Steps to complete the square used to solve the equation were discussed.
The given quadratic equation is:
[tex]5x+1=2x^{2} +9x[/tex].....(1)
What is a quadratic equation?Any equation of the form [tex]ax^{2} +bx+c=0[/tex] with [tex]a\neq 0[/tex] called a quadratic equation.
Rearranging the equation (1):
[tex]2x^{2} +9x-5x=1[/tex]
[tex]2x^{2} +4x=1[/tex]
[tex]2x^{2} +4x+2=1+2[/tex]
[tex]2x^{2} +4x+2=3[/tex]
[tex]2(x^{2} +2x+1)=3[/tex]
[tex]2(x+1)^2=3[/tex]........(2)
So, the required answer is equation (2).
Hence, steps in the process of completing the square used to solve the equation were discussed.
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I need help with this please.
The pentagons ABCDE and PQRST are similar.
Find the length x of ST.
D
S
2
4.
A
4.8
P
E
4.8
T
13
3.6
C
5
B
R
6
O
The value of x, which is the length of ST in the given similar polygons is: 2.4.
What are Similar Shapes?If two shapes are similar to each other, the ratio of their corresponding side lengths would be equal.
Thus, since both pentagons are similar, we would have:
CB/RQ = DE/ST
Plug in the values
5/6 = 2/x
Cross multiply
x = (6 × 2)/5
x = 12/5
x = 2.4
Therefore, the value of x, which is the length of ST in the given similar polygons is: 2.4.
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Amira is planning to plant a new food forest with papaya guava and banana trees she wants to plant a total of 36 trees in the forest and select 18 of them to be the buyer none of them to be guava she says that they're made in 25% of the forest will be banana trees is she correct? Explain.
Answer:
No
Step-by-step explanation:
If 18 are papaya or banana and none are guava then the remaining two trees would split the 36 50-50
a rectangle and a square have equal area.If the length of rectangle is 25 cm and breadth is 16 cm. Find the perimeter of the square.
answer:80cm
Please help me I can’t figure it out
Answer:
Your answer is 4
Step-by-step explanation:
(52 - 2(2)) / (9 + 3)
(52 - 4) / (9 + 3)
48 / 12 = 4
X^(2) + 6x - 9 = 0
solve by completing the square
write in (x+h)^2 = k form
Step-by-step explanation:
[tex]{x}^{2} + 6x - 9 = 0[/tex]
ADDING 18 ON BOTH SIDES[tex] { x }^{2} + 6x - 9 + 18 = 0 + 18[/tex]
[tex] {x}^{2} + 6x + 9 = 18[/tex]
[tex] {(x)}^{2} + 2(x)(3) + {(3)}^{2} = 18[/tex]
[tex] {(x + 3)}^{2} = 18[/tex]
rachel bought an equal number of bowls and plates for$96. each plate cost $2 and each bowl cost $4 more than each plate. how much did she spend on all the plates
Answer:
$24
Step-by-step explanation:
Cost per plate: $2
Cost per Bowl: $2 + $4 = $6
Cost of 1 Plate and 1 Bowl: $2 + $6 = $8
Total cost of $96 divided by Cost of 1 Plate and 1 Bowl $8 = 12 sets of 1 Plate and 1 Bowl
12 plates x $2 Cost per Plate = $24
Answer:
$24
Step-by-step explanation:
Let [tex]b[/tex] = bowl
Let [tex]p[/tex] = plate
Given:
Equal number of bowls and plates for $961 plate = $2 1 bowl = $4 + $2 = $61) We can translate these into algebra. Since Rachel has equal number of bowls and plates, [tex]b=p[/tex], totaling to $96.
[tex]b=p\\2p + 6b = 96[/tex]
2) We can solve for [tex]p[/tex] these two equations simultaneously using the substitution ot elimination method. I will demonstrate using the substitution method here.
[tex]2p + 6(p) = 96\\2p+ 6p = 96\\8p = 96\\p = \frac{96}{8} \\p = 12[/tex]
So, Rachel bought 12 plates and 12 bowls since plates are equivalent to bowls.
