The equation of the line that passes through the point (-5,7) with slope -5 in the point-slope form is 5x + y = -18 .
The Point - Slope form of the line passing through (x₁,y₁) with slope m is given by the equation
(y-y₁)= m(x-x₁)
In the question ,
it is given that the required line passes through the point(-5,7) and have the slope = -5 .
the point is (-5,7)
so x₁= -5 and y₁=7 and m = -5
Substituting the value in the equation of point slope form , we get
(y-y₁)= m(x-x₁)
(y-7)= (-5)(x-(-5))
simplifying further , we get
(y-7)= (-5)(x+5)
y-7 = -5x -25
5x + y = -25 +7
5x + y = -18
Therefore , the equation of the line that passes through the point (-5,7) with slope -5 in the point-slope form is 5x + y = -18 .
The given question is incomplete , the complete question is
Use point-slope form to write the equation of a line that passes through the point (-5,7) with slope -5 .
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PLEASEEEEEEEE HELPPP
If Greg has 1 1/2 servings of cereal for breakfast each day, he can consume 8 breakfasts from a box of cereal.
The price of one breakfast from a regular-sized box of cereal is $0.54 if the box costs $4.29.
Greg could consume 4 additional breakfast portions from a single family-sized box.
How to find unit rate of Greg's breakfast?A regular-sized box of cereal = 12 servings
If Greg eats 1 1/2 servings for breakfast every day
Number of breakfast Greg can eat in a regular-sized box = A regular-sized box of cereal / servings of breakfast eaten everyday
= [tex]\frac{12}{\frac{11}{2} }[/tex]
=[tex]\frac{12}{\frac{3}{2} }[/tex]
multiply by the reciprocal of [tex]\frac{3}{2}[/tex]
= 12 × [tex]\frac{2}{3}[/tex]
= [tex]\frac{24}{3}[/tex]
= 8 breakfast
Cost of regular-sized box of cereal = $4.29.
Cost of one breakfast from a regular-sized box of cereal = Cost of regular-sized box of cereal ÷ Number of breakfast Greg can eat in a box
= [tex]\frac{4.29}{8}[/tex]
= 0.53625
Approximately,
$0.54 per breakfast
If Greg purchased the family-sized box of cereal that contains 18 servings
Family-sized box of cereal divided by the daily serves of breakfast is the number of breakfasts Greg can consume.
= 18 servings / [tex]\frac{11}{2}[/tex]
= 18 ÷[tex]\frac{3}{2}[/tex]
= 18 × [tex]\frac{2}{3}[/tex]
= [tex]\frac{36}{3}[/tex]
= 12 servings
Consequently, the number of additional breakfasts Greg may consume from a single family-sized package
= Number of breakfast Greg can eat in a family-sized box - Number of breakfast Greg can eat in a regular-sized box
= 12 servings - 8 servings
= 4 servings
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Find the first 5 terms of the following sequence. For the first term let a_1=1. Round your answer to the nearest hundredth.a_n= \frac{2^n}{n^2} 1st term = Answer2nd term = Answer3rd term = Answer4th term = Answer5th term = Answer
1st term
Given:
[tex]a_1=1[/tex]With the formula of the sequence:
[tex]\begin{gathered} a_1=\frac{2^1}{1^2}=\frac{2}{1}=2 \\ \\ a_1=2 \end{gathered}[/tex]________
Second term:
[tex]\begin{gathered} a_2=\frac{2^2}{2^2}=\frac{4}{4}=1 \\ \\ a_2=1 \end{gathered}[/tex]____________
Third term:
[tex]\begin{gathered} a_3=\frac{2^3}{3^2}=\frac{8}{9}\approx0.89 \\ \\ a_3=0.89 \end{gathered}[/tex]_________
Fourth term:
[tex]\begin{gathered} a_4=\frac{2^4}{4^2}=\frac{16}{16}=1 \\ \\ a_4=1 \end{gathered}[/tex]-________________
Fifth term:
[tex]a_5=\frac{2^5}{5^2}=\frac{32}{25}=1.28[/tex]please answer asap im begging
Answer:
y = 3x + 3 :D
Step-by-step explanation:
Equation of line: y = mx + b :)
b: Y intercept
m: Slope
Now lets solve :)
Lets find M first :)
We need 2 points so lets use (0,3) and (1,6) :)
We fist need to subtract :)
6 - 3 = 3
1 - 0 = 1
Now we divide :)
3/1 = 3
Lets put that into our equation :)
y = 3x + b
Now lets find B :)
To find b, we need to see where the line intercepts the y axis! This will be at point (0,3)!
The y intercept will be 3 :)
The final equation will be y = 3x + 3 :)
Have an amazing day!!
Please rate!
The area of a trapezoid is given by the formula A = (a + b). Solve the formula for b.
Starting from the given formula:
[tex]A=\frac{h}{2}(a+b)[/tex]Multiply both sides of the equation by 2:
[tex]\begin{gathered} \Rightarrow2\times A=2\times\frac{h}{2}(a+b) \\ \Rightarrow2A=h(a+b) \end{gathered}[/tex]Divide both sides by h:
[tex]\begin{gathered} \Rightarrow\frac{2A}{h}=\frac{h(a+b)}{h} \\ \Rightarrow\frac{2A}{h}=a+b \end{gathered}[/tex]Substract a from both sides of the equation:
[tex]\begin{gathered} \Rightarrow\frac{2A}{h}-a=a+b-a \\ \Rightarrow\frac{2A}{h}-a=b \end{gathered}[/tex]Therefore:
[tex]b=\frac{2A}{h}-a[/tex]Julia sells subs for $6 each. How many subs will she need to sell to break even each month based on the costs listed below?
Labor costs (management & workers) = $11,000
Insurance = $400
Rent = $1300
Utilities = $300
Average cost of ingredients/packaging for each sub = $1.32
Answer:
2777.7777... subs
Step-by-step explanation:
11000+400+1300+300=13000
6-1.32=4.68
13,000/4.68
=2777.777777...
of one hundred and forty two students attending college , 23 are criminal justice majors. if 9 are selected at random, determine the probability each 9 criminal justice major. set up the problem as if it were to be solved but don't solve.
The probablity that first one selected is a criminal justice major is,
[tex]P_1=\frac{23}{142}[/tex]Now, the probablity that second one is a criminal justice major is when selected without replacement,
[tex]P_2=\frac{22}{141}[/tex]Simirally,
[tex]\begin{gathered} P_3=\frac{21}{140} \\ P_4=\frac{20}{139} \\ \ldots.\text{.} \end{gathered}[/tex]Thus, using the multiplication theorem,
[tex]\begin{gathered} P=P_1\times P_2\times\ldots\ldots.P_9 \\ =\frac{23}{142}\times\frac{22}{141}\times\frac{21}{140}\times\ldots\ldots\ldots\ldots\ldots\frac{15}{134} \end{gathered}[/tex]Thus, the above equation gives the requried probablity.
A florist has 60 tulips and 72 daffodils. The florist will make bouquets with the same number of tulips and the same number of daffodils in each, using all the flowers.
What is the greatest number of bouquets the florist can make?
Enter the correct answer in the box.
The greatest number of bouquets that the florist can make is 12.
What is the greatest number of bouquets that the florist can make?The greatest number of bouquets that the florist can make can be determined by calculating the highest common factor of 60 and 72. The factor of a number is the number that divides another number without any remainder. The highest common factor of two or more numbers is the highest factor that is common to two or more numbers.
Factors of 60 =1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Highest common factor = 12
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The following data are the ACT score of all student in the history class
The frequency means how many times specific data shows up in a set of values.
Score Frequency
1-6 2
7-12 4
13-18 5
...
And so on.
How to do this? Primary math please teach me
By using products and percentages, the grandson had the amount of $ 225 before to buy foods and beverages.
How much money did the grandson have at first?In accordance with the statement, the grandson spent 80 % of all his amount to buy some food, later 40 % of the remaining money to buy some beverages and there was $ 27 remaining. We need to determine the amount that the grandson had initially. Then, the situation can be described by the following mathematical expression:
(1 - 80 / 100) · (1 - 40 / 100) · x = 27
(20 / 100) · (60 / 100) · x = 27
(1200 / 10000) · x = 27
(12 / 100) · x = 27
12 · x = 2700
x = 2700 / 12
x = 225
By means of percentages, the grandson had an amount of $ 225 before buying foods and beverages.
RemarkThe name of the grandson cannot be added due to profanity detector.
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can you draw a quadrilateral with 2 pairs of congruent parallel sides and 4 right angles
ANSWER and EXPLANATION
We want to draw a quadilateral that has 2 pairs of congruent parallel sides and 4 right angles.
There are 2 quadilaterals that fit this description:
A square and a rectangle
QUESTION ATTACHED
PLEASE HELp
Answer:
yh no question....thanks for the points tho :)
El 30 % de que numero es el 30 % del 10 % de 700
Answer:
70
Step-by-step explanation:
[tex]\frac{(700)(0.1)(0.3)}{0.3}=70[/tex]
What is an equivalent expression to 20x - 45y
Equivalent linear expressions are expressions that have the same value. That is, if you have two linear expressions that are equivalent to one another, and you plug the same value in for the variable in each of them, you will get the same result in each of them.
In the case of this question, the equaivalent expression can be gotten by factorizing the expression
[tex]undefined[/tex]Use the given values to write an equation that relates x and y.
We are given that "x" and "y" vary inversely. This means that the variables follow the next relationship:
[tex]y=\frac{k}{x}[/tex]Where "k" is a constant to be determined. To determine "k" we will use the given values:
[tex]\begin{gathered} x=3 \\ y=6 \end{gathered}[/tex]Now, we plug in the values:
[tex]6=\frac{k}{3}[/tex]Now, we solve for "k" by multiplying both sides by 3:
[tex]\begin{gathered} 6\times3=\frac{k}{3}\times3 \\ \\ 18=k \end{gathered}[/tex]Therefore, the value of "k" is 18. Now, we substitute in the relationship:
[tex]y=\frac{18}{x}[/tex]And thus we get the equation.
I need help with this homework assignment it’s due by mid night
step 1
see the attached figure to better understand the problem'
step 2
Hypotenuse is AB
Opposite side is BC
Adjacent side is AC
because, the opposite side is the side opposite to the given angle (35 degrees)
adjacent side is the side adjacent to the given angle (35 degrees) and the hypotenuse is the greater side of a right triangle (is the opposite side to the angle of 90 degrees)
step 3
To find out the value of L
we use
cos(35)=40/L -----> adjacent side divided by the hypotenuse
step 4
solve for L
L=40/cos(35)
step 5
L=48.83 ft
step 6
the length of the ladder must be greater than 48.83 ft
step 7
A 50 ft ladder long is enought
because 50 > 48.83
What is the next fraction in the sequence 19/20,4/5,13/20,1/2
55 miles per hour Anserw
Answer: Uhm hold on
Step-by-step explanation:
help plwsty Graph the equation: y-1 = 2/3(x-3)?
The given expression : y-1=2/3(x-3)
Simplify the equation :
[tex]\begin{gathered} y-1=\frac{2}{3}(x-3) \\ y=\frac{2}{3}x-\frac{2}{3}(3)+1 \\ y=\frac{2}{3}x-2+1 \\ y=\frac{2}{3}x-1 \end{gathered}[/tex]for the graph we need atleast two coordinates
Let at x=0 then
y=2/3(0)-1
y=-1
Cooridnate = (0,-1)
Now, let x=9 then
y=2/3(9)-1
y=2(3)-1
y=5
Coordinate =(9,5)
Plot these point (0,-1) & (9,5)on the graph and join them by staright line
The graph will be ;
On Mrs. Sean's desk,there are pink and yellowmarkers. The ratio of pinkmarkers to total markersis 1:3. If there are 16yellow markers, then howmany markers are pink?
We know that the ratio of pink markers to total markers is 1:3.
This means that for every 3 markers, one of them is pink. The other 2 will be yellow markers.
We can write that the ratio of pink markers to yellow markers is 1:2, based on the last sentence. This means that if we have N yellow markers, we will have N/2 pink markers.
Then, if we have 16 yellow markers, then we will have 16/2=8 pink markers.
Ekua designs and sells T-shirts for $1 13 each. Ekua has to spend $280 per month, $9.50dollar per T-shirt ordered.
As Ekua has to spend $280 per month and the cost of each sheet is $9.50 / dollar. The inequality followed is T≤29.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.
To ascertain the maximum or lowest values of a scenario with many restrictions, a system of linear inequalities is frequently utilized. Inequalities reflect a limit of what is permitted or achievable rather than a precise quantity.
It is given that Ekua designs and sells T-shirts for $1 13 each. Ekua has to spend $280 per month, $9.50 dollar per T-shirt ordered.
We have to find the maximum number of T-shirts she can buy,
⇒ $280 / $9.50
⇒ 29.47 ≅29
Thus, Ekua has to spend $280 per month and the cost of each sheet is $9.50 / dollar. The inequality followed is T≤29.
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Function Notation - Transformationsill send a picture of the question
Let's see how two points on the left are mapped to their corresponding points on the right:
Point A has a corresponding point at A'. We have:
f(A) = A'
f(-6, -3) = (2, 4)
Point B has a corresponding point at B'. We have:
f(B) = B'
f(-4, -1) = (4, 6)
Now, notice that:
2 = -6 + 8
4 = -3 + 7
So, for (x, y) = (-6, -3), we have:
f(x, y) = (2, 4) = (x + 8, y + 7)
Notice that the same happens to the mapping of the other point:
4 = -4 + 8
6 = -1 + 7
So, for (x, y) = (-4, -1), we have:
f(x, y) = (4, 6) = (x + 8, y + 7)
Therefore, the rule for the transformation is
f(x, y) = (x + 8, y + 7)
Given that F( x) = x + 2, evaluate F(2)
Answer:
f(2) = 4
Step-by-step explanation:
Hello!
We can find f(2) by substituting 2 for x in the equation.
Evaluate f(2)f(x) = x + 2f(2) = 2 + 2f(2) = 4The value of f(2) is 4.
Jaylen's beta fish holds 4 1/2 gallons of water. It takes him 1 7/8 minutes to fill. What is the flow rate of the water in gallons per minute? show your work.
Let's begin by listing out the information given to us:
Jaylen's beta volume = 4 1/2 gallons = 4.5 gal
Time taken = 1 7/8 minutes = 1.785 min
[tex]Flowrate=\frac{volume}{time\text{ taken}}=\frac{4.5}{1.875}=2.4\text{ gal/min}[/tex]Flow rate = volume / Time taken = 4.5 / 1.875 = 2.4 gal/min
Peter's farm has 160 meters of fencing, and he wants to fence a rectangular field thatborders a straight river. He needs no fence along the river side. Find the largest areaof Peter's farm that can be fenced.
ANSWER
3200 m²
EXPLANATION
Peter wants to build a fence around a rectangular field, except for one side because the river is there,
So, the total perimeter of the fence is,
[tex]P=W+W+L=2W+L[/tex]And this is equal to 160 m. Solving for L,
[tex]160=2W+L\text{ }\Rightarrow\text{ }L=160-2W[/tex]The area of this field is,
[tex]A=WL[/tex]Replace L with the expression we found from the perimeter,
[tex]A=W(160-2W)=160W-2W^2[/tex]The area is given by a quadratic function whose leading coefficient is negative, which means that the graph is a downward parabola and, therefore, the vertex is the maximum value of the area.
The x-coordinate of the vertex is given by,
[tex]f(x)=ax^2+bx+c\text{ }\Rightarrow\text{ }x_{vertex}=\frac{-b}{2a}[/tex]In this case, x is W, a = -2, and b = 160, so the width of the field for the maximum area is,
[tex]W_{vertex}=\frac{-160}{2(-2)}=\frac{160}{4}=40m[/tex]And the length when W = 40 is,
[tex]L=160-2W=160-2\cdot40=160-80=80m[/tex]And the area is,
[tex]A=WL=40m\cdot80m=3200m^2[/tex]Hence, the largest area of Peter's farm that can be fenced is 3200 square meters.
A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers placed an ad online asking for volunteers to participate in the study, and 100 subjects replied. They are informed that one group of 50 will receive a new cream and the remaining group of 50 will receive a cream with no active ingredient. The subjects are numbered 1–100 and these numbers are put into a random number generator. The first 50 unique numbers will represent the subjects that will receive the new cream and the remaining 50 subjects will receive the inactive cream. All subjects are exposed to poison ivy and given their cream. They are asked to return in three days and report their level of irritation. The average scores for each cream are compared.
Does this procedure describe a completely randomized design for this experiment?
Yes, the subjects will be exposed to the poison ivy.
Yes, the subjects are randomly assigned to each treatment.
No, the subjects are asked to return in three days. It is possible that some of them may not return, which will introduce bias into the results.
No, the subjects are randomly assigned to the two treatment groups, but the groups are not guaranteed to have 50 subjects in each.
The procedure describe a completely randomized design for this research as B. Yes, the subjects are randomly assigned to each treatment.
How to illustrate the information?In a randomized block design, the experimental units are divided into groups that we refer to as blocks. The experimental units inside each of the blocks will then be randomly assigned treatments.
As we can see from the question, they were divided into Blocks based on how much sun exposure they received while engaging in outdoor activities. After that, random treatments are assigned to each group.
Here, the participants are divided into groups based on their sun exposure, and then both treatments are distributed at random among the groups.
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Find the average rate of change of k(x) = 4x + 11 over the interval [-19, -17].
Step 1:
Concept:
Use the rate of change formula below.
[tex]\begin{gathered} \text{Rate of change = }\frac{k(b)\text{ - k(a)}}{b\text{ - a}} \\ k(x)\text{ = 4x + 11} \\ a\text{ = -19} \\ b\text{ = -17} \end{gathered}[/tex]Step 2
Find k(a) and k(b)
[tex]\begin{gathered} k(-19)\text{ = 4(-19) + 11 = -76 + 11 = -65} \\ k(-17)\text{ = 4(-17) + 11 = -68 + 11= - 57} \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \text{Rate of change = }\frac{-57\text{ - (-65)}}{-17\text{ - (-19)}} \\ =\text{ }\frac{-57\text{ + 65}}{-17\text{ + 19}} \\ =\text{ }\frac{8}{2} \\ =\text{ 4} \end{gathered}[/tex]A change in temperature of 6°C is equivalent to achange in temperature of•F
A change in temperature of 6°C is equivalent to a
change in temperature of 10.8°F
Explanations:From the table drawn:
A change in temperature of 1°C is equivalent to 1.8°F
A change in temperature of 2°C is equivalent to 3.6°F
Following the relationships above, we can conclude that the relationship between °C and °F is:
°F = 1.8 °C
Therefore, a change in temperature of 6°C will be equivalent to:
°F = 1.8 °C
°F = 1.8 x 6
°F = 10.8°F
In the group of ordered pairs shown, the x-values are inputs and the y-values are outputs. Select all the statements that are true.
(2, 4), (6, 3), (5, 4), (7, 3), (8, 2)
A. There is only one input for every output.
B. There is only one output for every input.
C. There is more than one output for some inputs.
D. There is more than one input for some outputs.
E. The group of ordered pairs represents a function.
Since in this group of ordered pairs shown above, the x-values are inputs and the y-values are outputs, all the statements that are true include the following:
A. There is only one input for every output.
B. There is only one output for every input.
What is an ordered pair?An ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
Generally speaking, the values on the x-coordinate or x-axis (abscissa) of any graph represents all of the input values while the values on the y-coordinate or y-axis (ordinate) of any graph represents all of the output values.
In this context, we can reasonably and logically deduce that there is a unique input for every output and a unique output for every input.
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hello can you explain to me how I should write this out please
Here, we want to calculate the interquartile range
Mathematically, this is the difference between the lower quartile (1st quartile or 25th percentile) and the upper quartile (3rd quartile or 75th percentile)
We already have the numbers arranged from top to bottom
The count of numbers is 9 numbers
We have the first quartile as;
[tex]\frac{(n+1)}{4}\text{ = }\frac{10}{4}\text{ = 2.5th which is 3rd term}[/tex]The third term here is the weight of baby Selena
The 3rd quartile can be calculated as;
[tex]\frac{3(n+1)}{4}\text{ = }\frac{3(9+1)}{4}\text{ = 7.5 which is 8th term}[/tex]The 8th term is the weight of baby Me
The difference between these weights give the interquartile range as follows;
[tex]\text{Interquartile range =Q}_3-Q_1\text{ = 8 lbs 2 oz - 6 lbs 1 oz = 2 lbs 1 oz}[/tex]1. Solve the Systemy = 2x - 6y = -6x - 14
x = -1
Explanation:The given equations:
y = 2x - 6
y = -6x - 14
Since both equations are equal to y, we will equate the right hand side of both equations.
y = y
2x - 6 = -6x - 14
collect like terms:
2x + 6x = -14 + 6
8x = -8
divide both sides by 8:
8x/8 = -8/8
x = -1