The critical number are 0, 7 , -7.
Given function:
g(x) = [tex]\sqrt{49-x^{2} }[/tex]
first derivative is,
= -x/([tex]\sqrt{49-x^{2} }[/tex] )
-x = 0 or x = 0
[tex]\sqrt{49-x^{2} }[/tex] = 0
49 - [tex]x^{2} =0[/tex]
49 = [tex]x^{2}[/tex]
x = 7 , -7.
Therefore the critical number are 0, 7 , -7.
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Which expression is equivalent to 3x – 5?
Answer:
2x – 4 – 1 + x
Step-by-step explanation:
Answer:
Step-by-step explanation: -15
1. Given segment AB with A(-3, 2) and B (5, -4). If point P lies on segment AB such that the ratio of
AP to PB is 2:6. Find the coordinates of p
The coordinates of P is ( -1 , 0.5) .
What is section formula ?
We can get a point's coordinates using the section formula when it divides a line segment externally or internally in a certain ratio. It is a useful tool for determining the coordinates of the point that divides the line segment in a particular ratio. The midpoint of a line segment can be found using this section formula, and it can also be used to derive the midpoint formula.
Here Using the section formula, if a point P(x,y) divides the line joining the points A[tex](x_1,y_1)[/tex] and B[tex](x_2,y_2)[/tex] in the ratio of m:n then,
=> (x,y) = [tex](\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n} )[/tex]
Here A[tex](x_1,y_1)[/tex] =( -3,2) and B[tex](x_2,y_2)[/tex] = (5,-4) and m:n = 2:6
Then,
=> ( x,y ) = [tex](\frac{2(5)+6(-3)}{2+6} ,\frac{2(-4)+6(2)}{2+6})[/tex]
=> (x,y) = [tex](\frac{10-18}{8},\frac{-8+12}{8} )[/tex]
=> (x,y) = [tex](\frac{-8}{8} ,\frac{4}{8})[/tex]
=> (x,y) = (-1,0.5)
Hence the coordinates of P is (-1 , 0.5) .
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please help 25points, please show how you did it
Answer:
Angle 1: 27
2: 153
3: 58
4: 138
Step-by-step explanation:
1. 180-(116+37)=27
2. 180-27=153
3. 180-(48+74)=58
4. 122+16=138
180-138=42
180-42=138
A student requests a loan for $1178.80. The monthly payment of the loan is $42.10. So far, the student has paid $547.30. How many
more monthly payments must be maid to pay off the loan?
The number of months required to pay off the loan will be 15.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a student requests a loan for $1178.80. The monthly payment of the loan is $42.10. So far, the student has paid $547.30.
The number of the months will be calculated as,
N = ( 1178.8 - 547.30) / 42.10
N = 631.5 / 42.10
N = 15
Therefore, the number of months required to pay off the loan will be 15.
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Lets sets A and B be defined as follows:
A= {25, 26, 27, 28, 29}
B is the set of integers greater than or equal to -6 and less than or equal to 1.
(picture attached below)
a) The value sets of n(A) = 5, n(B) = 8
b) 33 ∈ A is false, -4 ∈ B is true, 25 ∈ A is true, 5 ∉ B is true.
What is set?Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set.
A = { 25, 26, 27, 28, 29}
B ( is greater or equal to -6 and equal to 1) = { -6, -5, -4, -3, -2, -1, 0, 1}
n(A) = number of elements in A which is 5 and n(B) = 8
33 ∈ A The symbol ∈ means element of. so 33 is not an element of A.
-4 is an element of B so it is true, -4 ∈ B is true
25 ∈ A is true because 25 is an element of A
5 ∉ B is true because 5 is not an element of B
In conclusion, n(A) = 5, n(B) = 8
-4 is an element of B so it is true, -4 ∈ B is true
25 ∈ A is true because 25 is an element of A
5 ∉ B is true because 5 is not an element of B
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Simon uses 121 one-inch tiles to make his square mosaic. What is the length of one side of his mosaic?
Which expression represents the number of tiles on Wendy's kitchen floor?
Wendy lays rows of 8 tiles each to cover her kitchen floor. Use t
for the number of rows.
t−8
8×8t
8t
8+t
The expression that represents the number of tiles on Wendy's kitchen floor is B. 8 × 8t.
What is an expression?An expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, Wendy lays rows of 8 tiles each to cover her kitchen floor.
Let t = the number of rows.
Therefore, the number of tiles on Wendy's kitchen floor will be:
= 8 × 8t.
Therefore, the correct option is B.
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~ ( ~ q → p) → ~ q is a tautology or not?
The proposition ~ (~ q ⇒ p) ⇒ ~ q represents a tautology, as it is true for all combinations of p and q.
Is a given proposition a tautology?
