An equation is formed of two equal expressions. The number is 4/3.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the unknown number be represented by x.
The given phrase can be written in the form of an expression "The sum of 1/2 and four times a number is equal to 5/6 subtracted from five times the number" as,
The sum of 1/2 and four times a number → (1/2) + 4x5/6 subtracted from five times the number → 5x - (5/6)Now, we can write the equation by equating the expressions together and then solving it for x,
(1/2) + 4x = 5x - (5/6)
(1/2) + (5/6) = 5x - 4x
x = (1/2) + (5/6)
x = (3/6) + (5/6)
x = 8/6
x = 4/3
Hence, the number is 4/3.
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Anya grandfather gives her a collection of souvenir subway tokens. He gives her 9 tokens from the 1980s. She wants to make a display of each type of token. She wants all three displays to have rows with the same number of tokens in them . Are the number of tokens in each of Anya's collections prime or composite numbers? Explain your reasoning
Please help! Need answered! Please and thank you.
Answer: (a) 5
Step-by-step explanation:
[tex]\lim_{x \to 2} 5[/tex] means what is the y-value when x = 2 .
The given equation is: y = 5 so the y-value is 5 for all values of x
Answer: (c) 13
Step-by-step explanation:
f(x) = x² + 5x
f'(x) = 2x + 5
f'(4) = 2(4) + 5
= 8 + 5
= 13
Answer: (c) 2
Step-by-step explanation:
The question is asking what the y-value is when x = -2. The graph shows that the coordinate (-2, 2) is on the curve. So, when x = -2, y = 2.
Answer:
lim x→2 5 =5
The slope is 13
lim x→-2 x^2 -2 =2
Step-by-step explanation:
lim x→2 5 =5
The limit of a constant is the constant
f(x) = x^2 +5x
We need to take the derivative
f'(x) = 2x+5
Then evaluate the derivative at x=4 (4,36)
f'(4) = 2*4 +5
= 8+5
= 13
The slope is 13
lim x→-2 x^2 -2 =2
Looking at the graph, the value of the function at -2 is about 2
We can also calculate it (-2)^2 -2 = 4-2 = 2
How much water should we add to 35kg of sugar syrup to change it's concentration from 30% to 25%
Answer:
Water = 1/5 of the volume of the syrup
Step-by-.step explanation:
Suppose we had 1000 cm^3 of syrup and the new volume after adding water is x cm^3. Now the amount of sugar stays the same so we have the equation 35 * 1000 = 25 * x
x = (30 * 1000) / 25 = 30,000 / 25
= 1200 cm^3
So we need to add 200 cm^2 of water .
In general terms, we need to add water which equals 1/5 of the volume of the syrup,
Use the substation to solve the system of equations choose the correct ordered pair y=6x-4 y=7x-7
Answer:
(x, y ) = (3, 14 )
Step-by-step explanation:
since both equations express y in terms of x, equate the right sides
7x - 7 = 6x - 4 ( subtract 6x from both sides )
x - 7 = - 4 ( add 7 to both sides )
x = 3
substitute x = 3 into either of the 2 equations for y
using y = 6x - 4 = (6 × 3 ) - 4 = 18 - 4 = 14
solution is (3, 14 )
Circle A has a radius with the length of 5 units. Calculate the exact length of the apothem, line segment AH . In your final answer, include your calculations.
ΔAED is the equilateral triangle. Therefore AH is a height of this triangle.
The formula of a height of an equilateral triangle:
[tex]h=\dfrac{a\sqrt3}{2}[/tex]
We have a = 5. Substitute:
[tex]\boxed{AH=\dfrac{5\sqrt3}{2}}[/tex]
You can use the Pythagorean theorem.
[tex]EH^2+AH^2=AE^2\\\\\left(\dfrac{5}{2}\right)^2+AH^2=5^2\\\\\dfrac{25}{4}+AH^2=25\\\\AH^2=25-\dfrac{25}{4}\\\\AH^2=\dfrac{100}{4}-\dfrac{25}{4}\\\\AH^2=\dfrac{75}{4}\to AH=\sqrt{\dfrac{75}{4}}\\\\AH=\dfrac{\sqrt{75}}{\sqrt4}\\\\AH=\dfrac{\sqrt{25\cdot3}}{2}\\\\\boxed{AH=\dfrac{5\sqrt3}{2}}[/tex]
If Circle A has a radius with the length of 5 units then the exact length of the apothem is 5√3/2
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Circle A has a radius with the length of 5 units.
