The number that has to fill the blank to make the trinomial a perfect square is 72x
Perfect square trinomialFrom the question, we are to determine the number that makes the given trinomial a perfect square
The given trinomial is
9x² + ___+ 144
For any given trinomial ax² + bx + c, the trinomial is a perfect square if
b² = 4ac
In given trinomial,
a = 9, c = 144, b = ?
Now, we will determine the value of b
Putting the values into the equation,
b² = 4ac
b² = 4×9×144
b² = 5184
b = √5184
b = 72
Thus,
The trinomial will become 9x² + 72x+ 144
Hence, the number that has to fill the blank to make the trinomial a perfect square is 72x
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a) The line y = 4 meets the line 2x + y = 8 at the point A
Fins the co-ordinates of A
b) The line 3x + y = 18 meets the x axis at the point B
Find the co-ordiantes of B
c) (i) Find the co-ordiantes of the mid-point M of the line joining A to B
(ii) Find the equation of the line through M parallel to 3x + y =18
answers :
a.
coordinates of A are (2,4)
b.
coordinates of B are (6,0)
i.
(4,2) is the midpoint
ii.
y = -3x + 18 is the parallel line
Step-by-step explanation:
a.
if two things are equal to the same thing then they are equal to each other
y = 4
2x + y = 8 is y = -2x +8 so
-2x +8 = 4
-2x = -4
x = 2
coordinates of A are (2,4)
b.
if two things are equal to the same thing then they are equal to each other
y=0
3x+y=18 is y = -3x+18 so
-3x+18=0
x = 6
coordinates of B are (6,0)
midpoint formula is
(X1+X2)/2 , (Y1+Y2)/2
(2,4) (6,0)
(X1+X2)/2 , (Y1+Y2)/2
(2+6)/2 , (4+0)/2
(4,2) is the midpoint
parallel line has the same x value
so for a line parallel to 3x+y=18 or y = -3x+18
the parallel line would be
y = -3x
point slope formula
point slope formulay - y1 = m (x - x1)
3x+y=18 or y = -3x+18 was 6,0 at y = 0
y - y1 = m (x - x1)
y - 0 = m (x - x1)
since it's a parallel line the m has to be the same
(6,0)
y - 0 = -3 (x - 6)
y = -3x + 18 is the parallel line
The height (in feet) of a rocket launched from the ground is given by the function f(t) = -16t2 160t. match each value of time elapsed (in seconds) after the rocket’s launch to the rocket's corresponding instantaneous velocity (in feet/second).
EachEach value of time elapsed (in seconds) corresponding instantaneous velocity (in feet/second) are:2s= 96, 3s = 64, 4s= 32, 5s = 0, 6s = -32, 7s = -64. 8s= -96, 9s= -128.
VelocityGiven equation:
f(t) = -16t² +160t
Velocity (v)=df(t)/dt
=-2×16t²+ 160t
=-32t+160
Hence:
-32t+160
1. -32×(1) + 160 = 128ft/s
2. -32×(2) + 160 = 96ft/s
3. -32×(3) + 160 = 64ft/s
4. -32×(4) + 160 = 32m/s
5. -32×(5) + 160 = 0m/s
6. -32×(6) + 160 = -32m/s
7. -32×(7) + 160 = -64m/s
8. -32×(8) + 160 = -96m/s
9. -32×(9) + 160 = -128m/s
The pairs are;
2s= 96
3s = 64
4s= 32
5s = 0
6s = -32
7s = -64
8s= -96
9s= -128
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A salesperson has 7 customers in denver and 13 customers in reno. in how many different ways could she telephone?
If a salesperson has 7 customers in denver and 13 customers in reno then there are 20 different ways in which he can make calls.
Given that the salesperson has 7 customers in denver and 13 customers in reno.
We are required to find the number of ways in which he can make use of telephone.
Number of customers in denver=7
Number of customers in reno=13
Total customers=20
Since he can talk to one customer at one time and he can either choose customer from denver or reno, the number of ways by using combinations will be [tex]7C_{1}[/tex]+[tex]13C_{1}[/tex]
=7+13
=20 ways.
Hence if a salesperson has 7 customers in denver and 13 customers in reno then there are 20 different ways in which he can make calls.
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10.
JKLM is a rhombus KLN is a triangle. Find MKN.
Answer:
65°
Step-by-step explanation:
JM = JK (all sides of a rhombus are equal)
Angle JKM = 25° (isosceles triangle)
Angle JKL = 50° (consecutive angles of rhombus)
Angle MKL = 25° (angle subtraction)
Angle MLK = 130° (opposite angles of a rhombus)
Angle KLN = 50° (angles on a straight line)
Angle LKN = 40° (angle sum of triangle)
Angle MKN = 65° (angle addition)
If $20.00 was spent on Shoes, what was the total amount spent on the shopping trip?