3) Use ratio to find the the cost of the plates.
[tex]1p[/tex] = $2
[tex]12p[/tex] = $24
Please help me with this question. Thank you
Answer:
9.
Step-by-step explanation:
6 9 12 15:- multiplying by 3.
Answer:
B) 9
Step-by-step explanation:
When looking in both the horizontal and vertical direction of the missing space, we can see that the difference between the two numbers, 12 and 15, is 3.
15 - 12 = 3
Using this, we can see that each space on the second row and second column change by 3. Therefore, when looking at the missing space in the sequence, we can figure out that it is 9 by adding 3 to 6.
Doesn’t it tell you the hight of the base I do not understand.
Answer:
Height of base (x) is 9cm exact
Step-by-step explanation:
8
5.1
What is the area of the parallelogram?
(Please my geometry is due tomorrow an I haven’t even started yet)
Answer:
s the answer is 40
n
Step-by-step explanation:
a the formula is A=bh
p so 8*5=40
dsan168
Alicia and Bennie have decided to play a game. They each draw as many flowers on paper as they can within one
minute, repeating this game many times. The number of flowers Alicia draws and the number of flowers Bennie
draws are independent. The number of flowers Alicia draws within 1 minute, A, is approximately Normally distributed
with a mean of 38 flowers and a standard deviation of 1. 8 flowers. The number of flowers Bennie draws in 1 minute,
B, is approximately Normally distributed with a mean of 41 and a standard deviation of 2. 6 flowers. Let D represent
the difference, A - B in the number of Alicia's and Bennie's flowers drawn in 1 minute
What is the probability that Alicia draws fewer flowers than Bennie in any 1 minute?
Answer:
0.829
Step-by-step explanation:
4
Select the correct answer.
Which expression is equivalent to the given expression?
3x2 + 5x – 7(x2 + 4)
-
O A.
x2 + 28
4
OB. x2 + 4
OC. -4x2 + 5x – 28
ОС
C
Answer:
C. -4x² + 5x - 28
Step-by-step explanation:
1. Expand -7(x² + 4):
-7x² - 28
3x² + 5x -7x² - 28
2. Group like terms:
-4x² + 5x -28
hope this helps :)
What is mZRST in degrees? O 78° O 84° O 120° O 156°
Answer:
rst = ust + usr
6x+12 = 78 + 3x - 12
3x = 54
3x+66 = 54 + 66
3x +66= 120
thus rst = 120
The measure of angle ∠RST in degree is 156°
What is measure of an angle?The measure of angle is the amount of rotation performed by initial side to get the terminal side. A complete angle is divided by 360 equal parts we get 360 number of small angles. Each of these small angle has measure 1 degree.
Given that, ∠RSU=78° , ∠UST=(3x - 11)° and ∠RST=(6x + 12)°
Now, ∠RSU+UST=∠RST
Putting the values of ∠RST and ∠UST we get,
78 + (3x - 12) = 6x + 12
78 + 3x - 12 - 6x - 12 = 0
54 - 3x = 0
3x = 54
So, x = 54/3=18
Therefore, (6x + 12)°=(6×18 + 12)°
=(144 + 12)°
=156°
Hence the measure of angle ∠RST is 156°
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#SPJ5
Can someone help me with this problem.?
Answer:
B -- Recipe 2 (Gluten-Free)
Step-by-step explanation:
Recipe 1
5 / 16 = 0.3125
Recipe 2
3 / 8 = 0.375
Recipe 2 (Gluten-Free) has a higher ratio so it must have a stronger taste.
Answer:
Your answer would be:
B.) The gluten-free batch has the stronger butterscotch
Regular batch:
5 / 21
5 / 21 = 25 / 110
Gluten-free batch:
3 / 11
3 / 11 = 30 / 110
Solution:
30 / 110 > 25 / 110
In conclusion, the gluten-free batch has the stronger butterscotch.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
If x2 mx m is a perfect-square trinomial, which equation must be true? x2 mx m = (x – 1)2 x2 mx m = (x 1)2 x2 mx m = (x 2)2 x2 mx m = (x 4)2
An expression has numbers, variables, and mathematical operations. The equation that must be true so that x²+mx+m is a perfect square trinomial is x²+mx+m=(x+2)².
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
A perfect square trinomial is in the form (a+b)²=a²+b²+2ab. If we compare the perfect square trinomial x²+mx+m, we will get that the value of m should be such that it satisfies the equation [tex]m^2+2m[/tex]. Since there is only one value that can satisfy this equation that is 2.
Therefore, the equation that must be true so that x²+mx+m is a perfect square trinomial is x²+mx+m=(x+2)².
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find the area figer
a 14
b 50
c 60
d 64
Answer:
64 cm²
Right corner rectangle:
Length * Width2 * 714 cm²Bottom rectangle:
Length * Width10 * 550 cm²Together:
50 cm² + 14 cm²64 cm²Answer:
d. 64 cm²
Step-by-step explanation:
Separate the shape into two rectangles (see attached image).
Formula
Area of a rectangle = width × length
Rectangle 1
Area = 2 × 12
= 24 cm²
Rectangle 2
Area = 5 × (10 - 2)
= 5 × 8
= 40 cm²
Total Area
Total area = Area of Rectangle 1 + Area of Rectangle 2
= 24 + 40
= 64 cm²
if two dice are thrown together , what is the probability of getting an even number on one die and odd number on the other die ?
Answer:
1/2
Step-by-step explanation:
the probability of the die rolling an even number = the probability of the die rolling an odd number =1/2
Let us name these 2 dice as A and B
One die can roll an even and the other can roll an odd, in the following cases
A rolls even and B rolls odd. The probability of this happening =1/2×1/2
A rolls odd and B rolls even. The probability of this happening =1/2×1/2
∴ The required probability
=1/2×1/2+1/2×1/2
=1/4+1/4
=1/2
What is 5/8 times 1/2
Answer:
5/16
Step-by-step explanation:
When multiplying fractions, you multiply the numerator by the numerator & the denominator by the denominator.
So 5/8 x 1/2 = 5 x 1/8 x 2 = 5/16
HELP ME PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]192cm^{2}[/tex]
Step-by-step explanation:
[tex]A = \frac{1}{2} bh[/tex]
We know that b is the measurement of the base, 12, and h is the height of the cone, 32. Now we can simply insert those numbers into the equation and solve it.
[tex]A = \frac{1}{2} (12*32)\\\\A = \frac{1}{2} (384)\\\\A = \frac{384}{2} \\\\A = 192[/tex]
651 x 5 porfavor ayudenme SIN CALCULADORA - please help me NO CALCULATOR
Answer:
3,255
Step-by-step explanation:
,
A right rectangular prism has a length of 2 1/2 feet, a width of 3 feet, and a height of 1 1/2
feet. Unit cubes with side lengths of 1/2 foot are added to completely fill the prism with no space remaining. What is the volume, in cubic feet, of the right rectangular prism?
Answer: 11.25 ft³
Step-by-step explanation:
We can use the volume formula to solve. I will turn the halves into 0.5 for calculation purposes.
V = L * W * H
V = 2.5 * 3 * 1.5
V = 11.25 ft³
The volume of the rectangular prism is 11.25 ft³.
Dana just finished paying off the $15,400 loan she took out four years ago. the loan had 6.68% interest, compounded monthly. if dana paid a total of $18,321.60, how much did she pay in service charges? a. $730.08 b. $366.49 c. $1,028.72 d. $266.76 please select the best answer from the choices provided a b c d
If Dana paid a total of $18,321.60, then the amount that she paid for in service charges will be $730.08
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
For service charge
[tex]\rm Pv = PMT[(1 - (1 + (r/k))^{-kn}) / (r/k)][/tex]
Where;
Pv is the amount of the loan = $15400
PMT is monthly payment
R is interest rate = 6.68% = 0.0668
K is number of times compounded monthly = 12
N is time = 4years
PMT the subject of the formula gives
[tex]PMT = Pv/ [(1 - (1 + (r/k))^{-kn}) /(r/k)][/tex]
PMT = 15,400 ÷ ((1 − (1 + 0.0668 ÷ 12)^(−12 × 4)) ÷ (0.0668 ÷ 12))
PMT = 366.49
Thus, the total amount paid
A = 366.49 × 12months × 4years
A = $17,591.52
Thus, the Service charge is
S.C = 18,321.60 − 17,591.52
S.C = $730.08
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Is this triangle acute, right or obtuse?
Triangle
Acute
Obtuse
Right
Answer:
ill say acute
Step-by-step explanation:
if im wrong tell me but if im not pls mark brainllest!
Answer:
This triangle is Acute.
Step-by-step explanation:
To figure this out you add the length of the two smaller sides if the sum is greater than the longest side then the answer is Acute. I really hope this helps have a wonderful day!
If f(x) = 3x 2 and g(x) = x2 1, which expression is equivalent to (f circle g) (x)? (3x 2)(x 2 1) 3x 2 1 2 (3x 2)2 1 3(x 2 1) 2
The expression is equivalent to (f circle g) (x) will be (3x+2)²+1. The correct option is D.
What is a factor?A number is obtained by dividing another number by itself without leaving a leftover. To put it another way, if multiplying two whole numbers produces a product,
The given expression is;
[tex]f(x) = 3x + 2 \\\\ g(x) = x_2 + 1[/tex]
[tex](f g)(x) =g(f(x)) =g(3x+2)=(3x+2)^2 +1[/tex]
The expression is equivalent to (f circle g) (x) will be (3x+2)²+1. Option D is correct.
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julie planned to walk 35 miles a week. On Monday and Wednesday she walked 5 miles each. tuesday and thursday she walked 3 miles each. friday she walked 2 miles, saturday she walked 7 miles. and sunday she walked 4 miles. she failed to reach her goal. what was julie's approximate percent error?
Answer:
11%.
Step-by-step explanation:
Total miles walked = 5+5+3+3 +2+7+4 = 29.
%age error = [(35-29)/35] * 100
= 4/35 * 100
= 11%.
=
An object moves at a speed of 20 yards per second.
What is the object's speed, in feet per second?
(1 yard = 3 feet)
A) 17
B) 23
C) 50
D) 60
Let's see
[tex]\\ \rm\Rrightarrow speed=20yd/s[/tex]
See unit given to change is ft/sSo only numerator we need to change[tex]\\ \rm\Rrightarrow Speed=20(3)=60ft/s[/tex]
Option D
From the top of a building 37 feet high, the angle of depression to a car stopped on the ground is 19 degrees. What is the distance from the car to the base of the building?
The distance from the car to the base of the building is 107.46 feet
Angle of elevation and depressionFrom the question We are given the following information
Angle of depression
Height of the building H = 37 feet
Required
distance from the car to the base of the building
Using the SOH CAH TOA identity
tan 19 = opp/hyp
tan 19 = 37/B
B = 37/tan 19
B = 37/0.34432
B = 107.46
Hence the distance from the car to the base of the building is 107.46 feet
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Find the are of the shaded region. Are of a triangle = 1/2 base x height . 2w+2 < height. Width is 3w-1
The formula for the area of a triangle is 1 / 2 × base × height. This formula can be more easily written as Area = 1 / 2 bh. The formula of Area = 1 / 2 bh works for all triangles, no matter what size or shape.
Can someone help me with this please
y – 6 ≥ 12
I NEED HELP PLSSSSS I HVA ENO TIME LEFT
Answer:
x=6
Step-by-step explanation:
FG is similar to MN just like GH is similar to NP. GH is 20, which is double NP,10. Then, MN should be half of FG, 12, so 6 is your answer.