We have to find the length of apothem
The formula of a height of an equilateral triangle
h=a√3/2
We have a = 5. Substitute:
h=5√3/2
Apply Pythagorean theorem.
(5/2)²+AH²=5²
25/4+AH²=25
AH²=25-25/4
AH²=75/4
Take square root on both sides
AH=5√3/2
Hence, if Circle A has a radius with the length of 5 units then the exact length of the apothem is 5√3/2
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Help with this question, please.
The limit of any constant function is the value of the constant, so the limit is just 5.
For this case we have that by definition:
The limit of a constant function of the form [tex]y = f (x)[/tex], where [tex]f (x) = c[/tex], is the same constant, whatever the value to which the limit tends.
Thus, the limit of "5" when x tends to "2", results in "5".
Answer:
5
Option A
Which statement correctly describes the end behavior of f(x)=ax+b, where a and b are positive numbers?
As x→∞, f(x)→∞, and as x→−∞, f(x)→∞.
As x→∞, f(x)→∞, and as x→−∞, f(x)→−∞.
As x→∞, f(x)→−∞, and as x→−∞, f(x)→∞.
As x→∞, f(x)→−∞, and as x→−∞, f(x)→−∞.
Answer:
The correct option is 2.
Step-by-step explanation:
The given function is
[tex]f(x)=ax+b[/tex]
Where, a and b are positive numbers.
The given function is the slope intercept form of a linear function. Where a is the slope and b is y-intercept.
Since slope is positive therefore function approaches to infinity as x approaches to infinity and function approaches to negative infinity as x approaches to negative infinity.
It is also proved by using limits.
[tex]lim_{x\rightarrow \infty}f(x)=lim_{x\rightarrow \infty}(ax+b)[/tex]
Apply limits.
[tex]lim_{x\rightarrow \infty}f(x)=a(\infty)+b=\infty[/tex]
Similarly,
[tex]lim_{x\rightarrow -\infty}f(x)=lim_{x\rightarrow -\infty}(ax+b)[/tex]
Apply limits.
[tex]lim_{x\rightarrow -\infty}f(x)=a(-\infty)+b=-\infty[/tex]
Therefore option 2 is correct.
[tex]f(x)\rightarrow \infty \text{ as }x\rightarrow \infty[/tex]
[tex]f(x)\rightarrow -\infty \text{ as }x\rightarrow -\infty[/tex]
Which choice does NOT represent the sample space for rolling a six-sided die one time?
Answer:
for imagine math it is the top left corner choice that says 1 with two lines coming from it and then a 2 and 3 from each line and so on until 6
Step-by-step explanation:
On Imagine math, It is the very first choice, with the 1 at the top and then the 2 and the 3, then the 4 and 5 and 6. Hope this helped!
Step-by-step explanation:
What is the distance to the earth’s horizon from point P?
Express your answer as a decimal
Answer:
The distance to the earth's horizon from point P is 216.2198187 mi, appriximately 216.22 mi
Step-by-step explanation:
This is a right triangle:
Hypotenuse: c=3959 mi + 5.9 mi → c=3964.9 mi
Leg 1: a=x=?
Leg 2: b=3959 mi
Using the Pytagorean theorem:
a^2+b^2=c^2
Replacing the known values:
(x)^2+(3959 mi)^2=(3964.9 mi)^2
Solving for x: Squaring:
x^2+15,673,681 mi^2=15,720,432.01 mi^2
Subtracting 15,673,681 mi^2 both sides of the equation:
x^2+15,673,681 mi^2-15,673,681 mi^2=15,720,432.01 mi^2-15,673,681 mi^2
x^2=46,751.01 mi^2
Square root both sides of the equation:
sqrt(x^2)=sqrt(46,751.01 mi^2)
x=216.2198187 mi
x=216.22 mi
The distance from the point P to the Earth’s horizon distance is approximately 216.22 mi.
To find the distance from the point P to the earth's horizon, we can use the concept of the earth's curvature.
The distance from the center of the earth to point P is the radius of the earth plus the distance from the center to the surface, which is 3959 + 3964.9 = 7923.9 miles.
The distance to the horizon can be found using the formula for the horizon distance, which is approximately equal to the square root of two times the product of the earth's radius and the total distance from P to the surface of the earth.
So, x = sqrt(2 * 3959 * 7923.9) = 216.22 mi.
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The probable question may be:
In the Earth center the radius of the earth is 3959 mi
P is a point outside the circle
the distance from center of the earth surface to point P is 3964.9 mi and the distance to the earth’s horizon from point P is x ?
Find x
Julia has 2 identical rooms in her house. If each room measures 8 fee on one side and 12 feet on another, what is the total area of the rooms?
Answer:
Step-by-step explanation:
all you have to is 8x12 multiplied by 2 since there is 2 rooms which is 192
What is the answer to this problem write the correct sign = or > or < 2/3 { } 4/5=
Answer:
2/3 < 4/5
Step-by-step explanation:
because:
2/3 = 0.666
4/5 = 0.8
Raul deposited $3000. Into a checking account that earned simple interest rate each year. After 3.5 years he earned $262.50 in interest. If no money was deposited or withdrawn from the account what was the annual interest rate?
It is 2.5 not what the other dude said it was
There are 32 students in Mrs. Worrell's Classroom. There 12 boys and 20 girls. She needs to select two students to represent her class for a Agora Student Math Department meeting. She will put all students names on a piece of paper and randomly select two names, one after the other. What is the probability that she will select a boy first and then a girl?
Answer:
15/64 = 23.4 %
Step-by-step explanation:
Let's consider the first two selections. Let's call B the case in which she extracts a boy and G the case in whish she extracts a girl.
For each selection, the probabilty of event B (selecting a boy) is
[tex]P(B)=\frac{12}{32}=\frac{3}{8}[/tex]
While the probability of event G (selecting a girl) is
[tex]P(G)=\frac{20}{32}=\frac{5}{8}[/tex]
We are asked to find the probability that the first two events are B and then G:
[tex]P(B,G)[/tex]
In the first two selections, we have 4 possible combinations:
BB, BG, GB, GG
The probability for each combination is given by:
[tex]P(BB)=P(B)\cdot P(B) = \frac{3}{8}\cdot \frac{3}{8}=\frac{9}{64}=14.1 \%[/tex]
[tex]P(BG)=P(B)\cdot P(G) = \frac{3}{8}\cdot \frac{5}{8}=\frac{15}{64}=23.4 \%[/tex]
[tex]P(GB)=P(G)\cdot P(B) = \frac{5}{8}\cdot \frac{3}{8}=\frac{15}{64}=23.4 \%[/tex]
[tex]P(GG)=P(G)\cdot P(G) = \frac{5}{8}\cdot \frac{5}{8}=\frac{25}{64}=39.1 \%[/tex]
The second one is the probability we are searching for, so the probability that she will select a boy first and then a girl is 15/64, or 23.4%.
Calculate the total cost of an item bought at a negotiated price of $17,250 with 7.7 percent sales tax and a $95 registration fee.
$17,250
$17,376.75
$18,673.25
$18,578.25
The answer is $18,673.25
use the given information to prove that m<QPS=m<TPV
To prove that m
To prove that m<QPS = m<TPV, we need to use the given information and apply the congruent triangles theorem. Let's assume that <QPS = <TPV. From the given information, we can determine that <QPS = I and <TPV = V. Since the angles are congruent and the corresponding sides are proportional, we can conclude that m<QPS = m<TPV.
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identify the value of p. Help Please!!
Answer:
Hello from MrBillDoesMath!
Answer:
p = 12
Discussion:
Assume we have a right trainload (looks like it but no angle indication given). By the Pythagorean Theorem
p^2 + 5^2 = (p+1) ^ 2 =>
p^2 + 25 = p^2 + 2p + 1 =>
25 = 2p + 1 => (subtract p^2 from both sides)
25 -1 = 2p => (subtract 1 from both sides)
24 = 2p =>
p = 24/2 = 12 => (divide both sides by 2)
Regards,
MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!
A recipe requires 1/4 lb of onions to make 3 servings of soup mark has 1.5 lbs of onions how amy sevings can mark make
Please give a step by step explanation if you can since I don't understand this.
Answer:
Red grapefruit costs more per pound.
Step-by-step explanation:
Red grapefruit
y =2x
This is in the form y= mx+b where m is the slope and b is the y intercept
The cost per pound is the slope, which is 2
The cost per pound is $2
Pink grapefruit
We need to find the slope
We have 2 points (0,0) and (4,4)
m = (y2-y1)/(x2-x1)
= (4-0)/(4-0)
=4/4
= 1
The slope is 1
The cost per pound is $1
Answer:
The red grapefruit.
Step-by-step explanation:
Let's think for a moment about what the equation [tex]y=2x[/tex] represents. For any value of x, our y is going to be double that. What do our y and our x represent, then? We're told that y represents the cost of the red grapefruit, and that x is the weight of that grapefruit in pounds. What our equation then tells us is that the cost (in dollars) of red grapefruit is always twice as much as its weight.
What about the pink grapefruit? Instead of an equation, we're given a line on a coordinate grid. Let's see if we can find a pattern here. The y axis is still cost, and the x axis is still weight. We see at the very beginning that when x = 0, y = 0 too. Finding a few more points, we can see that when x = 1, y = 1; when x = 2, y = 2; and when x = 3, y = 3. This pattern continues, and we can capture it with the equation [tex]y=x[/tex].
Comparing the two equations [tex]y=2x[/tex] (red grapefruit) and [tex]y=x[/tex](pink grapefruit) we can see that the cost of red grapefruit grows twice as fast as pink grapefruit. To see which one costs more per pound, we can simply set x = 1 to find that red grapefruit costs [tex]y=2(1)=\$2[/tex] per pound, while pink grapefruit costs [tex]y=\$1[/tex] per pound, and since [tex]\$2>\$1[/tex], the red grapefruit costs more.
Katherine is using a cone to fill a cylinder with sand. If the radius and height are equal on both objects, and Katherine fills the cone to the very top, how many cones will it take to fill the cylinder with sand? Explain your answer.
Using a stopwatch Tyrone determines it takes him 58.2 minutes to travel 30 miles to work the stopwatch measures to hundredths of a minute going by the accuracy of the stopwatch which is the most accurate determination for the number of feet per second Tyrone traveled on his way to work?
1 mile = 5,280 feet
1. 19.80 feet ps
2. 19.84 feet ps
3. 45.3 feet ps
4. 45.36 feet ps
Answer:
Correct choice is 4.
Step-by-step explanation:
Tyrone determines it takes him 58.2 minutes to travel 30 miles to work, then he travels with speed
[tex]\dfrac{30}{58.2}=\dfrac{300}{582}=\dfrac{50}{97}\ \text{miles per minute}.[/tex]
If 1 mile = 5,280 feet, then his speed is
[tex]\dfrac{50}{97}\cdot 5280=\dfrac{264000}{97}\ \text{feet per minute}.[/tex]
Since 1 minute = 60 seconds, then his speed is
[tex]\dfrac{264000}{97\cdot 60}=\dfrac{4400}{97}\approx 45.36\ \text{feet per second}.[/tex]
Answer:
45.36 feet ps IS THE ANSWER AND NOW GO AND SOLVE IT
Coco's garden has 88 tomato plants, 44 pepper plants, 33 squash plants, and 66 pumpkin plants. For every 77 plants in Coco's garden, there are 22 \_\_\_\_____ plants. Choose 1 answer: Choose 1 answer: (Choice A) A Tomato (Choice B) B Pepper (Choice C) C Squash (Choice D) D Pumpkin
Coordinate grid shown from negative 2 to positive 2 on x axis and negative 2 to positive 2 on y axis. There are increments of 1 over 4 for each grid line on each of the two axes. Only the whole numbers are labeled on either side of the axis. A point A is shown at the intersection of 5 grid lines to the left of the y-axis and 3 grid lines above the x-axis. What are the coordinates of point A? ( fraction negative 1 and 1 over 4, fraction 3 over 4) ( fraction 1 and 1 over 4, fraction negative 3 over 4) ( fraction negative 3 over 4, fraction 1 and 1 over 4) ( fraction 3 over 4, fraction negative 1 and 1 over 4)
Answer: (-5/4, 3/4) = (-1 1/4, 3/4)
Step-by-step explanation:
Left of y axis means x coordinate is negative
Above x axis means y coordinate is positive
Assume the vague description means there are 17 gridlines from -2 to 2,
-2.0, -1.75, -1.5, -1.25, -1.0, ..., 1.75, 2.0
A regulation soccer field has an area of 59,400 square feet. If the length is 330 feet, what is the width in feet
Answer:
The answer is 180 feet.
