The given expression √3x²+√4x is defined for x > 0
By property |f(x)| < c
⇒ f(x) < 0 and - f(x) < 0
⇒√3x²+√4x < 0 and -(√3x²+√4x) < 0
⇒ x < -√4/3 and x < -√4/3
Therefore x should be greater than 0.
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(6,- 8); 2x + 3y = 6
A. Write in slope intercept form
B. Write equation in the form Ax+By=C
Write the equation in slope-intercept form of the line that is parallel to the given line and passes through the given point.
y = 2x + 1; (6, -1)
The equation of line in slope - intercept form is, y = 2x - 13.
What is slope-intercept form of the line?
Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. y = mx + b is the equation in slope intercept form.
Consider the given equation of line y = 2x + 1.
And the point given is, (6, -1).
We have to find the equation of line parallel to the given line and passes through the point (6, -1).
First we have to find the slope of the parallel line.
Since, Slope of the parallel line is same as the slope of the given line.
Here, the slope of the line is 2.
So, the slope of the parallel line is also 2.
Now consider the point slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex](x_1, y_1)=(6, -1) , m = 2[/tex]
⇒
[tex]y-(-1)=2(x-6)\\y+1=2x-12\\y=2x-12-1\\y=2x-13[/tex]
Hence, the equation of the line parallel to the given line in slope intercept form is, y = 2x - 13.
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please help me with this im struggling :(
The equation that best represent the relationship on the scatter plot is y = 6 / 5 x + 18 / 5.
How to find the equation of a scatter plot?The line of best fit is used to express a relationship in a scatter plot of different data points.
The line of best fit (or trendline) is an educated guess about where a linear equation might fall in a set of data plotted on a scatter plot.
Therefore, the line of best fit will pass through (2, 6)(7, 12) and (12, 18).
Therefore, the equation of the line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = 12 - 6 / 7 - 2
m = 6 / 5
Let's find y-intercept using (2, 6)
6 = 6 / 5(2) + b
6 - 12 / 5 = b
b = 18 / 5
Therefore, the equation is y = 6 / 5 x + 18 / 5
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I need help please
In a test of a sex-selection technique, results consisted of female babies and male babies.
1. Based on this result, what is the probability of a female being born to a couple using this technique?
2. Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
The probability of a female being born to a couple using this technique is 0.923.
Yes, it is effective in increasing the likelihood that a baby will be a female.
Given:
In a test of a sex-selection technique, results consisted of 215 female babies and 18 male babies.
Total = 215+18
= 233
1.
The probability of a female being born to a couple using this technique is:
p = 215/233
p = 0.923.
hence the probability of the female being born to a couple is 0.923.
2.
Yes it is effective in increasing the likelihood that a baby will be a female because the probability of female is higher than the probability of male to be born.
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What would the domain and range be for a problem like this. I can’t seem to recall how to determine them
The domain and range are [−4, 1] & [−4, 5].
What are the domain and range of a graph?
Graphs can also be used to determine the domain and range of functions. Because the domain refers to the set of possible input values, the domain of a graph includes all of the input values shown on the x-axis. The range is the set of possible output values shown on the y-axis.
We have given the graph,
The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis.
The range is the set of possible output values, which are shown on the y-axis.
We can observe that the graph extends horizontally from −4 to the right 1. so the domain of function h is [−4, 1].
The vertical extent of the graph is 0 to –4, so the range of function h is [−4, 5].
Therefore, the domain and range are [−4, 1] & [−4, 5].
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use synthetic division to find the quotient and remainder of the following. Write your answer on the form of
Answer:
Step-by-step explanation:
1. x^2 + 4x + 5/x-1
2. x^3-3x^2 + 9x-2 + 3/x+3
3. 2x^2 - 2x+5- 14/3x+1
4.3x2^2- 4x+3 - 13/ 2x-1
5. 3x^2 + 6x + 7 + 12/2x-3
Select all the solutions to the inequality 2(7x + 1) < -26
_
A. -2
B. 9
C. -7
D. 4
Answer:X<-2
Step-by-step explanation:
7x+1<-13
7x<-13-1
7x<-14
Answer:
Step-by-step explanation:
the answer is A: x<-2
If you took out a loan for $10,000 with a 2% interest rate & it was for 18 months. How much interest would pay?
