Answer:
b=4
Step-by-step explanation:
b-14 =-10
b-14+14=-10+14
b=4
we want to factor the following expression: (x - 3)^2 - 64y^4 which pattern can we use to factor the expression? u and v are either constant integers or single variable expression.
The factored expression of (x - 3)^2 - 64y^4 is given as follows:
(x - 3)^2 - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).
What is the subtraction of perfect squares?The subtraction of perfect squares is a notable product that gives the simplification of an expression containing the subtraction of perfect squares as follows:
a² - b² = (a - b)(a + b).
In this problem, the expression is presented as follows:
(x - 3)^2 - 64y^4
This expression is a subtraction of perfect squares, as the terms are given as follows:
Term a: square root of (x - 3)² = x - 3.Term b: square root of 64y^4 = 8y².Then the expressions are given as follows:
a - b = x - 3 - 8y².a + b = x - 3 + 8y².Then the factored expression is presented as follows:
a² - b² = (a - b)(a + b).
(x - 3)² - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).
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Try It
Solving Equations with Rational Numbers
Solve this equation: -7x+12 - 2x = 23 + 13x
Step 1: Simplify by combining like terms that are on the
same side of the equation. Which terms can be
combined?
Check
-7x+12-2x = 23+13x
Answer:
-6/11
Step-by-step explanation:
please follow me to mark me on brainliest
draw the graph of the linear inequality 2x – 3y < 12?
Answer:
The following question has been answered in the attached document. If there are any queries kindly let me know they will be resolved shortly.
PRO TIP:
don't forget to mention y=0 on x axis and x=0 on y axis whenever you are drawing a graph as it accounts for 1/2 mark in board exams.
The line cuts the y axis at (0, -4) Also (0,0) satisfies the inequality So the shaded region is towards (0, 0). Since there is a strict inequality, the line is a broken line
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, [tex]\geq[/tex], [tex]\leq[/tex]
A one degree inequation is known as linear inequation.
The given linear inequality is
2x - 3y < 12
For the point on x axis for the line 2x - 3y = 12
we put y = 0
[tex]2x - 3\times 0 = 12\\2x = 12\\x = \frac{12}{2}\\x = 6[/tex]
The line cuts the x axis at (6, 0)
For the point on y axis for the line 2x - 3y = 12
we put x = 0
[tex]2\times 0 - 3y = 12\\-3y = 12\\y = \frac{12}{-3}\\y = -4[/tex]
The line cuts the y axis at (0, -4)
Also (0,0) satisfies the inequality
So the shaded region is towards (0, 0)
Since there is a strict inequality, the line is a broken line
The graph has been shown in the figure attached
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Jai read 3 books in 2 months. What was his rate of reading in books per month
Jai rate of reading in books per month is 1.5 books per month.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this case, Jai read 3 books in 2 month, his rate of reading in books per month will be:
= Number of books / Number of months
= 3 / 2
= 1.5 books per month
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Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52
Answer:
10
Step-by-step explanation:
I guess your question is
[tex] {(x - 3)}^{2} = 49[/tex]
[tex]x \: - 3 = \sqrt{49} \\ x - 3 = 7 \\ x = 7 + 3 \\ x = 10[/tex]
Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x = −7 and x = 5 and passes through the point (0, −2)
The equation for the parabola with the given characteristics is:
y = (2/35)*(x + 7)*(x - 5)
How to get the equation of the parabola?We know that for a parabola that has the zeros x₁ and x₂, and a leading coefficient a, can be written as:
y = a*(x - x₁)*(x - x₂)
In this case, the roots (zeros) are at X =-7 and x = 5
Then we can write:
y = a*(x + 7)*(x - 5)
Now we also know that it passes through the point (0, -2), then we can write:
-2 =a*(0 + 7)*(0 - 5)
-2 = a*-35
2/35 = a
Then the equation for the parabola is:
y = (2/35)*(x + 7)*(x - 5)
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1234567891011121314151617`81910
If you are god in math the I have a question do it
Answer:
I am definitely not one...Lol
Step-by-step explanation:
Please tell me answer ASAP
Adam has notes of RS.100, RS.50 and RS.10. The ratio of these notes is 2 : 3:5 respectively and the total amount is RS.200,000. Find the number of notes of each kind.
The number of notes of Rs. 100 is 1000, Rs. 50 is 1500, and Rs. 10 is 2500.
The ratio describes the number of times one number contains another. It helps to establish a relationship between two or three quantities.
The ratio between any two quantities is described as a:b. This can also be written as a to b or a/b.
The ratio of RS.100, RS.50, and RS.10 is 2:3:5.
From the given ratio, consider
the number of Rs. 100 is 2xthe number of Rs. 50 is 3xthe number of Rs. 10 is 5x.The total amount is given as RS.200,000. This can be written as,
[tex]\begin{aligned}100\times2x+50\times 3x+10\times5x&=200,000\\200x+150x+50x&=200,000\\400x&=200,000\\x&=\frac{200,000}{400}\\x&=500\end{aligned}[/tex]
Therefore,
the number of Rs. 100 is 2(500) = 1000the number of Rs. 50 is 3(500) = 1500the number of Rs. 10 is 5(500) = 2500To know more about ratios:
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25% of 0÷4 = 0÷1 True or False?
Answer:
false
Step-by-step explanation:
25% is equivalent to 0.25
Determine whether the series converges or diverges...
The series as represented in the task content is divergent and hence; diverges.
What convergence and divergence in series?It follows from the task content that the series defined by the summation expression as represented above is to be identified as divergent or convergent.
It is noteworthy to know that;
If a sequence converges, it means that the limit of the sequence exists as n → ∞. Also, if the limit of the sequence as n → ∞ does not exist, Then, such series is said to diverges.
Therefore, by evaluation as the limit of the expression k sin²k / 1 + k³ as k → ∞ is; Undefined and hence does not exist.
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1)if a number is trebled and 10 is subtracted from it and then multiply the result by 5 the answer is 55 what is the number
The number represented in the statement is 7
How to determine the number?The statements in the question can be highlighted as:
A number is trebled10 is subtracted from the resultThe result is then multiplied by 5The final result is 55When represented as an equation, we have
5(3x - 10) = 55
Where x represents the number
Divide both sides by 5
3x - 10 = 11
Add 10 to both sides
3x = 21
Divide by 3
x = 7
Hence, the result is 7
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Evaluate the expression 23.5 − 6.8x when x = 3.
Answer:
3.1
Step-by-step explanation:
23.5-6.8x
x=3
first put 3 in for x
23.5-6.8(3)
now solve the expression
23.5-20.4
3.1
50 POINTS!!
One Thursday night, Joel the delivery boy earned $43 in tips plus his usual $12/hr. He made $85. Write an equation for this situation.
Answer:
Step-by-step explanation:
This is a simple linear equation.
Y=12x + 43
The 12x represents the money he makes hourly, as x represents each hour he works
+43 represents the amount of money in tips he made since this was added on top of the hourly pay he was making.
Answer:
your welcome
Step-by-step explanation:
42+43=85$
to get the 42 you have to do 83-43 and that leaves you with 42
You have to make a balloon payment on your house five years from now of $15,000. If money can earn an average of 6 percent a year for the five-year period, how much will you have to place in the account today to have the $15,000 in five years?
The future value of an investment with such details must have a present value of $11120.58
Present ValuePresent value (PV) formula finds application in finance to calculate the present day value of an amount that is received at a future date. The present value formula (PV formula) is derived from the compound interest formula. The compound interest formula is,
FV = PV(1 + r/n)^nt
We can substitute the values into the formula
15000 = PV(1 + 0.06/12)^12*5
15000 = PV(1.005)^60
PV = 11120.58
The present value of an investment to give a future value of $15000 at 6% rate in 5 years is $11120.58
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The graph represents the function f(x) = x2 + 3x + 2. If g(x) is the reflection of f(x) across the x-axis, g(x) = . (Write the function in standard form. Use ^ to indicate an exponent.)
The reflection of the graph in the x-axis gives the function
g(x) = -x² - 3x - 2
The given function is of the form f(x) = x² + 3x + 2 which represents a parabola.
The vertex of the function is at (-3/2 , -1/4)
The focus is at ( 3/2 , 0 )
The axis of symmetry is 2x+3 = 0 and the directrix is at 2x + 1 = 0
Now when the parabola is reflected along the x-axis we get
the focus at ( -3/2 , 0 )
the vertex is at (-3/2 , 1/4)
Axis of symmetry remains the same
The directrix becomes 2y-1 =0
The red graph denotes the function f(x) while the blue graph denotes the function g(x) reflected on the x-axis.
Hence the reflection on the x-axis gives the function g(x) = -x² - 3x - 2
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A doctor prescribes 100 milligrams of a therapeutic drug that decays by about 15% each hour. To the nearest hour, what is the half-life of the drug?
The drug administered to the patient by the doctor has a half-life of 5 hours
Half-LifeHalf-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential decay.
The formula is given as;
T1/2 = ln2 / λ
Where;
λ = disintegration constant.But λ = 15% = 0.15/hr
t1/2 = ln2 / 0.15
T1/2 = 0.693/0.15
T1/2 = 4.62 = 5 hours.
The drug has an half-life of approximately 5 hours
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Which statement about odd functions is correct?
Answer:
at least put the possible answers
in a major need of help
Answer:
B and D are the correct answers.
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The equations that are true for x = –2 and x = 2 include the following:
x² – 4 = 0
4x² = 16
How to determine the true equations?In order to determine which x-values are true solutions based on the given equations, we would have to test each of the x-values by substituting their values into the equations as follows;
When x = -2, we have:
x² – 4 = 0
(-2)² – 4 = 0
4 - 4 = 0 (True).
When x = 2, we have:
x² – 4 = 0
(2)² – 4 = 0
4 - 4 = 0 (True).
When x = -2, we have:
x² = -4
(-2)² = -4
4 = -4 (False).
When x = -2, we have:
3x² + 12 = 0
3(-2)² + 12 = 0
3(4) + 12 = 0
12 + 12 = 0
24 = 0 (False).
When x = -2, we have:
4x² = 16
4(-2)² = 16
4(4) = 16 (True).
When x = 2, we have:
4x² = 16
4(2)² = 16
4(4) = 16 (True).
When x = -2, we have:
2(x – 2)² = 0
2(-2 – 2)² = 0
2(-4)² = 0
2(16) = 0
32 = 0 (False).
When x = 2, we have:
2(x – 2)² = 0
2(2 – 2)² = 0
2(0) = 0 (True).
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Complete Question;
Which equations are true for x = –2 and x = 2? Select two options
x² – 4 = 0
x² = -4
3x² + 12 = 0
4x² = 16
2(x – 2)² = 0
A population of 50 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 600 deer. Absent constraints, the population would grow by 70% per year.
If It is estimated that the sanctuary can sustain up to 600 deer. Absent constraints, the population would grow by 70% per year. After one year is 85 and after two years is 144.50.
How to find the population growth?Using this formula
A = P(1+r)t
Where:
A = Amount
P = Principal
r =Interest rate
t = time
Let plug in the formula
After one year:
A = 50(1+0.70)^1
A = 50(1.70)^1
A= 85 deer
After two years:
A = 50(1+.70)^2
A = 50(1.70)^2
A = 50(2.89)
A = 144.50 deer
Therefore the population growth is 85 deer and 144.5 deer.
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The complete question is:
A population of 50 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 600 deer. Absent constraints, the population would grow by 70% per year.
how many after one year
how many after two years
The length of the rectangular lot is 25 ft longer than twice the width. If the perimeter of the lot cannot exceed 350 ft, what is the greatest width possible?
The greatest width possible in line is 0.8.
What is line?
a line is an infinitely long to the object with no width, depth, or curvature. Thus, the lines are the one of one-dimensional objects, though they may exist on it two, three, or higher of the dimension spaces. The word line may also refer to a line are the segment in everyday life, which has two points to denote its ends.
Sol-As per the given question The line r has slope 8 and coordinate (0.8).
The slope of the line r will not change.
And intercept is the addition of their ordinate will be.
Intercept = 5+3
Intercept = 8
So, the line r has slope 8 and coordinate (0.8).
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can anyone help? thanks!
Answer: 175
Step-by-step explanation:
7 x 1 x 5^2
7 x 1 x 25
7 x 25
175
Answer:
175
Step-by-step explanation:
Since we have 7ca^2 and since we know a = 5 and c = 1, we can just plug in these values for a and c and follow the order of operations:
[tex]7ca^2\\7(1)(5)^2\\7(1)(25)\\7*25=175[/tex]
Determine an nth degree polynomial that satisfies the aforementioned conditions.
The polynomial of p(x) is 20/13(x³+4x²-9x-36) with the satisfying's conditions degree 3.
Given that,
An nth degree polynomial p meets the requirements listed below:
p is of degree 3.
-3 is a multiplicity 1 zero of p.
-4 is a zero, with multiplicity 1, of p.
3 is a root, with multiplicity 1, of p.
p(-2)=-40
We have to determine an nth degree polynomial that satisfier the conditions.
Let the polynomial be p(x) whose zero are -3,-4 and 3.
a be the coefficient.
p(x)=a(x+3)(x+4)(x-3)
p(x)=a(x²-3²)(x+4)
p(x)=a(x²-9)(x+4)
p(x)=a(x³+4x²-9x-36)
Now, take x=-2
p(-2)=a((-2)³+4(-2)²-(-2)-36)
-40=a(-8+16+2-36)
-40=a(-26)
a=-40/-26
a=40/26
a=20/13
We get,
p(x)=20/13((x+3)(x+4)(x-3))
p(x)=20/13(x³+4x²-9x-36)
Therefore, the polynomial of p(x) is 20/13(x³+4x²-9x-36) with the satisfying's conditions degree 3.
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HURRY PLS!! TEST!!!!
consider the line y=5x-5
find the equation of the line that is parallel to this line and passes through the point (3,4)
find the equation of the line that is perpendicular to this line and passes through the point (3,4)
Answer:
y=-5x+19
Step-by-step explanation:
yeah -ya...... right?
it takes matilda twice as long to complete a research project
UP FOR THE CHALLENGE?! PLEASE HELP!
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 110.5° is added to the data, how does the mean change and by how much?
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 101° is added to the data, how does the mean change?
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 71° is changed to 93°, which of the following measures changes the most and what is the new value?
Answer:50%
Step-by-step explanation:
What can be concluded about line that passes through the points (1,-2) and (4,-2)? Check all that apply.
The slope is 0.
The y-intercept is -2.
The line is vertical.
O The line is horizontal.
The line has no y-intercept.
The equation of the line is Y--2
All that apply are:
The slope is 0.
The y-intercept is -2
The line is horizontal.
The equation of the line is Y = -2.
Given points:
(1,-2) and (4,-2)
slope m = -2-(-2) / 4 - 1
= -2+2/3
= 0
so slope is 0
y = mx + c
(1,-2) passes
-2 = 0*1 + c
c = -2
y = 0*x + -2
y = -2
so the line is horizontal and equation of the line is y = -2.
The y-intercept is -2.
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what is y times equals negative 42
Answer:
I am thinking the answere is -6 x 7 but I'm not completely
write the number 4 as a fraction with a denominator of 15
Answer:
60/15
Step-by-step explanation:
A fraction is simply a portion of a whole number, so 1/15 is the number 1 split into fifteen equal parts, therefore 15/15 = 1.
So 4 as a fraction with fifteen as the denominator would be 15/15 x 4, which equals 60/15.