Propositions are constructions that contains a truth value, which are two according to classical logic (T - true, F - false). There are simple propositions and compound propositions. Compound propositions are formed by combining simple propositions and operators. There are the following operators:
∧ - Conjunction (operator "and")∨ - Disjunction (operator "or")~ - Negator (operator "not")⇒ - Implicator (operator "If-then")⇔ Double implicator (operator "if-only if")A tautology is a compound proposition that is always true. We can prove whether a proposition is a tautology by the use of a truth table:
p q ~ q ~ q ⇒ p ~ (~ q ⇒ p) ~ (~ q ⇒ p) ⇒ ~ q
T T F T F T
T F T T F T
F T F T F T
F F T F T T
The proposition ~ (~ q ⇒ p) ⇒ ~ q is a tautology.
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x^2-25 , (x+5) quotient and remainder
The quotient when ([tex]x^{2} -25[/tex]) is divided by (x+5) is (x-5) and the remainder is 0.
According to the question,
We have the following information:
([tex]x^{2} -25[/tex]) is divided by (x+5)
Now, we can solve this using two ways. First method is to use the long division method and second is to solve the expression using an identity.
We know that the following identity can used to expand the dividend:
[tex]a^{2} -b^{2} = (a+b)(a-b)\\[/tex]
In this case, we have a = x and b = 5.
[tex]x^{2} -(5)^{2} = (x-5) (x+5)[/tex]
Now, we have the following expression:
(x+5)(x-5)/(x+5)
(x-5)
Now, the remainder is 0.
Hence, the quotient when ([tex]x^{2} -25[/tex]) is divided by (x+5) is (x-5) and the remainder is 0.
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I’m doing my geometry homework and don’t remember the formula or way to solve the lengths of a triangle side with graph points. How do I solve both parts of #1?
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill EF=\sqrt{(~~ 3- 2~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill EF=\sqrt{( 1)^2 + ( -2)^2} \implies \boxed{EF=\sqrt{ 5 }}[/tex]
[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill FD=\sqrt{(~~ -1- 3~~)^2 + (~~ -1- 1~~)^2} \\\\\\ ~\hfill FD=\sqrt{( -4)^2 + ( -2)^2} \implies \boxed{FD=\sqrt{ 20 }} \\\\\\ D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill DE=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill DE=\sqrt{( 3)^2 + (4)^2} \implies DE=\sqrt{ 25 }\implies \boxed{DE=5} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{2}}} \implies \cfrac{ -2 }{ 1 } \implies - 2 \\\\[-0.35em] ~\dotfill[/tex]
[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{3}}} \implies \cfrac{ -2 }{ -4 } \implies \cfrac{1 }{ 2 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{3 +1}{2 +1} \implies \cfrac{4 }{ 3 }[/tex]
AB=18cm
BC=18cm
AC=16cm
What is the corresponding angles and sides?
The angle measurements are 5.38°, 87.31° and 87.31°.
What is triangle?
A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given are the sides of triangle as AB = 18cm, BC = 18cm, AC = 16cm.
The given triangle is a isosceles triangle with two sides equivalent. Angles opposite to these sides will be equal. So, we can write -
2∠x + ∠y = 180°
from the figure, it can be seen that angle B is 5.38 degrees.
2∠x + 5.38 = 180
2∠x = 174.62
∠x = 87.31°
Therefore, the angle measurements are 5.38°, 87.31° and 87.31°.
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Assignment Sowe for x and y
3x² - 4y =-1 2x -4=1
plss help me with it
Answer: x=25/4 or 6.25, y=79/16 or 4.9375
Step-by-step explanation:
Normally, we would have to set up a system of linear equations, but in this case we can solve for x and plug in from there. x=5/2 or 2.5 when solving for the variable. Now we go to the second equation, plug for x, and solve for y. 5/2 times 5/2 is 25/4, multiplied by 3 is 75/4. Subtract 75/4 from -1, and divide both sides by -4.
equation for the perpendicular bisector of the line segment whose endpoints
are (-9, 3) and (-3, -1).
Equation for the perpendicular bisector of the line segment is
2y = 3x +20.
A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector.
What is perpendicular bisector?A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.
Given coordinates of the endpoints of a line segment (-9, 3) and (-3,-1).
In order to find the equation of perpendicular line, we need to find the slope between given coordinates.
Slope between (-9, 3) and (-3, -1). :
slope = [tex]\frac{-1-3}{-3+9} =\frac{-2}{3}[/tex]
Slope of the perpendicular line is reciprocal and opposite in sign.
Therefore, slope of the perpendicular line = 3/2
Now, we need to find the midpoint of the given coordinates.
