Answer:
(a+b)(a+b-c)
Step-by-step explanation:
Formula:
(a+b)² = a² + b² + 2ab
Therefore,
a²+b²+2ab -ac-bc
= (a+b)² -ac-bc
Now take -c common in ac and bc
(a+b)² -c(a+b)
now take (a+b) common in both terms
(a+b)(a+b-c)
.
Hope it helps
The value of the equation is A = ( a + b ) ( a + b - c )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = a² + 2ab + b² - ac - bc be equation (1)
On simplifying the equation , we get
( a + b )² = a² + 2ab + b²
So ,
A = ( a + b )² - ac - bc
Taking the common factor in the equation , we get
A = ( a + b )² - c ( a + b )
Taking the common factor in the equation , we get
A = ( a + b ) ( a + b - c )
Hence , the equation is A = ( a + b ) ( a + b - c )
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∠MNQ and ∠PNR are vertical angles. What is the value of x?
Answer:
Step-by-step explanation:
I don’t know the answer
The value of x such that ∠MNQ and ∠PNR are vertical angles is 40
How to determine the value of x?The given parameters are:
MNQ = 3x - 6
PNR = 114
Vertical angles are equal.
So, we have:
3x - 6 = 114
Add 6 to both sides
3x = 120
Divide both sides by 3
x = 40
Hence, the value of x is 40
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PLZZZ HELP MEEE!!!!!!!!!!
Answer:
Step-by-step explanation:
Graph shown in the attachment,
- Since every value of x corresponds to a distinct value of y, so the graph represents a function.
- Every input value of x of the table has a output value of y, therefore, it's a function.
- In the set of ordered pairs (5, 8) and (5, 2), input value x = 5 has two output values for y,
y = 8 and y = 2
Therefore, it's not a function and (5, 8) should be changed to make the relation a function.
can someone do this ???
You get dressed in the morning without looking at the colours of the clothes you choose. Your shirts are white or blue, your pants are black, red, or yellow, and your shoes are brown or black. How likely are you to choose a white shirt, black pants, and brown shoes?
Answer:
add up all the colors
Step-by-step explanation:
If A(4 -6) B(3 -2) and C (5 2) are the vertices of a triangle ABC fine the length of the median AD from A to BC. Also verify that area of triangle ABD = Area of triangle ACD
Answer:
a) The median AD from A to BC has a length of 6.
b) Areas of triangles ABD and ACD are the same.
Step-by-step explanation:
a) A median is a line that begin in a vertix and end at a midpoint of a side opposite to vertix. As first step the location of the point is determined:
[tex]D (x,y) = \left(\frac{x_{B}+x_{C}}{2},\frac{y_{B}+y_{C}}{2} \right)[/tex]
[tex]D(x,y) = \left(\frac{3 + 5}{2},\frac{-2 + 2}{2} \right)[/tex]
[tex]D(x,y) = (4,0)[/tex]
The length of the median AD is calculated by the Pythagorean Theorem:
[tex]AD = \sqrt{(x_{D}-x_{A})^{2}+ (y_{D}-y_{A})^{2}}[/tex]
[tex]AD = \sqrt{(4-4)^{2}+[0-(-6)]^{2}}[/tex]
[tex]AD = 6[/tex]
The median AD from A to BC has a length of 6.
b) In order to compare both areas, all lengths must be found with the help of Pythagorean Theorem:
[tex]AB = \sqrt{(x_{B}-x_{A})^{2}+ (y_{B}-y_{A})^{2}}[/tex]
[tex]AB = \sqrt{(3-4)^{2}+[-2-(-6)]^{2}}[/tex]
[tex]AB \approx 4.123[/tex]
[tex]AC = \sqrt{(x_{C}-x_{A})^{2}+ (y_{C}-y_{A})^{2}}[/tex]
[tex]AC = \sqrt{(5-4)^{2}+[2-(-6)]^{2}}[/tex]
[tex]AC \approx 4.123[/tex]
[tex]BC = \sqrt{(x_{C}-x_{B})^{2}+ (y_{C}-y_{B})^{2}}[/tex]
[tex]BC = \sqrt{(5-3)^{2}+[2-(-2)]^{2}}[/tex]
[tex]BC \approx 4.472[/tex]
[tex]BD = CD = \frac{1}{2}\cdot BC[/tex] (by the definition of median)
[tex]BD = CD = \frac{1}{2} \cdot (4.472)[/tex]
[tex]BD = CD = 2.236[/tex]
[tex]AD = 6[/tex]
The area of any triangle can be calculated in terms of their side length. Now, equations to determine the areas of triangles ABD and ACD are described below:
[tex]A_{ABD} = \sqrt{s_{ABD}\cdot (s_{ABD}-AB)\cdot (s_{ABD}-BD)\cdot (s_{ABD}-AD)}[/tex], where [tex]s_{ABD} = \frac{AB+BD+AD}{2}[/tex]
[tex]A_{ACD} = \sqrt{s_{ACD}\cdot (s_{ACD}-AC)\cdot (s_{ACD}-CD)\cdot (s_{ACD}-AD)}[/tex], where [tex]s_{ACD} = \frac{AC+CD+AD}{2}[/tex]
Finally,
[tex]s_{ABD} = \frac{4.123+2.236+6}{2}[/tex]
[tex]s_{ABD} = 6.180[/tex]
[tex]A_{ABD} = \sqrt{(6.180)\cdot (6.180-4.123)\cdot (6.180-2.236)\cdot (6.180-6)}[/tex]
[tex]A_{ABD} \approx 3.004[/tex]
[tex]s_{ACD} = \frac{4.123+2.236+6}{2}[/tex]
[tex]s_{ACD} = 6.180[/tex]
[tex]A_{ACD} = \sqrt{(6.180)\cdot (6.180-4.123)\cdot (6.180-2.236)\cdot (6.180-6)}[/tex]
[tex]A_{ACD} \approx 3.004[/tex]
Therefore, areas of triangles ABD and ACD are the same.
I need help urgently
Solve the problem by entering and solving equation.
A rectangular picture frame has a perimeter of 56 inches. The height of the frame is 16 inches. What is the
width of the frame?
The solution is
+W)=
The width of the frame is
inches.
Answer:
12 inches
Step-by-step explanation
The perimeter of a rectangle is the sum of each of the sides. So, it would be Perimeter= width+width+height+height. Let's make x as the width as the variable. We already know the value of the perimeter and the height. We can then substitute these values in the above equation.
So, that would be 56=x + x +16 +16
Then we would solve for x. First combine like terms.
56=2x+32
Then, subtract 32 from each side.
24=2x
Finally, divide by 2 on both sides to get the answer.
x=12
Answer:
12 inches
Step-by-step explanation:
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The distance it takes a truck to stop can be modeled by the function Image description d = stopping distance in feet v = initial velocity in miles per hour f = a constant related to friction When the truck's initial velocity on dry pavement is 40 mph, its stopping distance is 138 ft. Determine the value of f, rounded to the nearest hundredth.
Answer: 0.39
Step-by-step explanation:
We are required to determine the the value of f, rounded to the nearest hundredth
The value of f, rounded to the nearest hundredth is 0.39
Given function:
[tex]d(v) = \frac{2.15 {v}^{2} }{64.4f} [/tex]
Where,
d = stopping distance in feet
v = initial velocity in miles per hour
f = a constant related to friction
When
v = 40 mph
d = 138 ft
f = ?
[tex]d(v) = \frac{2.15 {v}^{2} }{64.4f} [/tex]
[tex]138= \frac{2.15 {(40)}^{2} }{64.4f} [/tex]
138(64.4f) = 2.15(1600)
8,887.2f = 3440
f = 3440 / 8,887.2
f = 0.3870735439733
Approximately to the nearest hundredth f = 0.39
Therefore, the value of f, rounded to the nearest hundredth is 0.39
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On a road trip you see a sign "350 km to Indianapolis". About how many hours will it
take you to drive to Indianapolis if you are traveling at 68 mi/h (1 mile 1.61 km).
Round your answer to the nearest hundredth.
Answer: 3.20 hours
Step-by-step explanation:
Hi, to answer this question, first we have to convert the kilometers into miles:
Since: 1 mile = 1.61 km
For 350km:
350 /1.61 = 217.39 miles
Next, we have to apply the next formula:
Time = distance / speed rateReplacing with the values given:
Time = 217.39 mi / 68 mi/h = 3.20 hours
Feel free to ask for more if needed or if you did not understand something
Dave bought jeans at a store. • The jeans had an original price of $45.50 • The jeans were discounted 30% from the original price. • An 8% sales tax was added to the discounted price. What amount did Dave pay for the jeans?
Answer:$35.49
Step-by-step explanation:
1. Get sales tax from the original price
8/100*45.50=$3.64
2. Get the price after the discount which is 70% of the original price
45.50*70/100 = 31.85
3. Add the sales tax to the new price to get the amount paid
31.85+3.64= $35.49
Which of the following equations represents a proportional relationship?
A: y = 3x
B: y = 1/2x + 1
C: y = x/3 + 4
D: y = 2/5 - 5
Answer:
a
Step-by-step explanation:
y=3x
thus, a proportional relationship equation is y=kx .Where k is constant
Vicente has a prism- like water tank whose base area is 1.2 square meters. He bought 6 goldfish at the store and the store owner told him to make sure their density in the tank isn’t more than 4 fish per cubic meter. What is the lowest possible height so the fish aren’t too crowded
Answer: 1.25 m
Step-by-step explanation:
Area of base = 1.2 m²
Number of gold fish = 6
Density of the tank should be = 4 fish/m³
Height of the tank= ?
4 fish = 1 m³
6 fish = 6/4 = 1.5 m³
Volume required for 6 fish is 1.5 m³
V = area of base x height (h)
1.5 = 1.2 x h
h = 1.25 m
Hence, height of the tank is equal to 1.25 m.
On a coordinate plane, a straight line with a negative slope, labeled f of x, crosses the y-axis at (0, 4), and the x-axis at (4, 0). Which is true regarding the graphed function f(x)? f of 0 = 3 f of 5 = negative 1 f of 3 = 2 f of 2 = negative 2
Answer:
f of 5 equals negative 1
Step-by-step explanation:
equation- f(x) = -x + 4
f(5) = -5 + 4
f(5) = -1
Answer:
f(5)=-1
Step-by-step explanation:
What is the common ratio Between successive terms in the sequence? 1.5,1.2,0.96,0.768
Answer:
0.8
Step-by-step explanation:
0.768/0.96= 0.8
0.96/1.2 =0.8
Pls help me!!!!! I'm dead!!!!! I have like 40 of these things. Pls ;)
Answer:
4 and 5 are coefficients the rest are terms
Step-by-step explanation:
coefficients are the numbers not the letters
Answer:
Coefficient: 4, 5Term: 4p, 5b, 8cStep-by-step explanation:
The terms are the elements of the sum:
5b, 8c, 4p
The coefficients are the constant multipliers:
5, 8, 4
___
In your list of items to "drag and drop", you have ...
Coefficient: 4, 5
Term: 4p, 5b, 8c
The probability that a biased coin will land on Heads is 0.43
Azmol is going to throw the coin 600 times.
Work out an estimate for the number of times the coin will land on Tails.
Answer:
[tex]342[/tex]
Step-by-step explanation:
The probability of heads landing is 0.43.
The probability of tails landing is 1-0.43=0.57.
Azmol throws the coin 600 times, so:
[tex]600 \times 0.57[/tex]
[tex]=342[/tex]
Vertical angles are always adjacent.
True False
Answer:
False
Step-by-step explanation:
Vertical angles are opposite to each other, so they are not adjacent.
This recipe makes 5 portions of porridge. Complete the amount of each ingredient that is needed to make just 4 portions. Recipe: Serves 5 250 g oats 1.2 l milk 90 g sugar
Answer:
200g oats
0.96l milk
72g sugar
Step-by-step explanation:
250/5 * 4 = 50 *4 = 200g oats
1.2/5 * 4 = 0.96l milk
90/5 * 4= 18*4 = 72g sugar
if a sixth skateboard is added to the sample that has a price of $450, what happens to the standard deviation
Answer:
75
Step-by-step explanation:
i need help help pls
Answer:
MAD = 2
Step-by-step explanation:
First We'll find the mean of data
Mean = [tex]\frac{20}{5}[/tex]
Mean = 4
Then, we'll find absolute deviation
=> |4-3| = 1
=> |4-2| = 2
=> |4-1| = 3
=> |4-1| = 3
=> |4-3| = 1
Now, taking the mean of these absolute deviations:
MAD = [tex]\frac{1+3+3+2+1}{5}[/tex]
MAD = [tex]\frac{10}{5}[/tex]
MAD = 2
4432 buttons are made in three hours it takes 6 hours to make enough buttons to fill three boxes. When box B has been filled there are 3363 buttons remaining box C holds half of the amount of button as box A how many are there in A than C
Answer:
Box A has 1121 buttons more than Box C
Step-by-step explanation:
4432 boxes are made in three hours
Then in six hours, we would be making double of this
The number of boxes made is 4432 * 2 = 8864 boxes
Now,
we have boxes A B C to fill
Filling box B, we have 3363 boxes left to fill A and B
Now C holds half of what A hold
so we can say the ratio of buttons in C to A is 1:2
The number of buttons in C would thus be
1/3 * 3363 = 1121
Number of buttons in A would be 2/3 * 3363 = 2 * 1121 = 2242 buttons
Now the number of buttons with which the buttons in A exceeds that in C would be 2242 -1121 = 1121 buttons
) Sarah donated one-tenth of her salary to an orphanage, one-third of her salary is spent on food, one-fourth of salary on rent and electricity and one-twentieth of her salary on the telephone. She donated some amount to the Prime Minister's relief fund for the pandemic affected victims. She was left with ₹ 3000. If her monthly salary is ₹ 30,000: Find the amount she donated to the Prime Minister's Relief Fund
Answer:
₹ 4000
Step-by-step explanation:
Sarah's salary =₹ 30000
one-tenth of her salary to an orphanage= 1/10*₹ 30000= ₹ 3000one-third of her salary is spent on food= 1/3*₹ 30000= ₹ 10000one-fourth of salary on rent and electricity =1/4*₹ 30000= ₹ 7500one-twentieth of her salary on the telephone= 1/12*₹ 30000= ₹ 2500donated some amount to the Prime Minister's relief fund = xShe was left with ₹ 3000.x= ₹ 30000- (₹ 3000+₹ 10000+₹ 7500+₹ 2500+₹ 3000)= ₹ 4000
Can someone please explain the math on this one to me? Thanks!
Assume that is takes an average of 3 man-hours to stack 1 ton of a particular item. In order to stack 36 tons in 6 hours, the number of people required is _____
Answer:
18 men = 36 tons in 6 hours
Step-by-step explanation:
3 men = 1 ton in 1 hour
6 men = 2 ton in 1 hour
9 men = 3 tons in 1 hour
with this you find a pattern
3 men = 2 tons in 2 hours
3 men = 3 tons in 3 hours
3 men = 6 tons in 6 hours
6 men = 12 tons in 6 hours
9 men = 18 tons in 6 hours
12 men = 24 tons in 6 hours
15 men = 30 tons in 6 hours
18 men = 36 tons in 6 hours
(This is how i worked it out)
Answer:
18 people
Step-by-step explanation:
Method A:
3 man-hours to stack 1 ton
36 tons is 36 times 1 ton, so it takes 36 times as long to stack.
36 * 3 man-hours to stack 36 * 1 ton, or
108 man-hours to stack 36 tons
To do the job in 6 hours instead of 108, you need to do 108/6 = 18 times as much work per hour, so you need 18 times as many people.
