The equation of the line parallel to the given line is y + 4x = 22
The given line is y= -4x+1
Slope of the line = -4
Slope of the parallel line= -4
Equation of the line parallel to the given line which passes through C(6,4)
y - 6 = - 4 ( x - 4 )
y - 6 = -4x + 16
y + 4x = 22
Hence the equation of the parallel line is y + 4x = 22
One that stretches on all sides and has no width is referred to in geometry as a line. A straight line is, to put it simply, a line without bends. An non-curved line that extends to infinity on both sides is said to be straight.
The general equation for a straight line is y = mx + c, where m stands for the line's slope and c for its y-intercept. The most frequently used straight line equation is one that has to do with geometry.
The equation of a straight line can be written in a number of different ways, such as point-slope form, slope-intercept form, general form, standard form, etc.
To learn more about equation visit:
https://brainly.com/question/14200719
#SPJ9
Brainliest and 30 points
Determine which integers in the set S:{−2, 2, 12, 24} make the inequality 4(j − 2) > 4(6 − 3j) true.
{12 , 24} are the integers from the set S which makes the inequality 4(j − 2) > 4(6 − 3j} true.
Inequality are those mathematical expression where both the sides are not equal . Instead of equality sign , we use less than or greater than sign.
Given inequality is
4(j − 2) > 4(6 − 3j}
open the brackets ,
4j − 8 > 24 − 12j
bring right terms on left side,
4j − 8 - 24 + 12j > 0
adding j terms,
16j - 32 > 0
16j >32
j > 32/16
j > 2
Integers making inequality true should be greater than 2
From set S: {-2 , 2, 12, 24}
{12 , 24 } are integers that makes inequality 4(j − 2) > 4(6 − 3j) True .
To know more about Inequality here
https://brainly.com/question/20383699
#SPJ1
7. What is the domain of the relation? y у O D = (-4,00) OD = (-0,4) O D = (0,00 OD = (-4,5)
The domain of a function is the value x that varies.
here x is varying from -4 and it is going to infinity
so the answer is
the domain for the given graph is
[tex]D=(-4,\infty)[/tex]So the answer is option (A).
can anyone help me????
⇒The measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
[tex]2a=(a+10)+44\\2a=a+54\\2a-a=54\\a=54[/tex]
⇒The exterior angle in this case NOTE IT IS 2a NOT a
⇒Therefore Exterior angle is =2(54°)
=108°
The answer is 108°
Answer:
68°
Step-by-step explanation:
We know that,
the exterior angle of a triangle is equal to the sum of the interior opposite angles of a triangle.
Accordingly,
44 + a + 10 = 2a
First, subtract a from both sides.
44 + 10 = 2a - a
34 = a
Now let us find the measure of the exterior angle.
2a
2 × 34
68°
Determine the constant of variation for the direct variation given. 2 1
The constant of variation for the given direct variation is 2.
What is the constant of variation?The quantity that connects two variables that are directly or inversely proportional to one another is known as the constant of variation.So, the origin (0, 0) and the supplied line are intersected by it (3, 6)
The slope of the line is the variation constant for the direct variation.The two on line coordinates (0, 0) and (1, 1) can be used to determine the slope (3, 6).Slope formula: m = y2 - y1/x2 - x1
Where,
x₁ = 0y₁ = 0x₂ = 3y₂ = 6Substitute values as follows:
m = y2 - y1/x2 - x1m = 6-0/3-0m = 6/3m = 2Therefore, the constant of variation for the given direct variation is 2.
Know more about the constant of variation here:
https://brainly.com/question/25215474
#SPJ1
Correct question:
Determine the constant of variation for the direct variation given.
A. 1/2
B. 1
C. 2
I need to convert the numbers to presents then put them in order least to greatest
We have the next numbers
And we must put them in order least to greatest
In order to put them in order we can write all numbers as percents
- 1/3
[tex]\frac{1}{3}=0.333\cdot100\text{ \%}=33.333\text{ \%}[/tex]- 0.3
[tex]0.3\cdot100\text{ \%}=30\text{ \%}[/tex]- 8/25
[tex]\frac{8}{25}=0.32\cdot100\text{ \%}=32\text{ \%}[/tex]Now, we have all numbers in percents. So we can order them
30% -> 32% -> 33% -> 33.333% -> 33.6%
4x10 to the 8power/5x10 to the 3power
The value of the exponent is 80000000000.
