
The best way to solve this equation is by completing the square as the factors cannot be made directly.
3. 4x^2 -25 = 0
the best way to solve this equation is to solve by square root method as the 25 and 4 are perfect squares.
4. x^2-5x+ 6 = 0
The best way to solve this equation is to solve by factoring as it can clearly be seen that it is convenient to make factors ..
On a coordinate plane, point A is located at (7,4), and point B is located at (-8,4). What is the distance between the two points?
Answer:
15
Step-by-step explanation:
This problem is quite simple; that is, if you know the proper formula that must be applied in finding the distance. The formula for finding the distance between two coordinate points is: √(x2-x1)^2+(y2-y1)^2. Now, obviously, (x2-x1)^2 and (y2-y1)^2 are both under the radical, where x2 and y2 represent the xy coordinates of point A (7,4) and x1 and y1 represent the xy coordinates of point B (-8,4). Now, all you must do is plug the points into the distance formula to get the answer, 15.
The distance between the two points is 15 units.
The coordinate points are A (7, 4) and B (-8,4).
What is the formula to find the distance between coordinate points?The formula to find the distance between two coordinate points is Distance=[tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1} )^{2}}[/tex].
Now, the distance between two coordinate points=[tex]\sqrt{(-8-7)^{2} +(4-4)^{2}}[/tex]
=√225
=15 units
Therefore, the distance between the two points is 15 units.
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To make a students uniform, the tailor needs 15/4 m of cloth. To make 26 such uniforms. How much cloth will he need?
For one uniform 15/4 m of cloth is needed, since we need 26 uniforms week need 26 time that much cloth. Set up and multiply the equation like so...
[tex]\frac{15}{4}[/tex]*26
or you can write it like so...
[tex]\frac{15}{4} *\frac{26}{1}[/tex]
Multiply numerator by numerator and denominator by denominator...
[tex]\frac{15*26}{4*1}[/tex]
[tex]\frac{390}{4}[/tex]
^^^This can be further simplified to...
[tex]\frac{195}{2}[/tex]m
or
97.5 m
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
95 1/2 m of cloth
Step-by-step explanation:
Multiply:
(15/4 m)
------------ * 26 uniforms = 95.5 m of cloth needed, or 95 1/2 m of cloth
uniform