The amount of interest he would pay for a loan of $10,000 with a 2% interest rate and for 18 months is $300
Amount of money taken as a loan = $10000
The rate of interest = 2%
The time period of interest is 18 months = 1.5 year
Interst = prt/100
= 10000x 2 x 1.5/100
= 300
Therefore, the amount of interest he would pay for a loan of $10,000 with a 2% interest rate and for 18 months is $300
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Which triangle congruence postulate or theorem proves that these triangles
are congruent?
The Angle-Side-Angle Postulate (ASA) asserts that two triangles are congruent if their two angles and included sides are congruent with each other.
What is Angle-Side-Angle Postulate ?According to the definition of an angle side angle, two triangles are congruent to one another if two angles from one triangle and the side between them are, respectively, equal to two angles from another triangle and the side between them. If two triangles are congruent, thenOne triangle's three sides will be equivalent to its three sides, respectively.The three angles of one triangle will be equivalent to the three angles of the other, respectively.But we don't always need to know information about all the sides and angles of a triangle to be sure that two triangles are congruent. Let's use an example to illustrate ASA.Let's use an example to illustrate ASA. Take into account the triangles ABC and DEF:We are given that,
BC = EF
∠B = ∠E
∠C = ∠F
We say that by ASA criterion: Δ ABC ≅ ΔDEF.
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What is 6/21 + 6/7? Please help with question
Answer: 8/7 Or In Mixed Number Form 1 1/7
Step-by-step explanation: Get the common denominator which is 21 because you get 6/7 and multiply the number and denominator by 3. You will get 18/21. Now you add. 18/21 + 6/21 = 24/21. Simplify them by the greatest common factor and so I divide by 3 and get 8/7.
Hoped This Helped!
Answer:
Step-by-step explanation:
6/21 + 6/7
6/21 + 18/21
24/21 = 1 1 / 7
6 x 3 18
____ = __
7 x 3 21
- You need common denominators to add fractions together!!
Brandon made a model of a tower as shown below. It is composed of a square, prism, and a square pyramid. The height of the pyramid is 2 inches while The height of the prism 3 feet and the base of the prism is 8 inches long. What is the volume, to the nearest cubic inch, of the tower?
The volume, to the nearest cubic inch, of the tower is 2,347.
Brandon made a model of a tower, as shown in the figure. The tower is composed of a square prism and a square pyramid. The height of the pyramid is 2 inches. The height of the prism is 3 feet = 36 inches and the base of the prism is 8 inches long. Let the volumes of the tower, prism, and pyramid be represented by the variables V, V1, and V2.
V1 = L*B*H
V1 = 8*8*36
V1 = 2,304
The volume of the square prism is 2,304 cubic inches.
V2 = (1/3)a²h
V2 = (1/3)(8)²(2)
V2 = 42.67
The volume of the square pyramid is 42.67 cubic inches.
The volume of the tower is the sum of the volumes of the square prism and the square pyramid.
V = V1 + V2
V = 2,304 + 42.67
V = 2,346.67
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For some particular website, the password must start with one of the letters W, X, Y, or Z. Then there must be 5 more charaters, and each of those characters may be a numeric digit or a letter of the alphabet. How many different passwords are possible?
241,864,704 many different passwords are possible.
The total characters of the password is six in which it is given that first character should start with W, X, Y or Z. So the first character can be filled in 4 ways.
For next five characters it can be any letter of the alphabet or any numeric digit so it will be 26 + 10 = 36.
So second, third, fourth, fifth and sixth space can be taken by 36 characters.
Therefore the total no. of passwords will be 4 * 36 * 36 * 36 * 36 * 36 that is equal to 241,864,704.
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For the parallelogram, if m / 2 = 4x - 20 and m /4 = 3x - 11, find m / 1. The diagram is not drawn to scale.
For a parallelogram having (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles, if [∠2 = (4x - 20)] and [∠4 = (3x - 11)], then the measure of ∠1 will be 164°.
As per the question statement, a parallelogram has (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles, and [∠2 = (4x - 20)] and [∠4 = (3x - 11)],
Then, we are required to calculate the measure of ∠1.
To solve this question, first we will need to know about two important properties of a parallelogram,
(a) The sum of all the four interior angles of a parallelogram is equal to 360°,
(b) Opposite angles of a parallelogram are equal.
Now since our concerned parallelogram has (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles,
Therefore, (∠1 = ∠3) and (∠2 = ∠4),
And [(4x - 20) = (3x - 11)]...[∵(∠2 = ∠4)]
Or, [(4x - 3x) = (20 - 11)]
Or, [x = 9]
Therefore, [∠2 = ∠4 = (4x - 20) = 16°].
Now, [(∠1 + ∠2 + ∠3 + ∠4) = 360°]
Or, [(∠1 + ∠2 + ∠1 + ∠2) = 360°]...[∵(∠1 = ∠3) and (∠2 = ∠4)]
Or, [{(∠1 + ∠1 ) + (∠2 + ∠2)} = 360°]
Or, [(2∠1 + 2∠2) = 360°]
Or, [2∠1 = {360 - (2 * 16)}°]
Or, [2∠1 = (360 - 32)°]
Or, [2∠1 = 328°]
Or, [∠1 = (328/2)°]
Or, [∠1 = 164°]
That is, for a parallelogram having (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles, if [∠2 = (4x - 20)] and [∠4 = (3x - 11)], then the measure of ∠1 will be 164°
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If <1 and <2 are complementary, what are the measures of the backed when
The measures of the angles are m∠1 = 69° and m∠2 = 29°
How to find the measures of an angle?
*Triangles always have angles that add up to 180 degrees. As a result, you may find the unknown angles by taking the specified angles of a triangle and subtracting them from 180.
*Finding Unknown Measurements Using Exterior Angles
Two angles that together total 180 degrees are known as supplementary angles. These two angles combine to form a straight angle when put side by side
m∠1 = (4x-7)°
m∠2 = (x+12)°
As the two angles are complementary
4x-7+x+12=90°
5x+5=90°
5x=90-5
5x=85
x=[tex]\frac{85}{5}[/tex]
x=17
Therefore
m∠1 = 4(17)-7
m∠1 = 61°
m∠2 = 17+12
m∠2= 29°
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Write each set in the indicated form.
If you need to use "..." to indicate a pattern, make sure to list at least four elements of the set
a. Roster form: { 3, 4,5, 6}
b. Set-builder form : {x | x is an integer, where x ≥ -5}
What is a Roster form?
A list of the elements of a set, each separated by a comma, enclosed in a group of curly brackets, can be used to describe the contents of the set. Roster form is the term for this method of describing a collection.
What is a set-builder form?
Set builder notation is defining a set by expressing its properties rather than simply listing its constituents. One or more variables and a rule specifying which elements are part of the set and which are not are included in the set builder notation.
Here,
a. It is given the set is A={x:x is an integer 3 ≤ x ≤ 6}.
Then the integers lying between 3 and 6 are 3,4,5,6.
So the roster form is
A={3,4,5,6}.
b. It is given that A = { -5, -4, -3, -2......}
then the set-builder form is
A = {x | x is an integer, where x≤ -5}
Hence,
a. Roster form: { 3, 4,5, 6}
b. Set-builder form : {x | x is an integer, where x ≥ -5}
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5. Rewrite the expression as a single logarithm. (1 point)
We can rewrite the given logarithmic expression as [tex]ln(\frac{\sqrt{x}(x-1)^3 }{\sqrt[3]({x+1})^2 })[/tex].
So option (D) is the correct answer.
What is a logarithmic expression?
A logarithmic equation is one that involves the logarithm of a variable-containing expression. To solve exponential equations, first, determine whether both sides of the equation can be written as powers of the same number.
The given logarithmic expression can be expressed as
[tex]=\frac{1}{2}\ln}\left(x\right)+3\left(\ln\left(x-1\right)-\frac{2}{9}\ln\left(x+1\right)\right)[/tex]
[tex]=\frac{\ln\left(x\right)}{2}+3\left(\ln\left(x-1\right)-\frac{2}{9}\ln\left(x+1\right)\right)[/tex]
[tex]=\frac{\ln\left(x\right)}{2}+3\ln\left(x-1\right)-\frac{2\ln\left(x+1\right)}{3}[/tex]
By using the logarithmic properties, we get
[tex]=ln(\frac{\sqrt{x}(x-1)^3 }{\sqrt[3]({x+1})^2 })[/tex]
We can rewrite the given logarithmic expression as [tex]ln(\frac{\sqrt{x}(x-1)^3 }{\sqrt[3]({x+1})^2 })[/tex].
So option (D) is the correct answer.
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cual es la solucion de este numero entero (+4)+(+12)
Answer:
16
Step-by-step explanation:
12+1=13
13+1=14
14+1=15
15+1=16
1+1=2
2+1=3
3+1=4
---------
4+6=10
10+6=16
(6+6=12)
If f is a linear function for which f(4) = −13 and f(−4) = 19, find f(5). f(5) =
The value of the function f(5) is - 17.
How to solve linear function?A linear function is a function that represents a straight line on the coordinate plane.
A linear function in slope intercept form is as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, for the linear function, f(4) = −13 and f(−4) = 19.
f(5) can be found as follows;
-13 = 4m + b
19 = -4m + b
2b = 6
b = 6 /2
b = 3
-13 - 3 = 4m
-16 = 4m
m = -4
Hence,
f(5) = -4(5) + 3
f(5) = -20 + 3
f(5) = - 17
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Write the equation in standard form using integers.
y+3=3/4(x+5)
The equation in standard form is _____
Answer:
-3x + 4y = 3
Step-by-step explanation:
Ax + By = C standard form
y + 3 = 3/4 (x + 5) | ×4
4(y + 3) = 3(x + 5)
4y + 4·3 = 3x + 3·5
4y + 12 = 3x + 15
-3x + 4y = 15 - 12
The equation in standard form is -3x + 4y = 3
The longest runway at an airport has the shape of a rectangle and an area of 2,304,700 square feet. This runway is 190 feet wide. How long is the runway?
The runway is 12,130 feet long.
To find are you have to times the two sides, in this case it's 190 X 12,130. To find the length of one of these sides you must divide the area by one known side, in this case 2,304,700/190, which means the answer is 12,130 feet
Without computing, which best describes the value of (1/4) / 274?
(A) About one
(B) Much greater than one
(C) Much less than one
(D) There is not enough information
Answer:
Step-by-step explanation:
1/4 is already less than 1.
When you divide 1/4 by 274, you get much less than 1.
Much less than 1
Find the slope of the line that passes through the following points: (−4, 3) and (5, 4).
Answer:
The slope would be 1/9.
Step-by-step explanation:
From 3 to 4 it would be 1. From -4 to 5 it would be 9, the equation for slope is y/x so it would be 1/9.
solution
slope M =(Y' - Y)/(x' - x)
Indicated by (-4, 3) and (5 , 4)
x = -4 , x' = 5 , y = 3 , y' = 4
M = (4 - 3)/( 5 + 4)
M = 1/9 Ans
help by the end of the week.
Answer:
1 ) Slope of the line
[tex]m = 2[/tex]
2 ) Equation of the line
[tex]y=2x-2[/tex]
3 ) Values of a and b
a = 5
b = 6
4 ) What is the y-coordinate when?
The y-coordinate is the vertical position of a point in terms of distance and direction along the y-axis.
In this graph, when x = 2 they y-coordinate is also 2 so it is 2 units from the y-axis.
Hope this helps! :)
A car rental company charges an initial fee plus an additional fee for each mile driven. The charge depends on the type of car: economy or luxury.
The charge E (in dollars) to rent an economy car is given by the function E=0.70M+11.95, where M is the number of miles driven. The charge L (in dollars)
to rent a luxury car is given by the function L-1.25M+17.30.
Let C be how much more it costs to rent a luxury car than an economy car (in dollars). Write an equation relating C to M. Simplify your answer as much as
possible.
The equation to find rent difference C from given values of E and L is 1.75M + 3.25. After adding the values of E and L.
How to calculate cost difference ?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The meanings of the word equation and its translations into various languages can vary slightly.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables.
Let E represent Economy
Let L represent Luxury
Let M be the number of miles driven
Let C be how much it cost to rent a luxury car than economy
E = -0.70M + 11.95
L = 1.25M + 17.30
C = L - E
C =(1.25M + 17.30) - (-0.70M + 11.95)
C = 1.25M + 17.30 + 0.70M - 11.95
collect like terms
C = 1.25M + 0.70M + 18.20 - 14.95
C = 1.95M + 3.25
The rent difference between luxury car and economy car is 1.95M +3.25 .
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Work out the circumference of this circle.
Take pie T to be 3.142 and give your answer to 1 decimal place.
4 cm
Answer:
25.1 cm
Step-by-step explanation:
4 * 2 * 3.142 = 25.136 = 25.1 cm
Consider the following scenario: P(E) = 0.4, P(F) = 0.5
a. Find P(E or F) if E and F are disjoint
b. Find P(E or F) if E and F are independent
Part (a)
The term "disjoint" is the same as "mutually exclusive".
If events E and F are disjoint, then we know that P(E and F) = 0. In other words, the two events have nothing in common. Therefore, it's impossible for them both to occur simultaneously.
P(E or F) = P(E) + P(F) - P(E and F)
P(E or F) = 0.4 + 0.5 - 0
P(E or F) = 0.9
Answer: 0.9====================================================
Part (b)
If events E and F are independent, then P(E and F) = P(E)*P(F).
P(E or F) = P(E) + P(F) - P(E and F)
P(E or F) = P(E) + P(F) - P(E)*P(F)
P(E or F) = 0.4 + 0.5 - 0.4*0.5
P(E or F) = 0.4 + 0.5 - 0.2
P(E or F) = 0.9 - 0.2
P(E or F) = 0.7
Answer: 0.7A sweater has an original price of $65. It is on sale for 25% off. What is the amount of the discount?
Answer:
16.25
65 x 0.25 = 16.25
If another type of question the total price would be 48.75 :)
1. Corey buys a Toyota Yaris for $15,000 at 4.1% interest rate for 6 years.
How much interest will Corey pay on his Yaris?
What is the total amount that will paid?
What is his monthly payment?
Answer:
a) $4089.55
b) $19089.55
c) $56.80
Step-by-step explanation:
a) (100 + 4.1)/100 = 1.041. So, 15000 × 1.041⁶ = 19089.55. Interest that will be paid: 19089.55 - 15000 = $4089.55 (2 dp).
b) $19089.55 (with interest and principal)
c) 4089.55/72 = $56.80
Josie has $47 left on her checking account. If she writes a check for $55, what will Josie's balance be?
HALP PLEASE EMERGENCY
Answer:
a.) The relation is linear
b.) Plot the given (x,y) coordinates on the given graph and connect them.
c.) The y-intercept is at y=2.
d.) m=4
e.) y=4x+2
Step-by-step explanation:
a.) The relation is linear because the values in the sequence of first differences are all equal:
6-2=4 10-6=4 14-10=4 18-14=4
c.) The y-intercept is the point on the graph where x=0. According to the given points, the y-intercept must be y=2.
d.)
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\(x_1,y_1)=(0,2)\\(x_2,y_2)=(4,18)\\m=\frac{18-2}{4-0}\\m=4[/tex]
e.) Plug slope (m) and y-intercept into the slope-intercept form to get y=4x+2.