Answer: Total = $200
Step-by-step explanation:
Given information
Money spent on shoes = $20.00
Percent of Money spent on shoes = 10%
Given formula
The total amount of money spent × Percent = Money spent on shoes
⇵
The total amount of money spent = Money spent on shoes / Percent
Substitute values into the given formula
The total amount of money spent = Money spent on shoes / Percent
Total = (20.00) / (10%)
Convert percentage into decimal
Total = 20.00 / 0.1
Simplify the fraction
[tex]\Large\boxed{Total~=~200~Dollars}[/tex]
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Write the standard equation for the circle center left parenthesis negative 6 comma 7 right parenthesis, r = 9.
A. left parenthesis x minus 6 right parenthesis squared plus left parenthesis y plus 7 right parenthesis squared equals 9
B. left parenthesis x minus 7 right parenthesis squared plus left parenthesis y plus 6 right parenthesis squared equals 81
C. left parenthesis x plus 6 right parenthesis squared plus left parenthesis y minus 7 right parenthesis squared equals 81
D. left parenthesis x plus 6 right parenthesis squared plus left parenthesis y minus 7 right parenthesis squared equals 9
Answer:
Step-by-step explanation:
The standard form equation for a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where h and k are the coordinates of the center. Our center is given as (-6,7) and the radius is given as 9, so that information fits into our standard form like this:
[tex](x-(-6))^2+(y-7)^2=9^2[/tex] and simplified, it looks like this:
[tex](x+6)^2+(y-7)^2=81[/tex]
That's choice C
Joseph decided to solve the quadratic x² +8x=9. Which of the
following steps is where Joseph made his first mistake?
x² +8x=9
Step 1
Step 2
Step 3
0000
x+8x-9=0
(x+9)(x - 1) = 0
x= 9 and x = -1
Step 1
Step 2
Step 3
Joseph did not make any mistakes.
Answer:
he didn't mistake step 2
VERY URGENT: Alexis surveys a random sample of 80 students at his school and finds that 22 of them usually walk to school. There are 1,760 students at the school. Predict the number of students who usually walk to school.
Answer:
484 Students
Step-by-step explanation:
This is simple probability. Assuming 22/80 students walk to school within a small population, and there are 1760 students at the school, there should be (22/80)*1760 students that walk to school in total. (This is just theoretical). This is 484 students.
help i dont feel like doing the math
Answer:
A
Step-by-step explanation:
First, we should put this equation in slope-intercept form by isolating y.
Thus, we have:
[tex]2x-\frac{4}{3}y=4\\ -\frac{4}{3}y=4-2x\\ y=\frac{3}{2}x-3[/tex]
The slope-intercept equation shows that the y-intercept is -3 and the slope is 3/2.
Only answer A meets these requirements.
The formula c² = a² + b² is the Pythagorean Theorem used to find the sides of a right
triangle. Find the leg of the right triangle (b) if the hypotenuse (c) is 13 cm. and the other leg of
the right triangle (a) is 12 cm.
A. 4 cm
B. 18 cm
C. 5 cm
D. 14 cm
Answer: 5 cm
Step-by-step explanation:
B = [tex]\sqrt{13^{2} -12^{2} } = 5[/tex]
Answer:
OPTION C, 5
Step-by-step explanation:
Using the formula, substitute the hypotenuse and the other leg of the right triangle.
13²=12²+b²
Rearrange appropriately.
13²-12²=c²
Convert.
13²=169
12²=144
Apply and work out.
169-144= 25
c²=25
c=√25
c=5
OPTION C is therefore the answer.
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Can someone pls help me get the anwser for this question
Answer: [tex]\Large\boxed{x=6.5}[/tex]
Step-by-step explanation:
Given equation
-9 - (x + 1) = -2 - (3x - 5)
Expand the parenthesis
-9 - x - 1 = -2 - 3x + 5
Combine like terms
-9 - 1 - x = -2 + 5 - 3x
-10 - x = 3 - 3x
Add 3x on both sides
-10 - x + 3x = 3 - 3x + 3x
-10 + 2x = 3
Add 10 on both sides
-10 + 2x + 10 = 3 + 10
2x = 13
Divide 2 on both sides
2x / 2 = 13 / 2
[tex]\Large\boxed{x=6.5}[/tex]
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In c 11 you cannot use a range-based for loop to modify the contents of an array unless you declare the range variable as a reference variable. true false
This statement is true that the In c 11 you cannot use a range-based for loop to modify the contents of an array unless you declare the range variable as a reference variable.
According to the statement
we have given that the one statement and we have to tell that the those statement is true or false after analyzing it.
So,
In C++ 11 is a programming language which is used to write the coding. And in this language you cannot use a range-based for loop to modify the contents of an array unless you declare the range variable as a reference variable.
Because in the coding it is not possible that the you can make loop without declare the random variable in the loop.
Due to this reasons without declare the variable it is not possible.
So, This statement is true that the In c 11 you cannot use a range-based for loop to modify the contents of an array unless you declare the range variable as a reference variable.
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A supplier sold a scanner machine for Rs 41,400 with 15% VAT after allowing 10% discount on it's marked price and gained 20%. By how much is the discount percent to be reduced to increase the profit by 4%?
3%
Answer:
Selling price with VAT {15%} = Rs 41400
S.P +15% of S.P =Rs 41400
S.P(1+15%)=Rs 41400
S.P=Rs 41400/1.15
Selling price without VAT =Rs 36000
Again
Discount = 10%
M.P =S.P+ Discount % of M.P
M.P-Discount% of M.P= S.P
M.P(1-Discount%)=Rs 36000
M.P(1-10%)=Rs 36000
M.P=Rs 36000/0.9
Marked Price = Rs 40,000
again
Discount =Discount % of M.P
=10% of 40000
=Rs 4,000
Again
Profit=20%
For 20% profit
Cost price = (S.P*100)/(100+profit%)
=(36000*100)/(100+20)
= Rs 30000
For 24% profit
selling price = (100+profit%)*C.P/100
=(100+24)*30000/100
=Rs 37200
Again
Discount = 40000–37200 = Rs2800
Discount % = discount/M.P*100%
=2,800/40,000* 100 = 7%
Finally
Discount percent to be reduced =10%–7%= 3%
Given that it was less than 80º on a given day, what is the probability that it also rained that day? 0.3 0.35 0.65 0.7
The probability that it also rained that day is to be considered as the 0.30 and the same is to be considered.
What is probability?The extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
The probability that the temperature is lower than 80°F and it rained can be measured by determining the number at the intersection of a temperature that less than 80°F and rain.
So, This number is 0.30.
Hence, we can say that it was less than 80°F on a given day, the probability that it also rained that day is 0.30.
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The above question is incomplete.
The conditional relative frequency table was generated using data that compared the outside temperature each day to whether it rained that day. A 4-column table with 3 rows titled weather. The first column has no label with entries 80 degrees F, less than 80 degrees F, total. The second column is labeled rain with entries 0.35, 0.3, nearly equal to 0.33. The third column is labeled no rain with entries 0.65, 0.7, nearly equal to 0.67. The fourth column is labeled total with entries 1.0, 1.0, 1.0. Given that it was less than 80 degrees F on a given day, what is the probability that it also rained that day?
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Answer: Its 0.3 so the first one
Step-by-step explanation:
Im 101% sure
Write the following as an inequality:
x is less than or equal to negative 3 or greater than or equal to 4
The become in the inequality form is -3≥x≥4.
According to the statement
we have given that the statement and we have to write this condition in the form of the inequality.
So, we know that the
Inequality, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
It is represented with the grater than or less than or equal to signs.
so, the given statement is
x is less than or equal to negative 3 or greater than or equal to 4
and we have to write in the inequality condition so,
we have to write it but before this break the statement like
x is less than or equal to negative 3
And
x is greater than or equal to 4.
So,
-3≥x≥4.
So, The become in the inequality form is -3≥x≥4.
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Estimate each of these square roots.
a) √80
b) √27
c) √110
d) √0.03
e) √0.12
Answer:
a) √80 ≈ 9
b) √27 ≈ 5
c) √110 ≈ 10
d) √0.03 ≈ 0.2
e) √0.12 ≈ 0.3
Step-by-step explanation:
a) √8080 is close to 81
Therefore, √80 can be estimated as √81
√81 = 9
[tex]\Large\boxed{\sqrt{80}\approx9 }[/tex]
b) √2727 is close to 25
Therefore, √27 can be estimated as √25
√25 = 5
[tex]\Large\boxed{\sqrt{27}\approx5 }[/tex]
c) √110110 is close to 100
Therefore, √110 can be estimated as √100
√100 = 10
[tex]\Large\boxed{\sqrt{110}\approx10 }[/tex]
d) √0.030.03 is close to 0.04
Therefore, √0.03 can be estimated as √0.04
√0.04 = 0.2
[tex]\Large\boxed{\sqrt{0.03}\approx0.2 }[/tex]
e) √0.120.12 is close to 0.09
Therefore, √0.12 can be estimated as √0.09
√0.09 = 0.3
[tex]\Large\boxed{\sqrt{0.12}\approx0.3 }[/tex]
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x(x-5) (x+5) - (x+2) (x^2 - 2x +4) = 17
x[x²-25] - [x³+8] = 17
x³- 25x - x³- 8 = 17
-25x = 17 + 8
-25x = 25
x = -1
F = (x2 y2)i (x - y)j; c is the rectangle with vertices at (0, 0), (3, 0), (3, 9), and (0, 9)
I assume [tex]C[/tex] is oriented counterclockwise. If [tex]C[/tex] is the closed rectangle, then by Green's theorem we have
[tex]\displaystyle \int_C F\cdot dr = \int_0^3 \int_0^9 \frac{\partial (x-y)}{\partial x} - \frac{\partial (x^2+y^2)}{\partial y} \, dy \, dx \\\\ ~~~~~~~~~~~~ = \int_0^3 \int_0^9 (1 - 2y) \, dy \, dx = 3 \int_0^9 (1-2y)\, dy = \boxed{-216}[/tex]
It seems unlikely, but if you actually are omitting the integral along the line segment joining (0, 9) and (0, 0), let [tex]x=0[/tex] and [tex]y=9-t[/tex] with [tex]0\le t\le9[/tex]. Then the integral along this line segment would be
[tex]\displaystyle \int_{(0,9)\to(0,0)} F\cdot dr = \int_0^9 \bigg((0^2 + (9-t)^2) i + (0 - (9-t)) j\bigg) \cdot (0i - j) \, dt \\\\ ~~~~~~~~ = \int_0^9 (9-t) \, dt = \frac{81}2[/tex]
so that the overall integral would instead have -216 - 81/2 = -513/2.
What is the value of x in the equation7x+2y=48 , when y = 3?
Answer:
x = 6
Step-by-step explanation:
put '3' in where 'y' is :
7x + 2(3) = 48
7x + 6 = 48 subtract 6 from both sides of the equation
7x = 42 divide both sides by 7
x = 6
At a walk-in interview, 12% of candidates can be selected, and 28% of candidates can be put on hold for the next hiring date. if 75 candidates are interviewed, about how many are expected to be rejected?
45 candidates are expected to be rejected.
What is a percentage in math?
percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part. 100 percent represents the entirety and 200 percent specifies twice the given quantity.Here, we want to calculate the number of candidates to be rejected
The number of candidates to be rejected can be calculated from;
100% - (28% + 12%) = 60%
So 60% of the 75 interviewed are to be rejected
Thus, we have
60/100 * 75
= 45
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hi guys how do u order decimals like this
.76373
.5734
.432
and explain pls! i’ll mark u brainliest just please help me!
Answer:
Ascending Order: 0.432 < 0.5734 < 0.76373
Descending Order: 0.76373 < 0.5734 < 0.432
Step-by-step explanation:
Check the tenths place of the decimal number and order them accordingly. If the tenths place is the same for two decimal numbers, go on to the next corresponding place to compare their values.
2. (01.01 LC)
Which of the following is a defined term? (6 points)
Angle
Line
Point
Plane
Answer:
is there a picture I can look at?
Answer: Line
Step-by-step explanation:
can someone please help me(20 points will give brainliest!!!)
Answer:
a. 1080
b. 405
Step-by-step explanation:
Function evaluation is often conveniently done using a calculator. Many calculators know about the order of operations, so can be used without fear of an incorrect evaluation.
a)Put the value where the variable is and do the arithmetic.
f(x) = 40(3^x)
f(3) = 40(3^3) = 40(27) = 1080
b)g(x) = 5(3^(x+1))
g(3) = 5(3^(3+1)) = 5(3^4) = 5(81) = 405
There are two numbers between 30 and 40 that have just two factors.
What are they?
Answer:
31 and 37
Step-by-step explanation:
Those are the only two numbers
Answer:
The two numbers between 30 and 40 which have only 2 factors are -
31 and 37
Hope it helps you.
True or false: f(x) is a function
Answer Section 1. <3
Heyy, I'm sunny and I'm here to help you :)
(P.S: answer in explanation)
----------------------------------------------------------------------------------------------------------
Explanation Section:
It is false
If f(x) is a function , then for each value of x there should be a single y values
For input 0 there is a output 0
for input 10, the output is 2
for input 15, output is 3
For input 5, we have two output 1 and 3
for single input 5, the function cannot have two outputs 1 and 3
So this f(x) is not a function
Bye! - SunnyBunny <3
A 3.0-kg ball moving eastward at 4.0 m/s suddenly collides with and sticks to a 5.0-kg ball moving northward at 3.0 m/s. what is the magnitude of the momentum of this system just after the collision?
