The 7th term of the geometric sequence described by this explicit formula [tex]a_{n}=7*3^{(n-1)}[/tex] is 5103 ⇒ answer D
Step-by-step explanation:
The explicit formula of nth term in the geometric sequence is
[tex]a_{n}=a(r)^{n-1}[/tex] , where
a is the first termr is the common ratio between each two consecutive terms∵ The explicit formula of a geometric sequence is [tex]a_{n}=7*3^{(n-1)}[/tex]
∵ The explicit formula of nth term in the geometric sequence
is [tex]a_{n}=a(r)^{n-1}[/tex]
∴ a = 7 and r = 3
∵ We need to find the 7th term
∴ n = 7
- Substitute n by 7 in the formula
∴ [tex]a_{7}=7*3^{(7-1)}[/tex]
∴ [tex]a_{7}=7*3^{(6)}[/tex]
∵ [tex]3^{(6)}=729[/tex]
∴ [tex]a_{7}=7(729)[/tex]
∴ [tex]a_{7}=5103[/tex]
The 7th term of the geometric sequence described by this explicit formula [tex]a_{n}=7*3^{(n-1)}[/tex] is 5103
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Use substitution or elimination to solve each system of equations y=3x
X+y=4
Answer:
(1, 3 )
Step-by-step explanation:
Given the 2 equations
y = 3x → (1)
x + y = 4 → (2)
Substitute y = 3x into (2)
x + 3x = 4, that is
4x = 4 ( divide both sides by 4 )
x = 1
Substitute x = 1 into (1) for corresponding value of y
y = 3 × 1 = 3
Solution is (1, 3 )
Answer:
x = 1 & y = 3
Step-by-step explanation:
y = 3x -----(1)
x + y = 4 -------(2)
sub(1)into(2)
x + 3x = 4
4x = 4
x = 1
sub x=1 into(1)
y = 3(1)
y = 3
14 POINTS!!!!
Use the function to fill in the blanks in the table.
x f(x)
-2
-1
0
1
2
A computer repair company charges the free and an hourly change after 2 hours to repair bill is $110 and after 3 hours day is 150 how much would it cost for 1.5 hours of work
Answer:
$60
Step-by-step explanation:
Let the company's fixed charge be "x"
And let the the hourly rate be "h"
Firstly, 2 hours + fixed = $110, we can write:
2h + x = 110
Next, 3 hours + fixed = $150, we can write:
3h + x = 150
We multiply the first equation by "-1" to get:
-1 * [2h + x = 110] = -2h - x = -110
Now we add this equation to the 2nd:
3h + x = 150
-2h - x = -110
-------------------
h = 40
Hence, the hourly rate is $40
So, it would cost 1.5 * 40 = $60 for 1.5 hours
complete the square tov rewrite y=x^2+6x+2 in vertex form. then state whether the vertex is maximum or minimum and give its coordinates.
Answer:
x^2+6x+2 = (x+3)²-7
the vertex is minimum and its coordinates is (-3,-7)
Look at the photo below for more info.
(10.5-7)+(4x3) help please
Answer: 15.5
Step-by-step explanation:
(10.5-7)+(4x3)
following PEDAS we do operations in parentheses first
10.5-7=3.5
4x3=12
we now have 3.5+12 as our intermediate expression
and 3.5+12 = 15.5
Answer:
15.5
Step-by-step explanation:
(10.5-7)+(4*3)
3.5+12
15.5
Two identical cars need to fit into a small garage. The opening is 23 feet 6 inches wide, and there must be at least 3 feet 6 inches of clearance between the cars and between the edges of the garage. How wide can the cars be?
To fit two identical cars in a 23-foot 6-inch wide garage with 3 feet 6 inches clearance on each side and between the cars, the cars must each be 6 feet 6 inches wide.
Explanation:The subject matter of your question is a math problem involving subtraction and division. To find out how wide the cars can be, you first need to determine the total available space for the cars. The total width of the garage is 23 feet 6 inches. However, you need to leave room for clearance on either side of the cars and in between them. The clearance is a total of 3 feet 6 inches multiplied by 3 (one for each side and one for between the cars), which is 10 feet 6 inches. Subtract this from the total width of the garage, and you get 13 feet available for the cars. Since the cars are identical, you simply divide this by 2. Each car can be 6 feet 6 inches wide.
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daniella wants to run a total of 3,600 laps during the next 52 weeks. What is the total number of laps she will run if she runs 70 laps each week for 50 weeks? Write an equation
Answer:
3500
Step-by-step explanation:
I divided everything and I ended up just multiplying 70x50 which got me 3500. I'm sorry, but I don't know in what way to write the equation. I don't know if it's y=mx+b or some other way. all I was able to come up with was y=50x+70
What is the product of (-6)(-7)(-1)?
оооо
Answer:
-42
Explanation:
(-6)(-7)(-1)
do (-6)(-7)
-negative sign and -negative sign= +positive sign
(-6)(-7)=42
(42)(-1)
+positive sign and -negative sign=-negative sign
answer:
-42
The salaries of three employees are listed below. Each employee was recently given a raise. Which amount is closest to the total of all three raises?
Answer:
A
Step-by-step explanation:
We take the percentage raise and convert to decimal by dividing by 100. Then multiply this with the salary before raise. This will give us the "raise amount".
Then we will add up all of the "raises" of 3 employees to get our answer.
Jane = 4/100 = 0.04
0.04*41,500 = 1660
John = 4.5/100 = 0.045
0.045 * 44,100 = 1984.5
Jack = 3/100 = 0.03
0.03 * 39,600 = 1188
Sum of all 3 raises:
1660 + 1984.5 + 1188 = $4832.5
From the answer choices, A is the closest, $4833
erica says that the expression 4x has one term is she correct explain
Answer: Yes
Step-by-step explanation: Erica would be correct. 4x is called a term. When we see a variable next to a number which in this case is X, it's important to understand that this means multiplication.
We can also say that the expression 4x is a product of both 4 and X.
Final answer:
Erica is correct; the expression 4x is considered one term because it consists of a single element with a coefficient and a variable multiplied together.
Explanation:
Erica is correct in saying that the expression 4x has one term. In mathematics, a term is a single mathematical expression that may be a number, a variable, or numbers and variables multiplied together. The expression 4x consists of the number 4 and the variable x multiplied together, which forms a single term. It does not have any addition or subtraction signs that would separate it into multiple terms.
ANOTHER MATH QUESTION!! Please help me do this question and explain how you answer it thank you!!!
Answer:
[tex]y=8\cos \left(\dfrac{1}{2}x+\pi\right)+2[/tex]
Step-by-step explanation:
The equation of cosine function will be
[tex]y=a\cos (kx+b)+c[/tex]
Find [tex]a:[/tex]
The minimum y is [tex]y_{min}=-6,[/tex] the maximum y is [tex]y_{max}=10,[/tex] so
[tex]a=\dfrac{1}{2}\cdot |-6-10|=\dfrac{1}{2}\cdot 16=8[/tex]
Find [tex]k:[/tex]
The period of the function is [tex]T=4\pi,[/tex] so
[tex]T=\dfrac{2\pi }{k}\Rightarrow k=\dfrac{2\pi }{4\pi }=\dfrac{1}{2}[/tex]
Find [tex]b:[/tex]
At [tex]x=0,\ y=y_{min}=-6[/tex]
Function [tex]y=\cos x[/tex] at [tex]x=0[/tex] has the value [tex]y=y_{max}=1,[/tex] so [tex]b=\pi[/tex] [translate by one-fourth of the period]
Find [tex]c:[/tex]
The graph has the midline [tex]y=\dfrac{10-6}{2}=2,[/tex] so [tex]c=2.[/tex]
Hence,
[tex]y=8\cos \left(\dfrac{1}{2}x+\pi\right)+2[/tex]
Justin got a sack of Jelly beans in 5 different colors. Half if them were red,1/6 were green,1/6 were yellow,1/12 were orange, and 6 were black. How many of each color did he get, and how many jelly beans were there in all
Answer:
Total number of Jelly beans in the sack = 72
Number of red beans = 36
Number of green beans = 12
Number of yellow beans = 12
Number of orange beans = 6
Number of black beans = 6
Step-by-step explanation:
Let total number of jelly beans be =[tex]x[/tex]
We are given fractions of different colors of beans. To find the exact number of beans we need to multiply the fraction with the total number of beans.
Fraction of total are red beans = [tex]\frac{1}{2}[/tex]
Number of red beans = [tex]\frac{1}{2}\times x= \frac{x}{2}[/tex]
Fraction of total are green beans = [tex]\frac{1}{6}[/tex]
Number of green beans = [tex]\frac{1}{6}\times x= \frac{x}{6}[/tex]
Fraction of total are yellow beans = [tex]\frac{1}{6}[/tex]
Number of yellow beans = [tex]\frac{1}{6}\times x= \frac{x}{6}[/tex]
Fraction of total are orange beans = [tex]\frac{1}{12}[/tex]
Number of orange beans = [tex]\frac{1}{12}\times x= \frac{x}{12}[/tex]
Number of black beans = 6
Total number of beans can be given as
[tex] \frac{x}{2}+\frac{x}{6}+\frac{x}{6}+\frac{x}{12}+6[/tex]
Since we assumed total number of beans to be [tex]x[/tex], so we have.
[tex] \frac{x}{2}+\frac{x}{6}+\frac{x}{6}+\frac{x}{12}+6=x[/tex]
Multiplying each term by 12 to remove fractions.
[tex] (12\times\frac{x}{2})+(12\times\frac{x}{6})+(12\times\frac{x}{6})+(12\times\frac{x}{12})+(12\times6)=12\times x[/tex]
[tex]6x+2x+2x+x+72=12x[/tex]
combining like terms.
[tex]11x+72=12x[/tex]
Subtracting both sides by [tex]11x[/tex]
[tex]11x+72-11x=12x=11x[/tex]
[tex]72=x[/tex]
∴ [tex]x=72[/tex]
Total number of Jelly beans in the sack = 72
Number of red beans = [tex]\frac{1}{2}\times 72= 36[/tex]
Number of green beans = [tex]\frac{1}{6}\times 72= 12[/tex]
Number of yellow beans = [tex]\frac{1}{6}\times 72= 12[/tex]
Number of orange beans = [tex]\frac{1}{12}\times 72= 6[/tex]
number of black beans = 6
Justin has 72 jelly beans in total. By dividing the total number accordingly, he has 36 red, 12 green, 12 yellow, 6 orange, and 6 black jelly beans.
Explanation:Calculating the Number of Jelly BeansLet's assume the total number of jelly beans Justin has is represented by the variable x. We know that half of them are red, so there are x/2 red jelly beans. Similarly, since 1/6 are green and another 1/6 are yellow, there are x/6 green jelly beans and x/6 yellow jelly beans. As for the orange jelly beans, they represent 1/12 of the total, which means Justin has x/12 orange jelly beans. We are given that there are 6 black jelly beans, which do not need to be divided into fractions. To find the total, x, we can write an equation considering all the portions mentioned and the known number of black jelly beans:
x/2 (red) + x/6 (green) + x/6 (yellow) + x/12 (orange) + 6 (black) = x
Finding a common denominator (12), we rewrite the equation:
6x/12 + 2x/12 + 2x/12 + x/12 + 6 = x
Combine like terms:
(6x + 2x + 2x + x)/12 + 6 = x
11x/12 + 6 = x
To solve for x, subtract 11x/12 from both sides:
6 = x - 11x/12
6 = x(12/12) - 11x/12
6 = (12x - 11x)/12
6 = x/12
Multiplying both sides by 12 gives us:
x = 72
So, Justin has a total of 72 jelly beans. Calculating the number for each color:
Red: x/2 = 72/2 = 36 red jelly beansGreen: x/6 = 72/6 = 12 green jelly beansYellow: x/6 = 72/6 = 12 yellow jelly beansOrange: x/12 = 72/12 = 6 orange jelly beansBlack: Given as 6 black jelly beansIn conclusion, Justin has 36 red, 12 green, 12 yellow, 6 orange, and 6 black jelly beans, adding up to a total of 72 jelly beans.
Can someone help, I’ve been trying to figure this out but just can’t
Answer:
Step-by-step explanation:
Tip: say they are congruent if they have the same lines and seem to be same size of triangles.
For the how do you know part it can only be SSS, SAS, or SSA Good Luck Tried my best :).
