Answer:
a = x
b = 5
Step-by-step explanation:
for the polynomial x² + 10x + 25, b = 5 and a = x.
In the polynomial x² + 10x + 25, we can observe that the first term, x², is the square of x, and the last term, 25, is the square of 5. This suggests that the polynomial follows the perfect square trinomial identity.
The middle term, 10x, can be rewritten as 2ab, where a represents x and b represents a term that when squared equals the last term, 25.
In this case, b = 5, because 5² = 25.
To find a, we can take the square root of the first term, x². The square root of x² is x, so a = x.
Therefore, for the polynomial x² + 10x + 25, b = 5 and a = x.
Learn more about trinomial identity here
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The side of an Equileteral triangle is 12cm. What is its Area?
Answer:
A = 62.35 cm²
Step-by-step explanation:
Use the area formula A = [tex]\frac{\sqrt{3}a^2}{4}[/tex], where a is the side length.
Plug in the values:
A = [tex]\frac{\sqrt{3}(12^2)}{4}[/tex]
A = [tex]\frac{\sqrt{3}(144)}{4}[/tex]
A = 62.35 cm²
2 hundredths as a decimal
Answer:
0.02
Step-by-step explanation:
Answer:
.02
Step-by-step explanation:
need help will give 5 stars.
Answer:
t=0.64
Step-by-step explanation:
h = -16t^2 +4t +4
We want h =0 since it is hitting the ground
0 = -16t^2 +4t +4
Using the quadratic formula
a = -16 b = 4 c=4
-b ± sqrt( b^2 -4ac)
----------------------------
2a
-4 ± sqrt( 4^2 -4(-16)4)
----------------------------
2(-16)
-4 ± sqrt( 16+ 256)
----------------------------
-32
-4 ± sqrt( 272)
----------------------------
-32
-4 ± sqrt( 16*17)
----------------------------
-32
-4 ± sqrt( 16) sqrt(17)
----------------------------
-32
-4 ± 4 sqrt(17)
----------------------------
-32
Divide by -4
1 ± sqrt(17)
----------------------------
8
To the nearest hundredth
t=-0.39
t=0.64
Since time cannot be negative
t=0.64
Answer:
0.64
Step-by-step explanation:
0 = -16t^2 + 4t + 4
-4(4t^2 - t -1) = 0
t = [-(-1) +/- sqrt (1 - 4*4*-1)] / 8)
t = 0.64, -0.39
answer is 0.64
if 25% of a number is 75 find the number
Answer:
x = 300
Step-by-step explanation:
of means multiply and is means equals
25% * x = 75
Change to decimal form
.25x = 75
Divide each side by .25
.25x/.25 = 75/.25
x = 300
Answer:
300
Step-by-step explanation:
Assume the unknown value is 'Y'
75 = 25% x Y
75 = 25/100 x Y
Multiplying both sides by 100 and dividing both sides of the equation by 25 we will arrive at:
Y = 3 x 100/25
Y = 300%
Answer: 75 is 25 percent of 300
if AC= 40 find the length of jk
Answer:
JK = 24
Step-by-step explanation:
Δ BKJ and Δ BCA are similar and ratios of corresponding sides are equal, that is
[tex]\frac{JK}{AC}[/tex] = [tex]\frac{BK}{BC}[/tex] , substitute values
[tex]\frac{JK}{40}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )
5JK = 120 ( divide both sides by 5 )
JK = 24
What is the product?
8.25 x
1
5
0.82
O 1.65
0 8.25
16.5
Answer:
Answers
product, and assign a number to each person. ... 0.82. 12–13. 9. 0.18. 1.00. Total. 50. 1.00. F requency. 0. 1. 2. 3. 4. 5. 6. 7. 8 ... 3.12 (a) x = 25661.3333, ˜x = 25514.5 (b) Skewed ... N(8.25, 0.0002857).
Answer:
the answer is c
Step-by-step explanation:
i just took the test
I need help with this question. PLZZ HELP!!!
Answer: The solution of these inequalities are similar because they begin at two, however they are different because in the first inequality two cannot be an answer hence the open circle ⭕️, but the second inequality can have two as a solution hence the closed circle.
Step-by-step explanation:
To which set or sets below does the number -1/2 belong
Explanation:
The number -1/2 is rational as it is a fraction or ratio of two integers (-1 and 2). We can never have 0 in the denominator. Since it is rational, it means the number is not irrational. Recall that "irrational" means "not rational", so it is the opposite of rational.
