Jensen can send 4 messages for $1. This is calculated by using the concept of unit rate; first find the unit cost by dividing the total cost by the total number of messages, then divide $1 by the unit cost.
Explanation:The question is asking how many text messages Jensen can send for $1 if she usually spends $18 for 72 messages. This involves a concept in mathematics called unit rate, which identifies the cost (or quantity) per one unit. First, we figure out how much it costs to send one message by dividing the total cost by the total number of messages, i.e. $18/72. This gives us a unit cost of $0.25 per message. Therefore, to find out how many messages Jensen can send with $1, we divide $1 by the unit cost, giving us 4 messages. So, Jensen can send 4 messages for $1.
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There are 364 first-grade students in Park Elementary School. If there are 26 more girls than boys, how many girls are there?
There are 169 boys and 195 girls in the first-grade class at Park Elementary School.
Explanation:Let's assume the number of boys in the first-grade class is x. Since there are 26 more girls than boys, the number of girls would be x + 26. The total number of students in the class is 364, so we can calculate the equation:
x + (x + 26) = 364
Simplifying the equation, we get:
2x + 26 = 364
Subtracting 26 from both sides:
2x = 338
Dividing both sides by 2:
x = 169
So there are 169 boys and 169 + 26 = 195 girls.
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The area of a rectangle is 42 square inches the rectangle is 7 inches long how wide is the rectangle
Answer: 6 inches
Step-by-step explanation:
formula for area of a rectangle is length times width
LW=A
substitute
7(W)=42
divide 7 on both sides
42/7 = 6
Answer: 6
how do you know if two polygons are similar?
What is 12- 4/5(x+15)=4 please show me step by step.
Answer:
-5
Step-by-step explanation:
Explanation in the picture.
P(-2,2.5) Q(1.4,4) Find the midpoint
Answer:(-0.3,3.25)
Step-by-step explanation:
The midpoint of P(-2,2.5) and Q(1.4,4) is ( -0.3, 2.25)
What is Midpoint?A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.
Let two points A (x₁, y₁) and B (x₂, y₂), the midpoint between A and B is given by,
M(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2
Given P(-2,2.5) and Q(1.4,4)
So the midpoint = [(-2 + 1.4)/2, (2.5 + 4)/2]
The midpoint = [(-0.6)/2, (4.5)/2]
The midpoint = ( -0.3, 2.25)
Hence, the midpoint of P(-2,2.5) and Q(1.4,4) is ( -0.3, 2.25).
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What is the total cost of a $39.50 family dinner after you add a 20% tip
Answer:
$7.90 tip the total is $47.40
Step-by-step explanation:
Final answer:
To find the total cost of a $39.50 family dinner after adding a 20% tip, first calculate the amount of the tip by multiplying the cost of the dinner by the tip percentage. Then, add the tip to the cost of the dinner to get the total amount.
Explanation:
To find the total cost of a $39.50 family dinner after adding a 20% tip, you first need to calculate the amount of the tip. Tip is calculated by multiplying the cost of the dinner by the tip percentage. In this case, the tip would be 20% of $39.50, which is
$39.50 × 0.20 = $7.90
Next, you add the tip to the cost of the dinner to get the total amount:
$39.50 + $7.90 = $47.40
So, the total cost of the family dinner after adding a 20% tip is $47.40.
Problem Set#2:
In the cafeteria, 100 milk cartons were put on for breakfast. At the end of breakfast, 27 remained.
a. What is the ratio of the number of milk cartons taken to he total number of milk cartons?
b. What is the ratio of the number of milk cartons remaining to the number of milk cartons taken?
*Answer A-B
Answer:
a. the ratio is 73:100
b. the ratio is 27:73
Mike rides his motorcycle at an average speed (velocity) of 20 meters / second for
500 seconds how far did he ride?
Answer:
10,000 meter's is the answer
Step-by-step explanation:
multiply 20 and 500
30 POINTS!!
Karl is investigating two transformations.
Karl claims that a reflection over the line y=1 transforms a point (x,y) to the point (2−x,y). For example, (1,1) is reflected to (1,1).
Karl makes a second claim that a reflection over the line y=x transforms a point (x,y) to the point (y,x). For example, (2,2) is reflected to (2,2).
Which statement correctly classifies Karl’s claims?
A
Karl is correct regarding the first claim, but a reflection over y=x carries (x,y) to (x,y).
B
Karl is correct in both of his claims because each provided example supports the associated claim.
C
Karl is incorrect in both of his claims because neither example is enough to prove the associated claim.
D
Karl is incorrect as a reflection over line y=1 carries (x,y) to (x,2−y) but is correct in his second claim.
A doormat is 3 feet by 2 feet.
What is the area of the doormat?
2 1/2 ft
2
NI
3 ft
Factor the expression shown below completely.
18x^2-60x+50
A.
B.
C.
D.
Answer:D. 2(3x-5)^2
Step-by-step explanation:
18x^2-60x+50=2(9x^2-30x+25)
Answer:
D. 2(3x - 5)²
Step-by-step explanation:
18x² - 60x + 50
The expression can be factorize as follows;
18x² - 60x + 50
divide through by 2
2(9x² - 30x + 25)
The bracket equation can be factorized further
Find the square value that can be multiplied to get 9x² and 25
The values are 3x and 5
2( (3x- 5)(3x - 5) )
2(3x - 5)²
4* 5+ (14 + 8) - 369
Answer:
-327
Step-by-step explanation:
20+22-369=-327
how do make a rational to a fraction
Answer:
Step-by-step explanation:To convert part-to-part ratios to fractions:
Use the total number as the denominator: 6 + 8 = 14.
Use each of the ratio terms as the numerator in a fraction: ...
Reduce each fraction to lowest terms: ...
The part-to-part ratio 6 : 8 converts into the fractions:
To convert a rational expression to a fraction, create a common denominator, multiply by the inverse when dividing fractions, and simplify by canceling out common factors after prime factorization.
Converting a rational expression to a fraction involves creating a common denominator for the terms involved. When dividing fractions, the process is to change the division to multiplication by the inverse of the second fraction and then multiplying the numerators and denominators as above. A conversion factor in a measurement context is simply a fraction equal to one, with the original unit in the denominator to cancel it out and the new unit in the numerator.
When simplifying fractions it's useful to remember that multiplying or dividing both numerator and denominator by the same number does not change the value of the fraction; this is often referred to as multiplying by a fraction that equals one (1/2, 2/2, 3/3, etc.). Simplifying a fraction may involve finding these 'fractions equal to one' to cancel out the same factors in both the numerator and denominator.
you start at 11 ,10 and you move 7units left and 5 units down
Answer:
(4 , 5)
Step-by-step explanation:
Note the point: (x , y) = (11 , 10)
Note that if you are moving left or right, you are changing the x variable.
Note that if you are moving up or down, you are changing the y variable.
In this case, you are starting at (11 , 10)
You move 7 units left (subtract 7 from x):
(11 - 7 , 10) = (4, 10)
You then move 5 units down (subtract 5 from y):
(4 , 10 - 5) = (4 , 5)
(4 , 5) is your answer.
~
Determine whether each function is continuous at x=5. Justify your answer using the continuity test.
Answer:
2. [tex]f(x)=\frac{x^2}{x+5}[/tex]
Step-by-step explanation:
When you replace x=5 into those functions you obtain:
[tex]1. f(x)=\sqrt{x^2-36} = \sqrt{5^2-36} = \sqrt{-11} \\2. f(x)=\frac{x^2}{x+5}=\frac{5^2}{5+5}=\frac{25}{10}[/tex]
We can see that the function number 1, when the x=5 is replaced, falls into the imaginary numbers or complex domain, so the function is not continuous in the real domain.
On the other hand, the second function falls into the real domain whe x=5 is replaced, so the function is continuous in the real domain!
I hope you understand!
the difference between 33 1/3% and 33%
Answer:
_
1/3, or 0.3 is there difference
list the next 3 terms in the following sequence 1,2,4,8,16,32
Answer:
the next 3 terms are 64, 128, and 256
solve for x : 3/5(x + 2)= x-4
Answer:
x = 13
Step-by-step explanation:
Given
[tex]\frac{3}{5}[/tex](x + 2) = x - 4
Multiply through by 5 to clear the fraction
3(x + 2) = 5x - 20 ← distribute left side
3x + 6 = 5x - 20 ( subtract 5x from both sides )
- 2x + 6 = - 20 ( subtract 6 from both sides )
- 2x = - 26 ( divide both sides by - 2 )
x = 13
Describe a way to calculate 304-81 mentally by using reasoning other that the common subtraction algorithm. Then write a coherent sequence of equations that correspond to your reasoning
Answer:
See explanation
Step-by-step explanation:
To subtract mentally 81 from 304, complete following steps:
Step 1: Write number 304 as
[tex]304=300+4\\ \\304=200+100+3+1\\ \\304=200+20+80+3+1[/tex]
Step 2: Write number 81 as
[tex]81=80+1[/tex]
Step 3: Now subtract 80 and 1 from number 304:
[tex]304-81=(200+20+80+1+3)-(80+1)\\ \\304-81=200+20+3\\ \\304-81=223[/tex]
Final answer:
To mentally subtract 304-81, round 81 to 100, subtract from 304 to get 204, then add back the difference (19) for a result of 223.
Explanation:
To calculate 304-81 mentally, we can round 81 up to 100 to make the numbers easier to work with. We know that 304 - 100 = 204.
Since we've subtracted too much by rounding up, we need to add back the difference between 81 and 100, which is 19.
So the full calculation would be 304 - 81 = 304 - 100 + 19 = 204 + 19 = 223.
The coherent sequence of equations aligning with this reasoning would be:
304 - 100 = 204 (rounding 81 up to 100 and subtracting)100 - 81 = 19 (finding the difference between the rounded number and the original number)204 + 19 = 223 (adding the difference back)Please help me, please?
The answer is 14 2/3
I hoped this helped youuuuu!!!!!
Find the distance between (-7, 10) and (-3, 6). Round your answer to the nearest tenth, if necessary.
Answer:
5.7
Step-by-step explanation:
x^3-64 in factored form
Answer: (x−4)(x2+4x+16)
Step-by-step explanation:
x^3 − 64 ←is a difference of cubes
. xa^3 −b^3 = ( a − b ) (a^2 + ab + b^2)
here a = x and b =4 → (4)^3 = 64
⇒ x^3 − 64 = (x − 4) (x^2 + 4x + 16 )
Answer:
[tex][{x}^{2} + 4x + 16][x - 4][/tex]
Step-by-step explanation:
Take the cube root of this expression using the Difference of Cubes [(a + b)(a² - 2ab + b²)]:
[tex]x - 4 = \sqrt[3]{{x}^{3} - 64}[/tex]
Now, since the divisor\factor is in the form of [tex]x - c[/tex], use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:
4| 1 0 0 −64
↓ 4 16 64
__________
1 4 16 0 → [tex]{x}^{2} + 4x + 16[/tex]
You start by placing the c in the top left corner, then list all the coefficients of your dividend [x³ - 64]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², the 4x follows right behind it, and bringing up the rear, 16, giving you the other factor of [tex]{x}^{2} + 4x + 16[/tex]. Attach this to the first factor you started out your work on:
[tex][x - 4][{x}^{2} + 4x + 16][/tex]
I am joyous to assist you anytime.
Driving to your friend's house, you travel at an average rate of 35 miles per hour. On your
home, you travel at an average rate of 40 miles per hour. If the round trip took you 45 minutes
how far is it from your house to your friend's house?
Answer:
14 miles.
Step-by-step explanation:
Let the distance traveled from home to destination = x miles.
Speed while going to friend's house = 35 miles per hour.
Speed while coming back = 40 miles per hour.
Total Time taken for the journey = 45 minutes = 0.75 hours.
Let the time taken while going to friend's house = y hours.
Therefore, the time taken while going to friend's house = (0.75 - y) hours.
To find x and y, model the speeds of both the journeys.
Speed while going to friend's house = Distance/Time.
35 = x/y.
x = 35y (Equation 1).
Speed while coming back = Distance/Time.
40 = x/(0.75 - y).
x = 40(0.75 - y) (Equation 2).
Since x = x, therefore:
35y = 30 - 40y.
75y = 30.
y = 30/75.
y = 0.4 hours.
Put y = 0.4 hours in Equation 1:
x = 35y.
x = 35(0.4).
x = 14.
Therefore, the distance between my friend's house and my house is 14 miles!!!
Answer:
The distance from my house to friend's house is 14 miles
Step-by-step explanation:
* Lets explain how to solve the problem
- Driving to the friend's house rate is 35 miles per hour
- Driving to my home rate is 40 miles per hour
- The round trip took 45 minutes
- We need to find the distance from my house to my friend's house
* At first lets change 45 minutes to hour because the rate of driving
unit is miles per hour
∵ 1 hour = 60 minutes
∴ 45 minutes = [tex]\frac{45}{60}=\frac{3}{4}[/tex] hour
- Assume that the distance from my house to friend's house is d,
the time for the trip from my house to the friend's house is [tex]t_{1}[/tex]
and the time from friend's house to my house is [tex]t_{2}[/tex]
∵ The distance between the two houses is d
∵ Distance = rate of driving × time of the trip
∴ d = 35 × [tex]t_{1}[/tex] = [tex]35t_{1}[/tex]
∴ d = 40 × [tex]t_{2}[/tex] = [tex]40t_{2}[/tex]
- Equate the two equations
∴ [tex]35t_{1}[/tex] = [tex]40t_{2}[/tex]
- Divide both sides by 35
∴ [tex]t_{1}=\frac{40}{35}t_{2}=\frac{8}{7}t_{2}[/tex]
∴ [tex]t_{1}=\frac{3}{4}t_{2}[/tex] ⇒ (1)
- The time of the round trip is [tex]\frac{3}{4}[/tex] hour
∴ [tex]t_{1}+t_{2}=\frac{3}{4}[/tex] ⇒ (2)
- Substitute equation (1) in equation (2)
∴ [tex]\frac{8}{7}t_{2}+t_{2}=\frac{3}{4}[/tex]
∴ [tex]\frac{15}{7}t_{2}=\frac{3}{4}[/tex]
- Divide Both sides by [tex]\frac{15}{7}[/tex]
∴ [tex]t_{2}=0.35[/tex] hour
∵ d = [tex]40t_{2}[/tex]
- Substitute the value of [tex]t_{2}[/tex] in the equation above
∴ d = 40(0.35) = 14
∵ d represents the distance from my house to friend's house
∴ The distance from my house to friend's house is 14 miles
When writing an inequality how would you right x not equal to 25
Answer:
≠
Step-by-step explanation:
it would be unequal to
If, for a certain function, f(x)= 51, calculate the following values.
a.
f(x)-8
b.
1/2f(x)
c.
1/2f(x)-8
Answer: (a) 43 (b) 25.5 (c) 17.5
Step-by-step explanation:
f(x) = 51
Replace f(x) with 51
a) f(x) - 8 = 51 - 8 = 43
[tex]b)\quad \dfrac{1}{2}f(x)\qquad =\dfrac{1}{2}\cdot 51\qquad =\dfrac{51}{2}\qquad =25.5[/tex]
[tex]c)\quad \dfrac{1}{2}f(x)-8\qquad =25.5-8\qquad =17.5[/tex]
Select the correct answer.
If the function 5x + y=1 has the domain (-2, 1, 6), then what is the corresponding range?
A. {-9,6,31}
B. {9, -6, -31)
C. {-11, 4, 29}
D. (11,-4,-29)
Answer:
answer is D
Step-by-step explanation:
5(-2) + y = 1 5(1) + y = 1 5(6) + y = 1
-10 + y = 1 5 + y = 1 30 + y = 1
y - 10 = 1 y + 5 = 1 y + 30 = 1
y = 11 y = -4 y= -29
The corresponding range function 5x + y=1 which has the domain (-2, 1, 6) will be option (D) {11,-4,-29}
Corresponding rangeA function is a correspondence or rule that assigns to each element in one set, called the domain D, exactly one element from a second set, called the range R.
How to solve this problem?The Steps are as follow:
GivenFunction = 5x + y = 1
domain = (-2 , 1, 6)
Corresponding range = ?
According to subject x ∈ {-2,1,6}So we will put the value of x as -2 ,1, 6 in function to find corresponding range which will be as follow:let x = -2
∴ 5x + y =1
∴ 5(-2) + y =1
∴ -10 + y =1
∴ y = 11
x = 1
∴ 5x + y = 1
∴ 5(1) + y = 1
∴ 5 + y = 1
∴ y = -4
x = 6
∴ 5x + y =1
∴ 5(6) + y = 1
∴ 30 + y =1
∴ y = -29
So the corresponding range function 5x + y=1 which has the domain (-2, 1, 6) will be option (D) {11,-4,-29}
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“Seven less than a number squared”
Answer:
7-x^2
Step-by-step explanation:
The required expression will be x² - 7
Expressions are functions separated by an operation sign.
For the given statement:
Let the unknown number be xThe square of the number will be x²7 less than number means we are to subtract 7 from the result x² as shown
F(x) = x² - 7
Hence the required expression will be x² - 7
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L=4/3(C-30) solve for C literal equation
Answer:
C = [tex]\frac{3L+120}{4}[/tex]
Step-by-step explanation:
Given
L = [tex]\frac{4}{3}[/tex](C - 30)
Multiply through by 3 to clear the fraction
3L = 4(C - 30) ← distribute
3L = 4C - 120 ( add 120 to both sides )
3L + 120 = 4C ( divide both sides by 4 )
[tex]\frac{3L+120}{4}[/tex] = C
(PLEASE HELP ME IM STRUGGLING) (picture is shown) Here is an illustration of a four way stop. those roads are two lines and they intersect at a.....???
The roads are two lines and they intersect at 90° .
What is intersection of line?Intersecting lines cross each other at some arbitrary angle .
What are perpendicular lines?Two geometric objects are perpendicular if they intersect at a right angle. A line is said to be perpendicular to another line if the two lines intersect at a right angle.
According to the question
Roads have 2 lanes and have crossing lane .
Now,
Those roads are two lines and they intersect at a right angle by making 90° at there point of intersection .
So,
They are perpendicular lines .
Hence, the roads are two lines and they intersect at 90° .
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Simplify the square root of 16 plus the square root of 40
√16 + √40 = √4×4 + √4×10
= 4 + √2×2×10
= 4 + 2√10
If you need a better explanation just as in the comments.
Happy to help! Please mark as BRAINLIEST! Thanks
Answer:
4+ 2*√10
Step-by-step explanation:
√16 = 4
√40 = √4* √10
√4=2
√40 = 2 *√10
the square root of 16 plus the square root of 40 simplified is
4+ 2*√10