Answer:
y = 5x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 5, thus
y = 5x + c ← is the partial equation
To find c substitute (2, 6) into the partial equation
6 = 10 + c ⇒ c = 6 - 10 = - 4
y = 5x - 4 ← equation of line
An overweight dog is put on a special diet. use the table to determine the dogs average weight change per week.
TABLE: the week number
1,2,3,4,5
the weight change[oz]
- 1.5,2.2,-0.8,-1.6,-0.6
The dog's average weight change per week is -0.46 ounces, meaning that on average, the dog loses 0.46 ounces per week.
Explanation:To determine the dog's average weight change per week, we need to calculate the mean of the weight changes given in the table for weeks 1 through 5. The weights are measured in ounces, and we have the following weight changes: -1.5, 2.2, -0.8, -1.6, -0.6. To find the average, we add up these changes and divide by the number of weeks.
First, we calculate the sum of the weight changes:
Sum = -1.5 + 2.2 + (-0.8) + (-1.6) + (-0.6)
Sum = -2.3 ounces
Now we divide by the number of weeks, which is 5:
Average weight change per week = Sum / Number of weeks
Average weight change per week = -2.3 oz / 5
Average weight change per week = -0.46 ounces per week
Since the average is negative, this means the dog is losing weight on average, each week.
Final answer:
To calculate the average weight change per week for the dog, sum up the total weight change and divide by the number of weeks. The dog's total weight change is -2.3 ounces over 5 weeks, resulting in an average weight loss of -0.46 ounces per week.
Explanation:
The student is asking about calculating the average weight change per week for an overweight dog on a special diet. To find this, we need to sum up all the weight changes and then divide by the number of weeks. The weight changes given in ounces are: -1.5, 2.2, -0.8, -1.6, and -0.6 ounces.
First, let's add up these weight changes: -1.5 + 2.2 - 0.8 - 1.6 - 0.6 = -2.3 ounces over 5 weeks.
Now, let's calculate the average weight change per week: (-2.3 ounces) / (5 weeks) = -0.46 ounces per week.
It's important to note that a negative average indicates the dog is losing weight, which is the goal of the diet. In this case, the dog is losing an average of 0.46 ounces per week.
ChoiceA- f(x)axhk ChoiceB- f(x)axh2 k
ChoiceC- f(x)ax3 bx2 cxd ChoiceD- f(x)a xhk
ChoiceE- f(x) a k xh
Requirements:
*a should never equal 0
*h and k can’t both be 0
*b, c, and d can’t all be 0 *Can’t duplicate any values
TASK #2
1) Select 4 of the 5 graph choices to the left.
2) Fill in values/numbers for the generic equations, replacing variables
a, h, and k or a, b, c, and d as necessary, to create actual equations that can be graphed. You may use your calculator to help. Write this equation at the top of the graph page you use. Recommendation - use small #s☺(keep between -5 and 5)
3) Graph each of the 4 chosen graphs A - E, one on each of the graphs provided, #1 - 4. You may use your calculator to help. Requirements:
*Be sure that part of the graph drawn on its selected graph paper is actually located in the shaded region on the graph you choose. If not, select a different graph paper #1-4 or select different values/numbers for your equation. You may graph any of the equation choices on any of the graph papers.
*You must graph the entire function on the given graph paper for
the domain 15, 15 if the range is also between 15, 15. A
domain interval of at least 15 units wide must be present on the
graph.
4) Answer the questions below Graphs #1-4 in the spaces provided.
1) Take each shaded region (covering a domain interval of 5 units) of graphs 1-4 and graph ONLY that region from that graph onto Graph #5. (You should have a funky looking graph.) Be careful on the endpoints of your graph segment that you either graph a closed dot if including that value or an open dot if you are not including that value – see the domain intervals listed on the bottom of Graph #5 for help!
2) Fill in the information and answer the questions following the graph.
RUBRIC (Turn one copy in with your project):
Graph #1: Graph #2 Graph #3 Graph #4 Graph #5 Comments:
Equation: ____/1 Equation: ____/1 Equation: ____/1 Equation: ____/1 Equations: ____/4
Graph: _____/8 Graph: _____/8 Graph: _____/8 Graph: _____/8 Graph: _____/6
Questions: _____/11 = /20 Questions: _____/11 = /20 Questions: _____/11 = /20 Questions: _____/11 = /20 Questions: _____/10 = /20
TOTAL ______/100
did you ever complete this?
Step-by-step explanation:
If you ddi please send it to me
Ruby was paid $24 to sweep 4 walks which of the following can be represented by an equivalent ratio ?
•$6 to sweep 1 walk
•$12 to sweep 3 walks
•$30 to sweep 5 walks
Answer:
$6 to sweep 1 walk
Step-by-step explanation:
$24 : 4 walks can be simplified by dividing both sides by 4.
24/4:4/4=6:1
Write a subtraction story problem for a total of 14.solve it
A subtraction story problem for a total of 14 could be: Lucy has 17 cookies and she wants to share them with her friend Amanda. If Lucy gives Amanda some cookies and ends up with 14 cookies, how many cookies did Lucy give to Amanda?
Explanation:A subtraction story problem for a total of 14 could be:
Lucy has 17 cookies and she wants to share them with her friend Amanda. If Lucy gives Amanda some cookies and ends up with 14 cookies, how many cookies did Lucy give to Amanda?
To solve this, subtract the cookies Lucy ends up with (14) from the cookies she initially had (17):
17 - 14 = 3
Therefore, Lucy gave Amanda 3 cookies.
Nyasia spends a total of 7.5 hours playing sports each week. Basketball takes a total of 3.25 hours each week. If she plays sports for 4 days each week, write and solve an inequality that shows the average amount of tie per day she spends on OTHER sports.
Answer:
The Inequality which shows Amount of time spent on other sports each day is [tex]x\leq \frac{4.25}{4}[/tex].
Nyasia spends approximately 1 hour each day on Other sports.
Step-by-step explanation:
Total number of hours spent on sports each week =7.5 hrs
Time spent on basket ball each week = 3.25 hours
Number of days spent on sports = 4 days.
We need to find amount of time spent on other sports each day.
Let amount of time spent on other sports each day be 'x'.
First we will find amount of time spent on other sports each week.
Amount of time spent on other sports each week can be calculated by Subtracting Total number of hour spent on sports each week minus Time spent on basket ball each week.
Amount of time spent on other sports each week = 7.5 -3.25 = 4.25 hrs.
Now we can say amount of time spent on other sports each day we will less than or equal to Amount of time spent on other sports each week divided by number of days.
Framing in equation form we get;
[tex]x\leq \frac{4.25}{4}[/tex]
Hence The Inequality which shows Amount of time spent on other sports each day is [tex]x\leq \frac{4.25}{4}[/tex].
ON solving the inequality we get;
[tex]x\leq \frac{4.25}{4}\\\\x\leq1.0625\ hrs[/tex].
Hence we can say Nyasia spends approximately 1 hour each day on Other sports.
In each pair, tell if the fractions are equal by using cross multiplication.
a. 5/30 and 1/6
b.4/12 and 21/60
c. 17/34 and 41/82
d. 6/9 and 25/36
Answer:
a. 5/30 and 1/6 ---> are equal
b.4/12 and 21/60 ---> are not equal
c. 17/34 and 41/82 ---> are equal
d. 6/9 and 25/36 ---> are not equal
Step-by-step explanation:
case a) we have 5/30 and 1/6
equate the fractions
[tex]\frac{5}{30}=\frac{1}{6}[/tex]
using cross multiplication
[tex](5)(6)=(30)(1)[/tex]
[tex]30=30[/tex] ----> is true
therefore
The fractions are equal
case b) we have 4/12 and 21/60
equate the fractions
[tex]\frac{4}{12}=\frac{21}{60}[/tex]
using cross multiplication
[tex](4)(60)=(21)(12)[/tex]
[tex]240=252[/tex] ----> is not true
therefore
The fractions are not equal
case c) we have 17/34 and 41/82
equate the fractions
[tex]\frac{17}{34}=\frac{41}{82}[/tex]
using cross multiplication
[tex](17)(82)=(41)(34)[/tex]
[tex]1,394=1,394[/tex] ----> is true
therefore
The fractions are equal
case d) we have 6/9 and 25/36
equate the fractions
[tex]\frac{6}{9}=\frac{25}{36}[/tex]
using cross multiplication
[tex](6)(36)=(25)(9)[/tex]
[tex]216=225[/tex] ----> is not true
therefore
The fractions are not equal
Answer:
a. The fractions are equal.
b. The fractions are not equal
c. The fractions are equal.
d. The fractions are not equal
Step-by-step explanation:
By definition, equivalent fractions have the same value, but they look different.
In order to verify if two fractions are equivalent, you can use Cross multiplication.
The procedure is: multiply the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.
Then:
[tex]a.\ \frac{5}{30}=\frac{1}{6}\\\\5*6=1*30\\\\30=30\ (The\ fractions\ are\ equal)[/tex]
[tex]b.\ \frac{4}{12}=\frac{21}{60}\\\\4*60=21*12\\\\240=252\ (FALSE.\ The\ fractions\ are\ not\ equal)[/tex]
[tex]c.\ \frac{17}{34}=\frac{41}{82}\\\\17*82=41*34\\\\1394=1394\ (The\ fractions\ are\ equal)[/tex]
[tex]d.\ \frac{6}{9}=\frac{25}{36}\\\\6*36=25*9\\\\216=225\ (FALSE.\ The\ fractions\ are\ not\ equal)[/tex]
How many solutions does the system of equations have Y = 4x+3 and 2Y-8x = 3
Answer:
The system has no solution.
Step-by-step explanation:
Write the system as
y - 4x =3
2y - 8x = 3
The 2nd equation can be written as
2(y - 4x)
and the system would be
y - 4x =3
2(y - 4x) = 3
Now, call y -4x = z. Then we would have the system
z = 3
2z = 3
But if z =3 then 2z = 6 and we have a contradiction.
We conclude that the system has no solution.
A regular section of land made up of wheat farms has a length of 5x10^4 and the width of 6x10^3 what is the area of the length in square meters?
Answer:
The Area of land is 30 × [tex]10^{7}[/tex] meters² .
Step-by-step explanation:
Given as :
The length of rectangular wheat farm land = L = 5 × [tex]10^{4}[/tex] meter
The width of rectangular wheat farm land = w = 6 × [tex]10^{3}[/tex] meter
Let The Area of land = A meters²
Now, According to question
∵ Land is in rectangular shape
And we know, Area of rectangle = length × width
∴ Area of land = Area of rectangle = length × width
Or, A = L × w
Or, A = 5 × [tex]10^{4}[/tex] meter × 6 × [tex]10^{3}[/tex] meter
Or , A = 30 × [tex]10^{4+3}[/tex]
i.e A = 30 × [tex]10^{7}[/tex] meters²
So, The Area of land = A = 30 × [tex]10^{7}[/tex] meters²
Hence,The Area of land is 30 × [tex]10^{7}[/tex] meters² . Answer
There are 6 students. 2 of them are chosen for the position of president and Vice President. How many ways do we have to choose the students from the 6 students?
We have 15 ways to chose 2 students for the position of president and Vice President
Solution:
Given that,
There are 6 students. 2 of them are chosen for the position of president and Vice President.
To find: number of ways we have to choose the students from the 6 students
So now we have 6 students, out of which we have to choose 2 students
As we just have to select the students. We can use combinations here.
In combinations, to pick "r" items from "n" items, there will be [tex]^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}[/tex] ways
[tex]^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=\frac{n !}{(n-r) ! r !}[/tex]
Then, here we have to pick 2 out of 6:
Total students = n = 6
students to be selected = r = 2
[tex]\begin{aligned} 6 C_{2} &=\frac{6 !}{(6-2) ! 2 !} \\\\ 6 C_{2} &=\frac{6 !}{4 ! 2 !} \\\\ 6 C_{2} &=\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1 \times 2 \times 1} \\\\ 6 C_{2} &=15 \end{aligned}[/tex]
Thus we have 15 ways to chose 2 students for the position of president and Vice President
Two cars start from the same place driving at the same rate, one heading north and the other heading east. After two hours the car heading north has traveled 150 miles and the car heading east has traveled 100 miles. How far apart are the cars at this time?
A) 111.8 miles
B) 180.3 miles
C) 250 miles
D) 350 miles
Answer:
B: 180.3
Step-by-step explanation:
A^2 + B^2 = C^2
150^2 + 100 ^2 = 32500
square root of 32500
180.3
Subtract the sum of x2−3xy−y2 and 2x2+5xy−4y2 from 6x2−7xy+8y2
Answer:
[tex]3x^2-9xy+13y^2[/tex]
Step-by-step explanation:
We begin with : [tex]6x^2-7xy+8y^2-[(x^2-3xy-y^2)+(2x^2+5xy-4y^2)][/tex]
First, let us add the two portions within the brackets. To do this, we need to just combine the like terms
[tex]6x^2-7xy+8y^2-[(x^2-3xy-y^2)+(2x^2+5xy-4y^2)]\\\\6x^2-7xy+8y^2-[3x^2+2xy-5y^2][/tex]
Next, we need to distribute the negative to all the terms within the brackets
[tex]6x^2-7xy+8y^2-[3x^2+2xy-5y^2]\\\\6x^2-7xy+8y^2-3x^2-2xy+5y^2[/tex]
Now we can combine the like terms again
[tex]6x^2-7xy+8y^2-3x^2-2xy+5y^2\\\\3x^2-9xy+13y^2[/tex]
Answer:
Answer in image
Step-by-step explanation:
Answer in image
A motorboat traveling with a current can go 160km in 4 hours. against the current it takes 5 hours to go the same distance. find the speed of motorboat and speed of current
To find the speed of the motorboat and the current, two equations were set up based on the distances and times provided. The system of equations was solved to find the boat speed to be 36 km/h and the current speed to be 4 km/h.
Explanation:The student is asking a question related to the mathematical concept of relative motion involving a motorboat and a current.
To solve this problem we can set up two equations based on the information given:
With the current: Distance = (Boat Speed + Current Speed) * TimeAgainst the current: Distance = (Boat Speed - Current Speed) * TimeUsing the distances and times provided:
160 km = (Boat Speed + Current Speed) * 4 hours160 km = (Boat Speed - Current Speed) * 5 hoursWe can solve this system of equations to find the values for Boat Speed and Current Speed.
Let the speed of the boat be b and the speed of the current be c. From equation (1), we can express c in terms of b:
c = 40 - b (1)
Substitute c from equation (1) into equation (2):
160 = (b - (40 - b)) * 5
160 = (2b - 40) * 5
160 = 10b - 200
360 = 10b
b = 36 km/h
So the speed of the boat is 36 km/h. Now we can find the speed of the current using equation (1):
c = 40 - b
c = 40 - 36
c = 4 km/h
The speed of the current is 4 km/h.
write an expression for the sequence of operations described below. add s to t, add the result to r, then raise what you have to the 7th power
Answer:
[tex](s+t+r)^7[/tex]
Step-by-step explanation:
Sequential Operations
Mathematical operations can be done in sequence or in batches if they are of the same type. For example, we can add many terms in one single operation, but we cannot add and multiply in one go, because there are priorities when dealing with products and sums. Same happens with powers.
In our problem we are required to perform a sequence of operations like follows
Add s to t:
[tex]s+t[/tex]
Add the result to r
[tex]s+t+r[/tex]
Raise what you have to the 7th power
[tex]\boxed{(s+t+r)^7}[/tex]
This is the final result
44k5 – 66k4 + 77k3 =
you send out 20,000 emails of 6% are opened of those 9% clicked on the link to register for something of those who clicked on the link 30% complete the registration how many people completed the registration
Answer:
The answer is 32.
Step-by-step explanation
hope this helps :D
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+ 10 is the missing step in the given chart.
Step-by-step explanation:
Given data from the Flow chart,
Start = 20,
End = 6,
Second Step is ÷ 5.
Let us form the given information into two equations,
Consider the missing value as X.
20+X=Y ⇒1
Y÷5=6 ⇒2
where Y is the value of middle box.
From equation 1,
Y=6×5
Y=30.
From equation 2,
20+X=30.
X=30-20.
X= 10.
Thus + 10 is the missing step.
Measured in a map with a scale of 150 miles per inch, the distance from Chicago to Boston is 4.75. How many miles is it from Chicago to Boston if 1 inch equals 150 miles.
The actual distance from Chicago to Boston is 712.5 miles.
Step-by-step explanation:
Given,
Scale on map = 150 miles per inch
Distance from Chicago to Boston on map = 4.75 inches
Actual distance = Distance on map * 150 miles
Actual distance = 4.75 * 150
Actual distance = 712.5 miles
The actual distance from Chicago to Boston is 712.5 miles.
Keywords: scale, multiplication
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Dale Rodgers had the following for dinner: 2 pork chops, 1/2 cup broccoli, and one baked potato. How many calories did his meal have? 300 455 430 405
Answer:
The closest option is C. 430, but of course this estimation depends of the size of the serving, specially for the chops and the potato.
Step-by-step explanation:
Let's calculate the number of calories of this meal:
A. 2 pork chops: We could assume 145 calories in a 3-ounce serving, so we have 145 * 2 = 290
B. 1 baked potato: We could assume 130 in a baked small potato (around 130 grams)
C. 1/2 cup of broccoli: We could assume 15 calories
Then the total estimation of calories is:
290 + 130 + 15 = 435
The closest option is C. 430, but of course this estimation depends of the size of the serving, specially for the chops and the potato.
Answer:
The answer is 430.
Step-by-step explanation:
On the chart given with the question (which was not posted),
2 pork chops = 260 (on the chart the individual pork chop is 130)
1/2 broccoli = 25
1 baked potato = 145
Now you simply add the numbers together!
Hope this helps!
Abigail drives at an average speed of 60 miles per hour for 3 hours. The graph shows her distance versus time. Which statements are true? Check all that apply.
As Abigail’s time increases, her distance increases.
As Abigail’s time increases, her distance decreases.
At 2 hours, Abigail has traveled 120 miles.
At 1.5 hours, Abigail has traveled 100 miles.
At 3 hours, Abigail has traveled 180 miles.
Answer:
1,3,5
Step-by-step explanation:
not 1,3,4
Last Wednesday, students could choose ham or turkey sandwiches for lunch. The cafeteria made 60 sandwiches in all, 90% of which were turkey. How many turkey sandwiches did the cafeteria make?
Answer:
3
Step-by-step explanation:
Give me brainliest
Answer:
54 sandwiches were Turkey.
60 x .94 = 54
Step-by-step explanation:
Jeff is kepping Trace of his weight over several weeks. After 2 weeks, he weighs 194 pounds. After 6weeks , he weighs 186 pounds. Write and solve a linear equation to find Jeff’s weight after 12 weeks
The linear equation is y = -2 x + 198
Jeff’s weight after 12 weeks is 174 pounds
Step-by-step explanation:
Jeff is keeping Trace of his weight over several weeks
After 2 weeks, he weighs 194 poundsAfter 6 weeks , he weighs 186 poundsWe need to write a linear equation represents the Jeff’s weight, and find his weight after 12 weeks
The form of the linear equation is y = mx + b, where m is the slope of the line, and b is the y-intercept
The formula of the slope of a line which passes through points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let y represents Jeff's weight in x weeks
∵ After 2 weeks, he weighs 194 pounds
∴ [tex](x_{1},y_{1})[/tex] = (2 , 194)
∵ After 6 weeks , he weighs 186 pounds
∴ [tex](x_{2},y_{2})[/tex] = (6 , 186)
- Use these two points to find m
∵ [tex]m=\frac{186-194}{6-2}=\frac{-8}{4}=-2[/tex]
∴ m = -2
- Substitute the value of m in the form of the equation
∴ y = -2 x + b
- To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ x = 2 and y = 194
∴ 194 = -2(2) + b
∴ 194 = -4 + b
- Add 4 to both sides
∴ 198 = b
∴ y = -2 x + 198
The linear equation is y = -2 x + 198
To find his weight after 12 weeks substitute x by 12 in the equation
∵ x = 12
∴ y = -2(12) + 198
∴ y = -24 + 198
∴ y = 174
Jeff’s weight after 12 weeks is 174 pounds
Learn more:
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x+6/x+2=x+3/x-5
a. x=1
b. x=5
c. x=-9
d. x=-8
[tex]\dfrac{x+6}{x+2}=\dfrac{x+3}{x-5}\qquad\qquad\text{cross multiply}\\\\(x+6)(x-5)=(x+2)(x+3)\\\\x^2-5x+6x-30=x^2+3x+2x+6\\\\x^2+x-30=x^2+5x+6\\\\x^2+x-x^2-5x=6+30\\\\-4x=36\quad|:(-4)\\\\\boxed{x=-9}[/tex]
Answer C.
Which number line shows the solution set for |h-3|>5
Final answer:
The solution set for |h-3|>5 is h > 8 and h < -2, which on a number line is all values to the right of 8 and to the left of -2, with open circles at -2 and 8.
Explanation:
The question requires us to find the solution set for the inequality |h-3|>5 on a number line. To solve an absolute value inequality, we split the problem into two separate inequalities based on the definition of absolute value:
For h - 3 > 5, we add 3 to both sides to get h > 8.For h - 3 < -5, we again add 3 to both sides, which gives h < -2.
Therefore, the solution set on the number line includes all values to the right of 8 and all values to the left of -2. Remember, these are not included in the solution set because the inequality is strict (>). This means we use open circles or unshaded dots to represent -2 and 8, and shade the number line to the right of 8 and to the left of -2.
Which expression can be used to check the answer to 56 divided by negative 14 =n
Answer:
n=-4
Step-by-step explanation:
n=56/-14
n=-4
−
1
⋅
f
(
−
8
)
−
4
⋅
g
(
4
)
=
−1⋅f(−8)−4⋅g(4)=
Answer:
-7
Step-by-step explanation:
The question is a mathematics problem related to evaluating functions, but it cannot be answered without additional information about the functions f and g.
Explanation:The question asks for the result when evaluating two functions f and g at given arguments and then combining these evaluated results with given coefficients. Specifically, it asks to compute the value of − 1 ⋅ f(− 8) minus 4 ⋅ g(4). However, without additional information about the functions f and g, it's not possible to calculate the exact numeric answer. Students usually encounter this type of problem while learning about functions and their evaluations in algebra.
Garrett brown bought $200,000 of term life insurance at the rate of $5.40 per thousand dollar unit how much is the annul premium
Answer:
The annual premium will be = $1080
Step-by-step explanation:
Total life insurance term amount = $200,000
The term life insurance rate per $1000 = $5.40
Let’s divide total term amount i.e. $200,000 by $1000 unit to get the total number of $1000 units in $200,000
So, $200,000 ÷ $1000 = 200
So, it is clear that 200 would be the total number of $1000 units in total term life insurance amount of $200,000.
Therefore, if rate per unit $1000 is $5.40, then we must have to multiply $5.40 by 200 to find the annual premium as the total number of $1000 units in total term life insurance amount
of $200,000 is 200.
So, $5.40 × 200 = $1080
Hence, the annual premium will be = $1080
Keywords: insurance, premium, annual premium
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Please help me on these two questions
[tex]\bf \begin{array}{|ll|ll} \cline{1-2} bridge&\stackrel{tons}{materials}\\ \cline{1-2} concrete&1,000\\ \textit{steel structure} & 400\\ \textit{glass and granite}&200\\ \cline{1-2} \end{array}\qquad \qquad \stackrel{~\hfill \textit{total weight}}{1000+400+200=1600} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{\stackrel{\textit{steel structure}}{400}}{\underset{\textit{total weight}}{1600}}\implies \stackrel{\textit{simplified}}{\cfrac{1}{4}}~\hfill \cfrac{\stackrel{\textit{glass and granite}}{200}}{\underset{\textit{total weight}}{1600}}\implies \stackrel{\textit{simplified}}{\cfrac{1}{8}}[/tex]
WILL GIVE BRAINLIEST . (06.02) Which of these is the algebraic expression for "eight less than some number?" (3 points) 8 − b b − 8 Fraction 8 over b Fraction b over 8
Answer: b - 8
Step-by-step explanation:
Answer:
same
Step-by-step explanation:
In which quadrant is the point (-7, 4)?
Answer:
2nd
Step-by-step explanation:
The point (-7, 4) is located in the second quadrant of the Cartesian coordinate system because it has a negative x-coordinate and a positive y-coordinate.
Explanation:The point (-7, 4) is located in the second quadrant of the Cartesian coordinate system. In the second quadrant, the x-coordinate is negative and the y-coordinate is positive. This is in line with the definition that axes divide the plane into four quadrants, where the sign of the coordinates determines the quadrant in which the point lies.
Understanding Quadrants
To better understand which quadrant a point falls into, consider the following general rules for the Cartesian coordinate system:
The first quadrant contains points where both x and y are positive.The second quadrant, where our point lies, contains points with a negative x-coordinate and a positive y-coordinate.The third quadrant contains points with both x and y negative.The fourth quadrant contains points with a positive x-coordinate and a negative y-coordinate.As the point (-7, 4) has a negative x-coordinate and a positive y-coordinate, it falls into the second quadrant, confirming our original statement.
7. Which of the following equations illustrates the associative property of addition?
(1) (3+7)+(2+8)=(7+3)+(8+2)
(2) (5)(3-4)=(5-3)(4)
(3) (4+5)+5 = 4 +10
(4) 2(5+4)=10+8
3
Answer:
3. (4+5)+5 = 4 +10 expresses the ASSOCIATIVE PROPERTY OF ADDITION.
Step-by-step explanation:
The associative property of addition is given as:
For any three numbers A, B and C
(A +B) + C = A + ( B+ C)
Here, the ORDER OF ADDITION is not important, answer is always the SAME.
Now, in the following given expressions:
1. (3+7)+(2+8)=(7+3)+(8+2)
Here, ( 3+ 7)in L H S is replaced with ( 7 + 3) in R H S
Similarly, ( 2+ 8)in L H S is replaced with (8 + 2) in R H S
Hence, the given expression is expresses the Commutative PROPERTY OF ADDITION.
2. (5)(3-4)=(5-3)(4)
Here, the operation between 5 and (3-4) is MULTIPLICATION
Hence, the given expression DO NOT expresses the ASSOCIATIVE PROPERTY OF ADDITION.
3. (4+5)+5 = 4 +10
Here, the form of ASSOCIATIVE PROPERTY OF ADDITION is
(4 +5 )+5 = 4 + (5 + 5) = 4 + (10)
So, the given expression expresses the ASSOCIATIVE PROPERTY OF ADDITION.
4. 2(5+4)=10+8
Here, the operation between 2 and (5 + 4) is MULTIPLICATION
Hence, the given expression DO NOT expresses the ASSOCIATIVE PROPERTY OF ADDITION.
The associative property of addition means the way numbers are grouped in an addition does not change the sum. From the given equations, equation (1) illustrates this property as shown by the same results 20 in both groupings (3+7)+(2+8) or (7+3)+(8+2).
Explanation:The associative property of addition is a property in Mathematics that states that the way in which numbers are grouped when added does not change the sum. From the given equations, equation (1) (3+7)+(2+8)=(7+3)+(8+2) perfectly shows this property. It demonstrates that it doesn't matter how we group the numbers when we're adding them - the result will be the same.
For example, in equation (1), (3+7)+(2+8), if we add the numbers in brackets first, we get 10 + 10 = 20. This is the same result we get if we re-group the numbers like this: (7+3)+(8+2), that is, 10 + 10 = 20.
Learn more about Associative Property of Addition here:https://brainly.com/question/34210744
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