[tex]Mid points : \\x= \frac{ -9-3}{2} =-6\\ y= \frac{3-1}{2} = 1\\ pint = (-6,1)[/tex]
Let us apply point-slope form of the linear equation:
y-y1 = m(x-x1)
y - 1 = 3/2 (x + 6)
2y = 3x +20
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Please refer to picture
Using the corresponding angle theorem, the value of x is 15 and y is 12.
In the given question we have to find the value of x and y.
From the graph we can see that
From the corresponding angle theorem
4x+2=62
Subtract 2 on both side, we get
4x=60
Divide by 4 on both side, we get
x=15
So the value of x is 15.
Similarly from the corresponding angle theorem
12y=144
Divide by 12 on both side, we get
y=12
So the value of y is 12.
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Solve the value of (a-b)^2 given that a^2+b^2=15 and ab=3.
Answer:
(a - b)² = 9Step-by-step explanation:
Givena² + b² = 15,ab = 3.FindValue of (a - b)²SolutionUse identity:
(a - b)² = a² - 2ab + b²Substitute values:
(a - b)² = a² + b² - 2ab = 15 - 2*3 = 15 - 6 = 9Answer:
(a - b)² = 9
Step-by-step explanation:
Expand (a - b)²:
[tex]\begin{aligned}\implies (a-b)^2&=a^2-2ab+b^2\\&=a^2+b^2-2ab\end{aligned}[/tex]
Given:
a² + b² = 15ab = 3Substitute the given values into the expanded equation:
[tex]\begin{aligned}\implies (a-b)^2&=a^2+b^2-2ab\\&=15-2(3)\\&=15-6\\&=9\end{aligned}[/tex]
Therefore, (a - b)² = 9.
Don’t get how I can figure out the Explicit Equation from this
The four terms of the series will be equal to 14,20,26, and 32.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the equation for the series is given as, t(n) = 6n + 8. The series will be formed as,
t(n) = 6n + 8.
t(1) = 6 x 1 + 8 = 6 + 8 = 14
t(2) = 6 x 2 + 8 = 12 + 8 = 20
t(3) = 6 x 3 + 8 = 18 + 8 = 26
t(4) = 6 x 4 + 8 = 24 + 8 = 32
Therefore, the four terms of the series will be equal to 14,20,26, and 32.
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Solve for x. Enter the solutions from least to greatest. (x + 6)^2 - 16=0 lesser x = greater x =
Answer:
x= -2, -10
Step-by-step explanation:
(x+6)^2-16=0
(x+6)(x+6)-16=0
x^2+6x+6x+36-16=0
x^2+12x+20=0
10+2=12
10(2)=20
(x+2)=0
(x+10)=0
x= -2, -10
A company has 35% and 3% hydrogen peroxide solutions. They need an 8 L container with a 12% concentration of hydrogen peroxide. How much of the 3% hydrogen peroxide solution should they include in the container?
Answer:
2 L
Step-by-step explanation:
If the first one is 12% then the 3% one would be 2L because of algebra
5.75 liters of 3 percent hydrogen peroxide solution are included by the company in the container.
What is the percentage?A measurement used to determine a number's value out of 100 is the percentage.
Hydrogen peroxide solutions in various containers have concentrations of 35% and 3%.
Since the corporation wants an 8-liter container with a 12% hydrogen peroxide concentration.
Use mixture and allegation property,
35 3
12
9 : 23
Total quantity = 23x + 9x = 32x
Since, the company wants 8 liters,
therefore, 32x = 8 ⇒ x = 1/4
3.5 percent hydrogen peroxide solution will be equal to = 23x = 23/4 = 5.75. 5.75 liters of 3 percent hydrogen peroxide solution are needed.
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August hosted two dinner parties for his friends. Twenty guests attended the first party, and twenty-seven guests attended the second party. What is the percentage increase of the number of guests from the first party to the second party?
A.
35%
B.
30%
C.
65%
D.
70%
Answer:
A 35%
Step-by-step explanation:
take the higher number (27) and subtract the smaller number (20) from it. there's your difference. afterwards, take the difference (7) and divide it by the smaller number (20). this gives you .35. convert it into percentage move the decimal point to the right two spots and slap a percentage sign onto it (shift+3). giving you 35%, or A.
Answer:
a) 35%
Step-by-step explanation:
Given information,
→ 20 guests attended the 1st party, and 27 guests attended the 2nd party.
Now we have to,
→ find the % increase of number of guests from first party to second party.
Let's solve the problem,
→ ((27 - 20)/20) × 100
→ (7/20) × 100
→ 0.35 × 100
→ 35%
Hence, the answer is 35%.
I need help answer please
Teddy and Henry both bought a used car on the same day. Teddy's used car has
4,298 miles on it already, and he drives 426 miles per month. Henry's car has 6,129
miles on it already, and he drives 223 miles per month. After how many months will
each car have the same nulaber of miles on it?
After 9 months each car will have the same number of miles on it.
What is a linear equation?
Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Here,
Let miles per month be x.
then, by a linear equation, we get
4298 + x(426) = 6129 + x(223)
203x = 1831
x = 9 months
Hence, after 9 months each car will have the same number of miles on it.
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In a factory, 40% of k liters of acid are added to 60% of w liters of water.
Express the total volume of the solution as an algebraic expression. Pls help
Answer: (0.4k+0.6w)
Step-by-step explanation:
the answer would be (0.4k+0.6w) Since we do not know the values of k nor w, their coefficients cannot be added together.
The total volume of the solution as an algebraic expression is
0.4k + 0.6w.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Amount of acid added to the solution = 40% of k
Amount of water added to the solution= 60% of w
Now,
The total volume of the solution.
= 40% of k + 60% of w
= 40/100 x k + 60/100 x w
= 0.40k + 0.60w
Thus,
The volume is 0.4k + 0.6w.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representations of the given inequality -3(2x - 5) < 5(2 - x) include the following:
-6x + 15 < 10 - 5xAn open circle is at 5 and a bold line starts at 5 and is pointing to the right.What is an inequality?An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numbers and variables in an algebraic equation, especially based on any of the following inequality symbols:
Greater than (>).Greater than or equal to (≥).Less than (<).Less than or equal to (≤).For this exercise, we would evaluate and simplify the given inequality so as to enable use determine its solution as follows:
-3(2x - 5) < 5(2 - x)
Opening the bracket, we have:
-6x + 15 < 10 - 5x (correct representation)
Rearranging the algebraic equation by collecting terms, we have:
-6x + 5x < 10 - 15
-x > -5
x > 5 (correct representation)
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12u–9u–5u+13= -5
find u
There are 4 green apples and 7 red apples in a basket.
(a) What is the ratio of all apples in the basket to red apples?
0
(b) What is the ratio of green apples to all apples in the basket?
0
Answer:
1) 7:4
2) 11: 7
Step-by-step explanation:
7. In one week, Sabrina received 18 letters and
8 bills. What was the ratio of bills to letters?
71,72×35,36 =2536.0192
give your answer to 2 decimal places
Answer:
the answer to 2dp is 2536.02
About 53% of adults in the US have traveled with a commercial airline. A random sample of 400 adults was selected
and whether they have traveled with a commercial airline was recorded.
Calculate the standard deviation of the sampling distribution of
O 0.00062
O 0.00086
* 0.00125
O 0.02495
B
M
B
1
■
▬
T
U
Done
♥
The standard deviation of the sampling distribution is 0.01767.
What is a standard deviation?Standard deviation is a measure of the amount of variability or spreads in a set of data.
It is calculated as the square root of the variance and is often denoted by the symbol σ (sigma) for a population and s for a sample.
We have,
Given that the sample size is sufficiently large (n=400) and the population proportion is known, we can use the formula for the standard deviation of the sampling distribution of the sample proportion, which is:
[tex]\sigma_{\hat{p}} = \sqrt((p (1 - p)) / n)[/tex]
where p is the population proportion and n is the sample size.
In this case,
p = 0.53 (as given in the problem) and n = 400.
Substituting these values into the formula, we get:
[tex]\sigma_{\hat{p}} = \sqrt((0.53 (1 - 0.53)) / 400)\\\sigma_{\hat{p}} = \sqrt((0.53 0.47) / 400)\\\sigma_{\hat{p}} = \sqrt(0.0003121)\\\sigma_{\hat{p}} = 0.01767[/tex]
(rounded to five decimal places)
Therefore,
The standard deviation of the sampling distribution is 0.01767.
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Write an exponential function in the form y = ab^x that goes through points (0, 14)
and (4,8750).
The exponential function will be written as y = 14⁰.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given exponential function is [tex]y = ab^x[/tex]. The equation of the exponential function passing through the point is,
[tex]y = ab^x \\[/tex]
14 = ab⁰
a = 14
The equation will be written as,
y = 14b⁰
y = 14⁰
Therefore, the exponential function will be written as y = 14⁰.
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Describe in words where the square root of 50 minus 10 would be plotted on a number line.
Between −3 and −2, but closer to −3
Between −3 and −2, but closer to −2
Between 6 and 7, but closer to 6
Between 6 and 7, but closer to 7
The required value lies Between 6 and 7, but closer to 6. Option C is correct.
Given that,
The square root of 50 minus 10 would be plotted on a number line.
A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.
According to the question,
= √[50-10]
= √40
= 6.32
Which is closer to 6.
Thus, the required value lies Between 6 and 7, but closer to 6. Option C is correct.
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