Step-by-step explanation:
Here's your equation. (330 x W = 59,400). If you want to find the width then divide 59,400 by 330 and you get 180 feet.
You can check by multiplying 330 and 180 which will result in 59,000.
So the correct answer is 180 feet.
Sophie and Elizabeth go to the movie theater and purchase refreshments for their friends. Sophie spends a total of $72.50 on 5 drinks and 5 bags of popcorn. Elizabeth spends a total of $163.50 on 15 drinks and 3 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a drink, to the nearest cent.
Find the value of 7v-10 given that -11v-7=4. Simplify your answer as much as possible.
First thing to do is solve the given equation for v
-11v-7 = 4
-11v = 4+7
-11v = 11
v = 11/(-11)
v = -1
Once we know this, we can use it to compute the following
7v-10 = 7*(-1) - 10 = -7 - 10 = -17
--------------------------------
Answer: -17
A case of pencils cost $15.If the academic team spends $135 on pencils for the school tournament,how many cases of pencils did the academic team buy?
Answer:
9
Step-by-step explanation:
135 / 15
During Christmas a book store sold 72 books. If the ratio of books to books marks sold was 9:2,how many bookmarks did the store sell
Answer:
16
Step-by-step explanation:
the 9 parts of the ratio is equivalent to 72 books
divide number of books by 9 to find one part of the ratio
[tex]\frac{72}{9}[/tex] = 8 ← 1 part of the ratio
2 parts = 2 × 8 = 16 ← number of bookmarks sold
This upcoming week is finals week, and I need help lol
Answer:
k=3
Step-by-step explanation:
Given equation is
[tex]x^2+y^2 -6y-12=0[/tex]
First we move -12 to the other side by adding 12 on both sides
[tex]x^2+y^2 -6y =12[/tex]
We apply completing the square method to get square form (y-k)^2
Lets take coefficient of y and then divide it by 2
-6 divide by 2 is -3
Then we square it (-3)^2 = 9
We add 9 on both sides
[tex]x^2+y^2 -6y + 9=12+9[/tex]
[tex]x^2+(y^2 -6y + 9)=21[/tex]
Now we factor, y^2 - 6y +9 is (y-3)(y-3)= (y-3)^2
[tex]x^2+(y-3)^3=21[/tex]
Now we compare with x^2 + (y-k)^2 = 21 and find the value of k
The value of k = 3
PLEASE HELP ME WITH THIS PROBLEMS 2.
Answer: y = 8ˣ
Step-by-step explanation:
y = bˣ substitute the coordinate (1, 8) for x and y and solve for b:
8 = b¹ ⇒ 8 = b
**********************************************************************************
Answer: [tex]P = 10e^{.22t}[/tex], 1964
Step-by-step explanation:
[tex]P = P_{0}e^{kt}[/tex]
= [tex]10e^{.22t}[/tex]
= [tex]10e^{.22(24)}[/tex]
= 1964
********************************************************************************
Answer: 10,147.47 ; 29,881.05
Step-by-step explanation:
[tex]A = Pe^{rt}[/tex]
= [tex]9000e^{.06(2)}[/tex]
= 10,147.47
[tex]A = Pe^{rt}[/tex]
= [tex]9000e^{.06(20)}[/tex]
= 29,881.05
Which of the following names a line segment
Answer:
The answer is C.
Step-by-step explanation:
A. name of ray
B. name of line
C. name of line segment
D. length of segment
Answer:
B is the answer
Step-by-step explanation: