Question:
Let [tex]p=x^2-2[/tex] .
Which equation is equivalent to in terms of p ?
Answer:
[tex]p^2+18=9p[/tex] or [tex]p^2+18 - 9p = 0[/tex]
Step-by-step explanation:
Given
[tex]p=x^2-2[/tex] .
Required
Find the equation equivalent to [tex](x^2-2)^2+18=9x^2-18[/tex]
To get the equation equivalent to the given expression, we simply simplify [tex](x^2-2)^2+18=9x^2-18[/tex] and solve in terms of p
[tex](x^2-2)^2+18=9x^2-18[/tex]
Factorize expression on the right hand side
[tex](x^2-2)^2+18=9(x^2-2)[/tex]
Substitute [tex]x^2 - 2[/tex] for p
[tex](x^2-2)^2+18=9(x^2-2)[/tex] becomes
[tex]p^2+18=9p[/tex]
Hence, equation [tex]p^2+18=9p[/tex] is equivalent to [tex](x^2-2)^2+18=9x^2-18[/tex]
Solving further to get the value of p
[tex]p^2+18=9p[/tex]
Subtract 9p from both sides
[tex]p^2+18 - 9p = 9p - 9p[/tex]
[tex]p^2+18 - 9p = 0[/tex]
Rearrange
[tex]p^2 - 9p +18 = 0[/tex]
Factorize
[tex]p^2 - 6p - 3p +18 = 0[/tex]
[tex]p(p - 6) - 3(p -6) = 0[/tex]
[tex](p - 3)(p -6) = 0[/tex]
p - 3 = 0 or p - 6 = 0
p = 3 or p = 6
Answer:
p^2-18+9p=0
Step-by-step explanation:
Khan
Given that sinθ=3/5
, find cosθ
and tanθ
. Write your answers as fractions in simplest form.
Answer:
cos θ = 4/5.
tan θ = 3/4.
Step-by-step explanation:
Given sin θ = 3/5, we can find the value for the other side of the right triangle.
Using the Pythagorean formula, we can derive the value of this other leg.
5² = 3² + x²
x = 4.
Since sin θ is O/H, the Hypoteneus is 5 and the Opposite side is 3. The Adjacent side is 4, which will be used when finding cos θ and tan θ.
cos θ= A/H --> cos θ = 4/5.
tan θ= O/A --> tan θ = 3/4.
Find the solution to this system:
Equation 1: 5x – 2y = -11 (2)
Equation 2: -2x + 5y = 17
Step #2
Multiplying Equation 2 by will create additive
inverses for the x-coefficients.
Answer:
Step 1: Equation 1 can be multiplied by 2, Multiplying Equation 2 by 5
Step 2: divide by 21
Step 3: substitute 3 for y in one of the equations
Step 4: add 6
Step 5: divide both sides of the equation by 5
Step-by-step explanation:
The solution for the given set of equation 5x - 2y = -11 and -2x + 5y = 17 is x = -1 and y = 3.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given set of equation is,
5x - 2y = -11 (1)
-2x + 5y = 17 (2)
Find the value of x from equation (2),
-2x + 5y = 17
2x = 5y - 17
x = (5/2)y -17/2
Substitute the value of x in equation (1),
5((5/2)y -17/2) - 2y = -11
25y/2 - 85/2 - 2y = -11
21y/2 = 63/2
y = 3
Substitute the value of y in equation (2) to get the value of x,
-2x + 15 = 17
x = -1
The value of x is -1 and y is 3.
The additive inverse for the x coefficient in equation (2) is 2x.
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Find the zeros of the function h(x)=x^2+23x+60 by factoring.
Answer:
x = - 20, x = - 3
Step-by-step explanation:
To find the zeros, let h(x) = 0, that is
x² + 23x + 60 = 0
Consider the factors of the constant term (+ 60) which sum to give the coefficient of the x- term (+ 23)
The factors are + 20 and + 3, since
20 × 3 = 60 and 20 + 3 = 23, thus
(x + 20)(x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 20 = 0 ⇒ x = - 20
x + 3 = 0 ⇒ x = - 3
Find f(–2) for the function f(x) = 3x2 – 2x + 7
Answer: The Answer Is 23
Step-by-step explanation:
Answer:
the answer is 23,
Step-by-step explanation:
i took the test and got it right!!!
How would you solve dy/dx = 4x - 2, y(-1) = 1 using differential equations?
Answer:
y=2(x square)-2x-3
Step-by-step explanation:
Let dy with y varibles in a hand
And dx with x variables on the other hand
dy=(4x-2)dx
Then by integration
y=2(square x)-2x+constant
Then substitute by x=-1 and y=1 to find the value of the constant
1=2(1)-2(-1)+ constant
Then constant=-3
Then the equation is
y=2(x square)-2x-3
An octopus weighed 5 6 kilograms. After two weeks, its weight was increased by 3 10 kilograms. But afterward, it lost 1 5 kilograms in weight as it was sick. What is its current weight?
Answer:
The current weight of the octopus is:
[tex]w = \frac{14}{15}\,kg[/tex]
Step-by-step explanation:
The current weight is determine by addition and subtraction of rational numbers:
[tex]w = \frac{5}{6}\,kg + \frac{3}{10}\,kg -\frac{1}{5}\,kg[/tex]
[tex]w = \frac{50 + 18}{60}\,kg - \frac{1}{5}\,kg[/tex]
[tex]w = \frac{68}{60}\,kg - \frac{1}{5} \,kg[/tex]
[tex]w = \frac{17}{15}\,kg - \frac{1}{5}\,kg[/tex]
[tex]w = \frac{85-15}{75} \,kg[/tex]
[tex]w = \frac{70}{75}\,kg[/tex]
The current weight of the octopus is:
[tex]w = \frac{14}{15}\,kg[/tex]
Find the sum. 1/6+ √6
Answer:
2.6
Step-by-step explanation:
Answer:
2.6161564..
Step-by-step explanation:
12 is 3/4 of what number
Answer:
Step by step: you need to divide the top and multiple by the bottom. 12 divided by 3 is 4, and 4 times 4 is 16
Answer:
16
Step-by-step explanation:
The formula to solve for this is [tex]\frac{is}{of}=\frac{percent}{100}[/tex]
Here the 12 is our "is", the "of" is the [tex]\frac{3}{4}[/tex] , and the "percent" is what we are solving for so we can replace it for "x"
So now replacing our values we have [tex]\frac{12}{\frac{3}{4} } =\frac{x}{100}[/tex]
Cross multiplying we get [tex](12)(100) = (x)(\frac{3}{4} )[/tex]
Which then simplifies to
Then multiplying both sides by 4 to get rid of the fraction we get 4800% = 3x
The we need to divide by 3 and we get 1600% = x
Now this is in a percentage, so we need to divide 1600 by 100 to turn it into a whole number which comes out to x = 16
Which equation represents the sum of eight times a number and seven is twice the number
Answer:
8n + 7 = 2n
Step-by-step explanation:
A locker combination consists of two non-zero digits, and each combination consists of different digits. Event A is defined as choosing an even number as the first digit, and event B is defined as choosing an even number as the second digit. If a combination is picked at random, with each possible locker combination being equally likely, what is P(A and B) expressed in simplest form? A. 1/6 B. 5/18 C. 1/2 D. 5/9
Answer:
B. 5/18
Step-by-step explanation:
We have to digits taking the 0, they are as follows:
1, 2, 3, 4, 5, 6, 7, 8, 9
In other words, there are 9 in total.
Odd are 5 (1, 3, 5, 7, 9)
Pairs are 4 (2, 4, 6, 8)
Now, we have that the probability of drawing an odd one would be: 5/9
and that also, already selected that number, there would be 8 in total.
Therefore, drawing another number that is even the probability would be: 4/8
So the final probability is:
(5/9) * (4/8) = 20/72, we simplify (divide by 4) and we have 5/18 left
In other words, the answer is B. 5/18
Answer:
b
Step-by-step explanation:
x more than the square root of 400 is 50.
Answer:
Step-by-step explanation:
x + sqrt(400) = 50
x + 20 = 50
x = 30
what is (18-7)+(5+7)
Answer:
its 23!
Step-by-step explanation:
18-7=11
5+7=12
11+12=23!
what are the domain and range of f(x)=log x-5
Answer:
Is this what you needed?
RELATED QUESTION..........
BCGF is a quadrilateral, angles sum to 360 degrees.
B+C+G+F=360
B and G are right angles, formed by a radius and a tangent.
90+C+90+F=360
C+F=180
C and F are supplementary.
2x + 146 + 4x + 238 = 180
6x + 384 = 180
6x = -204
x = -34
Answer: -34, second choice
Emilio worked for 19.5 hours. He earned $497.25.
How much did Emilio earn per hour?
A: 26.16
B: $25.50
C: $20.88
B: $20.37
Answer:
B
Step-by-step explanation:
497.25/19.5=25.50
Answer:
B. $25.50
Step-by-step explanation:
if Emilio worked for 19.5 hours to earn $497.25 then how much wldid he earn perhour? ylwhen you put this in equation form
19.5h=$497.25
1h=? (so you crisscross them)
so 1h×$497.25÷19.5h (hour is divided by itself=1)
so Emilio earned $25.50 per hour.
What is the volume of the rectangular prism? 21 mm3 76.5 mm3 80 mm3 267.75 mm3
Please consider the complete question.
A prism has a length of 9 millimeters, height of 3 and one-half millimeters, and width of 8 and one-half millimeters. What is the volume of the rectangular prism?
We know that volume of rectangular prism is product of its length, width and height.
[tex]V=\text{Length}\times\text{Width}\times \text{Height}[/tex]
[tex]V=9\text{ mm}\times8\frac{1}{2}\text{ mm}\times 3\frac{1}{2}\text{ mm}[/tex]
Let us convert our given mixed fraction into decimal.
[tex]V=9\text{ mm}\times8.5\text{ mm}\times 3.5\text{ mm}[/tex]
[tex]V=267.75\text{ mm}^3[/tex]
Therefore, the volume of the given prism would be [tex]267.75\text{ mm}^3[/tex] and option D is the correct choice.
Answer:
D
Step-by-step explanation:
The ladder of a slide forms a 67 degree angle with the ground. The distance from the top of the ladder to the bottom of the ladder is 10 feet. The slide is 15 feet long. What angle does the slide make with the ground?
A. 71.9
B.47.9
C.37.9
D.23.0
Answer:
71.9 i think
Step-by-step explanation:
PEMDAS is used to help us remember the "order of operations." What do we use to help us remember the right triangle trig formulas? Hint: It start with s and ends with a.
Answer:
SOH CAH TOA
(Sine,opposite,Hypotenuse) - SOH
(Cosine, adjacent, Hypotenuse) - CAH
(Tangent,opposite,adjacent) - TOA
Step-by-step explanation:
Answer:
SOH CAH TOA
is the answer
You roll a fair 6-sided die.
What is P(roll greater than 6)?
If necessary, round your answer to 2 decimal places.
Answer:
1/3
Step-by-step explanation:
3(x + 2) + 4(2x - 1) = 5(x - 2)
may I ask how to do
????????
Answer:
it's 2 I already took the quiz
Use the Pythagorean theorem to find b .
Answer:
b = 5
Step-by-step explanation:
We can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
12^2 + b^2 = 13^2
144+b^2 =169
Subtract 144 from each side
144-144+b^2 = 169-144
b^2 = 25
Take the square root on each side
sqrt(b^2) = sqrt(25)
b = 5
Answer:
B= 5
Step-by-step explanation:
Jorge is making 6 large salads and 4 small salads how many cherry tomatoes does he need.
Which inequality statement describes the two numbers on a number line?
*6 and a number 10 units to the left of 6"
A)
10 > 6
B)
10 < 6
C)
-4> 6
D)
Answer:
-4 > 6
Step-by-step explanation:
So it would be -4 > 6 because you have 6 on the right, and 6 - 10 is -4, which is on the left.
A cone is of radius 6 cm and its height is 10 cm . The volume of the cone is __________ π cm3
please help
20 pointss
Answer:
376.99 cm
Step-by-step explanation:
V=πr2h^3
Only do question 5
50 points
Topic: Percentage
Answer:
.2%
.6%
40.25%
Step-by-step explanation:
There are 100 blocks in a grid so a complete grid is 100 %
a 2/10 out of 1 block is shaded
2/10 out of 100
.2 out of 100
out of 100 means percent
.2 %
b 3/5 out of 1 block is shaded
6/10 out of 100
.6 out of 100
out of 100 means percent
.6%
c 40 /100 + 1/4 out of 1 block
40% + .25 %
40.25%
A country's population in 1991 was 26 million.
In 1999 it was 28 million. Estimate
the population in 2006 using the exponential
growth formula. Round your answer to the
nearest million.
P = Aekt
Answer:
30 million
Step-by-step explanation:
i just spared my question to get the answer. it is 30 million. have a good day.
The estimated population in 2006 was 33 million.
What is the exponential function?Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round.
The exponential growth formula is:
Pn = Po × (1 + r)ⁿ⁻¹
Where:
Pn = the population at time n
Po = the population at time 0
r = the rate of growth
n = the number of years after time 0
In this case, Po = 26 million, n = 15 (2006 - 1991 = 15 years), and r can be calculated as follows:
Pn = 28 million
Po = 26 million
n = 15
r = (Pn - Po) / (Po × n)
r = (28 - 26) / (26 × 15)
r = 0.0077
Therefore, the population in 2006 can be calculated as follows:
P2006 = 26 × (1 + 0.0077)¹⁵
P2006 = 33.02 million
Therefore, the estimated population in 2006 was 33 million.
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Which is true about the product of 3/8 and 7/2. 1.The product is less than 3/8. 2.The product is greater than 1/8 and less that 1/2. 3.The product is greater than 7/2. 4.The product is greater that 3/8 and less than 7/2.
Answer:
4.The product is greater that 3/8 and less than 7/2.
Step-by-step explanation:
The product of 3/8 and 7/2 is:
[tex]\frac{3}{8} * \frac{7}{2} \\\\= \frac{21}{16} = 1\frac{5}{16}[/tex]
This number is greater than 3/8.
It is greater than 1/8 but not less than 1/2.
This number is less than 7/2.
This number is greater than 3/8 and it is less than 7/2.
Hence, the correct options is 4.
A quadrilateral with 90 degree angles is shown. The lengths of the left and right sides are 10 and 2 y + 4. The lengths of the top and bottom sides are 18 and 10 + 2 x. What is the value of x? 3 4 6 8
Answer:
4
Step-by-step explanation:
i just answered it.
The value of the variable x will be 4. Then the correct option is B.
What is a quadrilateral?It is a polygon with four sides. The total interior angle is 360 degrees.
A quadrilateral with 90 degree angles.
If all the angles are right angle, then the quadrilateral should be either rectangle or square.
The lengths of the left and right sides are 10 and 2y + 4.
The lengths of the top and bottom sides are 18 and 10 + 2x.
If the adjacent side of the rectangle are same, then the rectangle will become square.
So, the quadrilateral is a rectangle.
Opposite sides of the rectangle are congruent.
Then the value of the variable x will be
10 + 2x = 18
2x = 18 – 10
2x = 8
x = 8 / 2
x = 4
The value of the variable x will be 4.
Then the correct option is B.
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Find the 82nd term of the arithmetic sequence
-8, 9, 26, ...
Please help with this question
In a symmetric histogram, you have the same number of points to the left and to the right of the median. An example of this is the distribution {1,2,3,4,5}. We have 3 as the median and there are two items below the median (1,2) and two items above the median (4,5).
If we place another number into this distribution, say the number 5, then we have {1,2,3,4,5,5} and we no longer have symmetry. We can fix this by adding in 1 to get {1,1,2,3,4,5,5} and now we have symmetry again. Think of it like having a weight scale. If you add a coin on one side, then you have to add the same weight to the other side to keep balance.