18 * 1 person = 18 people
Answer: 18 people
Method B:
1 person works 3 hours and stacks 1 ton. That same person works another 3 hours and stacks another ton. In a total of 6 hours, 1 person stacked 2 tons. Since you need 36 tons stacked in the same 6 hours, and 36 = 18 * 2, you need 18 times the number of people, so you need 18 people.
How much is (2.5-3 minutes)
Answer:
150 - 180 seconds
Step-by-step explanation:
Let change minutes to seconds
1 minute = 60 seconds
2.5 minutes * 60 =150 seconds
3 minutes * 60 = 180 seconds
150 - 180 seconds
Let $\overline{XY}$ be a tangent to a circle, and let $\overline{XBA}$ be a secant of the circle, as shown below. If $AX = 15$ and $XY = 9$, then what is $AB$?
Answer:
AB=5.4 units
Step-by-step explanation:
We using the theorem of intersecting tangent and secant to solve this.
By this theorem:
[tex]XY^2=XB \times AX\\9^2=15(15-XB)\\81=225-15XB\\15XB=144\\XB=9.6\\$Therefore:\\AB=AX-XB\\AB=15-9.6\\AB=5.4$ units[/tex]
Answer:
Its 9.6, the other guy got it wrong, he already got it but accidentally added a step. Its 9.6 :)
Step-by-step explanation:
trust me :).
A bicycle wheel turns at 80 rpm. If the rider travels 27.227 m in 10 seconds, what is the radius of the wheels of the bicycle?
Answer:
2.042 meters
Step-by-step explanation:
We have that the angular speed is 80 rpm and we can calculate the linear speed, we know that the linear speed is equal to the radius times the angular speed, like this:
v = w * r
w = 80 rpm, but we must pass it to seconds, that is:
80/60 = 1,333 rps, that is, revolutions per second, to have the same time unit as the linear speed.
v = distance / time = 27,227 / 10 = 2.7227
therefore, the radius would be:
r = v / w = 2.7227 / 1,333
r = 2.042
Which means that the radius is 2.042 meters.
Make K the subject of the formula
[tex]t = \frac{mu {}^{2} }{k} - 5mg[/tex]
Answer:
Step-by-step explanation:
[tex]t = \frac{mu^{2} }{k} -5mg\\kt = mu^{2} -5mg\\k = \frac{mu^{2} -5mg}{t}[/tex]
To make k subject of the fomula :
Step 1 : cross multiply
Step 2 : Divide both side of the equation to isolate k
The solution of the expression for the value of k will be k = (mu² - 5mgk)/t.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is t = (mu²)/k - 5mg. The value of the expression for the value of k will be,
The value of k will be written as,
t = (mu²)/k - 5mg
k = (mu² - 5mgk)/t
Therefore, the solution of the expression for the value of k will be k = (mu² - 5mgk)/t.
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Which graph matches the equation y+3=2(x+3)?
Answer:
The leftmost graph [with the points (-3,-3) and (0,3)]
Step-by-step explanation:
y+3=2(x+3)
y+3=2x+6
y=2x+3
The y-intercept is 3, meaning that the line passes through the point (0,3), and it's slope is 2, so it travels 2 units up and 1 unit over. Thus the correct graph is the top left graph, with the two points (-3,-3) and (0,3).
The graph is considered as the creation of a diagram that depicts a relationship connecting two or more items, and further discussion can be defined as follows:
Given:
[tex]\bold{y+3=2(x+3)}[/tex]
To find:
graph=?
Solution:
[tex]\bold{y+3=2(x+3)}[/tex]
Solving the given equation:
[tex]\to \bold{y+3=2(x+3)}\\\\\to \bold{y+3=2x+6}\\\\\to \bold{y=2x+6-3}\\\\\to \bold{y=2x+3}\\\\[/tex]
In this, the y-intercept is 3, indicating that the line crosses through the point (0,3), and the slope is 2, showing that it moves 2 units up and 1 unit over. And as a result, the proper graph is the upper left graph, with two points [tex]\bold{(-3,-3)\ and\ (0,3)}[/tex].Please find the graph in the attached file.
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What is the solution to this system of equations
Sorry, Please rewrite it again.
help plzzzz asap i need the answer right now