What are exponents?Exponentiation is a mathematical operation that involves the base number and the exponent (or power) number (n), and is represented as bn. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to base multiplication when n is a positive integer; therefore, bn is the result of multiplying n bases: Exponent-related problems are solved using the rules of exponents or the properties of exponents. These characteristics are regarded as major exponents rules that must be adhered to when solving exponents.acc to our question-
4x10 to the 8power/5x10 to the 3power is = 80000000000.learn more about exponents here:
https://brainly.com/question/13669161
#SPJ13
True or False?
Point (5,y) is a solution of the inequality y+9x>0 for any value of y.
Answer:
False
Step-by-step explanation:
Determine the value of altitude BD to the nearest tenth.
1) Given the altitude BD, let's find its measure using some trigonometric relations on the Right Triangle:
1.2) Pythagorean Theorem to find the other leg
b²=a²+c² The hypotenuse, in this case, is labeled as "b"
32²=16²+a²
1024=256+a²
1024-256=a²
768=a²
√768=√c²
a=16√3
2) Now, let's use one trigonometric relation on the Right Triangle, based on the similarity of the triangles:
ah=bc Adjusting it:
bh=ac
32h=16√3*16
32h=256√3
h=256√3/32
h=8√3 ≈ 13.85 ≈13.9
3) So the altitude BC of that triangle is approximately 13.9
let f(x) = 3/3-× and g (×) = 11+x find the domain of (f/g) (x)
Answer:
[tex]\lbrace x|x\text{ is a real number and x }\ne\text{ -11},3\rbrace[/tex]Explanation:
Here, we want to get the domain of the given function
We start by dividing the two as follows:
[tex](\frac{f}{g})(x)\text{ = }\frac{f(x)}{g(x)}[/tex][tex]\begin{gathered} So,\text{ we have it that:} \\ \frac{3}{3-x}\times\frac{1}{11+x}\text{ = }\frac{3}{33+3x-11x-x^2}\text{ = }\frac{3}{33-8x-x^2} \end{gathered}[/tex]The domain refers to the possible x-values
To get that, we need to solve the quadratic equation in the denominator
We have that as:
[tex]\begin{gathered} 33-8x-x^2=0 \\ 33-11x+3x-x^2=0 \\ 11(3-x)+x(3-x)=\text{ 0} \\ (11+x)(3-x)\text{ = 0} \\ x\text{ = -11 or 3} \end{gathered}[/tex]So, we have the domain as:
[tex]\mleft\lbrace x|x\text{ is a real number and x }\ne\text{ -11},3\mright\rbrace[/tex]Factor the quadratic expression.5x2 – 17x - 405x2 - 17x - 40 = (Factor completely.)
The general form of a quadratic polynomial is given by:
[tex]ax^2+bx+c[/tex]You have the following quadratic expression:
[tex]5x^2-17x-40[/tex]In order to factorize the previous expression, you first use the quadratic formula, which is given by;
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a = 5, b = -17, c = -40. You replace these values into the quadratic formula:
[tex]\begin{gathered} x=\frac{-(-17)\pm\sqrt[]{(-17)^2-4(5)(-40)}}{2(5)} \\ x=\frac{17\pm\sqrt[]{1089}}{10}=\frac{17\pm33}{10} \\ x_1=5 \\ x_2=\text{ -}\frac{16}{10}=-\frac{8}{5} \end{gathered}[/tex]The factors of the quadratic polynomial, based on the previous calculated zeros of the piolynomial are as follow:
[tex](x-x_1)(x-x_2)=(x-5)(x+\frac{8}{5})[/tex]Cindy spent $65.25 on ingredients for blueberry pies and $62.84 on ingredients for cherry pies.Each slice of pie sells for $3.50.Part A:Write an expression to represent Cindy's profit is she sells b slices of blueberry pie and c slices of cherry pie. Part B:Cindy sells 24 slices of blueberry pie and 15 slices of cherry pie. The next day, she sold 26 slices of blueberry pie and 17 slices of cherry pie. What was her total profit?