-1/2 = -0.5 is not a whole number as it has a fractional or decimal portion. This means -1/2 is not an integer either, nor is it a natural number. The negative portion is another reason to exclude -1/2 from the list of whole numbers and natural numbers.
But we can say that -1/2 = -0.5 is a real number. Any number you encountered so far is a real number until you get to the complex numbers.
What is the scale factor of abc to def
Answer:
[tex]\large \boxed{\mathrm{B. \ 6}}[/tex]
Step-by-step explanation:
Length AB is similar to length DE.
Scale factor = DE/AB
Scale factor = 12/2
Scale factor = 6
The required Scale factor would be 6 to transform triangle ΔABC to triangle ΔDEF which is the correct option (B).
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.
Length AB is similar to length DE.
Here triangle ΔABC is dilated to form triangle ΔDEF
Length of the side DE = 12
Length of the side AB = 2
As we know scale factor is the ratio of sides in the original image and the image after dilation.
Scale factor = DE/AB
Substitute the values of the length of the side DE and AB,
Scale factor = 12/2
Apply the division operation, and we get
Scale factor = 6
Therefore, the required Scale factor would be 6 to transform triangle ΔABC to triangle ΔDEF.
Learn more about the Scale images here:
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At a furniture shop, every chair came with either 1 or 2 cushions. The ratio of
the number of chairs to the number of cushions was 7:11, what fraction of
the chairs came with 2 cushions?
Answer: 4/7
Step-by-step explanation:
the number of chairs = 7
the number of cushions = 11
Every chair has at least 1 cushion. There are 7 chairs so 7 cushions are used.
There is a total of 11 cushions and 7 cushions are already distributed to the chairs so there are 4 chairs with a 2nd cushion.
Chairs with 2 cushions ÷ Total chairs = 4/7
ITS REALLY IMPORTANT
can somebody please explain how to find the surface and lateral area please and thank you!!
Answer:
The lateral area of the figure = 480 m²
The surface area = 720 m²
Step-by-step explanation:
By definition, we have;
The lateral area is the area of the vertically facing sides of or the area of the triangular faces of a pyramid
The surface area is the area of the entire surface = Lateral area + The other surface areas of the object
For a pyramid, the surface area = Lateral area + Area of base
The figure in the question is a pentagon based pyramid with five triangles on the sides
The lateral area of the figure = 5 × area of the 5 triangles = 5 × Base × Height
The lateral area of the figure = 5 × 12 × 8 = 480 m²
The lateral area of the figure = 480 m²
The surface area = Area of the base + Lateral surface area
Area of the regular pentagon base = 1/2 × Perimeter of the pentagon × Apothem
Perimeter of the pentagon = 5 × 12 = 60 m
Apothem = Perpendicular distance from the pentagon's side to the center = 8.3 m
∴ Area of the regular pentagon base = 1/2 × 60 × 8 = 240 m²
∴ The surface area = 240 +480 =720 m²
The surface area = 720 m²
How many of the positive integer factors of 15552 are perfect squares? (WILL MARK BRAINLIEST IF CORRECT)
Answer:
The positive integer factors of 15552 that are perfect squares are;
1, 4, 9, 16, 36, 64, 91, 144, 324, 576, 1296, 5184
Step-by-step explanation:
The positive integer factors of 15552 are;
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 243, 288, 324, 432, 486, 576, 648, 864, 972, 1296, 1728, 1944, 2592, 3888, 5184, 7776, 15552
The perfect square integers are;
1 = 1 × 1
4 = 2 × 2
9 = 3 × 3
16 = 4 × 4
36 = 6 × 6
64 = 8 × 8
91 = 9 × 9
144 = 12 × 12
324 = 18 × 18
576 = 24 × 24
1296 = 36 × 36
5184 = 72 × 72
Therefore, the positive integer factors of 15552 that are perfect squares are;
1, 4, 9, 16, 36, 64, 91, 144, 324, 576, 1296, 5184.
Evaluate the expression 5^-2
Hi there! :)
Answer:
[tex]\huge\boxed{\frac{1}{25}}[/tex]
When evaluating an expression with a negative exponent, the reciprocal will need to be taken. Therefore:
[tex]5^{-2} = \frac{1}{5^{2} } = \frac{1}{25}[/tex]
Can you help me find all the seventh roots of unity? what do they look like graphed?
Answer:
There are seven seventh roots of unity, e2πki7 , all on the unit circle, r=1 above.
The first one is at θ=2π7=360∘7=5137 ∘ , and there are others at 4π7,6π7,8π7,10π7,12π7 and of course at 0 radians, i.e. unity itself.
How to find?
There are 4 fourth roots of unity and they are 1, i,−1 and−i
Each of the roots of unity can be found by changing the value of k k k in the expression e 2 k π i / n e^{2k\pi i/n} e2kπi/n. By Euler's formula, e 2 π i = cos ( 2 π ) + i sin ( 2 π ) = 1.
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps west and finally 50 steps on a bearing of 3150 . i. Sketch Musah's movement [Mark 4] ii. How far west is Musah's final point from the centre?
Answer:
Musah's final point from the centre = 60.355 steps
Step-by-step explanation:
From the given information:
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps west and finally 50 steps on a bearing of 315°
The sketch for this information can be seen in the attached file below.
How far west is Musah's final point from the centre?
In order to determine how far west is Musah's,
Let d be the distance of how far;
Then d = QR + RS cos θ
In the North West direction,
cos θ = cos 45°
d = 25 + 50( cos 45°)
d = 25 + 50( [tex]\dfrac{1}{\sqrt{2}}[/tex] )
d = 25 + 50( 0.7071)
d =25 + 35.355
d = 60.355 steps
Musah's final point from the centre = 60.355 steps
Find h, k, and p
Write the equation in standard form
Identify the missing pieces
Vertex (0,0); focus (0,-4)
Answer:
Step-by-step explanation:
This is a parabola. If we plot the vertex and the focus, we see that the focus is below the vertex. What this tells us is that the parabola opens "upside down" since the parabola wraps itself around the focus. If it opens upside down, then the format for the equation is
[tex]4p(y-k)=-(x-h)^2[/tex]
where p is the distance between the vertex and the focus (4), h is the first coordinate of the vertex (0), and k is the second coordinate of the vertex (0). Filling in the formula then:
[tex]4(4)(y-0)=-(x-0)^2[/tex] which simplifies down to
[tex]16y=-x^2[/tex] and then finally,
[tex]y=-\frac{1}{16}x^2[/tex]
Suppose the radius of a circle is 2. What is its circumference?
Answer:
12.57
Step-by-step explanation:
The formula to solve the circumference of a circle is:
2 x PI x R (radius)
=> 2 x PI x 2
=> 4 PI or 12.57
this is urgent...please help!
the brown family is ordering pizza. they are trying to decide whether to order a large pizza or a monster pizza. a monster pizza (m) has six fewer slices than twice the number of slices on a large pizza (l). the difference between the number of slices on a monster pizza and the number of slices on a large pizza is five slices. which system of equations below can be used to determine the number of slices on a large pizza and a monster pizza?
a) m - 2 l = 5
m - l = 6
b) 2m - l = 6
m - l = 5
c) 2m - l = -6
m - l = 5
d) m - 2 l = - 6
m - l = 5
Answer:
d) m - 2 l = - 6; m - l = 5
Step-by-step explanation:
Twice the number of slices on a large pizza is 2l. 6 fewer than that is 2l-6. This is the number on a monster pizza, so we have ...
m = 2l -6
Subtracting 2l from both sides gives the equation ...
m -2l = -6 . . . . . matches choice D
Simplify the following expression -10x + 10x
Answer:
0
Step-by-step explanation:
the x after the 10 is literally just 1
so 10 x 1 =10
-10 + 10 = 0
simplify (y+x) 2-2xy
Answer:
y² + x²
Step-by-step explanation:
Given
(y + x)² - 2xy ← expand (y + x)² using FOIL
= y² + 2xy + x² - 2xy ← collect like terms
= y² + x²
Ans2x + 2y -2xy
Step-by-step explanation:
First You need to distribute 2 to both x and y. 2x + 2y-2xy
Find the radius of a circle that has an area of 6.76 cm². Use it for pi.
Answer:
radius = 1.47 cmStep-by-step explanation:
Area of a circle = πr²
where
r is the radius
From the question
Area = 6.76 cm²
To find the radius substitute the value of the area into the above formula and solve for the radius
That's
[tex]6.76 = \pi \: {r}^{2} [/tex]
Divide both sides by π
We have
[tex] {r}^{2} = \frac{6.76}{\pi} \\ r = \sqrt{ \frac{6.76}{\pi} } [/tex]
r = 1.46689291
We have the final answer as
radius = 1.47 cm
Hope this helps you
One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hour is desired. Past studies suggest that a population standard deviation of hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Complete question:
One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hours is desired. Past studies suggest that a population standard deviation of 1.5 hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Answer:
111 students
Step-by-step explanation:
Given the following :
Margin of Error (E) = 0.28
Population standard deviation (sd) = 1.5
Recall:
Margin of Error(E) = Z * (sd/√n)
Taking a confidence interval of 95%
The Z value at a 95% confidence interval is 1.96
Plugging our values, we have :
Margin of Error(E) = Z * (sd/√n)
0.28 = 1.96 * (1.5/√n)
0.28 = 2.94 / √n
√n × 0.28 = 2.94
√n = 2.94 / 0.28
√n = 10.5
Square both sides to obtain n
n = 10.5^2
n = 110.25
2x + 3y = 40
5x + 2y = 30
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Hi my lil bunny!
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A) Let's solve for x. [tex]2x + 3y = 40[/tex]
Step 1: Add -3y to both sides.
[tex]2x + 3y + -3y = 40 + -3y[/tex]
[tex]2x = -3y + 40[/tex]
Step 2: Divide both sides by 2.
[tex]\frac{2x}{2} = \frac{-3y + 40}{2}[/tex]
[tex]x = \frac{-3}{2} y + 20[/tex]
Answer : [tex]\frac{-3}{2} y + 20[/tex]
~~~~~~~~~~~~~~~~~
B) Let's solve for x. [tex]5x + 2y = 30[/tex]
Step 1: Add -2y to both sides.
[tex]5x + 2y + -2y = 30 + -2y[/tex]
[tex]5x = -2y + 30[/tex]
Step 2: Divide both sides by 5.
[tex]\frac{5x}{5} = \frac{-2y + 30}{5}[/tex]
[tex]x = \frac{-2}{5} y + 6[/tex]
Answer : [tex]\frac{-2}{5} y + 6[/tex]
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Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
If the graphs of the linear equations in a system are the same line, what does that mean about the possible solution or solutions of the system?
Answer:
If we have a system of linear equations:
y = a*x + b
y = c*x + d
And the graphs of the equations are the same line, this means that both lines have the same equation, then:
a = c and b = d.
Then we have only one equation (but repeated) and two variables, then we have infinite solutions for our system.
Another way to see this is:
When we have a system of linear equations, the solution is the point where the lines intersect.
But if both lines are the same line, then the lines intersect in infinite points, then we have infinite solutions.
Evaluate the following expression if a=-9, b=-7,c=9 and d=3
2cd + 3ab =
Answer:
The answer is 243.Step-by-step explanation:
To evaluate the expression substitute the values of a , b , c and d into the above expression
a = - 9
b = - 7
c = 9
d = 3
So we have
2cd + 3ab = 2(9)(3) + 3(-9)(-7)
= 2(27) + 3( 63)
= 54 + 189
We have the final answer as
243Hope this helps you
Em um posto de combustível, o litro da gasolina estava custando R$2,40.Um cliente gastou R$72,00 para encher o tanque de seu carro. O valor do litro da gasolina sofreu 2 aumentos sucessivos,ambos de 10%. Quando o mesmo cliente gastara para encher o tanque do seu carro, após esees aumentos
Answer:
english i think u need hekp
factor of x^3+x^2y+xy^2
Answer:
[tex] x(x {}^{2} + xy + y {}^{2})[/tex]
Step-by-step explanation:
[tex]x {}^{3} + x {}^{2}y + xy {}^{2} = x(x {}^{2} + xy + y {}^{2})[/tex]
Hope this helps ;) ❤❤❤
Please help At a party of 102 people, 72 lb of potato salad is served. Write and solve and equation to find how many people each pound of potato salad serves.
Answer:
1.417
Step-by-step explanation:
102/72=1.417
2 Mayra is a caterer and charges $75 per plate plus a
set up fee of $30. The cost per person is represented
by C = 30+75p. If she is catering a wedding for 150
people, how much does the bride and groom spend
on food?
Answer:
$11,280
Step-by-step explanation:
Plug in 150 as p into the equation to solve for the cost, C:
C = 30 + 75p
C = 30 + 75(150)
C = 30 + 11,250
C = 11,280
= $11,280
y=-2x+4 missing value
Answer:
y=-2x+4
x | y
0 | 4
2 | 0
Step-by-step explanation:
