Answer: B. y = 2/3 x - 13/3
Step-by-step explanation:
two lines are said to be parallel if they have the same slope.
To find the slope of line K we will use the formula fro calculating slope which is :
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = 2
[tex]x_{2}[/tex] = 8
[tex]y_{1}[/tex] = -3
[tex]y_{2}[/tex] = 1
substituting into the values into the formula , we have :
m = [tex]\frac{1-(-3)}{8-2}[/tex]
m = [tex]\frac{4}{6}[/tex]
m = [tex]\frac{2}{3}[/tex]
Therefore : the slope of line K = [tex]\frac{2}{3}[/tex] , this means that any line that will be parallel to K must have a gradient of [tex]\frac{2}{3}[/tex].
The only line that has a gradient of [tex]\frac{2}{3}[/tex] is the line y = 2/3x - 13/ 3 ,this means that the line is parallel to Line K
Figure ABCD is a kite.
Kite A B C D is shown. Sides A B and B C are congruent. The length of A B is 3 x + 1 and the length of B C is 22. Sides A D and C D are congruent. The length of A D is 4 x.
What is the length of line segment CD?
7 units
8 units
28 units
35 units
Answer:
I think 28. Sorry if its wrong
Step-by-step explanation
The kite is a quadrilateral with 4 sides and angles. The length of line segment CD from the given kite is 28 units
Properties of a kiteThe kite is a quadrilateral with 4 sides and angles.
From the given diagram,
AB = 3x + 1
BC = 22
Since AB = BC, hence;
3x + 1 = 22
3x = 22 - 1
3x = 21
x = 7
Since AD = CD = 4x, hence;
CD = 4x
CD = 4(7)
CD = 28 units
Hence the length of line segment CD from the given kite is 28 units
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Find the missing height
Answer:
5
Step-by-step explanation:
Solve this exercise using the fact that the sum of the measures of the three angles of a triangle is 180degrees°.
In a triangle, the measures of the three angles are x, x+14, and x−38. What is the measure of each angle
Answer:
68°, 82°, and 30°
Step-by-step explanation:
x+x+14+x-38=180
combine like terms
3x-24=180
put variables on one side
3x=204
divide
x=68
substitute
x=68
x+14=82
x-38=30
By using the triangle angle sum theorem, we find that the measures of the angles of the triangle in question are 68 degrees, 82 degrees, and 30 degrees.
Explanation:This question involves using the fact that the sum of internal angles in any triangle totals 180 degrees. In this triangle, the three angles are given as x, x+14, and x-38. To find the measures of these angles, we set up the below equation:
x + (x+14) + (x−38) = 180
The step above incorporates the triangle angle sum theorem. Now we simplify and solve for 'x':
3x - 24 = 180
3x = 204
x = 68
So the measure of the angles in the triangle are 68 degrees, 82 degrees, and 30 degrees.
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Jackie says that the fraction 7/8 is equivalent to 3/4. Is she right? Explain
Answer:
Jackie is incorrect.
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] [tex]\left {x2} \atop {x2}} \right.[/tex] = [tex]\frac{6}{8}[/tex]
[tex]\frac{3}{4}[/tex] is equivalent to [tex]\frac{6}{8}[/tex] not [tex]\frac{7}{8}[/tex]
Jackie is mistaken when she claims that the fraction 7/8 is equal to 3/4. We compare the numerator (the top number) and denominator (the bottom number) of two fractions to see if they are equal.
In this instance, 3/4 has a denominator of 3 and a numerator of 4, whereas 7/8 has a numerator of 7 and a denominator of 8, respectively. The fractions cannot be equal since the numerators and denominators vary.
Two fractions must have the same numerator to denominator ratio in order for them to be equal. In this situation, 7/8 is a bigger fraction than 3/4. Jackie's assertion that 7/8 is comparable to 3/4 is therefore false.
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If a function uses variables other than xand y for its input and output
variables, you take the original equation and solve for the input variable to
find the inverse.
A. True
B. False
Answer:
True
Step-by-step explanation:
Sorry if it's wrong lol
Which pair of angles are corresponding angles? 1 and 4, 2 and 3, 3 and 6, 4 and 8 Please answer ASAP
Answer:
4 and 8
Step-by-step explanation:
corresponding angles are two angles that have the same angle degree and are on the same side of the graph if you were to take the bottom part and move it up to the top part
17•blank=1. As a fraction ASAP pls
the answer for this question is:
1/17
Write a minor function for the line with the slope of -5 that passes through points (7,3)
The equation of the line is [tex]5x+y-38=0[/tex]
Step-by-step explanation:
The slope is [tex]m=-5[/tex]
Also, the line passes through the points [tex](7,3)[/tex]
To find a line with slope [tex]m=-5[/tex] that passes through the points [tex](7,3)[/tex], let us use the equation of a line with slope that passes through the point is given by [tex](y-y_{1} )=m(x-x_{1} )[/tex] where m is the slope and [tex](x_{1} ,y_{1} )[/tex] are the points [tex](7,3)[/tex].
Thus, substituting the values in the equation of a line, we get,
[tex](y-3)=-5(x-7)[/tex]
Multiplying the term [tex](x-7)[/tex] by -5, we get,
[tex]y-3=-5 x+35[/tex]
Adding both sides by 5x,
[tex]5x+y-3=35[/tex]
Subtracting 35 from both sides of the equation,
[tex]5x+y-38=0[/tex]
Thus, the equation of the line is [tex]5x+y-38=0[/tex]
write and solve the differential equation that models the following statment. "the rate if change of W with respect to x is proportional to x+18."
Answer:
[tex]\int k(x + 18)dx = \int kx + 18k dx[/tex] = [tex]k\frac{x^{2} }{2}[/tex] + [tex]18kx[/tex] + C where C is the constant of integration.
Step-by-step explanation:
i)it is given that the rate of change of W with respect to x is proportional to
x + 18. Therefore [tex]\frac{dW}{dx}[/tex] = k(x + 18) where k is a constant.
ii) Therefore [tex]\int k(x + 18)dx = \int kx + 18k dx[/tex] = [tex]k\frac{x^{2} }{2}[/tex] + [tex]18kx[/tex] + C where C is the constant of integration.
iii) the complete solution can only be found if we know the constant of proportion and also the constant of integration.
What is the perimeter of 10 ft long and 9 feet wide?
Answer: Answer is 38ft.
Step-by-step explanation: The figure that measures 10ft by 9ft is a rectangle which means two sides measure 10ft each (length) and two sides measure 9ft each (width). A perimeter simply measures all sides of the entire shape, that is;
10ft + 9ft + 10ft + 9ft = 38ft.
At the grocery store, Lily spent $m$ dollars on milk, twice that amount on fruit, and $6$ dollars less than $3$ times the amount spent on milk for bread. If she entered the store with $\$80$, how much money did she have when she left? Write your answer in terms of $m$.
Answer:
$remaining=86-6m
Step-by-step explanation:
$remaining = 80 - (m + 2m) - (3m-6)
$remaining = 80 - 3m - 3m +6
$remaining = 86 - 6m
80 -> total amount she brings into the store
m -> money spent on milk
2m -> money spent on fruit (two x m)
3m-6 -> bread (six dollars less than three times the milk value)
Simplify and the result is 86-6m
Which absolute value expression represents the distance between 3 and
9
2
on a number line?
A) |3 −
9
2
|
B) |3 − (−
9
2
)|
C) |−3 + (−
9
2
)|
D) |−3 −
9
2
)|
From other source on the internet this question is:
Which absolute value expression represents the distance between 3 and - 2 on a number line?
Answer:
|3 - (-2) |, or|-2 - 3|Both are equivalent.
Explanation:
The distance between two numbers in a number line is the absolute value of the difference between the two numbers.
Thus, the distance between a number x and a number y is |x - y|, which is also equivalent to |y - x|.
In this case the distance between 3 and - 2 can be represented by either of the expressions:
|3 - (-2) |, or|-2 - 3|Note that when you simplify them you get the same value:
|3 - (-2) | = |3 + 2| = |5| = 5|-2 - 3| = | -5| = 5Answer:
The distance between 3 and
9
2
on a number line is |3 −
9
2
|. The distance between two numbers is equal to the absolute value of their difference.
|3 −
9
2
| = |−
3
2
| =
3
2
Step-by-step explanation:
so the answer is A
I need help on this problem( picture included)
hmmm first off, let's convert the decimal to a fraction, and then the mixed fraction to an improper fraction and proceed from there.
[tex]\bf 6.\underline{2}\implies \cfrac{62}{1\underline{0}}\implies \cfrac{31}{5}~\hfill \stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] ~\dotfill\\\\ 6.2\div (2x+1)=2\frac{1}{3}\div 4\implies \cfrac{31}{5}\div (2x+1) = \cfrac{7}{3}\div 4[/tex]
[tex]\bf \cfrac{31}{5}\div \cfrac{(2x+1)}{1} = \cfrac{7}{3}\div \cfrac{4}{1}\implies \cfrac{31}{5}\cdot \cfrac{1}{(2x+1)} = \cfrac{7}{3}\cdot \cfrac{1}{4}\implies \cfrac{31}{5(2x+1)}=\cfrac{7}{12} \\\\\\ \cfrac{31}{10x+5}=\cfrac{7}{12}\implies \stackrel{\textit{cross multipling}}{372 = 7(10x+5)}\implies 372=70x+35\implies 337=70x \\\\\\ \cfrac{337}{70}=x\implies 4\frac{57}{70}=x\implies 4.81\approx x[/tex]
please help me with #4
The chances of it being less than 5 is 4/6
So if he spins it 150 times the chances of it landing on 5 or less than it will be: 4/6 * 150 = 100 (c)
Answer:
i think its c 100
Step-by-step explanation:
sorry if it makes no sense
i go backwards 8m in 4s what is my velocity
Answer:2m/s
Step-by-step explanation:
Velocity=distance÷time
Velocity=8÷4
Velocity=2m/s
Need help with question number 13. Can’t figure it out.
Answer:
least common multiple
Step-by-step explanation:
Find the lcm of the given numbers, do you know how to do that?
Alright, so you're looking for the GCF.
Greatest Common Factor
I don't wanna go into detail of what that is (if you don't already know what it is, please watch a video on what it is and how to find it.)
Our numbers are 18, 36, 54
What is the gcf of these numbers? They all are both divisble by 18 and that's the largest 18 can go, so 18 is the GCF.
18 is the answer.
Line b passes through the Point(-3, -4) and has a slope of -1/2. What is the equation of Line b in standard form?
x + 2y = -11
x + 2y = -10
2x + y = -11
2x + y = -10
Answer:
[tex]x+2y=-11[/tex]
Step-by-step explanation:
Slope intercept form of a line is given by:
[tex]y=mx+b[/tex]
Where
m is the slope and b is the y-intercept
Given slope is [tex]-\frac{1}{2}[/tex]
We can write:
[tex]y=-\frac{1}{2}x+b[/tex]
Now to find b, we replace x with -3 and y with -4, given, so we have:
[tex]y=-\frac{1}{2}x+b\\-4=-\frac{1}{2}(-3)+b\\-4=\frac{3}{2}+b\\b=-5.5[/tex]
So, the equation is:
[tex]y=-\frac{1}{2}x-\frac{11}{2}[/tex]
Now,
The standard form is given by:
[tex]Ax+By=C[/tex]
So, we take x and y to left side and the constant to right side. Rearranging, we get:
[tex]y=-\frac{1}{2}x-\frac{11}{2}\\2y=-x-11\\x+2y=-11[/tex]
The first answer choice is right.
Final answer:
The equation of line b that passes through the point (-3, -4) and has a slope of -1/2 in standard form is x + 2y = -11.
Explanation:
To find the equation of line b that passes through the point (-3, -4) and has a slope of -1/2, we will start with the slope-intercept form of a line equation y = mx + b, where m is the slope and b is the y-intercept. While we know the slope (-1/2), we do not yet have the y-intercept. We can use the given point to solve for b. Plugging the point into the equation gives -4 = (-1/2)(-3) + b, which simplifies to -4 = 3/2 + b. Solving for b yields b = -11/2.
Now we have the slope-intercept form of the line: y = (-1/2)x - 11/2. To convert this to standard form, which is Ax + By = C, we multiply through by 2 to clear the fractions, which gives us 2y = -x - 11. Rearranging this, we add x to both sides to get x + 2y = -11. Therefore the correct equation in standard form is x + 2y = -11.
log2 (32) =
Answer this
Answer: 5
Step-by-step explanation:
[tex]log_{2}[/tex] 32
32 can be written in index form as 2x2x2x2x2 , which could be written as [tex]2^{5}[/tex].
[tex]log_{2}[/tex] 32 the becomes
[tex]log_{2}[/tex] [tex]2^{5}[/tex]
Which could be written as
5 [tex]log_{2}[/tex] 2
From law of logarithms; [tex]log_{2}[/tex] 2 = 1
Therefore : 5 [tex]log_{2}[/tex] 2 = 5 x 1 = 5
Bob bought 24 hockey tickets for $83. Adult tickets cost $5.50 and child tickets cost $2.00. How many child tickets did he buy?
Answer:
Step-by-step explanation:
a + c = 24......a = 24 - c
5.5a + 2c = 83
5.5(24 - c) + 2c = 83
132 - 5.5c + 2c = 83
-5.5c + 2c = 83 - 132
-3.5c = - 49
c = -49 / -3.5
c = 14 <==== 14 child tickets
a + c = 24
a + 14 = 24
a = 24 - 14
a = 10 ........and 10 adult tickets
Twice a number x plus 8 is greater than 12
Answer:
2x+8>12
Step-by-step explanation:
24 cupcakes for 168$ what is unit rate
Answer:
$7 per cupcake
Step-by-step explanation:
A unit rate is the cost of one item. So we would do $168 divided by twenty-four. That would be equivalent to seven.
What value of x is in the solution set of 4x – 12 ≤ 16 + 8x?
Answer:
4x – 12 ≤ 16 + 8x; x>-7
Step-by-step explanation:
i dont remember how i did it
Answer:
x≥-7
Hope this helps
Hawaii has an area of 1.1 × square miles and a population of 1.2 × people. Which key strokes on a calculator will give the population density of Hawaii?
The population density of Hawaii is 109.09 with an area of [tex]1.1 \times 10^4[/tex]square miles and a population of [tex]1.2 \times 10^6[/tex] people.
Given that:
The area of Hawaii is 1.1 × 10^4 square miles
The population of Hawaii is 1.2 × 10^6 square miles
The population density of Hawaii can be calculated as:
[tex]Population \ density = \dfrac{Number \ of \ people} {land\ area}[/tex]
Substitute the values in the given formula:
[tex]Population \ density = \dfrac{ 1.2 \times 10^6} {1.1 \times 10^4}[/tex]
This can be further solved as:
[tex]Population \ density = \dfrac{ 1.2 \times 10^{(6 -4)}} {1.1}[/tex]
The laws of exponent are used here,
Where, [tex]\dfrac{x^m}{x^n} = x^{(m-n)[/tex]
This can be solved as:
Population density = [tex]1.0909 \times10^2[/tex]
= [tex]1.0909 \times 100[/tex]
= 109.09
The population density of Hawaii is 109.09.
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The complete question is :
Hawaii has an area of [tex]1.1 \times 10^4[/tex] square miles and a population of [tex]1.2 \times 10^6[/tex] people. Which keystrokes on a calculator will give the population density of Hawaii?
Final answer:
To find the population density of Hawaii, divide the population by the area. The key strokes on a calculator would be 1.2 divided by 1.1 equals 1.09. The population density of Hawaii is approximately 1.09 people per square mile.
Explanation:
To calculate the population density of Hawaii, you will need to divide the population by the area. The formula for population density is: Population Density = Population / Area. Using the provided information, the key strokes on a calculator to find the population density of Hawaii would be: 1.2 / 1.1 = 1.09. Therefore, the population density of Hawaii is approximately 1.09 people per square mile.
Jason bought n candy bars. Write an expression to show the total cost of the candy bars if each candy bar cost $5.
HELP ME !
Answer:
5n
Step-by-step explanation:
Answer:
total cost of the candy bars = 5 x n
Step-by-step explanation:
What is 2/20 + 10/75
[tex]\text{Hey there!}[/tex]
[tex]\text{What is }\dfrac{2}{20}+\dfrac{10}{75}[/tex]
[tex]\text{For the LCD (Lowest Common Denominator) it should be equal to 300}[/tex]
[tex]\dfrac{2\times15}{20\times15}+\dfrac{10\times4}{75\times4}[/tex]
[tex]\bf{2\times15=30}\\\bf{20\times15=300}\\\\\bf{10\times4=40}\\\bf{75\times4=300}[/tex]
[tex]\text{Your new equation}\rightarrow\dfrac{30}{300}+\dfrac{40}{300}[/tex]
[tex]\text{With the denominators being alike we can leave the same}[/tex]
[tex]\text{New equation}\rightarrow\dfrac{30+40}{300}[/tex]
[tex]\text{30 + 40 = 70}[/tex]
[tex]\text{New equation}\rightarrow\dfrac{70}{100}[/tex]
[tex]\text{Since both of the terms have 10 in their like terms, let's divide both sides by it}[/tex]
[tex]\dfrac{70\div10}{300\div10}[/tex]
[tex]\bf{70\div10=7}[/tex] [tex]\leftarrow\text{Your numerator}[/tex]
[tex]\bf{300\div10=30}[/tex] [tex]\leftarrow\text{Your denominator}[/tex]
[tex]\boxed{\bf{Thus,\ your\ answer\ should\ be:\dfrac{7}{30}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
[tex]\frak{LoveYourselfFirst:)}[/tex]
P=v/1+kM^-t solve for k
Answer: [tex]k=\frac{M^t(v-P)}{P}[/tex]
Step-by-step explanation:
Given the following equation provided in the exercise:
[tex]P=\frac{v}{1+kM^{-t}}[/tex]
You can follow these steps in order to solve for "k":
1. You must multiply both sides of the equation by [tex]1+kM^{-t}[/tex]:
[tex](P)(1+kM^{-t})=(\frac{v}{1+kM^{-t}})(1+kM^{-t})\\\\P+PkM^{-t}=v[/tex]
2. The next step is to subtract "P" from both sides of the equation:
[tex]P+PkM^{-t}-(P)=v-(P)\\\\PkM^{-t}=v-P[/tex]
3. Now apply the Negative Exponent Rule, which states that:
[tex]a^{-n}=\frac{1}{a^n}[/tex]
Then:
[tex]\frac{Pk}{M^{t}}=v-P[/tex]
4. Multiply both sides of the equation by [tex]M^t[/tex]:
[tex](M^t)(\frac{Pk}{M^{t}})=(M^t)(v-P)\\\\Pk=M^t(v-P)[/tex]
5. And finally, you must divide both sides of the equation by "P":
[tex]\frac{Pk}P=\frac{M^t(v-P)}{P}\\\\k=\frac{M^t(v-P)}{P}[/tex]
A rectangle has an area of 18 square centimeters.
Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:
A
1 cm and 18 cm
®
4 cm and 5 cm
2 cm and 9 cm
0
3 cm and 6 cm
Eduardo has 45 yards of rupe light.
Exactly how many more yards does he need to finish the car's ceiling?
Item
Length of Rope Light (yds)
Front spoiler
Rear spoiler
Ceiling
DONE
Naimmis
Dashboard
What is the fraction
Answer: 2 1/6
Step-by-step explanation:
Because the denominators are different, and there are whole numbers involved, then first make the fractions improper.
4 1/2 -> 9/2
6 2/3 -> 20/3
Next, make the denominators the same by multiplying each fraction by the denominator of the other.
9/2 * 3 = 27/6
20/3 * 2 = 40/6
Then you can subtract the numerators because the denominators are the same:
40/6-27/6= 13/6
Then you can convert to a mixed fraction if need be.
find one terminating decimal and one repeating decimal between -1 1/2 and -1 7/9
Answer:
-1.777...
Step-by-step explanation:
Using the LCM of 18 for the denominator, these values are:
-1 7/9 -1 1/2
-32/18 -27/18 0
--------------|-------------------|-------------------------------------|-----------
So, the easy values to identify are: -31/18, -30/18, -29/18, and -28/18
All of these numbers have repeating decimals (because 9 is a factor of the denominator).
Now, you may realize that -1 3/4 is within the range specified.
-1 7/9 -1 1/2
-32/18 -27/18 0
--------------|-------------------|-------------------------------------|-----------
|
-1 3/4
-1.75
This is because -1.75 is between -1.5 and -1.7777.... Note that it is not repeating.
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what is 5 13.5% of ?
Answer:
67.5
Step-by-step explanation:
Okay so I spent way to long overthinking this problem but in the end, I just used common sense to figure this one out. *it still may be wrong though...
A way to check if this is correct is dividing 67.5 by 5 and it equals to 13.5 which should make that answer correct?
Answer:
67.5
Step-by-step explanation:
Okay so I spent way to long overthinking this problem but in the end, I just used common sense to figure this one out. *it still may be wrong though...
A way to check if this is correct is dividing 67.5 by 5 and it equals to 13.5 which should make that answer correct?