The variable 'a' in Albin's equation represents the number of minutes Albin was late for picking up from the daycare, with 3 dollars as the base fee and 0.50 dollars charged for each minute late.
Explanation:The variable a in Albin's equation, 10.50 = 0.50a + 3, represents the number of minutes of Albin's late pick-up from the daycare. The base fee of the daycare is 3 dollars, which is a fixed amount, while 0.50 dollars is the rate charged per minute for being late. The equation is a way to calculate the total fee based on the minutes Albin is late.
For comparison, if we look at Aaron's Word Processing Service, the total cost of services would be represented by y = 31.50 + 32x, where 31.50 is a fixed cost and the cost for word processing is 32 dollars per hour (x). Similarly, for Svetlana's tutoring sessions, the total income she earns is given by y = 25 + 15x, where 25 is a one-time fee and 15 dollars per hour is her rate of earning.
The diagram represents a flower border that is 3 feet wide
surrounding a rectangular sitting area. Write an expression in
factored form that represents the area of the flower border.
(50 points)
The factored form of the expression representing the area of the flower border surrounding a rectangular sitting area with dimensions 3x by 5 feet is 18x + 66 square feet.
The flower border surrounds a rectangular sitting area with dimensions 3x by 5 feet. To find the area of the flower border, we need to consider the difference in the areas of the outer rectangle (which includes the border) and the inner rectangle (the sitting area). The outer rectangle has dimensions (3x + 6) by (5 + 6), accounting for the 3-foot wide flower border on each side.
The expression for the area of the flower border can be written as follows:
Area of Flower Border = (Length of Outer Rectangle) * (Width of Outer Rectangle) - (Length of Inner Rectangle) * (Width of Inner Rectangle)
= (3x + 6) * (5 + 6) - (3x) * (5)
Now, let's factor the expression:
= (3(x + 2)) * (11) - (3x) * (5)
= 33x + 66 - 15x
Combining like terms, we get:
= 18x + 66
So, the factored expression representing the area of the flower border is 18x + 66 square feet.
1,773 divided by 3 is what?
Answer: 591
Step-by-step explanation:
1773/3= 591
Sum of 2 numbers are 83. Difference is 7. Find the numbers
The two numbers that add up to 83 with a difference of 7 are 45 and 38. We can find these numbers by setting up a system of linear equations and solving for each variable.
To find the two numbers where the sum is 83 and the difference is 7, we can set up two equations based on the information provided:
Let the first number be x and the second number be y.The sum of the two numbers is x + y = 83.The difference of the two numbers is x - y = 7.To solve the system of equations, we can use the method of addition. Add the two equations together to eliminate the variable y:
(x + y) + (x - y) = 83 + 72x = 90x = 90 / 2x = 45With the value of x known, you can substitute it into the first equation to find y:
45 + y = 83y = 83 - 45y = 38Therefore, the two numbers are 45 and 38.
Mr. Killarney has 25 students, 3/5 ride the bus home, how many students ride the bus?
Answer:
15 students ride the bus home.
Step-by-step explanation:
Divide 25 by 5. Next multiply the product by 3 and you have your answer.
A car travels on a highway at a constant speed of 67 miles per hour. Which equation and table shows the correct relationship between , the number of hours, and , the distance traveled
Answer:
Theres no tables but y=67x would be the equation
since 67 is the constant which =m in y=mx+b
How many solutions does 2(x-3)=10x-6-8x
Answer: Infinitely many
Step-by-step explanation: 2(x-3)=10x-6-8x
2x-6=10x-6-8x
2x-6=2x-6
What would be the slope-intercept function for a line that crosses points (3, -2) &
(1, 4)?
Answer:
[tex]y=-3x+7[/tex]
Step-by-step explanation:
The slope of the line passing through the points (3,-2) and (1,4) is
[tex]\dfrac{4-(-2)}{1-3}=\dfrac{4+2}{-2}=\dfrac{6}{-2}=-3[/tex]
Hence, the equation of the line is
[tex]y-(-2)=-3(x-3)[/tex]
Rewrite it:
[tex]y+2=-3x+9\\ \\y=-3x+9-2\\ \\y=-3x+7[/tex]
The last equation is the slope-intercept equation of linear function.
Bianca filled 2 same-sized jars with flavored popcorn as a gift. She wants to glue a piece of ribbon around the edge of each lid.
The radius of each jar lid is 5 centimeters. Approximately what is the total length of ribbon she will need for the two jar lids? (Use 3.14 for pi .)
A.
157 cm
B.
78.5 cm
C.
31.4 cm
D.
62.8 cm
Answer: D
Step-by-step explanation:
You have to multiply 2 times pi.
Use the Remainder Theorem to evaluate f(x)=2x5−3x4−9x3+8x2+2 at x=−3
Answer:
i think its -412 but im not sure
Step-by-step explanation:
The value obtained by using the remainder theorem for the the f(x)=2x5−3x4−9x3+8x2+2 at x=−3 will be 2x⁴-9x³+18x²-46x+138-(412)/(x+3).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that,use the Remainder Theorem to evaluate f(x)=2x5−3x4−9x3+8x2+2 at x=−3
A method for Euclidean polynomial division is the remainder theorem. This theorem states that if we divide a polynomial, P(x), by a factor, (x - a), which isn't really an element of the polynomial, we get a smaller polynomial and a remainder.
[tex]=\frac{2x^5-3x^4-9x^3+8x^2+2}{\left(x+3\right)} \\\\ =2x^4+\frac{-9x^4-9x^3+8x^2+2}{x+3} \\\\ =2x^4-9x^3+18x^2+\frac{-46x^2+2}{x+3}\\\\ =2x^4-9x^3+18x^2-46x+\frac{138x+2}{x+3} \\\\ =2x^4-9x^3+18x^2-46x+138+\frac{-412}{x+3} \\\\ =2x^4-9x^3+18x^2-46x+138-\frac{412}{x+3}[/tex]
Thus, the value obtained by using the remainder theorem for the the f(x)=2x5−3x4−9x3+8x2+2 at x=−3 will be 2x⁴-9x³+18x²-46x+138-(412)/(x+3).
Learn more about the function here:
brainly.com/question/5245372
#SPJ2
Solve for x, where x is a real number.
3/2x – 14 – 2=0
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
Answer:
Step-by-step explanation:
3/2x - 14 - 2 = 0
3/2x - 12 = 0
3/2x = 12
2x = 36
x = 18
Lin and Noah are solving the equation 7(x+2)=91. Lin starts by using the distributive property. Noah starts by dividing each side by 7. Show what Lin's and Noah's full solution methods might look like. What is the same and what is different about their methods?
The solution is x = 11
Step-by-step explanation:
The original equation is
[tex]7(x+2)=91[/tex]
Lin uses the distributive property, which states that
[tex]a(x+y)=ax+ay[/tex]
By applying the property to this case,
[tex]7(x+2)=91\\7x+14=91[/tex]
Then we subtract 14 on both sides:
[tex]7x+14-14=91-14\\7x=77[/tex]
Finally, we divide by 7 on both sides:
[tex]\frac{7x}{7}=\frac{77}{7}\\x=11[/tex]
Noah starts by dividing each side by 7, so he gets
[tex]\frac{7(x+2)}{7}=\frac{91}{7}\\x+2=13[/tex]
Then he can subtract +2 from both sides:
[tex]x+2-2=13-2\\x=11[/tex]
So, they get the same result. The similarity between the two methods is that they both divide by 7, while the difference is that Lin has to subtract 14, while Noah has to subtract 2.
Learn more about solving equations:
brainly.com/question/11306893
brainly.com/question/10387593
#LearnwithBrainly
Lin's solution method: 7x+14=91, 7x=77, x=11
Noah's solution method: x+2=13, x=11
Both methods involve dividing by 7, but Noah does the division first, while Lin does the division last. Also, Lin's method involves subtracting 14, while Noah's method involves subtracting 2. Both solutions are correct and valid. Noah's solution could be considered more efficient for this example, because it takes fewer steps and has equally complicated arithmetic work.
Philip got a ride with a friend from Denver to Las Vegas, a distance of 750 miles. If the trip took 10 hours, how fast was the friend driving?
Answer:
The friend was driving at the speed of 75 miles per hour.
Step-by-step explanation:
Given:
Philip got a ride with a friend from Denver to Las Vegas, a distance of 750 miles.
If the trip took 10 hours.
Now, to find the speed the friend was driving.
As, given:
Distance = 750 miles.
Time = 10 hours.
Now, to get the speed we put formula:
[tex]Speed=\frac{Distance}{Time}[/tex]
[tex]Speed=\frac{750}{10}[/tex]
[tex]Speed=75\ miles\ per\ hour.[/tex]
Therefore, the friend was driving at the speed of 75 miles per hour.
how do you solve y=1/2x-4
Answer: x = 2y + 4
Step-by-step explanation:
y=1/2x-4
multiply both sides by 2
2y=x-4
substract from both sides 2y
0=x+–2y-4
substract from both sides x
-x=-2y-4
multiply both sides by -1 to get positive x
x=2y+4
In a sequence of numbers, a1=0, a2=6, a3=12, a4=18, and a5=24.
Based on this information, which equation can be used to find the nth term in the sequence, an?
an=−6n+6
an=−6n−6
an=6n+6
an=6n−6
To find the nth term in the following sequence we can use an = 6n-6 equation
Step-by-step explanation:
From the given equations it is clear that the series is in arithmetic progression (AP).So the series can be written as 0,6,12,18,24.Thus by substituting the value in the equation which is used for finding the value of the nth term in the arithmetic progression (AP) is an = a + ( n-1 ) × dHere a is the first term , n is the number of the term to be founded and d is the common difference between the two consecutive number in the series. Thus by substituting the value we get an = 0 + ( n-1 ) × 6 By solving we get an = 6n - 1.
-2(x-2)=-16 answer.
Answer:
-2x+4=-16
-2x = -16-4
-2x = -20
x = -20/-2
x = 10
Kim wants to earn at least $65 from her two jobs next week. At most, she can work 15 hours. Her first job pays $5 per hour, and her second job pays $7 per hour. Let x represent the number of hours worked at the first job and y represent the number of hours worked at the second job. Which system of linear inequalities models Kim's situation?
A)
+>15
x
+
y
>
15
5+7<65
5
x
+
7
y
<
65
B)
+≤15
x
+
y
≤
15
5+7≥65
5
x
+
7
y
≥
65
C)
+≤65
x
+
y
≤
65
5+7≥15
5
x
+
7
y
≥
15
D)
+>65
x
+
y
>
65
5+7<15
Final answer:
The correct system of linear inequalities that models Kim's work situation is option B, which includes the inequalities x + y ≤ 15 and 5x + 7y ≥ 65. These inequalities account for the maximum hours she can work and the minimum income she wants to earn. The correct option is B.
Explanation:
The student is asking for the system of linear inequalities that models Kim's work situation based on the hours she can work at two different jobs with different hourly rates. To model this situation, we have two variables: x for the number of hours worked at the first job and y for the hours at the second job. The first inequality comes from the maximum hours she can work, which is 15. Therefore, the combined hours worked at both jobs cannot exceed 15, which gives us:
x + y ≤ 15
The second inequality is derived from Kim's target earnings, which is at least $65. So, the income from both jobs combined must be at least $65, which gives us:
5x + 7y ≥ 65
Taking into account the given options, the correct system of linear inequalities is represented by option B:
x + y ≤ 15
5x + 7y ≥ 65
Find the probability of having 2, 3, or 4 successes in five trials of a binomial experiment in which the probability of success is 40%.
Round to the nearest tenth of a percent
[?]%
Final answer:
To find the probability of having 2, 3, or 4 successes in five trials where the probability of success is 40%, we calculate each scenario's probability using the binomial probability formula and sum them. The total probability is 65.3%, rounded to the nearest tenth of a percent.
Explanation:
To calculate the probability of having 2, 3, or 4 successes in five trials of a binomial experiment where the probability of success is 40%, we use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability of k successes in n trials
C(n, k) is the combination of n trials taken k at a time
p is the probability of success on an individual trial
(1-p) is the probability of failure on an individual trial
Let's calculate each probability:
P(X = 2) = C(5, 2) * 0.4² * 0.6³
P(X = 3) = C(5, 3) * 0.4³ * 0.6²
P(X = 4) = C(5, 4) * 0.4⁴ * 0.6¹
To find the total probability of having either 2, 3, or 4 successes (P(X = 2 or 3 or 4)), we add up these probabilities:
P(X = 2 or 3 or 4) = P(X = 2) + P(X = 3) + P(X = 4)
Let's use the combination formula to calculate these probabilities:
P(X = 2) = 10 * 0.4² * 0.6³ = 0.2304
P(X = 3) = 10 * 0.4³ * 0.6² = 0.3456
P(X = 4) = 5 * 0.4⁴ * 0.6 = 0.0768
Therefore:
P(X = 2 or 3 or 4) = 0.2304 + 0.3456 + 0.0768 = 0.6528 or 65.3% (rounded to the nearest tenth of a percent)
Mariah lives in a $75,000 wood house in the country with contents valued at
$10,000. Use the table below to calculate her monthly property insurance
premium
Annual Premium per $100 of coverage
Brick
Steel
Mixed
Wood
Area
Building Contents Building Contents Building Contents Building
rating
City 039
0 39 043 05 0.54 0.55 0.65 0.66
Suburb 0.45 052 056 0.63 0 .72 0.74 0.83
Rural 0.6 0.69 0.71 0.
8 0 .89 0.91 1 1
Contents
0.76
0.85
.02
The correct answer is $71.
Mariah's monthly property insurance premium, given that her $75,000 wood house and $10,000 contents are situated in a rural area, would be approximately $71.67.
Explanation:Calculating Mariah's Monthly Property Insurance Premium
To calculate Mariah's monthly property insurance premium, we need to note that her house is made of wood and that she lives in a rural area. In the table, the annual premium per $100 coverage for a wood building in a rural area is 1.0 and for the contents, it is 1.1.
Following the steps below, we can calculate Mariah's monthly property insurance premium:
First, we calculate the annual premiums by dividing the value of the house and the contents by $100 and multiply by the annual premium rates.
So, Mariah's monthly property insurance premium would be approximately $71.67.
Learn more about Property Insurance Premium here:https://brainly.com/question/29771572
Fraction between 1/2 and 1/4 that has denominator of 19
Answer:
6/19
Step-by-step explanation:
Sine 19 divided by 2 is 9.5 and 19 divided by 4 is 4.75, you can choose any number from 4.75 to 9.5.
The fraction which falls within the given range with a denominator of 19 is 5/19
Fraction between 1/2 and 1/4 which has a denominator of 19
1/2 = 0.5
1/4 = 0.25
Value between 0.25 and 0.5 The fractional representation the value has a denominator of 19We could use trial and error method :
2/19 = 0.1025
3/19 = 0.1578
4/19 = 0.210
5/19 = 0.263
6/19 = 0.315
7/19 = 0.368
8/19 = 0.421
9/19 = 0.474
10/19 = 0.526
From the values above, the fractions which fall in range are ;
5/196/197/198/199/19Hence, any of the given fractions could be selected.
Learn more : https://brainly.com/question/13497040
PLZ HELP WILL GIVE BRAINLIEST
A new juice stand is serving free drinks at a community festival. It offers the following drink options.
Fruit: apple, mango, orange, lime
Cup size: small, regular, large
Ice: cubed, crushed
If drinks are randomly passed out from each of the options, what is the probability that the next drink given out will be a regular apple juice with cubed ice?
a. 1/9
b. 1/12
c. 1/24
d. 1/4
THX SO MUCH!!!!
The correct answer is 1/24
Fruit: apple, mango, orange, lime
Cup size: small, regular, large
Ice: cubed, crushed
If you count every variation you'll get to 24.
The chances are 1 in 24.
For what value of x is the equation 22x + 7 = 215 true?
Answer:
x = 9 5/11
Step-by-step explanation:
22x + 7 = 215
22x = 215-7
22x = 208
x = 208/22
x = 9 5/11
[tex]\text{Hey there!}[/tex]
[tex]\text{For what value of x is the equation 22x + 7 = 215?}[/tex]
[tex]\mathsf{22x+7=215}\\\mathsf{Subtract\ by\ 7\ on\ your\ sides}\\\mathsf{22x+7-7=215-7}\\\mathsf{7-7=0\leftarrow cancel\ that\ because\ we\ DO\ NOT\ need it}\\\mathsf{215-7= 208\leftarrow keep\ that\ because\ helps\ us\ solve\ for\ x}\\\mathsf{Equation:22x=208}\\\mathsf{Divide\ by\ 22\ on\ your\ sides}\\\mathsf{\dfrac{22x}{22}=\dfrac{208}{22}}\\\\\mathsf{\dfrac{22x}{22}\leftarrow cancel\ out\ this\ because\ it\ gives\ you\ the\ value\ of\ 1}[/tex]
[tex]\mathsf{\dfrac{208}{22}\leftarrow keep\ this\ because\ it\ helps\ us\ solve\ for\ x}\\\\\mathsf{x=208\div22}\\\\\mathsf{\uparrow Solve\ that\ and\ you\ have\ the\ value\ of\ x}\\\\\boxed{\boxed{{\mathsf{Answer:x=\dfrac{104}{11}}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
I'LL GIVE BRAINLIEST....PLZ HELP ME!!
Solve the following system of equations using substitution. Be sure to show all work and check your answer.
y=5x+2
3x=-y+10
Answer:
Step-by-step explanation:
y = 5x + 2.....so we will sub in 5x + 2 for y, back into the other equation
3x = -y + 10
3x = - (5x + 2) + 10
3x = -5x - 2 + 10
3x + 5x = 8
8x = 8
x = 8/8
x = 1
y = 5x + 2
y = 5(1) + 2
y = 5 + 2
y = 7
check it... (1,7)
3x = -y + 10 y = 5x + 2
3(1) = -7 + 10 7 = 5(1) + 2
3 = 3 (correct) 7 = 7 (correct)
so ur solution is : x = 1 and y = 7...or (1,7) <=====
Answer:
(1,7)
Step-by-step explanation:
Since we know that y=5x+2, we replace y in the bottom equation with 5x+2.
3x=-(5x+2)+10
Then distribute the - into both of the parentheses (multiply both terms by -1):
3x=-5x-2+10
Then add like terms:
3x=-5x+8
Add 5x to both sides:
8x=8
Divide both sides by 8:
x=1
Plug the known x value into y=5x+2:
y=5(1)+2
Multiply:
y=5+2
Add:
y=7
Put values into (x,y) form:
(1,7)
The Murphy family is on a road trip. On the first day, they traveled 30% of their total distance. On the second day, they traveled another 1/4 of the total distance. What fraction of the total distance do they have left after the second day? What percent?
Answer:
55% or 55/100 or 11/20
Step-by-step explanation:
1/4 is equal to 25%
Add: 30+25=55
So the percent will be 55%
Percents are always out of 100, so to convert 55% into a fraction, you simply have to put 55 over 100: 55/100
Find the greatest common factor, which is 5.
Divide:
55÷5=11
100÷5=20
So the simplified fraction will be 11/20.
A rectangular carport has an area 28 square feet. The height of the carport is 1 feet less than 2 times its length. Find the height and the length of the carport.
Answer:
Dimension= [tex](4\times 7)\ feet[/tex]
Step-by-step explanation:
Given: Area of Carport= 28 feet²
The height of the carport is 1 feet less than 2 times its length.
Lets assume the length of Carport be "w"
∴ Height of carport= [tex](2w-1)\ feet[/tex]
We know, Area of rectangle= [tex]width\times length[/tex]
∴[tex]28= w\times (2w-1)[/tex]
Using distributive property of multiplication.
⇒ [tex]28= 2w^{2} -w[/tex]
Subtracting both side by 28.
⇒ [tex]2w^{2} -w-28= 0[/tex]
Using the quadratic formula to solve the equation.
⇒ [tex]2w^{2} -w-28= 0[/tex]. what are the values of w.
Solving by using quadratic formula.
Formula: [tex]\frac{-b\pm \sqrt{b^{2}-4(ac) } }{2a}[/tex]
∴ In the equation [tex]2w^{2} -w-28= 0[/tex] , we have a= 2, b= -1 and c= -28.
Now, subtituting the value in the formula.
= [tex]\frac{-(-1)\pm \sqrt{(-1)^{2}-4(2\times -28) } }{2\times 2}[/tex]
= [tex]\frac{1\pm \sqrt{1 - 4(-56) } }{4}[/tex]
Opening parenthesis.
= [tex]\frac{1\pm \sqrt{1+224 } }{4}[/tex]
= [tex]\frac{1\pm \sqrt{225}}{4}[/tex]
We know 15²=225
= [tex]\frac{1\pm \sqrt{15^{2}}}{4}[/tex]
we know √a²=a
= [tex]\frac{1\pm 15 }{4}[/tex]
Now we have two solution
= [tex]\frac{16}{4} \ or\ \frac{-14}{4}[/tex]
Ignoring negative base or width or carport
∴ w= [tex]\frac{16}{4} = 4[/tex]
Hence, Length of carport is 4 feet
next subtituting the value of length to get height of carport
Height of carport= [tex](2w-1)\ feet[/tex]
⇒ Height of carport= [tex](2\times 4-1)[/tex]
⇒ Height of carport= [tex]7\ feet[/tex]
Hence dimension of rectangular carport= [tex](4\times 7)\ feet[/tex]
Please help! My teacher didn't teach us this and idk what to do
Answer:
A. 112 feet
B. 3 seconds
C. 256 feet
Step-by-step explanation:
The function [tex]d(t)=-16t^2+96t+112[/tex] describes the height of the quarter above the water.
When [tex]t=0,[/tex] then
[tex]d(0)=-16\cdot 0^2+96\cdot 0+112\\ \\d(0)=112\ feet[/tex]
Part A. The quarter was tossed from 112 feet.
Find the vertex of parabola represented by quadratic function d(t):
[tex]t_v=\dfrac{-b}{2a}=\dfrac{-96}{2\cdot (-16)}=3\\ \\d(t_v)=d(3)=-16\cdot 3^2+96\cdot 3+112\\ \\d(3)=-144+288+112\\ \\d(3)=256\ feet[/tex]
Hence,
Part B. It will take 3 seconds to reach the maximum height.
Part C. The maximum height is 256 feet
CL 6-131. Solve each system using the method of your choice.
I. 2x + 3y = 7
−3x − 5y = −13
II. 8 − y = 3x 2y + 3x = 5
System 1: The solution is (x, y) = (-4, 5)
System 2: The solution is [tex](x, y) = (\frac{11}{3}, -3)[/tex]
Solution:
Given system of equations are:
2x + 3y = 7 ------ eqn 1
-3x - 5y = -13 --------- eqn 2
We can solve by elimination method
Multiply eqn 1 by 3
6x + 9y = 21 ------ eqn 3
Multiply eqn 2 by 2
-6x - 10y = -26 ------- eqn 4
Add eqn 3 and eqn 4
6x + 9y -6x - 10y = 21 - 26
-y = -5
y = 5
Substitute y = 5 in eqn 1
2x + 3(5) = 7
2x + 15 = 7
2x = -8
x = -4
Thus the solution is (x, y) = (-4, 5)
Second system of equation is:8 - y = 3x ------ eqn 1
2y + 3x = 5 ----- eqn 2
We can solve by susbtitution method
From given,
y = 8 - 3x ----- eqn 3
Substitute eqn 3 in eqn 2
2(8 - 3x) + 3x = 5
16 - 6x + 3x = 5
3x = 16 - 5
3x = 11
[tex]x = \frac{11}{3}[/tex]
Substitute the above value of x in eqn 3
y = 8 - 3x
[tex]y = 8 - 3 \times \frac{11}{3}\\\\y = 8 - 11\\\\y = -3[/tex]
Thus the solution is [tex](x, y) = (\frac{11}{3}, -3)[/tex]
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of y plus StartFraction one-half EndFraction equals 3 left-parenthesis x minus 2 right-parenthesis.?
Answer:
[tex]y-2=3(x-3)[/tex]
Step-by-step explanation:
We want to write the equation of a line in point-slope form.
This is given by:
[tex]y-y_1=m(x-x_1)[/tex]
We have that line passes through (3,2).
Assuming the line has a slope of m=3, then the equation in point slope form is:
[tex]y-2=3(x-3).[/tex]
Final answer:
The point-slope form of the line that passes through the point (3, 2) with a slope of ½ is represented by the equation y - 2 = ½(x - 3).
Explanation:
The equation that shows the point-slope form of the line that passes through the point (3, 2) with a slope of ½ is derived from the point-slope equation format: y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope. Plugging the given point and slope into this formula, we get the equation y - 2 = ½(x - 3).
When solving for y to get the slope-intercept form, it's important to distribute the slope ½ across the (x - 3) term resulting in the equivalent equation: y = ½x + ¼.
Which number has a 7 that is 1/10 the value of the 7 in 3,762?
A.4,071
B.738
C.297
D.107
For a 7 to have a value that is 1/10 of the 7 in 3,762, it needs to be in the tens place of a number. Only choice B, 738, meets this requirement.
Explanation:To solve this question, we need to first understand the place value of numbers. In the number 3,762, the 7 is in the hundreds place, which signifies that it represents 700. A 7 that has 1/10 of this value would, therefore, represent 70. So, we're looking for a number where 7 appears in the tens place.
By reviewing choices A through D, we can determine that the correct answer is B. 738. In this number, the 7 is in the tens place, which means it is worth 70, or 1/10 of the value of the 7 in 3,762.
Learn more about Place Value here:https://brainly.com/question/35447631
#SPJ2
Joseph will have a 200-foot-long fence installed
around his yard. The A+ Fence Company charges a
$500.00 fee, plus a set amount per foot of fence. The
A+ Fence Company has given Joseph an estimate of
$2,200.00 to install the fence around his yard. What is
Che set amount per foot of fence?
Answer:$8.50
Step-by-step explanation:
The answer would be. $8.50 per foot. $8.50 times 200 is $1700 plus the $500Company fee equals to $2200
60 more than 9 times la number is the same as 2 less than 10 times the number what is the number?
Answer:
Step-by-step explanation:
let x represent the number
9x + 60 = 10x - 2
60 + 2 = 10x - 9x
62 = x <===