Hello, the product of the roots is
[tex]\dfrac{3p}{2}[/tex]
So, if there are reciprocal roots, their product is 1, and then
[tex]\dfrac{3p}{2}=1<=> p=\dfrac{2}{3}[/tex]
Thank you
how to solve the quadratic equation y = 15x2 + 4x - 4 using the factoring method.
Which of the following is an example of the difference of two squares? x2−9x2−9 (x−9)2 x3−9x3−9 (x+9)2
Answer: x²−9
Step-by-step explanation:
A square number is obtained ehen we multiply a number to itself.
For example: 5 × 5 = 5² = 25 [It is a square number]
We can do this in expression too, For example: z×z =z²
From all the given options, only x²−9 has both terms as square.
∵ x² = x × x
and 9 = 3×3= 3²
So that, x²−9 =(x)²-(3)²
Hence, the correct option is x²−9.
the square of an integer creates a
Answer:
It creates a positive integer.
Step-by-step explanation:
Integers are whole number which could be negative or positive. Examples are; 2, 3, -1, -7 -5 etc.
Whenever an integer is squared, a positive integer is created. For example, let us consider integers; 3, 4, -3 and -4.
[tex](3)^{2}[/tex] = 3 × 3 = 9
[tex](-3)^{2}[/tex] = -3 × -3 = 9
Also,
[tex](4)^{2}[/tex] = 4 × 4 = 16
[tex](-4)^{2}[/tex] = -4 × -4 = 16
Therefore, the square of an integer creates a positive integer.
The perimeter of a rectangle is 24 m. The length is 30 m less than five times the width. Find the dimensions of the rectangle. List answer as follows: width, length.
Answer:
width = 7 mlength = 5 mStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
where
l is the length
w is the width
From the question
Perimeter = 24m
The statement
The length is 30 m less than five times the width is written as
l = 5w - 30
Substitute the expression into the above formula and solve for the width
That's
24 = 2( 5w - 30) + 2w
24 = 10w - 60 + 2w
84 = 12w
Divide both sides by 12
w = 7
Substitute this value into l = 5w - 30
That's
l = 5(7) - 30
l = 35 - 30
l = 5
Therefore the dimensions are
width = 7 m
length = 5 m
Hope this helps you
Solve the following
equation
85= -5(1 - 2n)
n=12
n = 15
n = -15
n=-8
Answer:
n = 9
Step-by-step explanation:
Step 1: Solve the equation
85 = -5 + 10n
90 = 10n
n = 9
Therefore n is equal to 9
Which expression is equivalent to y.y.y.z.z.z.z
Answer:
y^3z^4
Step-by-step explanation:
y*y*y*z*z*z*z
y*y*y=y^3
z*z*z*z=z^4
Together,
y^3z^4
Hope this helps ;) ❤❤❤
Answer:
your answer is A, y³ z⁴
Step-by-step explanation:
it was correct for me.
If there is a discount of 40% on an article costing #7000, then the price after discount is
Answer:
The answer is # 4200Step-by-step explanation:
A discount of 40% was allowed on the price
To find the price after the discount first calculate the discount and subtract it from the original price
That's
[tex] \frac{40}{100} \times 7000[/tex]
= 2800
So the price after the discount is
#7000 - #2800
Which is
# 4200Hope this helps you
Solve for x
-2x+2-7x= -70
Answer:
x=8
Step-by-step explanation:
-2x+2-7x=-70
Minus two from each side.
-2x-7x=-72
Combine like terms.
-9x=-72
Divide -9 from each side.
x=8
please someone help me...
2cos pi/13 cos 9pi/13+ cos 3pi/13 +cos 5pi/13
=cos 10 pi/13 +cos 8 pi/13 +cos 3pi/13 +cos 5pi/13
=cos 10 pi/13 +cos 3pi/13 +cos 8pi/13 +cos 5pi/13
=2 cos pi/2 .cos 7 pi/26 +2 cos pi/2 .cos 3 pi /26
=2 (0)cos 7 pi /26 + 2(0) cos 3pi/26
=0 =R.H.S.
Answer: see proof below
Step-by-step explanation:
Use the following identities:
2cos x · cos y = cos(x + y) + cos(x - y)
cos x + cos y = 2 cos (x + y)/2 · cos(x - y)/2
Use the Unit Circle to evaluate: cos(π/2) = 0
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad 2\cos \dfrac{9\pi}{13}\cos \dfrac{\pi}{13}\quad +\quad \cos \dfrac{3\pi}{13}+\cos \dfrac{5\pi}{13}\\\\\text{Identity:}\qquad \quad \cos\bigg(\dfrac{9\pi}{13}+\dfrac{\pi}{13}\bigg)+ \cos\bigg(\dfrac{9\pi}{13}-\dfrac{\pi}{13}\bigg)+\quad \cos\bigg(\dfrac{3\pi}{13}\bigg)+\cos \bigg(\dfrac{5\pi}{13}\bigg)[/tex]
[tex]\text{Simplify:}\qquad \qquad \cos\bigg( \dfrac{10\pi}{13}\bigg)+\cos \bigg(\dfrac{8\pi}{13}\bigg)+\qquad \cos\bigg(\dfrac{3\pi}{13}\bigg)+\cos \bigg(\dfrac{5\pi}{13}\bigg)[/tex]
[tex]\text{Regroup:}\qquad \qquad \cos\bigg( \dfrac{10\pi}{13}\bigg)+\cos \bigg(\dfrac{3\pi}{13}\bigg)\quad +\quad \cos\bigg(\dfrac{8\pi}{13}\bigg)+\cos \bigg(\dfrac{5\pi}{13}\bigg)[/tex]
[tex]\text{Identity:}\qquad 2\cos \bigg(\dfrac{10\pi+3\pi}{13\cdot 2}\bigg)\cdot \cos \bigg(\dfrac{10\pi-3\pi}{13\cdot 2}\bigg)+\quad 2\cos\bigg(\dfrac{8\pi+5\pi}{13\cdot 2}\bigg)\cdot \cos\bigg(\dfrac{8\pi-5\pi}{13\cdot 2}\bigg)[/tex]
[tex]\text{Simplify:}\qquad 2\cos \bigg(\dfrac{13\pi}{26}\bigg)\cdot \cos \bigg(\dfrac{7\pi}{26}\bigg)+\quad 2\cos\bigg(\dfrac{13\pi}{26}\bigg)\cdot \cos\bigg(\dfrac{3\pi}{26}\bigg)\\\\\\.\qquad \qquad =2\cos \bigg(\dfrac{\pi}{2}\bigg)\cdot \cos \bigg(\dfrac{7\pi}{26}\bigg)+\quad 2\cos\bigg(\dfrac{\pi}{2}\bigg)\cdot \cos\bigg(\dfrac{3\pi}{26}\bigg)\\\\\\\text{Factor:}\qquad =2\cos\bigg(\dfrac{\pi}{2}\bigg)\bigg[ \cos \bigg(\dfrac{7\pi}{26}\bigg)+ \cos \bigg(\dfrac{3\pi}{26}\bigg)\bigg][/tex]
[tex]\text{Unit Circle:}\quad 2(0)\bigg[ \cos \bigg(\dfrac{7\pi}{26}\bigg)+ \cos \bigg(\dfrac{3\pi}{26}\bigg)\bigg][/tex]
Product of Zero 0
LHS = RHS: 0 = 0 [tex]\checkmark[/tex]
The temperature of a freezer started at 18 degrees Celsius.After cooling for a few hours, the freezer had a temperature of -12 degrees Celsius. What is the difference between the new,colder temperature and the original temperature?
Answer:
Step-by-step explanation:
Difference = New temperature - original temperature
= -12 - (18)
= - 30
New temperature is 30° less than the original temperature
what value of x that will make x/3 - 2 = - 11/4
Answer:
x = -9/4
Step-by-step explanation:
x/3 - 2 = - 11/4
Add 2 to each side
x/3 - 2+2 = - 11/4+2
Get a common denominator on the right
x/3 = -11/4 + 8/4
x/3 = -3/4
Multiply each side by 3
x/3*3 = -3/4 *3
x = -9/4
Answer:
[tex]$ x= -\frac{9}{4} $[/tex]
Step-by-step explanation:
[tex]$\frac{x}{3} - 2 = -\frac{11}{4} $[/tex]
[tex]$\frac{x}{3} -\frac{6}{3} = -\frac{11}{4} $[/tex]
[tex]$ \frac{x-6}{3} = -\frac{11}{4} $[/tex]
Multiply both sides by 3
[tex]$ x-6 = -\frac{33}{4} $[/tex]
[tex]$ x= -\frac{33}{4} + 6$[/tex]
[tex]$ x= -\frac{33}{4} + \frac{24}{4} $[/tex]
[tex]$ x= -\frac{9}{4} $[/tex]
what is a postulate?
Answer:
A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived.
Step-by-step explanation:
The Addition Postulate: If you have one apple and Sally has one apple, when you both add the same quantity to your existing number of apples, you'll still have the same number of apples. Using algebra, the postulate states:
If x = y, then x + 4 = y + 4
The Subtraction Postulate: If you have ten apples and Sally has ten apples, when you both subtract the same quantity of apples from your existing number of apples, you'll still have the same number of apples.
If x = y, then x - 3 = y - 3
Without being repetitive, these same principles apply to both multiplication and division.
The Multiplication Postulate: If x = y, then x * 3 = y * 3
The Division Postulate: If x = y, then x / 7 = y / 7
Answer:
suggest or assume the existence, fact, or truth of (something) as a basis for reasoning, discussion, or belief.
Step-by-step explanation:
A bricklayer is building a wall. Each layer of the wall has the same number of bricks. The points on the following coordinate plane show how many bricks he used to make 2, 3, and 4 layers of the wall.
Answer:
50
Step-by-step explanation:
Follow the graph and the bricks go up by 50 per 1 layer
For 1 layer 50 bricks, for 2 layers 100 bricks, for 3 layers 150 bricks, and for 4 layers he uses 200 bricks.
What is a linear graph?The graph for a straight line is called the linear graph in the linear graph the increment of the data for both the axes is constant so it gave a linear relationship.
As we can see in the graph there is a relationship between the number of bricks and the layers of the bricks.
Therefore, for 1 layer 50 bricks, for 2 layers 100 bricks, for 3 layers 150 bricks, and for 4 layers he uses 200 bricks.
To know more about linear graphs follow
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Simplify the expression -1/2(-5/6 + 1/3)
Answer: 1/4
Step-by-step explanation:
-
Answer:
5/12 - 1/6
Step-by-step explanation:
Took the diagnostic
-6 + x = -5
Solving one and two step equations
Answer:
1
how did i get it:
-6 - (-5) = 1
is y = -5x a function
Answer:
Yes, it is.
Step-by-step explanation:
For each x we get y, and no two xes give the same y
Write a problem based on the given information.
P = Cost of dinner
0.15p = cost of a 15% tip
P + 0.15p = 23
Answer:
Total cost of dinner = P + 0.15p = 23
Step-by-step explanation:
Consider the information provided.
The cost of dinner at a restaurant is $P.
The tip offered for the service was, $0.15p.
The total of the cost of dinner and the tip offered for the service is:
T = P + 0.15p = 23
Suppose Mr. Swanson turns in a late order for 1 veggie sandwich and 1 chicken sandwich. What is the new ratio of chicken sandwiches to veggie sandwiches?
Answer:
6 chicken sandwiches to 4 veggie sandwiches
Step-by-step explanation:
edge 2020
What is the first derivative of r with respect to t (i.e., differentiate r with respect to t)? r = 5/(t2)Note: Use ^ to show exponents in your answer, so for example x2 = x^2. Also, type your equation answer without additional spaces.
Answer:
The first derivative of [tex]r(t) = 5\cdot t^{-2}[/tex] (r(t)=5*t^{-2}) with respect to t is [tex]r'(t) = -10\cdot t^{-3}[/tex] (r'(t) = -10*t^{-3}).
Step-by-step explanation:
Let be [tex]r(t) = \frac{5}{t^{2}}[/tex], which can be rewritten as [tex]r(t) = 5\cdot t^{-2}[/tex]. The rule of differentiation for a potential function multiplied by a constant is:
[tex]\frac{d}{dt}(c \cdot t^{n}) = n\cdot c \cdot t^{n-1}[/tex], [tex]\forall \,n\neq 0[/tex]
Then,
[tex]r'(t) = (-2)\cdot 5\cdot t^{-3}[/tex]
[tex]r'(t) = -10\cdot t^{-3}[/tex] (r'(t) = -10*t^{-3})
The first derivative of [tex]r(t) = 5\cdot t^{-2}[/tex] (r(t)=5*t^{-2}) with respect to t is [tex]r'(t) = -10\cdot t^{-3}[/tex] (r'(t) = -10*t^{-3}).
what is 8.5 divided by 390
0.2017 this is the answer i got
Answer:
0.02179
Step-by-step explanation:
8.5÷390 = 0.02179
Factorise: 5(2^n)+2^n+2
Answer:
2 ( n + 2 ) ( n + 1 2 )
Step-by-step explanation:
coefficient of the first term:
2 = 2 × 1
coefficient of the last term:
2 = 2 × 1
coefficient of the middle term (using only the factors above):
5 = 2 × 2 + 1 × 1
2 n 2 + 5 n + 2 = ( 2 n + 1 ) ( n + 2 )
Alternative method:
Treat the given expression as a quadratic set equal to zero, with the form
a n 2 + b n + c
and use the quadratic formula
− b ± √ b 2 − 4 a c 2 a
This will given solutions
n = − 2 and n = − 1 2
for a factoring
2 ( n + 2 ) ( n + 1 2 )
Hope this helped
Find the value of x. A. 13 B. 9 C. 12 D. 10
Answer:
D. 10
Step-by-step explanation:
9+4=13
x+3=13
x=10
The value of x is 10 which is correct option (D).
What is the Angles of Intersecting Secants Theorem?Angles of Intersecting Secants Theorem states that, If two lines intersect outside a circle, then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs.
Given that,
Length of CW = 9 units,
Length of WV = 4 units,
Length of WU = 3 units,
Length of TW = x units,
⇒ Length of CW + Length of WV = Length of CV
⇒ 9 + 4
⇒ 13
⇒ Length of TW + Length of WU = Length of CV
⇒ x + 3 = 13
⇒ x = 10 - 3
⇒ x = 10
Hence, the value of x is 10 which is correct option (D).
Learn more about Secants theorem here:
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Give an example of an exponential function that includes the following transformations: o Vertical Compression o Reflection in the y-axis o Horizontal Stretch o Horizontal Translation to the left o Vertical Translation down
Step-by-step explanation:
A transformation may be defined as taking a basic function and then changing it slightly with the predetermined methods. This changes will cause the required graph of that function to shift, move or stretch, which depends on the type of the transformation.
For example:
Let a function be : [tex]$f(x)= B^x$[/tex]
For any constants m and n, the function [tex]$f(x)= B^{x+m}+n$[/tex] shifts the parent function.
- vertically n units and in same direction of the sign of n.
- horizontally m units and towards the opposite direction of the sign of m.
- The y-intercept becomes ([tex]$0, b^m+n$[/tex])
- The horizontal asymptote becomes y = n.
- the reflection about x -axis becomes [tex]$f(x)=- B^x$[/tex]
On a map, two locations are 0.75 cen timeter apart. Their actual distance is 15 kilometers apart. What scale could be shown on the map? Select three options.
Options:
A.0.25 centimeter = 3 kilometers
B.0.4 centimeter = 8 kilometers
C.0.75 centimeter = 15 kilometers
D.3 centimeters = 60 kilometers
E.6 centimeters = 144 kilometers
Answer:
B, C, D
Step-by-step explanation:
Distance between the two locations :
On map = 0.75 centimeter
Actual = 15 km
Using the scale drawing notation :
On map : actual
0.75 cm : 15 km
Therefore,
Actual / on map
15 / 0.75 = 20
This means :
1 cm on map represents 20 km on land
0.25 cm on map = (20 * 0.25) = 5 kilometers
0.4 cm on map = (20 * 0.4) = 8 kilometers
0.75 cm on map = (20 * 0.75) = 15 kilometers
3 cm on map = (20 * 3) = 60 kilometers
6 cm on map = (20 * 6) = 120 kilometers
Hence, only options B, C and D are correct
Answer:
b,c,d are correct.
Step-by-step explanation:
just shortened the answer above me°∪°
can i get the answer for number 16
Answer:
25
Step-by-step explanation:
For each problem, the two numbers on the left are perfect squares. The number in the upper right is the square of the difference between the two numbers on the left. The number on the bottom right is equal to the number on the upper right plus the number on the upper left.
For problem 16, we know that the square of the difference between 36 and the missing number is 121. The square root of 121 is 11, so the missing number is 36 - 11 = 25 which fits the pattern because it is also a perfect square.
(Also if you look at problem 15, it basically gives you the answer to problem 16.)
Answer:
See below
Step-by-step explanation:
The upper left box and the bottom left box are being subtracted. When the result is obtained we square it and the squared answer is written in the top right box. After that , the squared answer and the top left answer are added to get the bottom left answer.
See the attached file.
how would i find y in this situation
Answer:
C.) 7√2/2
Step-by-step explanation:
tan¤ = opp/adj
tan 45° = y/7√2/2
1 = y/7√2/2
1 = 2y/7√2
7√2 = 2y
2y = 7√2
y = 7√2/2
NOTE: ¤ = Theta
The table represents the total miles traveled, y, after a number of hours, x.
Hours, x
Miles, y
2.5
150
4.0
240
5.5
330
7.0
420
Which linear equation represents the situation?
y = 60 x
y = 60 x + 480
y = 4 x + 240
y = 270 x
Answer: Y=60x
Step-by-step explanation:
find the slope (Y2-Y1)/(X2-X1)
(240-150)/4-2.5)
90/1.5 =60
It's multiple choice so it can only be a or b. If you do 60 x 2.5 you get 150 so there's no way you will add 480 so you are done it's A. If it's not a multiple choice question then you would do the who y=mx+b and plug in x, y and m and then find the b which in this case would be 0.
Answer:
(2.5,150)(4,240)
slope = (240 - 150) / (4 - 2.5) = 90 / 1.5 = 60
y = mx + b
slope(m) = 60
(4,240)...x = 4 and y = 240
now we sub and find b, the y int
240 = 60(4) + b
240 = 240 + b
240 - 240 = b
0 = b
so ur equation is : y = 60x + 0 which is written as : y = 60x <==
A body at rest and of mass
5kg is acted upon by a force
for 0.2s. Find the increase in
momentum.
f(x) = x; translation
6 units down followed by a
vertical stretch by a factor
of 5
g(x) = 5x = 6
Answer:
the transformed function becomes: g(x) = 5 x - 30
Step-by-step explanation:
When the function f(x) = x is shifted down by a factor of 6 we have the following transformation:
f(x) --> x - 6
After this, a vertical stretch by a factor of 5 should affect the full functional expression in the following way:
5 ( x - 6) = 5 x - 30
Therefore the transformed function becomes: g(x) = 5 x - 30
can some one solve this pls[tex]\int\limits^\frac{1}{\sqrt{2}}_0 \frac{1}{\sqrt{1-x^{2} } }[/tex]
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]x(t)=sin(t)\\\\dx=cos(t)dt\\\\\text{For x = }\dfrac{1}{\sqrt{2}}=\dfrac{\sqrt{2}}{2} \text{ we have } t = \dfrac{\pi}{4}[/tex]
So, we can write.
[tex]\displaystyle \int\limits^{\dfrac{1}{\sqrt{2}}}_0 {\dfrac{1}{\sqrt{1-x^2}}} \, dx =\int\limits^{\dfrac{\pi}{4}}_0 {\dfrac{cos(t)}{\sqrt{1-sin^2(t)}}} \, dt\\\\=\int\limits^{\dfrac{\pi}{4}}_0 {\dfrac{cos(t)}{\sqrt{cos^2(t)}}} \, dt\\\\=\int\limits^{\dfrac{\pi}{4}}_0 {\dfrac{cos(t)}{cos(t)}} \, dt \\\\=\int\limits^{\dfrac{\pi}{4}}_0 {1} \, dt\\\\=\large \boxed{\sf \bf \dfrac{\pi}{4}}[/tex]
Thank you
Answer: [tex]\bold{\dfrac{\pi}{4}}[/tex]
Step-by-step explanation:
Note the following integral formula: [tex]\int\limits^a_b {\dfrac{1}{\sqrt{1-x^2}}} \, dx =\sin^{-1}(x)\bigg|^a_b[/tex]
We can rationalize the denominator to get: [tex]\dfrac{1}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)=\dfrac{\sqrt2}{2}[/tex]
*************************************************************************************
[tex]\int\limits^{\frac{\sqrt2}{2}}_0 {\dfrac{1}{\sqrt{1-x^2}}} \, dx \\\\\\=\sin^{-1}(x)\bigg|^{\frac{\sqrt2}{2}}_0\\\\\\= \sin^{-1}\bigg(\dfrac{\sqrt2}{2}\bigg)-\sin^{-1}(0)\\\\\\=\dfrac{\pi}{4}-0\pi\\\\\\=\large\boxed{\dfrac{\pi}{4}}[/tex]