A) 3.5a +3.5b ≥ 128.09 B) Total profit: $158.91
1) Gathering the data
$65.25 ingredients for blueberry pies
$62.84 cherry pie
Each slice
3.50
A) Since Cindy's profit relies on her sales we can write
b = slices of blueberry
c = cherry pie slices
3.50b +3.50a ≥ 65.25+62.84
3.5a +3.5b ≥ 128.09
B) Gathering those data and adding the number of slices that were sold:
1st day
b= 24
a =15
2nd day
b=26
a=17
Plug into that:
Profit: 3.5(15+17) + 3.5(24+26)
P =287
$287 was the total revenue
Cherry pie cost of production 62.84
3.5(15+17)=112
Profit = 112 -62.84
Profit = $49.16
Blueberry cost of production: $65.25
3.5(24+26) =175
175 - 65.25 =109.75
Profit $ 109.75
Total profit: $158.91
Every day, an automobile factory assembles 12 more cars than trucks.
Let t represent the number of trucks assembled and c represent the number of
cars assembled.
Use the function c = t + 12 to find the value of c when t = 1.
C=
The value of C is 13.
What is mean by mathematical operation ?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.
An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.
Given ,
The automotive manufacturer produces 12 more automobiles than trucks each day.
T is the input and c is the output in this connection. Therefore, by adding 12 to t, you may calculate c.
Write this connection as a function.
c = t + 12
To determine the value of c, replace t in the function with 1 instead.
c = t+12
c = 1 + 12
c = 13.
Therefore the value of C is 13
To learn more about mathematical operator refer to:
https://brainly.com/question/28294142
#SPJ1
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 3.4 meters, Length = 6.4 meters
Step-by-step explanation:
If the width is [tex]w[/tex], then the length is [tex]w+3[/tex].
[tex]w(w+3)=22\\\\w^2 +3w=22\\\\w^2 +3w-22=0\\ \\ w=\frac{-3 \pm \sqrt{3^2 -4(1)(-22)}}{2(1)}\\\\w \approx 3.4 \text{ } (w > 0)\\\\\implies w+3 \approx 6.4[/tex]
Andrew spent $12 on 25 Twix bars.How many did each twixt bar cost him?
Answer: 48 cents on each twix bar
Step-by-step explanation: divide 12 by 25, which would come out to 0.48, to ensure this is correct you can multiply 0.48x25 and it would be 12
he spent 48 cents on each twix bar
(division)
Emma went to the movie theater for her birthday. A mix of adults and children attended, making a total of 19 people. Each adult ticket was $9 and each child’s ticket was $5.50. If the total cost for the party was $150, then how many adults and how many children attended
Solving the equations for the total number of adults and children and respective ticket costs, we find out that the number of adults and children that attended the movie theater are 13 adults and 6 children.
It is given to us that -
A total of 19 people attended the movie theater which was a mix of adults and children
Each adult ticket was $9
Each child’s ticket was $5.50.
Total cost for the party was $150
We have to find out the number of adults and children that attended the movie theater.
Let us assume that the number of adults and children that attended the movie theater be [tex]x[/tex] and [tex]y[/tex] respectively.
Since, a total of 19 people attended the movie theater including both adults and children, we can say that -
[tex]x+y=19[/tex] ------ (1)
It is also given that each adult ticket was $9 and each child’s ticket was $5.50. So,
For [tex]x[/tex] adults, the ticket price = [tex]9x[/tex], and
For [tex]y[/tex] children, the ticket price = [tex]5.5y[/tex]
It is given that the total cost for the party was $150
[tex]= > 9x+5.5y=150[/tex] ------- (2)
From equation (1), we have
[tex]x+y=19\\= > y =19-x[/tex] ------ (3)
Substituting this value of [tex]y[/tex] in equation (2),
[tex]= > 9x+5.5y=150\\= > 9x+5.5(19-x)=150\\= > 9x +104.5-5.5x=150\\= > 3.5x=45.5\\= > x=13[/tex]------ (4)
Substituting this value of [tex]x[/tex] from equation (4) in equation (3), we get
[tex]y=19-x\\= > y=19-13\\= > y=6[/tex]
Thus, solving the equations, we find out that the number of adults and children that attended the movie theater are 13 adults and 6 children.
To learn more about equations visit https://brainly.com/question/14686792
#SPJ9
If a line bisects a segment, then the segment is divided into two congruent parts.
Converse:
Inverse:
Contrapositive:
In converse, a segment is divided into two congruent portions if a line bisects it.
What is converse?A line bisects a segment if it can be divided up into two congruent portions. A line does not cut a section in half if it is not separated into two equal parts.A line is split into two equal parts by a bisector. Therefore, when we refer to a perpendicular bisector of a line segment AB, we mean that it bisects or divides AB into two equal halves. It is perpendicular to AB or at right angles to it. The distance between each point on the perpendicular bisector from points A and B is equal.Contrarily, if two segments are congruent, they have the same length. Inverse: Two segments have different lengths if they are not congruent.To learn more about line bisector refer to :
https://brainly.com/question/27948960
#SPJ1
select all the points that are on the graph of the linr 2x + 4y =20
Answer: y-intercept (0,5)
slope is -1/2
Step-by-step explanation:
Just put it on a graph.
If the total price for two cars at the dealership is $87,000, where one car’s price is $6000 less than twice the other, what is the price of the cheaper vehicle?
The price of the cheaper vehicle, given the total price of the two cars can be found to be $40, 500
How to find the price?Assuming the price of the cheaper car is denoted as x, the formula for the price of the more expensive car would be:
= Price of cheaper car + $6, 000
= 6, 000 + x
Finding the value of the cheaper car in the dealership can be found by the formula:
x + (6, 000 + x) = 87, 000
2x + 6, 000 = 87, 000
2x = 87, 000 - 6, 000
x = 81, 000 / 2
x = $40, 500
Find out more on car price at https://brainly.com/question/28611283
#SPJ1
9. A variety box of donuts has 4 sprinkle
donuts, 5 glazed donuts, and 3 cream filled
donuts. The expression 4b + 5b + 3b
represents the total number of donuts in
b boxes. Write an expression in simplest
form to represent the total number of
donuts. (Example 2)
It is as simple as adding the probability of each event and then subtracting the probability of both events occurring to calculate the probability of either one of two events occurring: P(A or B) = P(A) + P(B) - P(A or B)
What are the addition Rule probability of two or more events occurring .
P (A or B) denotes the probability of two or more events occurring. The symbol represents the outcomes of event A or event B and means "union" (or both).
P(A) = P(A) + P(B) - P(AB)
The events have no outcomes in common if they are mutually exclusive (disjoint).
Then P(A) = 0.
Here are some simple examples to get you started...
A box includes three glazed doughnuts, four jelly doughnuts, and five chocolate doughnuts. Determine the probability that a person will choose a glazed doughnut or a chocolate doughnut at random.
If the two events are mutually exclusive (also known as disjoint), they cannot both occur!
If neither can happen, P(A and B) is 0. Therefore,
P(A) + P(B) = P(A) + P(B).
to learn more about addition Rule probability refer to :https://brainly.com/question/28710004
#SPJ1
please help i have 10 mins to be doing this
Height of nth stair from the ground be 18n.
What do you mean by airthmetic sequence?
A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence.
The common difference of the sequence is d, and the number a is the first term. [tex]a_{n}[/tex] = a + (n - 1)d is the formula for an arithmetic sequence's nth term.
The common difference, or d, is the difference between any two consecutive terms in an arithmetic sequence, and it may be calculated by deducting any pair of terms beginning with a and ending with [tex]a_{n+1}[/tex] Accordingly, d = [tex]a_{n+1}[/tex] - [tex]a_{n}[/tex]
It is given that height of each stair is 18 cm
Height of first stair = 18 cm
Height of second stair = 18 + 18 = 36 cm
Height of third stair = 36 + 18 = 54 cm
and so on.
This data will make a sequence such as 18 , 36 , 54 , 72 ..........
Here first term , a = 18
Common difference , d = 36 - 18 = 18
For the height of nth stair , use the formula of [tex]a_{n}[/tex]
[tex]a_{n}[/tex] = a + (n-1) d
where a is the first term , d id the common difference and n is the number of terms
Here, [tex]a_{n}[/tex] = 18 + (n-1)18 = 18 + 18n - 18 = 18n
Hence, height of nth stair from the ground be 18n .
To learn more about the airthmetic sequence from the given link.
https://brainly.com/question/7882626
#SPJ1
Circle M dilated by a scale factor of 3 gives circle N. If the circumference of circle N is 6 cm, what is the circumference of circle M?
For this problem, we are given two circles, M and N, that are related by a scale factor of 3, we know that the circumference of the larger circle is 6 cm, and we need to determine the circumference of the smaller one.
The circumference of a circle can be found by using the following expression:
[tex]C=2\pi r[/tex]Where 'r' is the radius. When the circles are scaled, their radii should be scaled at the same proportion, so the following demonstrates the relation between both radii:
[tex]r_n=3\cdot r_m[/tex]We know that the circumference for the circle N is equal to 6 cm, therefore we have:
[tex]6=2\pi\cdot r_n[/tex]If we replace the radius for circle n, with the second expression, we will obtain:
[tex]\begin{gathered} 6=2\pi\cdot(3\cdot r_m) \\ 6=3\cdot(2\pi r_m) \\ \frac{6}{3}=C_m \\ C_m=2 \end{gathered}[/tex]Circle M's circumference is equal to 2 cm.
Answer:
2cm
Step-by-step explanation:
I Just Took the Test.
Graph h(x) = 32(0.45)x. What is the constant percent rate of change of f(x) with respect to x? Does the graph show growth or decay?
45% growth
45% decay
55% growth
55% decay
Answer:
55% decay, the other guy is wrong
Step-by-step explanation:
Trust me
Factor. 4y - 32 Factor
Notice that:
[tex]\begin{gathered} 4y=4\times y, \\ 32=4\times8 \end{gathered}[/tex]Therefore:
[tex]4y-32=4\times y-4\times8.[/tex]Grouping like terms we get:
[tex]4\times y-4\times8=4\times(y-8)\text{.}[/tex]Answer:
[tex]4(y-8)\text{.}[/tex]Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. y=3(7/5)^t
The function y=3[tex](7/5)^t[/tex] In the function f (x) = bx when b > 1, the function represents exponential growth represents exponential growth.
What is the difference between exponential growth and exponential decay?An exponential function has the generic formula y = abx, where a = 0 and b = a positive real number. When describing an exponential function, the base b is a constant. When the domain is a set of real numbers, the independent variable is the exponent x.Exponential growth and decay: When b > 1, the function f (x) = bx represents exponential growth. If 0 b 1, the function f (x) = bx illustrates exponential decay.To calculate the growth rate, subtract the current value from the previous value. The percentage growth rate is calculated by multiplying the difference by the previous number and dividing by 100.Therefore,
The function y=3[tex](7/5)^t[/tex] In the function f (x) = bx when b > 1, the function represents exponential growth represents exponential growth.
Exponential growth and decay are the two different kinds of exponential functions.
When b > 1, the function
f (x) = bx represents exponential development.
If 0 b 1, then the function
f (x) = bx depicts exponential decay.
To learn more about Exponential growth, refer to:
https://brainly.com/question/27161222
#SPJ1
Write an equation of the parabola that has the same shape as the graph of f(x)= 3x², but with the point (3,-4) as the vertex.
Answer: y = 3(x-3)^2-4
==================================================
Explanation:
The graph of y = 3x^2 has (0,0) as the vertex.
To move from (0,0) to (3,-4) we will shift 3 units right and 4 units down.
Therefore, we will have y = 3(x-3)^2-4 as the answer
It is of the form y = a(x-h)^2+k with (h,k) being the vertex.
The 'a' value out front vertically stretches or compresses the parabola. Also if a > 0, then the parabola opens upward; or if a < 0, then the parabola opens downward.
We keep the same value of 'a' so that both parabolas have the same shape.
2x^2-3x=1
i need a step by step please
The solutions of the quadratic equation are:
x = 7/4
x = -1/4
How to solve the quadratic equation?Here we have the quadratic equation:
2x^2 - 3x = 1
Remember that the general quadratic equation:
a*x^2 + b*x + c = 0
Has the solutions:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Then our quadratic equation:
2x^2 - 3x = 1
2x^2- 3x - 1 = 0
The solutions are:
[tex]x = \frac{3 \pm \sqrt{(-3)^2 - 4*2*-1} }{2*2}\\\\x = \frac{3 \pm 4}{4}[/tex]
So the two solutions are:
x = (3 + 4)/4 = 7/4
x = (3 - 4)/4 = -1/4
Learn more about quadratic equations:
https://brainly.com/question/1214333
#SPJ1
2.Which data set is more likely to produce a histogram with a symmetric distribution? Explain yourreasoning.Data on the number of seconds on a track of music in a pop album.Data on the number of seconds spent talking on the phone yesterday by everyone in theschool.
A histogram with a symmetric distribution looks like this:
Leaving aside the quality of the drawing, the left and the right side of the histogram are identical if we split it by the red line. Is like having a reflexion axis.
Now, we have to discuss what of the 2 data sets may have such an histogram. This means that we must think which of them may have the same number of ocurrences for very short and very long durations, for regular to short and regular to long durations, and so on and so furth.
Pop album tracks:
In the same album we may have arround 12 tracks (small number), all of them with a duration of arround 3 minutes. We could imagine a histogram like the following:
All the songs last between 170 and 190 seconds, and one or two last a little bit more.
Phone talks:
In this case, we can think that there are some calls to say something like "mom, I'm on my way home" and other like "let me tell you the hole movie I saw yesterday night", so very short and very long calls, but they are no so common. There are a lot of "regular" calls that might last for 60 seconds.
Also, in this case, we are taking into account all the calls from people in the school in one day (yesterday), so, may be 1.000 calls? The actual number really doesn't matter, but the fact that the number is very big. Because of the big number, we can expect a symmetric distribution.
a box of 210 tissues for 3.19
The unit rate is $0.015 per tissue
The total number of tissues in the box = 210 tissues
The cost of 210 tissues = $3.19
Here we have to apply the unitary method
The unitary method is defined as the method of finding the value of the single unit. The value of the single unit is call the unit rate
Then the unit rate of tissue = The cost of 210 tissues / The total number of tissues in the box
Substitute the values in the equation
The unit rate = 3.19 / 210
= $0.015 per tissue
Hence, the unit rate is $0.015 per tissue
The complete question is :
Express the rate as unit rate, a box of 210 tissues for $3.19
Learn more about unit rate here
brainly.com/question/28572142
#SPJ1
The cost of producing pens is $5.00 to set up the machine and $0.10 per pen. Each pen sells for $0.30. How many pens must be sold for the cost of production to equal the income?
Answer:
x=25
Step-by-step explanation:
0.3x = 5+0.1x
0.3x-0.1x = 5
0.2x = 5
x = 5/0.2
x= 50/2
x=25
Use the line tool to graph the line passing through (3,-2) whose slope is m = -2
Given:
P(3, -2)
m = -2
The linear equation is of the form y = mx + b where m is the slope and b is y-intercept. So we find b:
[tex]\begin{gathered} y=mx+b \\ -2=-2(3)+b \\ -2=-6+b \\ -2+6=-6+b+6 \\ b=4 \end{gathered}[/tex]Therefore, the equation is:
[tex]y=-2x+4[/tex]Graphing: