Answer:
Option A is correct.
d = 50t shows the relationship between d and t
Step-by-step explanation:
Point slope form: For a point [tex](x_1, y_1)[/tex] and a slope m, the equation of the line can be written as
[tex]y-y_1=m(x-x_1)[/tex] ......[1], where m is the slope of the line.
Here, d represents the total distance ( in miles) and t represents the time (in hours).
From the given table:
Consider any two points (1, 50) and (2, 100).
Calculate slope:
Slope(m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{100-50}{2-1}=\frac{50}{1} =50[/tex]
⇒[tex]m= 50[/tex]
Now, by point slope intercept form:
Substitute m= 50 and (1, 50) in [1]
we have;
[tex]y -50 = 50(x-1)[/tex]
Using distributive property: [tex]a\cdot(b+c) = a\cdot b+ a\cdot c[/tex]
y -50 = 50x -50
Add both sides 50 we get;
y -50+ 50= 50x -50 + 50
Simplify:
[tex]y =50x[/tex]
∵y = d represents the distance and x = t represents the time;
then, our equation become:
[tex]d = 50t[/tex]
The equation representing the relationship between the distance covered (d) and time (t) in the given situation is d = 50t. This signifies that the distance covered is equal to 50 times the time.
In the given data, we observe that the total distance (d) travelled by the car in an hour is always 50 miles. This means that every hour, the car covers a distance of 50 miles.
Therefore, the relationship between the distance covered (d) and time (t) can represent this situation is d = 50t.
This signifies that 'd', the distance covered, is equal to 50 times 't', the time in hours. For example, when t=1 hour, d = 50*1 = 50 miles. Similarly, when t=2 hours, d = 50*2 = 100 miles. This continues accordingly.
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There are 3.79 L in every gallon how many liters of gas does a 13.6 gallon tank hold
Answer:
51.544 L in our tank
Step-by-step explanation:
We have a 13.6 gallon tank
Our conversion factor is 3.79 L = 1 gallon. We want liters on top since that is where we want to end up
3.79 L /1 gallon is what we want to use
13.6 * 3.79L/1 gallon = 51.544 L in our tank
Which inequality is represented by the number line graph?
A) x > -6
B) x < -6
C) x ≥ -6
D) x ≤ -6
The correct answer is option (D).
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The graph shows an open circle at -6,
which implies that -6 is not a solution to the inequality.
The shaded arrow on all values shows that values are smaller than -6 and x < -6 is the inequality that represented on the line graph.
The required inequality is x < -6.
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which has less water a swimming pool that is 5/10 full or a glass that is 9/10 full
Answer: A swimming pool that is 5/10 full.
Which equation represents the following word sentence? The opposite of g times the quantity 2 plus 5.
Answer:
-g * (2+5)
Step-by-step explanation:
The opposite of g times the quantity 2 plus 5
Opposite means put a negative sign
times means multiply
Quantity means parenthesis
plus means addition
-g * (2+5)
The problem 'The opposite of g times the quantity 2 plus 5' translates into the mathematical equation -g*(2+5) or -g*7 in which g is multiplied by 7, and the result is negated.
Explanation:The word sentence 'The opposite of g times the quantity 2 plus 5' can be represented by the equation -g*(2+5) or -g*7, where * denotes multiplication, + denotes addition, and - denotes opposite or negation. Therefore, the interpretation of the sentence is 'multiply g by 7 and then take the opposite or negative of the result'. The use of parentheses ( ) in the equation ensures we first perform the addition within, according to the order of operations in math, most commonly known as BIDMAS/BODMAS or PEMDAS rules.
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A rectangular flowerbed at a city park has an area of 126 sou area meters the width of the flowerbed is 3 meters what is the perimeter of the flowerbed
Answer: The Perimeter is 90 meters
Step-by-step explanation:
Area = 126
Width = 3
Length = L
3 x L = 126
3 x L / 3 = 126/3
L = 42
Check:
3 x 42 = 126
126 = 126
Perimeter = L2 + W2
P = 42 x 2 + 3 x 2
P = 84 + 6
P = 90
Layla and Carson work at the same store. Last week, Layla worked 8.75 hours, which was 25% of the amount of the time that Carson worked. How many hours did Carson work last week
Divide 8.75 by 35 and multiply the result by 100 to get 25 hours.
Given f(x)=5x+5, find f(-4)
f(-4) This means that x is -4, so you can plug in -4 for "x" in the equation
f(x) = 5x + 5
f(-4) = 5(-4) + 5
f(-4) = -20 + 5
f(-4) = -15
Luz reads for 1/4 hours every night. After 8 nights, how much total time has she been reading?
Answer:
2 hours
Step-by-step explanation:
To find out how much she has read, we multiply the number of nights by how much read per night
time read = 8 nights * 1/4 hours per night
time read = 8/4 hours
time read = 2 hours
Answer: 2 weeks?
Step-by-step explanation: 1/4 x 8= 2
The angle bisector of a triangle divides the triangle into two similar triangles
-always
-sometimes
-never
The angle bisector of a triangle divides the triangle into two similar triangles sometimes true and sometimes not true. Because the sum of the angle of the triangle is 180 degrees. But all three angles are not equal.
TriangleTriangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
Given
Angle bisector of the triangle.
To find
The angle bisector of a triangle divides the triangle into two similar triangles always, sometimes, or never.
How to show the condition?The angle bisector of a triangle divides the triangle into two similar triangles sometimes true and sometimes not true. Because the sum of the angle of the triangle is 180 degrees. But all three angles are not equal.
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The angle bisector divides a triangle into two similar triangles Option B) sometimes, specifically when the triangle is isosceles.
1. Isosceles Triangle: In an isosceles triangle, two sides are equal in length. When the angle bisector of the vertex angle is drawn, it also bisects the base, creating two congruent triangles (by the Angle Bisector Theorem). Congruent triangles are always similar, so in this case, the statement holds true.
2. Scalene Triangle: In a scalene triangle, none of the sides are equal. When you draw the angle bisector of one of the angles, it won't necessarily bisect any other side into two equal lengths. Hence, the resulting triangles formed by the angle bisector won't necessarily be similar.
So, the angle bisector divides the triangle into two similar triangles sometimes (when it's an isosceles triangle) but not always (when it's a scalene triangle).
There were 27 balloons at the beginning of a party. By the end of the party, c of them had popped. Using c , write an expression for the number of balloons that were left.
Answer: 27-c =x
Step-by-step explanation:
We'll use c to represent the amount taken away (subtracted) and x to represent the amount left (the answer).
We begin with 27 balloon, and take away c amount to make x.
27-c =x
The number of balloons left after c balloons have popped from an initial number of 27 balloons can be represented by the mathematical expression 27 - c.
Explanation:In order to determine the number of balloons that were left after some of them had popped, we can use a simple mathematical expression. If there were initially 27 balloons and c balloons popped, then the number of balloons left would be the initial number of balloons minus the number popped.
Mathematically, this can be represented by the expression: 27 - c.
The variable c is used to represent the number of balloons that popped during the party. By subtracting this from the total number of balloons, we're left with the number of balloons that survived the party.
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A problem states: "There are 9 more pencils than pens in a container. There are 25 writing utensils in the container in all. How many pens are there in the container?" Let p represent the number of pens. Which equation represents the situation?
Answer:
the answer is 16
Step-by-step explanation:
25-9=16 pens
Answer:25-9= 16 pens
Step-by-step explanation:
Evaluate (precalculus)
Answer:
Option 4 which is 1,430.
Step-by-step explanation:
Step 1
In this this step we will break up the terms in the summation symbol using the rules for manipulation summations.
[tex]\sum_{i=1}^{n}(aX^2_i+k)=\sum_{i=1}^{n}(aX)+\sum_{i=1}^{n}k\\\\\sum_{i=1}^{n}(aX^2_i+k)=a\sum_{i=1}^{n}X^2+nk.[/tex]
This means that for our case, the sum can be simplified to be,
[tex]\sum_{i=1}^{11}(3i^2_i-8)=3\sum_{i=1}^{11}i^2+11\times(-8)\\\\\sum_{i=1}^{11}(3i^2_i-8)=3\sum_{i=1}^{11}i^2-88[/tex]
Step 2
In this step we use the formula for the sum of the first n squares to evaluate the first part of the sum in step 2. The formula for the sum of the first n squares is,
[tex]\sum_{i=1}^{n}n^2=\frac{n(n+1)(2n+1)}{6} \\\\\implies\sum_{i=1}^{11}i^2=\frac{11(11+1)(2\times 11+1)}{6} =506[/tex]
Step 3
In this step we use the result from step 1 to evaluate the sum.[tex]3\sum_{i=1}^{11}i^2-88=3(506)-88=1,430.[/tex]
The correct answer is Option 4,which is 1,430.
Answer:
[tex]\boxed{\boxed{\sum_{i=1}^{11}(3i^2-8)=1430}}[/tex]
Step-by-step explanation:
The given expression is,
[tex]\sum_{i=1}^{11}(3i^2-8)[/tex]
[tex]=\sum_{i=1}^{11}(3i^2)-\sum_{i=1}^{11}(8)[/tex]
[tex]=3\sum_{i=1}^{11}(i^2)-\sum_{i=1}^{11}(8)[/tex]
we know that,
[tex]\sum_{i=1}^{n}i^2=\dfrac{n(n+1)(2n+1)}{6}[/tex] and
[tex]\sum_{i=1}^{n}c=cn,\text{ Where c is a constant}[/tex]
Hence,
[tex]3\sum_{i=1}^{11}(i^2)-\sum_{i=1}^{11}(8)=3\left(\dfrac{11(11+1)(2(11)+1)}{6}\right)-8(11)[/tex]
[tex]=3\left(\dfrac{11(12)(23)}{6}\right)-8(11)[/tex]
[tex]=3\left(506}\right)-8(11)[/tex]
[tex]=1518-88[/tex]
[tex]=1430[/tex]
Please help I don’t know how to do this at all!
Answer:
16 times the square root of 6
Step-by-step explanation:
2 radical54 simplifies:
2(radical6 x radical9), which is 6 radical6
and 5 radical24 simplifies:
5(radical6 x radical4), which is 10 radical6,
10 radical6 + 6 radical6=
16 radical6
What is the value of arcsin (0) in degrees
Answer:
0
Step-by-step explanation:
full answer guide attached
Will give lots of points/write a rule to describe each transformation
Step-by-step explanation:
What number(s)?
what is the name of the angle formed by the rays please show the work
Answer:
∠RQP
Step-by-step explanation:
What is the value of cos 0 given that (-2,9) is a point on the terminal side of 0?
Answer:
The value of cos 0 = - 2 sqrt(85) / 85 = - 0.216930458
Step-by-step explanation:
cos 0 = ?
Point on the terminal side of 0 : (-2,9)=(x,y)→x=-2, y=9
cos 0 = x/r
r=sqrt(x^2+y^2)
Replacing the known values:
r=sqrt( (-2)^2+(9)^2)
r=sqrt(4+81)
r=sqrt(85)
cos 0 = x/r
cos 0 = -2 / sqrt(85) = -2/9.219544457 = -0.216930458
Rationalizing:
cos 0 = -[2 / sqrt(85)] [sqrt(85) / sqrt(85)]
cos 0 = - 2 sqrt(85) / [sqrt(85)]^2
cos 0 = - 2 sqrt(85) / 85
a 33 m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 36m Find the length of the shadow
Answer:
14.39
Step-by-step explanation:
a^2 + b^2 = c^2
33^2 + b^2 = 36^2
1089 + b^2 = 1296
1089 - 1089 + b^2 = 1296 - 1089
b^2 = 207
b = 14.39
Matthew jogged to his friend’s house 12 miles away and then got a ride back home. It took him 2 hours longer to jog there than ride back. His jogging rate was 25 mph slower than the rate when he was riding. What was his jogging rate?
Answer:
The jogging rate of Matthew is 5 mph.
Step-by-step explanation:
Let the jogging rate of Matthew be x mph.
It is given that his jogging rate was 25 mph slower than the rate when he was riding. So, the riding rate is (x+25) mph.
The distance between Matthew and his friend's house is 12 miles.
[tex]Speed=\frac{Distance}{Time}[/tex]
[tex]Time=\frac{Distance}{Speed}[/tex]
The time taken by Matthew in jogging is [tex]\frac{12}{x}[/tex] and the time taken by Matthew in riding is [tex]\frac{12}{x+25}[/tex].
It took him 2 hours longer to jog there than ride back.
[tex]\frac{12}{x}=\frac{12}{x+25}+2[/tex]
[tex]\frac{12}{x}-\frac{12}{x+25}=2[/tex]
[tex]\frac{12(x+25)-12x}{x(x+25)}=2[/tex]
[tex]12x+300-12x=2x(x+25)[/tex]
[tex]300=2x^2+50x[/tex]
[tex]0=2x^2+50x-300[/tex]
[tex]0=x^2+25x-150[/tex]
[tex]0=x^2+30x-5x-150[/tex]
[tex]0=(x+30)(x-5)[/tex]
Equate each factor equal to 0.
[tex]x=5,-30[/tex]
The speed cannot be negative, therefore the jogging rate of Matthew is 5 mph.
Answer:
the answer is D
Step-by-step explanation:
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 18 N acts on a certain object, the acceleration of the object is 6 /ms2 . If the acceleration of the object becomes 5 /ms2 , what is the force?
Answer: [tex]F=15N[/tex]
Step-by-step explanation:
1. You know that the force acting on the object varies directly with the object's acceleration. Then, by definition, you have:
[tex]F=ka[/tex]
Where [tex]F[/tex] is the force acting on the object, [tex]a[/tex] is the object's acceleration and [tex]k[/tex] is the constant of proportionality.
2. Keeping this on mind, you can calculate the constant of proportionality by substituting [tex]F=18[/tex] and [tex]a=6[/tex] into the equation and solving for [tex]k[/tex]:
[tex]18=k6\\k=\frac{18}{6}\\k=3[/tex]
3. Now, you can calculate the force when the acceleration of the object becomes 5 m/s², as following:
[tex]F=3(5)\\F=15[/tex]
3. The result is:
[tex]F=15N[/tex]
The acceleration that an objects gains is given by the mass of the object.
If the acceleration of the object becomes 5 m/s² the force is 15 N.Reason:
The given parameters are;
The acting force ∝ The acceleration of the object.
The acceleration given by an amount of force, F, of 18 N = 6 m/s²
Required:
The force acting on the object acceleration, a, is 5 m/s².
Solution:
According to Newton's Second Law of motion, we have;
F = m·a
Where;
m = The mass of the object
Therefore, we have;
[tex]Mass, \, m = \dfrac{F}{a}[/tex]
From the conditions, F = 18 N, when a = 6 m/s², we have, the mass of the
given object is given as follows;
[tex]Mass \ of \ the \ object, \, m = \dfrac{18 \, N}{6 \ m/s^2} = 3 \, kg[/tex]
The force acting when the the acceleration, a = 5 m/s², is therefore;
F = 3 kg × 5 m/s² = 15 N
If the acceleration of the object becomes 5 m/s² the force is 15 N.
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What is the diameter of a circle that has a circumference of 56.52 feet? Round your answere to the nearest whole number
Answer:
18 = diameter
Step-by-step explanation:
Solve for x
3x-xy=4z-5y
Is it no solutionn????
From algebra1
HELP PLZZZZZZ
Answer:
x = (4z -y)/(3 – y); y ≠ 3
Step-by-step explanation:
3x – xy = 4z - 5y Factor
x(3-y) = 4z - y Divide each side by 3-y
x = (4z -y)/(3 – y); y ≠ 3
x is undefined when y = 3, so we must include the condition that y ≠ 3.
Look at the table below showing an example of a checkbook ledger. Adrienne has several receipts from recent transactions that she entered in her records. The receipts include an ATM receipt for a $60.00 withdrawal (plus a $2.00 transaction fee), a grocery store receipt for $32.50, and a $1,200 paycheck deposit slip. When she finishes entering her transactions, Adrienne realizes that her balance is incorrect. Assuming that Adrienne’s beginning account balance was $320.00, why is her balance incorrect?
I think it's "Adrienne did not enter her ATM withdrawal correctly"
Answer:
" Adrienne did not enter her ATM withdrawal correctly."
D.
Step-by-step explanation: <3
The cost of a car rental is twenty-five dollars a day plus ten cents a mile. What is the total cost, in dollars, if the car is rented for three days and driven a total of six hundred and sixty miles? A) 86 B) 91 C) 97 D) 141
Answer:
The total cost is D) $141
Step-by-step explanation:
To solve we can use the equation: [tex]y=25d+0.10m[/tex]
d= number of days m= number of miles
We know both of these values so we can plug them in and solve.
y= 25(3) + 0.10(660)
y= 75 + 66
y = 141
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Find the area of a regular hexagon with the given measurement. 48-inch perimeter A = sq. in.
Answer:
Step-by-step explanation:
It is given that the perimeter of the regular hexagon is 48 inch. Thus,
Perimeter of the regular hexagon = 48
⇒[tex]Sum of all the sides=48[/tex]
⇒[tex]6x=48[/tex]
⇒[tex]x=8inch[/tex]
Thus, the side of the regular hexagon is 8 inch.
Now, [tex]area of the regular hexagon=\frac{3\sqrt{3}}{2}(x)^2[/tex]
⇒[tex]A=\frac{3\sqrt{3}}{2}(8)^2[/tex]
⇒[tex]A=\frac{3\sqrt{3}}{2}(64)[/tex]
⇒[tex]A=96\sqrt{3}[/tex]
⇒[tex]A=166.03 sq inches[/tex]
Thus, the area of the regular hexagon is 166.03 sq inches.
The area of the regular hexagon that's given will be 166.03 inches².
How to calculate the area of the hexagonFrom the information, it was stated that the regular hexagon has a perimeter of 48 inches.
Therefore, the length of each side will be:
= 48/6
= 8 inches
The area of a regular hexagon calculated as:
= 3✓3/2 × x²
= 3✓3/2 × 8²
= 96✓3
= 166.03
In conclusion, the area is 166.03 inches².
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Mindy opens a bank account with $55 and start saving five dollars per week. Sean’s grandma gives him $100 for his birthday, but he spends $10 every week. After how many weeks would they have the same amount of money, how much will that be?
Answer:
3 weeks, $45
Step-by-step explanation:
So we can make an equation!
55+5x=100-10x
So solving for x,
X=3
Final answer:
After solving the equations, Mindy and Sean will have the same amount of money, which is $70, after 3 weeks.
Explanation:
The question is about finding after how many weeks Mindy and Sean would have the same amount of money and how much that amount would be. Let's denote the number of weeks as w. For Mindy, who starts with $55 and saves $5 per week, her amount of money as a function of weeks is 55 + 5w. For Sean, who starts with $100 and spends $10 every week, his amount of money as a function of weeks is 100 - 10w.
To find out after how many weeks they would have the same amount of money, set the two expressions equal to each other:
55 + 5w = 100 - 10w
Add 10w to both sides and subtract 55 from both sides to solve for w:
15w = 45
Therefore, w = 45 / 15 = 3
To find out how much money they would have, substitute w = 3 into one of the original equations:
Mindy: 55 + 5(3) = 70
So, after 3 weeks, both Mindy and Sean will have $70
Someone please help!!!!!
I'm bad at math!!!
(5b - 9) - 3(8 - 2b)
Also, could you give me tips on how to solve these kind of problems?
Thanks.
- A Math Disaster
Denise’s rock sample weighs 684 grams Pauline’s rock sample weighs 29,510 centimeters how much heavier is Denise’s sample than Pauline’s
Answerenise's rock sample has
38
,
890
centigrams more mass than that of Pauline
:
Step-by-step explanation:
at a farmers market two vendors sell fresh milk. one vendor sells 2 liters for $3.80, and another vendor sells 1.5 liters for $2.70. which is the better deal?
Answer:
The second dealer is better.
Step-by-step explanation:
To figure this out we need to divide the price by the amount of milk. Lets do both at the same time.
3.8/2= 2.7/1.5=
3.8/2=1.9 2.7/1.5=1.8
The second dealer is better.
Price per unit is the cost of the sing unit or measure of goods or the service provided.The second vendor sells 1 liter of fresh milk at $1.80 which is $0.10 less than the first vendor. Therefore the second vendor gives the better deal.
Given information-
First vendor sells 2 liters for $3.80.
Second vendor sells 1.5 liters for $2.70.
What is price per unit?Price per unit is the cost of the sing unit or measure of goods or the service provided.
Price per unit helps to compare the two product with there cost. The less will be the price per unit of a product the product will be more cheaper.
Price per unit is the ratio of the total cost to the number of units.
The vendor which provide more milk in less rate will be the better deal.
As first vendor sells 2 liters for $3.80. Thus the price of milk per liter is,
[tex]P_1=\dfrac{3.80}{2} \\P_1=1.90[/tex]
Hence the first vendor sells the 1 liter milk in $1.90.
As Second vendor sells 1.5 liters for $2.70. Thus the price of milk per liter is,
[tex]P_2=\dfrac{2.70}{1.5} \\P_2=1.80[/tex]
Hence the second vendor sells the 1 liter milk in $1.80.
Hence the second vendor sells 1 liter of fresh milk at $1.80 which is $0.10 less than the first vendor. Therefore the second vendor gives the better deal.
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I need help with number 14 please