Answer:
y = [tex]\frac{7}{6}[/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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, 2 ) and (x₂, y₂ ) = (3, - 5 )
m = [tex]\frac{-5-2}{3-9}[/tex] = [tex]\frac{-7}{-6}[/tex] = [tex]\frac{7}{6}[/tex]
• Parallel lines have equal slopes , so
m = [tex]\frac{7}{6}[/tex] is the slope of the parallel line
the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = [tex]\frac{7}{6}[/tex] x - 3 ← equation of parallel line
Hey there!
[tex] \\ [/tex]
Answer:[tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}[/tex]
[tex] \\ [/tex]
Explanation:To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.
Let the line that we are trying to determine its equation be [tex] \: \sf{d_1} \: [/tex] and the line that is parallel to [tex] \: \sf{d_1} \: [/tex] be [tex] \: \sf{d_2} \: [/tex] .
[tex] \sf{d_2} \:[/tex] passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:
[tex] \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}} [/tex]
[tex] \\ [/tex]
⇒Subtitute the values :
[tex] \sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )} [/tex]
[tex] \implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}[/tex]
[tex] \sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}} [/tex].
Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:
Slope-Intercept Form:
[tex] \sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.} [/tex]
[tex] \implies \sf{y = \bold{\dfrac{7}{6}}x + b} [/tex] [tex] \\ [/tex]
We know that the coordinates of the point (0 , -3) verify the equation since it is on the line [tex] \: \sf{d_1} \: [/tex]. Now, replace y with -3 and x with 0:
[tex] \implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Therefore, the equation of the line [tex] \: \bold{d_1} \: [/tex] is [tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}} [/tex]
[tex] \\ [/tex]
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HELP HELP HELP HELP
HELP HELP HELP HELP
PLSSSSS
Answer:
5 (rounded)
Step-by-step explanation:
by using the Pythagorean theorem you can calculate b
[tex]a^{2} + b^{2} = c^{2}[/tex]
here we have a and c
first lets times it by themselves
16 + b^2 = 36
now lets isolate b^2
b^2 = 36-16
= 20
now we have to get rid of the exponent ^2
b = 4.47....
rounding it would be 5!
Hope that helps :>
What was the ratio of the number of goggles sold to the number of swimsuits sold?
Answer: Give me the full answer and i will be able to answer it
Step-by-step explanation:
Which function is represented by the graph?
The parent absolute value function is translated
3 units and
1 unit.
The function that is graphed is f(x) =
✓.
The function that is graphed is f(x) = |x - 3| + 1
How to determine the graphed function?The parent absolute function is:
f(x) = |x|
From the graph, we have the following transformations:
3 units left1 unit upThis is represented as:
(x, y) = (x - 3, y + 1)
So, we have:
f(x) = |x - 3| + 1
Hence, the function that is graphed is f(x) = |x - 3| + 1
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Find the equivalent expression of 12.6 − (5.1 + 2.2).
12.6
5.1
5.3
2.2
Answer: 5.3
Step-by-step explanation:
[tex]12.6-(5.1+2.2)\\\\=12.6-7.3\\\\=5.3[/tex]
Which angle is an exterior angle?
k°
i°
g°
Answer:
k
Step-by-step explanation:
For the upcoming parade, Lauren needed to make her school's triangular flag into a larger, similar triangular flag. Using the information given, determine which (if any) similarity postulate she used in making her school's new flag. Pls help
The ratio of corresponding sides of the triangle are not in the same proportion, hence they are not similar.
What are similar triangles?Two triangles are said to be similar if they have the same shape and angles. Also, the ratio of their corresponding sides are to be in the same proportion.
From the image shown, if the triangles are similar, hence:
AB / DE = AC / DF = BC / EF
Hence:
5.6 / 4 = 4.9 / 3.5 ≠ 2.4 / 1.5
1.4 = 1.4 ≠ 1.6
The ratio of corresponding sides of the triangle are not in the same proportion, hence they are not similar.
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-A farmer decides to pack 1,231 mangoes into sacks If a sack contains 25 mangoes, how many sacks can be parked full / Can fully be packed. How many remained?
The sum of the measures of the angles of a triangle is 180°. The middle-sized angle measures 3° more than 2 times the smallest angle. The middle-sized angle measures 109° less than the largest angle. Find the measure of each angle.
Answer:
13° , 29° , 138°
Step-by-step explanation:
let x be the smallest angle , then
2x + 3 is the middle angle and
2x + 3 + 109 is the largest angle
summing the 3 angles and equating to 180
x + 2x + 3 + 2x + 3 + 109 = 180 , that is
5x + 115 = 180 ( subtract 115 from 180 )
5x = 65 ( divide both sides by 5
x = 13
2x + 3 = 2(13) + 3 = 26 + 3 = 29
2x + 3 + 109 = 29 + 109 = 138
the 3 angles are 13° , 29° , 138°
A cone and a cylinder have the same base and height, as shown below.
A cone is inside of a cylinder with same base and height.
The volume of the cylinder is 84 pi inches squared What can be concluded about the volume of the cone? Check all that apply.
The volume of the cone is One-third the volume of the cylinder.
The volume of the cylinder is 2 times the volume of the cone.
The volume of the cone is less than the volume of the cylinder.
The statement that apply is that the volume of the cone is One-third the volume of the cylinder
How to find the volume of a cone and cylinder?volume of a cone = 1 / 3 πr²h
where
r = radiush = height of the coneVolume of a cylinder = πr²h
where
r = radiush = heightThe cone and the cylinder has the same base and height. Therefore, the radius and height are the same .
volume of the cylinder = 84π
Therefore, the volume of the cone is One-third the volume of the cylinder.
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Area=
Stuck help me please thanks
Answer: 112
Step-by-step explanation:
area of the parallelogram is base times height
Please help!! What is the product of the 2x and...
Answer:
The answer is option c
Answer:
The answer is B.
Find 0,8,3 round the nearest degree
The measure of [tex]\theta[/tex] is 68 degrees
How to solve the angle?The complete question is in the attached image
The value of [tex]\theta[/tex] is calculate using the following cosine function
[tex]\cos(\theta) = \frac 38[/tex]
Evaluate the quotient'
[tex]\cos(\theta) = 0.375[/tex]
Take the arc cos of both sides
[tex]\theta = \cos^{-1}(0.375)[/tex]
Evaluate the arc cos
[tex]\theta = 67.97[/tex]
Approximate to the nearest degree
[tex]\theta = 68[/tex]
Hence, the measure of [tex]\theta[/tex] is 68 degrees
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Name an angle supplementary to
Helpppp find the missing angles for 5 and 6
Answer:
5. 68 degrees :)
6. 55 degrees :)
Step-by-step explanation:
5.
A flat line is 180 degrees so we subtract to find x :)
Lets do that now :)
180 - 112 = 68
x = 68 degrees
6.
X will be the same as 55 degrees.
All lines are tipped the same what so that is why it is 55 degrees :)
Have an amazing day!!
Please rate and mark brainliest!!
Simplify the expression to a polynomial in standard form:
(−x+1)(x^2+6x−4)
Answer:
-x^3-5x^2+10x-4
Step-by-step explanation:
(−x + 1) (x ^ 2 + 6x − 4) = (-x)(x ^ 2 + 6x − 4) + 1(x ^ 2 + 6x − 4)
= -x^3-6x^2+4x+x^2+6x-4 = -x^3-5x^2+10x-4
A basketball hoop is shown. Lisa is standing 10 feet from the basketball net. The basketball net is 8.5 feet high. Lisa apostrophe s line of vision is 5 feet off the ground. When she looks up to the net, a right triangle is formed.
Use the diagram and complete the steps to find the measure of the angle of depression from the top of the hoop to Lisa.
The length of the shortest leg of the right triangle that is formed is
feet.
The angle of depression from the hoop to Lisa is
to the angle of elevation from Lisa’s line of sight to the hoop.
Because the lengths of the opposite and adjacent sides are known, use the
function.
The angle of depression, rounded to the nearest degree, is approximately
degrees.
By critically observing the basketball hoop (see attachment), we can logically deduce that the basket's height from Lisa's horizontal sight is the same as the length of the shortest leg of the right-angle triangle:
Shortest leg = 8.5 - 5
Shortest leg = 3.5 feet.
In Geometry, the sum of all the angles in a triangle is equal to 180°:
x + y + z = 180
x + y + 90 = 180
x + y = 180 - 90
x + y = 90° (complementary angle).
Therefore, the angle of depression is complementary to the angle of elevation.
Also, you should use the inverse tangent function because the lengths of the opposite and adjacent sides of the right-angle triangle are known.
How to find the angle of depression?Angle of depression = tan⁻¹(Opposite/Adjacent)
Angle of depression = tan⁻¹(3.5/10)
Angle of depression = 19.29° ≈ 19°.
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Answer:
3.5
congruent
inverse tangent
19
Step-by-step explanation:
soybeans have a conversion factor of 36.744 (bu/t). how much do 45 bushels weight. Show your work pls
The weight of 45 bushels of soya beans is 1.2247 Tons
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The conversion factor of soyabeans is 36.744 (bu/t). Hence:
45 bushels = 45 bushels / 36.744 (bu/t) = 1.2247 Tons
The weight of 45 bushels of soya beans is 1.2247 Tons
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ASAP!!! Question 7 (Essay Worth 5 points)
(02.03)
Part A: Use ratio language to describe the relationship of any two things you can think of.
Example: For every 5 minutes of jogging, I ran 500 yards.
Be creative and come up with your own idea.
Part B: Determine the unit rate in your example.
this is what i have for part a: For every 1 student out of school, there are 10 students going to school
help me with part B pls I need to find the unit rate for my part a.
The unit rate for every 1 student out of school, there are 10 students going to school is 10 students going to school per 1 student out of school
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A unit rate is a ratio between two different units with a denominator of one.
If For every 1 student out of school, there are 10 students going to school, hence:
Unit rate = 10/1 = 10 students going to school per 1 student out of school
The unit rate for every 1 student out of school, there are 10 students going to school is 10 students going to school per 1 student out of school
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PLSS HELPP DUE IN 20 MIN. I NEED SOME STEP BY STEP TOO.
What is the length of GH?
5
10
15
25
Question 3
What is the value of y?
2
4
16
20
Question 4
What is the measure of angle DBE?
20
30
40
6
Question 5
If the measure of angle ABE?
20
30
40
60
Question 6
Which ray is a bisector of angle ABC?
ray BC
ray BD
ray AB
ray BF
The length of GH is 15.
How to calculate the length?GH = IG
GH = 5x - 10
IG = 3x
5x - 10 = 3x
5x - 3x = 10
2x = 10
x = 10/2 = 5
GH = 5x - 10
= 5 * 5 - 10 = 25 - 10
GH = 15
<ABD = < DBC
<ABD = 10y°
<DBC = (8y + 4)°
10y° = (8y + 4)°
10y = 8y + 4
10y - 8y = 4
2y = 4
y = 4/2 = 2
The value of y is 2
<DBE = <DBC + <CBE
<DBC = 10y°
<CBE = <DBC = 10y°
y = 2
<DBC = <CBE = 10y° = 10*2° = 20°
<DBE = 20° + 20° = 40°
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−5(5x+3)−5x+1= -44
solve for X
Answer:
x=1
Step-by-step explanation:
Original Equation:
[tex]-5(5x+3)-5x+1= -44[/tex]
Distribute the -5
[tex]-25x-15-5x+1= -44[/tex]
Add like terms
[tex]-30x-14=-44[/tex]
Add 14 to both sides
[tex]-30x=-30[/tex]
Divide both sides by -30
[tex]x=1[/tex]
Answer:
x = 1
Step-by-step explanation:
-5(5x+3) - 5x + 1 = -44
(-5*5x -5*3) - 5x + 1 = -44
(-25x - 15) - 5x + 1 = -44
-25x - 5x - 15 + 1 = -44
-30x - 14 = -44
-30x = -44 + 14
-30x = -30
x = -30/-30
x = 1
Check:
-5(/5*1) + 3) - 5*1 + 1 = -44
-5(5+3) - 5 + 1 = -44
-5*8 - 5 + 1 = -44
-40 - 5 + 1 = -44
-45 + 1 = -44
Customers can pick blueberries for $1.75 per quart. How much would one dozen quarts of berries cost?
Aiden and Jacob share a reward of $60 in a ratio of 2:3. what fraction of the total reward does Jacob get?
What is the equation in point-slope form for the line parallel to y=5x-4 that contains p(-6,1)
Answer:
[tex]\displaystyle{y-1=5(x+6)}[/tex]
Step-by-step explanation:
A point-slope form is written in the equation of [tex]\displaystyle{y-y_1=m(x-x_1)}[/tex]. Where [tex]\displaystyle{(x_1,y_1)}[/tex] is a coordinate point and [tex]\displaystyle{m}[/tex] is slope.
The definition of parallel is to both lines have same slope. The given line equation has slope of 5. Therefore, we can write the equation in point-slope form as:
[tex]\displaystyle{y-y_1=5(x-x_1)}[/tex]
Next, we are also given the point p(-6,1). Substitute [tex]\displaystyle{x_1}[/tex] = -6 and [tex]\displaystyle{y_1}[/tex] = 1 in:
[tex]\displaystyle{y-1=5[x-(-6)]}\\\\\displaystyle{y-1=5(x+6)}[/tex]
Hence, the line equation that’s parallel to y = 5x - 4 and passes through a point (-6,1) is y - 1 = 5(x + 6)
Answer:
y - 1 = 5 ( x + 6 )
Step-by-step explanation:
We know that when two lines are parallel the slope of both lines is equal.The formula that we use to find an equation of a line is y = m x + cHere,
m ⇒ slope
Now let us take a look at the given equation which is already drawn.y = 5x - 4 ← equation of the old line
Now it is clear to us that,
m ⇒ slope of the line ⇒ 5
c ⇒ y-intercept ⇒ -4
Therefore, the slope of the new line also will be 5.That is, m = 5
The question asked us to write the equation in point-slope form.The formula to write the equation in the line in point-slope form is :y - y₁ = m ( x - x₁ ).
Here,m = slope
Also, we can use the given coordinates to write the equation in point-slope form( -6 , 1 ) ⇔ ( x₁ , y₁ )
So, to find the equation of the new line we can replace m, y₁ & x₁ with 5, 1 & -6 respectively.Let us solve this now
y - y₁ = m ( x - x₁ )
y - 1 = 5 ( x - ( -6) )
y - 1 = 5 ( x + 6 )
And now let us write the equation of the new line in point - slope form.y - 1 = 5 ( x + 6 )
Alan bought 3 pencils and a notebook. The notebook cost $6, and he spent a total of $12. How much did each pencil cost? Use p to represent how much each pencil costs.
Answer:
$2
Step-by-step explanation:
If the total is $12, and he spent $6 on a notebook, he has $6 left for his 3 pencils. If each pencil costs the same, he paid $2 for each pencil.
the area of a quadrilateral whose vertices is ABCD taken in order are (1,2) (-5,6) (7,-4) and (-2,t) be 0 ,find the value of t
What are the solutions to the system of equations?
y = 2x² + 6x - 10
\ y =
y = -x + 5
Answer:
x= 1.5, y= 3.5
or x= -5, y= 10
Step-by-step explanation:
Let's solve by substitution.
Label the two equations:
y= 2x² +6x -10 -----(1)
y= -x +5 -----(2)
Substitute (2) into (1):
2x² +6x -10= -x +5
2x² +6x +x -10 -5= 0
Simplify:
2x² +7x -15= 0
Factorise:
(2x -3)(x +5)= 0
2x -3= 0 or x +5= 0
2x= 3 or x= -5
x= 1.5
Now that we have found the value of x, we can find the value of y through substitution.
Substitute into (2):
y= -1.5 +5 or y= -(-5) +5
y= 3.5 or y= 10
Supplementary:
Do check out the following should you wish to learn more about solving quadratic equations!
https://brainly.com/question/12187987Find the tangent of angle Θ in the triangle below.
A. 4(sqroot)65/65
B. 9/5
C. 4/9
D. (sqroot)65/4
E. 9/4
Answer: [tex]\frac{\sqrt{65}}{4}[/tex]
Step-by-step explanation:
By the Pythagorean theorem, the unknown side has length
[tex]\sqrt{9^{2}-4^{2}}=\sqrt{65}[/tex]
Therefore,
[tex]\tan \theta=\boxed{\frac{\sqrt{65}}{4}}[/tex]
Which is the best estimate of StartRoot 47 EndRoot to the nearest tenth?
6.8
6.9
7.0
7.1
The closest value will be 6.9 since the value is close to 49
Square root of prime numbersThe square root of a number can both be negative or positive. According to the question, we are to determine the square root of 47
The square root of 47 must be between the square root of 36 and square root of 64
√36 = 6
√64 = 8
This shows that the answer must be between 6 and 8. Hence the closest value will be 6.9 since the value is close to 49
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Answer: 6.9
Step-by-step explanation: just did the test
What is this problem
The coordinate of the vertex is; (h, k) = (3, -5)
The final equation of the parabola is; y = 5(x - 3)² - 5
How to find the vertex of a Parabola?The vertex is the coordinate of the crest or trough of the curve. Now, in the given graph, we only have a Trough which is the lowest point of the graph.
The coordinate of the vertex is; (h, k) = (3, -5)
2) Since the general equation is;
y = a(x - h)² + k
We will have;
y = a(x - 3)² - 5
At x = 2, y = 0. Thus;
0 = a(2 - 3)² - 5
a - 5 = 0
a = 5
3) The final equation of the parabola is;
y = 5(x - 3)² - 5
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The expression x-y equals 0.7 if x and y have certain values. Evaluate the following expression with the same values of x and y
5(x-y)
Answer:
3.5Step-by-step explanation:
We already know that x-y equals to 0.7,so 5(x-y) would just be 5(0.7), with this the answer would equal to 3.5.***I hope this helps and the explanation is helpful!***
Step-by-step explanation:
5 x 0.7 = 3.5