Answer:
[tex]\boxed{y = \dfrac{1}{4}x -4}[/tex]
Step-by-step explanation:
The slope-intercept form of a line equation is y = mx + b[tex]\sf\\\\To\;find\;b, \;plug \;in \;the \;values\; of\; (4, - 3) \;which \;corresponds\; to\; x = 4, y = -3 \;into \;the \;above \;equation:\\== > - 3 = \dfrac{1}{4}\cdot 4 + b\\\\Switching\;sides,\\\dfrac{1}{4}\cdot 4 + b = -3\\\\Simplifying\\1 + b = -3\\\\b = -3 -1 = -4\\So\; the\; equation \;of \;the\; perpendicular\; line \;is: \boxed{y = \dfrac{1}{4}x -4}[/tex]
A perpendicular line will have slope is [tex]-\dfrac{1}{m}[/tex]
The perpendicular line will have a slope which is the negative of the reciprocal of the first line
Here the line is 4x + y =3
This can be re-written as y = -4x + 3
Slope of this line is -4
[tex]\sf Reciprocal \; of-4 = -\dfrac{1}{4}[/tex]
[tex]\sf Negative \; of \; reciprocal = -(-\dfrac{1}{4}) = \dfrac{1}{4}[/tex]
[tex]\sf So\;slope\;of\;perpendicular\;line=\dfrac{1}{4}\\Equation \;of \;the \;perpendicular\; line\; is \;y = \dfrac{1}{4}x + b \;where \;b \;is \;the\; y\; intercept[/tex]
Make a conjecture about each possible value for the following scenario:
The relationship between the area of a rectangle and a
triangle with the same base and equal heights.
The conjecture that can be made with regards to the given scenario is, given that the variable in the equation for the areas of the triangle and rectangle are the same;
The area of the triangle is half the area of the rectangle What is a conjecture?A conjecture is a conclusion or opinion which is based on partial or incomplete details or information ;
An appropriate conjecture that can be made with regards to the areas of the rectangle and triangle is obtained as follows;
Let the b represent the common base length, and let h represent the common height, we have;
Area of a triangle, At = 0.5•b•h
Area of a rectangle, Ar = b•h
Which gives;
At/Ar = (0.5•b•h/b•h) = 0.5The conjecture that can be made is that the area of the triangle is half the area of the rectangle.
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A weaver needs 7.8 meters of yarn for one project and 2.6 meters of yarn for a second project. What is the total amount of yarn, in meters, the weaver will need for both projects, written as a decimal?
Answer:10.4 written as a decimal is 0.104
Step-by-step explanation:
right or wrong tell me in comment
c. Estimation Estimate when first-class postage was 37 cents.
Estimation Possible year, 2005, when first-class postage was 37 cents, between 2001 and 2006.
What does that mean First class postage?First-Class mail is sent when a stamp is applied to an envelope and deposited in a mailbox. First-Class Mail is thus equivalent to "ordinary" mail. The ever-popular First-Class Mail is just one; the postal rate of the several services or "classes" that the Estimation Possible year, 2005, when first-class postage was 37 cents, between 2001 and 2006.
What is the postal rate?A fee will be assessed by a government postal service for the shipping and delivery of letters.
Assuming the value is supplied,
a) POSTAGE RATES L1=x
L2=y
y= -0.004x2+0.859x+27.53
y=28.381
b) Integers from -10 to 17 are the domain. Range: whole number between 18 and 42
c) From 2001 to 2006, first class postage cost 37 cents.
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Can some one pls help me it is my last question. Thank you!
Answer:
17.91!
Step-by-step explanation:
It would be, 17.91044776, so if you round it, you should get 17.91!
Hope this helps!!
Find the nth term of this quadratic sequence
4, 9, 16, 25, 36,
Answer:
(n+1)^2.
Step-by-step explanation:
Term: 1 2 3 4 5
Value 4 9 16 25 36
= 2^2 3^2 4^2 5^2 6^2
So, the nth term is (n + 1)^2.
what effect does eliminating the lowest value -6 from the data set have on the mean and median
By eliminating values from the given the given set , it will reduce the mean and median value. Mean = 23.5 and Median = 5
According to the question, the given set of values for the calculation of mean and median is as follows:
Values: = (-6, 3, 3, 3, 3, 5, 6, 6, 8, 10)
After eliminating -6 from the given set of values:
Values: = (3, 3, 3, 3, 5, 6, 6, 8, 10)
Now the median is the middle tern from the given set of the values:
Median = 5
And mean is : 3 + 3 + 3 + 3 + 5 + 6 + 6 + 8 + 10 / 2 = 47/2 = 23.5
Hence, the correct answer is median = 5 and mean = 23.5
What is mean and median?
The mean is the average value of the given set of the data. It is the addition of all the values and later divide it by two. Similarly, median is the middle value from the set of values provided it should be arranges in the order ascending to descending.
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Solve each system.
4y = 2x , 2x + y = (x/2) + 1
After solving each system, 4y = 2x , 2x + y = (x/2) + 1 , the values of x and y are calculated to be 0.5 and 0.25 respectively.
The first equation, 4y = 2x is a linear equation whereas the second equation, 2x + y = (x/2) + 1 is considered a rational equation as it contains a fraction.
By rearranging the linear equation, the value of x can be found to be,
4y = 2x
x = 4y ÷ 2
x = 2y
Putting the calculated value of x in the rational equation,
2x + y = (x/2) + 1
2(2y) + y = (2y/2) + 1
4y + y = y + 1
Rearranging,
4y + y - y = 1
4y = 1
y = 1/4 = 0.25
To solve for x, put y = 0.25 in the linear equation as follows,
4y = 2x
4(0.25) = 2x
1 = 2x
x = 1/2 = 0.5
Thus the value of x and y in these systems are calculated to be 0.5 and 0.25 respectively.
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Determine whether \triangle X Y Z is an acute, right, or obtuse triangle for the given vertices. Explain.
X(1,2), Y(4,6), Z(6,6)
The triangle having vertices X(1,2), Y(4,6), Z(6,6) is obtuse.
According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:
acute if [tex]c^{2} < a^{2} + b^{2}[/tex]obtuse if [tex]c^{2} > a^{2} + b^{2}[/tex]right if [tex]c^{2} = a^{2} + b^{2}[/tex]XY = [tex]\sqrt{(4-1)^{2} + (6 - 2)^{2} }[/tex]
∴ XY = 5
YZ = [tex]\sqrt{(6 - 4)^{2} + (6 - 6)^{2} }[/tex]
∴YZ = 2
ZX = [tex]\sqrt{(6 - 1)^{2} + (6 - 2)^{2} }[/tex]
∴ ZX = 6.4
∴The longest side is ZX = 6.4
Hence, a = XY, b = YZ and c = ZX;
Consider [tex]a^{2} + b^{2}[/tex]:
= [tex]XY^{2}[/tex] + [tex]YZ^{2}[/tex]
= [tex]5^{2} + 2^{2}[/tex]
= 29.
Now consider [tex]c^{2}[/tex]:
= [tex]6.4^{2}[/tex]
= 40.96.
Thus, [tex]c^{2} > a^{2} + b^{2}[/tex]
Hence, the triangle is obtuse.
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a rectangular prism has a volume of 125 cubid inches. its width is four times its lenght. its height is one-fourth the lenght. what are the dimensions of the prism? (Please help me)
A rectangular prism has a volume of 125 cubid inches. its width is four times its lenght.
Given:
the volume of rectangular prism = 125 cubic inches
Let the length of the rectangular prism be 'x'.
width = 4x
height = x/4
volume =( x)(4x)(x/4)=125
x^3=125
x=5
Length=5
Hieght=5/4
Width=20
Rectangular prism:
In terms of geometry, a rectangular prism is a solid 3-dimensional object having six faces and a rectangular base. Rectangular prisms can be of two types, namely right rectangular prisms and non-right (oblique) rectangular prisms.
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what is monomial,binomial,trinomial and polynomial
Find the slope of the line that passes through the points (8, -2) and (-13, 7). Enter answer as a fraction
Answer:
[tex] \frac{ - 9}{21} [/tex]
then simplify
Step-by-step explanation:
Slope =
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Rise
(-2)-(7)=-9
Run
[tex]8 - ( - 13) = 21[/tex]
Answer: 3/-7
Step-by-step explanation:
y2-y1 over x2-x1 is slope. your parenthesis go in the order of (x,y)
8=x1 -2=y1 -13=x2 7=y2
7 - -2 = 9
-13 - 8 = -21
9/-21
simplify to get 3/-7
find the volume of this object.
PLEASE HURRY
Answer:
24 maybe?
Step-by-step explanation:
I think 24 because if you multiply all of them it gives you this answer.
Answer: Total volume= 71.21 in^3
Step-by-step explanation:
The volume of the sphere= (4/3)*π*(2^3) = 33.51 in^3
The volume of the cylinder= π*(2^2)*3 = 37.7 in^3
Total volume= 71.21 in^3
I NEED THIS ASAP
(4r–4)(r–1) solve and simplify
Answer: 4r2−8r+4
Step-by-step explanation:
(4r−4)(r−1)
=(4r+−4)(r+−1)
=(4r)(r)+(4r)(−1)+(−4)(r)+(−4)(−1)
=4r2−4r−4r+4
=4r2−8r+4
Hope u get it Correct <3
State whether sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
The ₋Law of Sines can be used to find an angle measure when given three side lengths.
Given statement 'The ₋Law of Sines can be used to find an angle measure when given three side lengths.' is False.
The correct statement is 'The ₋Law of cosines can be used to find an angle measure when given three side lengths.'
We know that an oblique triangle is a triangle which is either acute triangle or obtuse triangle but not a right triangle.
We know that the Law of Sines defines the relationship between the sides and angles of an oblique triangle.
And to use the Law of Sines we must know either two angles and one side of the triangle or two sides and one of the opposite angle to them (SSA).
But, the Law of Cosines is used to find the remaining parts of an oblique triangle.
This means, in case of the Law of Cosines when either the two sides and the angle included is given or the lengths of the three sides are given then we find the remaining angle measure.
Therefore, given statement 'The ₋Law of Sines can be used to find an angle measure when given three side lengths.' is False.
The correct statement is 'The ₋Law of cosines can be used to find an angle measure when given three side lengths.'
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Simplify
63 ÷ (7-4) X 2=
Answer: 63 ÷ (7-4) x 2=42
Step-by-step explanation:
Answer:
The answer is 42
Step-by-step explanation:
We can solve this by using Order of Operations
1. Solve whats inside the parentheses (7-4) =3
63÷3×2
2. Now solve from left to right
63÷3 =21
21 ×2= 42
And we get a final answer of 42.
Hope this helps!
What is an equation of the line that passes through the points (−2,5) and (−2,−8)?
Answer:
Y=5
Step-by-step explanation:
1) find gradient
2) find equation of line using the formula y-y1=m(x-x1) where m is the gradient.
SENSE-MAKING Determine whether ΔM N O ≅ ΔQ R S . Explain.
M(4,7), N(5,4), O(2,3), Q(2,5), R(3,2), S(0,1)
A translation maps one triangle onto the other. Each pair of corresponding sides has the same measure, so they are congruent. △MNO ≅ △QRS by SSS.
What exactly do you mean by congruent?
If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.Use the Distance Formula to find the lengths of.
MN , NO , OM
MN has end points M(4 , 7) And N( 5, 4 )
MN = [tex]\sqrt{ (x_{2} - x_{1}^{2}+ ( y_{2} - y_{1} )^{2}[/tex]
= [tex]= \sqrt{(1)^{2} + ( -3)^{2} }[/tex]
[tex]= \sqrt{ 1 + 9 }[/tex]
[tex]= \sqrt{10}[/tex]
NO has end points N(5, 4) and O(2, 3).
NO = √( 2 - 5 )² + ( 3- 4 )²
= √( - 3)² + ( -1)²
= √ 9 + 1 = √10
OM has end points O(2, 3) and M(4,7)
OM = √( 4 - 2 )² + ( 7 - 3 )²
= √ (2)² + ( 4 )²
= √20
Similarly, find the lengths of QR, RS , SQ
QR has end points Q(2, 5) and R(3, 2).
QR = √( 3 - 2)² + ( 2 - 5 )²
= √(1)² + ( -3)²
= √ 1 + 9
= √10
RS has end points R(3, 2) and S(0, 1).
RS = √( 0- 3)² + ( 1 - 2 )²
= √( -3)² + (-1)²
= √9 + 1 = √10
SQ has end points S(0, 1) and Q(2, 5).
SQ = √ ( 2 - 0 )² + ( 5 - 1 )²
= √ 4 + 16 = √20
So, MN ≅ QR , NO ≅ RS and OM ≅ SQ
A translation maps one triangle onto the other. Each pair of corresponding sides has the same measure, so they are congruent. △MNO ≅ △QRS by SSS.
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the difference between the areas of the figures is less than 2
Answer:
Step-by-step explanation:
Complete the pattern:
2 +
20 +
200 +
2,000 +
= 6
= 60
= 600
= 6,000
Answer:
2+4=6
20+40=60
200+400=600
2,000+4,000=6,000
Step-by-step explanation:
Evaluate a +6 for a = 10.
06
60
16
Answer:
16
Step-by-step explanation:
a+6 where a=10
You'd substitute the number 10 where the variable 'a' is.
(10)+6
Then, you'd solve the expression.
10+6=16.
Thus, the answer is 16.
Hope this helps.
Simplify the expression 9x-4-12x-3
Answer:
-3x - 7 is the answer
Step-by-step explanation:
your welcome
===================================================
[tex]9x-4-12x-3\\\\\\9x-12x-4-3\\\\\\-3x-7[/tex]<--------- SOLUTION=====================================================
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[tex]\textcopyright ELIZA[/tex]
Given the figure below, find the values of x and y.
Answer:
x= 8, z= 118
Step-by-step explanation:
To find x, solve the equation with the one unknown x given by supplementary angles definition.
Supplementary angles sum up to 180° there for
8x +54 + 7x +6 = 180, group like terms
8x + 7x = 180 -54-6, combine like terms
15x = 120, divide both sides by 15
x = 8
To find z, solve for z the equation given by vertical angles definition.
Vertical angles are congruent there for
8x +54 = z, substitute x for 8
8·8 +54 = z, multiply then add
z = 118
Based on the definition of supplementary angles, x = 8; z = 118
How to Apply the Definition of Supplementary Angles?Based on the definition of supplementary angles we have:
7x + 6 + 8x + 54 = 180
Solve for x
15x + 60 = 180
15x = 180 - 60
15x = 120
x = 120/15
x = 8
z = 8x + 54 (vertical angles)
Plug in the value of x
z = 8(8) + 54
z = 118
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You have 7 quarters, 6
dimes, 4 nickels and 25
pennies. How much money
do you have?
Answer:2.80
Step-by-step explanation:
Answer:
$2.80
Step-by-step explanation:
One quarter is worth 25 cents. 4 quarters is a dollar.
0.25 x 7 = $1.75
----------------
One dime is worth 10 cents
0.10 x 6 = 0.60 cents
----------------
One nickel is worth 5 cents
0.5 x 4 = 20 cents
One penny is worth 1 cent
It's rather simple here. 25 pennies is 25 cents
----------------
Now, you have to add all the numbers together.
1.75 + 0.60 + 0.20 + 0.25 = 2.80
Add the correct label and your final answer is $2.80
--------------------------------------------------------------------------
Hope this helps!
Have a great day and God bless! :)
70. The histogram below shows the heights of 300 ran-
domly selected high school students. Which of the
following is the best description of the shape of the
distribution of heights?
I
(a) Roughly symmetric and unimodal
(b) Roughly symmetric and bimodal
(c) Roughly symmetric and multimodal
(d) Skewed to the left
(e) Skewed to the right
The histogram is unimodal as it has only one peak point and roughly symmetric because both sides of the histogram when flipped across the axis of symmetry does not overlap completely.
What is Histogram?Histogram is a diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.
Given is histogram that shows heights of 300 randomly selected high school students.
The shape that best describes the distribution of heights is - Roughly symmetric and unimodal. Unimodal histograms have only one peak in the distribution. It can be seen from the image that the graph has only one peak point. However, if we check the symmetry of this histogram by drawing the axis of symmetry, then both sides will not overlap completely. So it is Roughly symmetric.
Therefore, the histogram is unimodal as it has only one peak point and roughly symmetric because both sides of the histogram when flipped across the axis of symmetry does not overlap completely.
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what is 4+7-2+9 im not able to figure it out
Answer:
18
4+7-2+9
11-2=9+9=18
Answer:
18
Step-by-step explanation:
Since according to PEMDAS, the value of when addition and subtraction is used is the same. Basically, in this equation you should do it in order. So, 4+7=11. Then 11-2 is 9. 9+9 is 18. So, the answer is 18.
After 8 years, what is the total amount of a compound interest investment of $25,000 at 3% interest, compounded quarterly?
The correct answer is: D) $31,752.78
Explanation:
The formula for compound interest is:
where A is the total amount, p is the principal invested, r is the interest rate as a decimal number, n is the number of times per year the interest is compounded, and t is the number of years.
The principal in this problem is 25,000; the interest rate is 3% = 3/100 = 0.03; the number of times the interest is compounded is 4; and the number of years is 8:
Solve the following system of equations for all three variables.
-x+ 5y + 4z = 7
x+10y + 4z = -1
x + 8y + 4z = -5
Answer: 1. x=−7+5y+4z, y=7/5+x/5−4z/5, z=7/4+x/4−5y/4
2. x=−1−10y−4z y=−1/10−x/10−2z/5 z=−1/4−x/4−5y/2
3. x=−5−8y−4z y=−5/8−x/8−z/2 z=−5/4−x/4−2y
Step-by-step explanation:
Write the expression as a number in scientific notation.
7.2 x 107
7.2 x 104
6.4 x 107
6.4 x 104
Answer:
7.2 × 10⁷ = 72,000,000
7.2 × 10⁴ = 72,000
6.4 × 10⁷ = 64,000,000
6.4 × 10⁴ = 64,000
*image* = 64,000
Step-by-step explanation:
Solve the equation.
( 8 × 10² ) ( 3.2 × 10⁵ )
4 × 10³
Step 1: Solve the parenthesis
( 8 × 10² ) ( 3.2 × 10⁵ )
↓ ↓
= (800) = (320,000)
Step 2: Solve for the denominator
4 × 10³
↓
= 4,000
Step 3: Plug in the answers & solve
1. ( 800 ) ( 320,000 )
2. 4,000
1. 800 × 320,000
↓
= 256,000,000
2. 256,000,000
4,000
↓
256,000,000 ÷ 4,000
↓
= 64,000
I hope this was helpful! (✿◠‿◠)
Have a blessed day!
Write an equation in slope-intercept form for the line described.
passes through (0,7), parallel to y=4 x-19
The equation in slope-intercept form for the line that passes through (-0,7), parallel to y = 4x-19 is y = 4x + 7.
The slope intercept form of a line is:-
y = mx + b
Where:-
m represents the slope of a line
b represents the y-intercept of a line
x and y represent the ordered pairs (x,y) throughout a line
We are given the line y = 4x-19 is parallel to the line whose equation we have to find.
Hence,
slope of the line = 4 = slope of the given line
Also, (0,7) passes through the line,
Hence,
7 = 4*(0) + b
7 = 0 + b
b = 7
Hence, the equation of the line in slope intercept form is y = 4x + 7.
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Is division of integers commutative? Give an example supporting your answer.
Answer:
No. When we change the places of the number, the results also changes
Step-by-step explanation:
4 / 2 = 2
2 / 4 = 0.5
