As the length of the sides AD ≠ BC the given quadrilateral ABCD is not a parallelogram.
What approach proves the lines are parallel?To prove that the given lines are parallel we have to determine their slope if the slope if equal then the lines are parallell.
We know that a quadrilateral is a parallelogram when opposite lines are of the same length and opposite lines are parallel to each other.
Given a quadrilateral, ABCD has coordinates A(−6,−1), B(−5,2), C(−1,−5), and D (0,−2).
∴ The quadrilateral ABCD t be a parallelogram length of AB = DC and length of AD = BC.
We know the distance formula is [tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
So, lenght of AB = [tex]\sqrt{ (-5+6)^2 + (2 + 1)^2[/tex].
AB = [tex]\sqrt{ 1 + 9}[/tex].
AB = [tex]\sqrt{10}[/tex] units.
Lenght of DC = [tex]\sqrt{(0+1)^2 + (-2+5)^2}[/tex].
DC = [tex]\sqrt{10}[/tex] units.
Now length of AD = [tex]\sqrt{0+6)^2 + (-2+1)^2[/tex].
AD = [tex]\sqrt{ 37}[/tex] units.
Length of BC = [tex]\sqrt{(-1+5)^2 + (-5+2)^2[/tex].
BC = [tex]\sqrt{25}[/tex].
BC = 5 units.
As BC ≠ AD therefore quadrilateral ABCD is not a parallelogram.
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How to find the slope intercept form for the equation of the line through (5,1) and (3,-7)
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{5}}} \implies \cfrac{-7 -1}{3 -5} \implies \cfrac{ -8 }{ -2 }\implies 4 \\\\\\ \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-\stackrel{y_1}{1}=\stackrel{m}{4}(x-\stackrel{x_1}{5})[/tex]
[tex]y-1=4x-20\implies y=4x-19\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
2. Gwen uses 3 teaspoons of sweetener for every 5 cups of iced tea. How many teaspoons of sweetener should she
add to 30 cups of iced tea if she wants the same flavor?
A. 9
B. 18
C. 28
D. 50
Answer:
B: 18
Step-by-step explanation:
3 t for every 5 c
30/5 = 6, 6 groups of 5
6 x 3 (3 for every 5 cups, but x by the 6 groups)
6 x 3 = 18.
At how many points does the graph of the function below intersect the x-
axis?
y = 4x²-9x+9
O A. 1
OB. 2
О с. о
SUBMIN
The points does the graph of the function below intersect the x-axis equation is= y = 4x²-9x+9 is C) - 0
because this equation does not have any x intercept
Y = 4x² -9x +9 is a quadratic equation
To know at what point this equation intersect x axis we have to put the value of y= 0
Y = 4x²2 -9x +9
0 = 4x² -9x + 9
4x²-9x+9=0
This equation can be solved using quadratic formula
We need to find the value of discriminant
D= √(b²-4ac)
D=√((-9)²-4(4)(9))
D= √(81-144)
D=√(-63)
As the value of discriminate is not a real number so reel roots does not exit and hence this equation does not have any x intercept
Hence, option c is correct because this equation does not have any x intercept
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Select all equations that are equivalent to -8x - 6 15. 2 - (Select all that apply.) 4x+3= 15 -4x-3=15 8x+6=30 (-4x - 3) = 15 — − ½ ( 8x + 6) = 15 -
I need help with this algebra problem
The mean of all ninth grader's scores in the city is 80.32
Calculating meanFrom the question, we are to determine the mean score for all ninth graders in the city
From the given information,
Mariner High school
Mean score is 75 and the frequency is 265
Everett High school
Mean score is 90 and the frequency is 326
Jackson High school
Mean score is 69 and the frequency is 154
Thus,
The mean score for all ninth graders
= (265×75 + 326×90 + 154×69)/ (265 + 326 + 154)
= (19875 + 29340 + 10626)/745
= 59841/745
= 80.32
Hence, the mean is 80.32
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In a particular parking lot with 24 cars in it, 18 are blue. What fraction of the cars in the parking lot are blue?