Magnitude of the momentum of this system just after the collision = 19.2Kgm/s
What is law of conservation of momentum?Law of conservation of momentum states that the total momentum after the collision must be equal to the total momentum before the collision.
The momentum of each ball is given by:
p = mv
where m is the mass of the ball and v its velocity.
The momentum of ball 1 is:
p = mv
= (3.0 kg)(4.0 m/s)
= 12.0 kg m/s in the eastward direction
The momentum of ball 2 is:
p = mv
= (5.0 kg)(3.0 m/s)
= 15.0 kg m/s in the northward direction
The two momenta are in perpendicular directions, so the magnitude of the total momentum can be found as:
[tex]p = \sqrt{p1^{2} +p2^{2} }[/tex]
[tex]p = \sqrt{12^{2} +15^{2} }\\p = \sqrt{144 + 225} \\p = \sqrt{369}\\ p = 19.2 kgm/s[/tex]
and due to the law of conservation of the momentum, this is also equal to the total momentum after the collision.
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if 1+sin² =3sin *cos, prove that tan = 1 or 1/2
Step-by-step explanation:
hif 1+sin² =3sin *cos, prove that tan = 1 or 1/2A dealer marked the price of a digital watch as Rs 6,000. She then allowed 20% discount to make 20% profit. If she increased the discount to 25%, by how much was the profit percent decreased?
Profit decreased by 7.5%
Answer:
Solution Given:
Marked Price= Rs 6,000
discount =20%
Selling Price =M.P- discount% of M.P
=M.P(1-discount%)
=6000(1-20%)
= Rs 4,800
Again
Profit = 20%
Cost Price=(S.P*100)/(100+profit%)
= (4800*100)/(100+20%)
= Rs 4,000
For discount 25%
Marked Price =Rs 6,000
Selling Price =M.P - discount% of M.P
=M.P(1-discount%)
=6000(1-25%)
=Rs 4,500
Profit = S.P- C.P= Rs 4,500- Rs 4,000=Rs 500
Profit %=Profit/C.P* 100%= 500/4000*100 = 12.5%
Profit % decreased from 20% to 12.5%
Profit decreased by 7.5%
Answer:
7.5%
Step-by-step explanation:
Marked Price
Rs 6,000
Discounted Price
If the price is discounted by 20%, then the discounted price is 80% of the marked price:
[tex]\implies \sf Discounted\:Price =80\% \textsf{ of marked price}[/tex]
[tex]\implies \sf Discounted\:Price =0.8 \times 6000[/tex]
[tex]\implies \sf Discounted\:Price = 4800\:Rs[/tex]
Cost Price
If the dealer makes 20% when selling the watch at the discounted price, then the cost price is:
[tex]\implies \sf Cost\:Price=\dfrac{100\%}{120\%} \times 4800[/tex]
[tex]\implies \sf Cost\:Price=\dfrac{4800}{1.2}[/tex]
[tex]\implies \sf Cost\:Price=4000\:Rs[/tex]
Discount of 25%
If the price is discounted by 25%, then the discounted price is 75% of the marked price:
[tex]\implies \sf Discounted\:Price =75\% \textsf{ of marked price}[/tex]
[tex]\implies \sf Discounted\:Price =0.75\times 6000[/tex]
[tex]\implies \sf Discounted\:Price = 4500\:Rs[/tex]
Profit after 25% discount
[tex]\implies \sf Profit=\dfrac{discounted\:price}{cost\:price}-1 \times 100[/tex]
[tex]\implies \sf Profit=\dfrac{4500}{4000}-1 \times 100[/tex]
[tex]\implies \sf Profit=12.5\%[/tex]
Therefore, the profit decreased from 20% to 12.5% which means the profit percent decreased by 7.5%.
Build Your Math Skills 2B, Round decimals to the nearest hundredth (0.01): 1223.075
Answer: 1223.07
Step-by-step explanation: you don't round up
pls help me urgetnly pls help me
The size of the largest angle of the pentagon will be 150°.
How to illustrate the information?A pentagon is the polygon that has five sides. It should be noted that the interior angle of a regular pentagon is 540°.
The given ratio is 2:3:4:4:5. Therefore, the size of the largest angle of the pentagon will be:
= 5/(2+3+4+4+5) × 540
= 5/18 × 540
= 150°
In this case, the size of the largest angle of the pentagon will be 150°.
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