Answer:
3/4
Step-by-step explanation:
If you do a ratio, 18 blue cars to 24 total cars, that would be 18:24. If you simplify that, then you would be left with 3:4. So for every 4 cars, 3 are blue. So 3/4 of the cars in the parking lot are blue.
evaluate this please
Answer:
32⅘
(using indices)
32 = 2⁵
= 2⁵ × 1⅘
= 2²⁰
⁵
= 2⁴ = 16
A water tank measures 5 in. by 6 in. by 6 in. If each dimension of the tank were doubled, approximately how many more gallons can the larger tank hold? (Hint : There are 231 cubic inches in 1 gallon.)
Answer:
6.23376623 gallons
Step-by-step explanation:
5×2 is 10
6×2 is 12
10x12x12 is 1440 inches
1440/231 is 6.23376623 gallons
round if you need to
In a particular class of 26 students , 13 are men. What fraction of the students in the class are women?
Answer:
1/2
Step-by-step explanation:
Since 13+13= 26 we know that 13 or 1/2 are girls
If Samantha moved point A 9 units down and 6 units to the right, at what point would she end up?
Based on the transformaion of point A, the coordinate of the point she would end up is (3, -4)
How to determine the point she would end up?The complete question is added at the end of this solution
From the question, we have the following point
Starting point = (-3, 5)
The movement is given as
9 units down and 6 units to the right
The above can be represented mathematically as
(x, y) = (x + 6, y - 9)
When the above translation is applied on point A, we have the following equation
A' = (-3 + 6, 5 - 9)
Evaluate the sum and he difference in the above equation
A' = (3, -4)
Hence, the coordinate of the point she would end up is (3, -4)
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Complete question
The coordinates (the x- and y-values) for point A are (−3, 5).
If Samantha moved point A 9 units down and 6 units to the right, at what point would she end up?
Match each number to a point on the number line.
Answer:
I dont understand it bc the pic is blurry
Step-by-step explanation:
Please mark Branliest
Drag the numbers below to put them in order from least to greatest: 1.393 1.3 1.43 1.47 1.301 1.45
The order of the number from least to greatest is 1.30, 1.301, 1393, 1.43, 1.45, 1.47.
What is the order of the numbers?
Decimal is used to denote integers and non-integers. The integers are separated by non-integers using a decimal point. An example of a decimal is 1.393.
The place value of 1.393 is
1 - unit value 3 = tenth value 9 = hundredth value 3 = thousandth valueThe further away a number is from zero on the number line, the higher the value of the number.
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Four friends went scuba diving today. Ali dove 70 feet, Tim went down 50 feet, Carl dove 65 feet, and Brenda reached 48 feet below sea level. Write the 4 friends’ names in order from the person whose depth was closest to the surface to the person whose depth was the farthest from the surface.
The orders from the person whose depth was closest to the surface to the person whose depth was the farthest from the surface as:
Brenda < Tim < Carlton < Ali
Ascending order is a method of arranging numbers from smallest value to largest value. The order goes from left to right. Ascending order is also sometimes named as increasing order. For example, a set of natural numbers are in ascending order, such as 1, 2, 3, 4, 5, 6, 7, 8… and so on.
If the information is sorted from highest to lowest, it is said to be in descending order. For example 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 are arranged in descending order. In other words, if the numbers are arranged from the largest to the smallest number, it is said to be in descending order.
We can write, four friends went scuba diving today,
Ali dove = 70 feet,
Tim went down = 50 feet,
Carl dove = 65 feet,
Brenda reach = 48 feet below sea level.
To determine the order from the person whose death was closest to the surface to the person whose death was the farthest from the surface.
Arrange in ascending order of distance from sea level.
Brenda < Tim < Carlton < Ali
48feet < 50 feet < 65 feet < 70 feet
Therefore,
The order from the person whose depth was closest to the surface to the person whose depth was the farthest from the surface as:
Brenda < Tim < Carlton < Ali.
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For the linear function f (x) = mx + b, f (-3) = 23 and f (2) = -7.
Find m and b.
Answer:
b = 8 , m = - 5
Step-by-step explanation:
For this question we can use simulteanous equations to solve for m and b.
We first come up with 2 equations.
Given the first condition:
23 = -3m + b
b - 3m = 23 (Equation 1)
Now the Second Condition:
-7 = 2m + b
b + 2m = -7 (Equation 2)
Now, we will use Equation 1 - Equation 2 to eliminate b to solve for m.
-3m - (+2m) = 23 - ( - 7)
- 5m = 30
m = 30 ÷ -6 = -5
Now we substitute m into Equation 1 to solve for b.
b - 3(- 5) = 23
b + 15 = 23
b = 23 - 15 = 8
Answer: m=-6 b=5
Step-by-step explanation:
f(x)=mx+b
f(-3)=23 f(2)=7
[tex]\displaystyle\\\left \{ {{23=(m)(-3)+b} \atop {-7=(m)(2)+b}} \right. \ \ \ \ \left \{ {{23=-3m+b\ \ \ \ (1)} \atop {-7=2m+b\ \ \ \ (2)}} \right.[/tex]
Subtract equation (2) from equation (1):
-30=5m
Divide both parts of the equation by 5:
-6=m
Thus, substitute m=-6 in (2):
-7=(-6)(2)+b
-7=-12+b
-7+12=-12+b+12
5=b
Hence,
y=-6x+5
Which expression is equal to (-3- i)+ (5 +6i)?
A.2 +5i
B. -7
C.-4+11i
D.77
Answer:
A
Step-by-step explanation:
[tex](-3-i)+(5+6i) \\ \\ =-3-i+5+6i \\ \\ =2+5i[/tex]
Can’t figure it out I need help on how to do this
Answer: 11
Step-by-step explanation:
the answer is 11 all it is asking for is finding the mode which simply means the highest group of repeated numbers
The mode of the frequency distribution based on the table is age 11 with 12 students.
What is the mode?Mode can be defined as the most occurring value in a statistical distribution. It is also the most repeated number.
According to the table given;
Age 9 = 3 students
Age 10 = 10 students
Age 11 = 12 students
Age 12 = 1 students
Based on this information, the age with the most number of students is age 11.
Therefore, the mode is 11
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Find the equation of the line through (7,−2) which is parallel to the line y=−x−4.
Give your answer in the form y=mx+b.
Answer:
y = -x + 5
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line we need to find is -1. Substituting into point-slope form, we get the equation to be
[tex]y+2=-(x-7)[/tex]
which rearranges into slope-intercept form as follows:
[tex]y+2=-x+7 \\ \\ y=-x+5[/tex]
Answer:
y=-x+5
Step-by-step explanation:
Needed help asap please and thank you so much !
Step-by-step explanation:
based on the story told I expected completely different questions.
but for the actually asked question the whole thing about gaining our not gaining weight is competent irrelevant. ignore it.
so, all we need to do is looking at the row totals.
27.4% of the participants took 1 vitamin.
49.5% of the participants took more than 1 vitamin.
so, 49.5% + 27.4% = 76.9% of all participants are taking vitamins in some form.
therefore, the second answer option is correct.
Is −5 greater than, less than, or equal to |−5|?
Answer: Less than
Step-by-step explanation:
The symbols || indicate absolute value.
Absolute value changes a number into it's distance from 0 on the number line. As such, |27| = 27, but |-9| = 9.
Thus, |-5| = 5, and 5 > -5
|-5| > -5
Hope it helps
Answer:
Less than
Step-by-step explanation:
-5 is negetive 5 and |−5| means "positive 5", or just 5
what is the actual awnser to find the length x 14cm and 7 cm
Hi could u ask the question a bit clearer?
Perimeter of the computer chip. Length 7.18×10⁻⁷ meters, width 3.4×10⁻⁹ meters
Perimeter of computer chip = 14.428 * ( [tex]10^{-7}[/tex] ) meters .
Given : length = 7.18×10⁻⁷ meters
breadth = 3.4×10⁻⁹ meters
To find = perimeter of computer chip
Formula for perimeter of a rectangle :
Perimeter = 2 ( length + breadth )
Calculations :
Perimeter = 2 [ ( 7.18×10⁻⁷ ) + ( 3.4×10⁻⁹ ) ]
On simplifying ,
= 2 [ [tex]10^{-7}[/tex] ( 7.18 + 0.034 )
= 2 [ [tex]10^{-7}[/tex] ( 7.214 ) ]
= 14.428 * ( [tex]10^{-7}[/tex] ) meters
Hence , perimeter = 14.428 * ( [tex]10^{-7}[/tex] ) meters .
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A cube-shaped shed has 6-foot high walls. If all the shed's walls are painted (not including the floor or ceiling), how much area will be painted?
The area that would be painted will be 144 square feet
Calculating surface areaFrom the question, we are to determine the area of the cube-shaped shed that was painted
From the given information,
The cube-shaped shed has 6-foot high walls
From the formula for the surface area of a cube,
Surface area = 6s²
Where s is the measurement of a side
A cube has six sides
Since, the floor and ceiling are not painted,
The area of the shed that was painted will be
Surface area painted = 4s²
s = 6 feet
Thus,
Surface area painted = 4 × 6²
Surface area painted = 4 × 36
Surface area painted = 144 square feet
Hence, the area that would be painted will be 144 square feet
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How many solutions does this equation have? 6(x + 1) + 5 = 13 - 2 + 6x
Answer:
Step-by-step explanation:
So you start out with this equation
6(x+1)+5=13-2+6x
you simplify it down to get
6x+11=6x+11 if they are the same then there fore you answer is
Infinite solutions
Drag the tiles to the boxes to form correct pairs.
Multiply the pairs of numbers, and match them with their products.
The expressions matched with their correct pairs is
(-8)(-2.2) → 17.6
(-3.4)(5) → -17
(-9.5)(-2) → 19
(3.8)(-5) → -19
From the question, we are to match the tiles to the boxes to form correct pairs
To do this, we will simplify the expressions
(-8)(-2.2)Multiplying
-8 × -2.2
= 17.6
(-3.4)(5)Multiplying
-3.4 × 5
= -17
(-9.5)(-2)Multiplying
-9.5 × -2
= 19
(3.8)(-5)Multiplying
3.8 × -5
= -19
Hence, the expressions matched with their correct pairs is
(-8)(-2.2) → 17.6
(-3.4)(5) → -17
(-9.5)(-2) → 19
(3.8)(-5) → -19
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After a storm, Michael measured 6 inches of
snow. What is this amount as a decimal?
Answer:
0.5 feet of snow
Step-by-step explanation:
6 inches is half of a foot because 1 foot = 12 inches.
6 inches / (12 inches / 1 foot) = 0.5 feet of snow
The mean life of a tire is 30,000 km. The standard deviation is 2000 km.
Then, 68% of all tires will have a life between ___________ km and __________ km.
Answer:between 28000 km and 32000 km
Step-by-step explanation:
4. Stanley quilts a square rug that has an area of 400 square inches. What is the length of each side of the
rug?
A. 14 inches
B. 16 inches
C. 18 inches
D. 20 inches
Answer:
D. 20 inches
Step-by-step explanation:
Area = length * width
20 * 20 = 400 square inches
20 inches
Find the value of each follow expression use a title diagram or a number line to help you 3(4)
The value of the expression 3(4) can be expressed as 12 with the help of a title diagram or a number line and the explanation for this same can be done easily if we take into consideration a number line.
What does the math number line mean?A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It can also be assumed that every point present on a number line corresponds to a real number, and that every real number also corresponds to a point.
To solve this expression, we can deduce as follows:
As per the number line, for the expression 3(4).
Since it is absolutely positive, thus we will get the final answer in positive that means on the side of the number line lying right to zero.
To express this expression,
3 (4) means we have to move towards the right side of the number line from zero for 4 times and each time covering a total of 3 units each.
Thus, we start from zero, first time we reach 3 then 6, then 9 and then finally 12.
Thus, the value of the expression is received as 12.
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For a recent year, 34 more Democrats than Republicans represented a country. If the total number of representatives of the country from these two parties was 484, find the number of representatives from each party.
In linear equation the number of Republicans are 225 and the number of Democrats are 259 .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Let Republicans = x
then Democrats = x + 34
x + x + 34 = 484
2x + 34 = 484
2x = 484 - 34
2x = 450
x = 450/2
x = 225
x + 34 = 225 + 34 ⇒ 259
Therefore ,the number of Republicans are 225 and the number of Democrats are 259 .
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. Jason pays $3.60 for 2 bottles of
water. What is the unit price of each bottle?