Which polynomial is in standard form? A) 5x6 − 6x8 + 7x9 + 9 B) x2 + 2x3 − 3x4 + 3x5 C) 3x3 − 5x2 + 7x4 + 9x3 D) 2x5 − 6x3 + 3x2 − x
Answer: choice D
2x^5 - 6x^3 + 3x^2 - x
Explanation:
Polynomials in standard form always have the exponents decrease (ie go from largest to smallest) when we read from left to right. For choice D, the exponents from left to right are: 5, 3, 2, 1. This is decreasing order. The other answer choices do not have the exponents in decreasing order. The degree of the polynomial in choice D is a 5th degree polynomial since 5 is the largest exponent.
If the measure of angle QNT is 74,what is the measure of QPN?
Answer:
The answer is 148 degrees
Step-by-step explanation:
I'm pretty sure it is 148°... In my notes it says "if a tangent to a circle & a chord intersect at a point on the circle, then the measure of each angle they form is one-half the measure of its intercepted arc." Hope this helps...
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The measure of arc QPN is 148° if the measure of angle QNT is 74°.
Given a circle with center O.
TS is the tangent of the circle at point N.
From the figure, we have, ∠ONT = 90°, since the angle formed at the tangent by the diameter is always the right angle.
Now,
m∠ONT = m∠QNT + m∠ONQ
Substitute the values.
90° = 74° + m∠ONQ
m∠ONQ = 90 - 74 = 16°
Now, from triangle QNO, OQ = ON, since, both are radii of the same circle.
The angle which lies opposite to these sides will be also equal.
So, m∠ONQ = m∠OQN = 16°.
Now, by the angle sum property of a triangle, the sum of the interior angles of a triangle is 180°.
So,
m∠ONQ + m∠OQN + m∠QON = 180°
16° + 16° + m∠QON = 180°
m∠QON = 180° - (16° + 16°)
m∠QON = 148°
The measure of arc QPN is equal to the central angle = 148°
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The complete question is given below:
Bill wants to make 22 small pizzas for a party. He has 16 cups of flour. Each pizza crust takes - cup of flour. Doe
he have enough flour?
3
You left out how much flour each pizza needs. Without that info no one can answer teh question.
the following frequency table shows the number of hours of sleep that each of the staff members at tia’s toy store got on thanksgiving night . How many employees work at Tia’s toy store?
Answer:
Total number of employees at Tia's toy store [tex]=9[/tex]
Step-by-step explanation:
To find the number of employees who worked on Tia's store .
We have to add the total number of values from the employee column.
As the question mentioned.
Each of the staff members have different number of hours of sleep on thanksgiving night.
So
The summation of the number of employees from the frequency table
[tex]=(1+0+4+2+1+1)=9[/tex]
So there are [tex]9[/tex] employees working on thanksgiving night in Tia's store.
A line that is perpendicular to y = -1 is a vertical line. Vertical lines have an undefined slope. True False
Answer:
True
Step-by-step explanation:
Horizontal lines with equation y = c where c is the value of the y- coordinates the line passes through are parallel to the x- axis and have a slope of zero.
Vertical lines with equation x = c where c is the value of the x- coordinates the line passes through are parallel to the y- axis and have an undefined slope.
Please help! The question is in the pic!
Answer:
B. -x + 8
Step-by-step explanation:
Given expression
[tex]\dfrac{8-4(x-6)}{4}[/tex]
Consider the numerator [tex]8-4(x-6).[/tex]
First, use distributive property:
[tex]8-4(x-6)=8-(4x-24)[/tex]
Open the brackets:
[tex]8-(4x-24)=8-4x+24[/tex]
Combine the like terms:
[tex]8-4x+24=(8+24)-4x=32-4x[/tex]
Again use distributive property:
[tex]32-4x=4\cdot 8-4x=4(8-x)[/tex]
Now, the expression is
[tex]\dfrac{4(8-x)}{4}=8-x\ \text{or}\ -x+8[/tex]
At an all you can eat barbecue, adults pay $8 and children pay $5. 140 people attend you raise $856. What’s the total number adults and children?
The number of adults was 52 and number of children was 88.
Step-by-step explanation:
Cost for one adult = $8
Cost for one child = $5
People attended = 140
Amount raised = $856
Let,
x be the number of adult
y be the number of children
According to given statement;
x+y=140 Eqn 1
8x+5y=856 Eqn 2
Multiplying Eqn 1 by 8'
[tex]8(x+y=140)\\8x+8y=1120\ \ \ Eqn\ 3\\[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](8x+8y)-(8x+5y)=1120-856\\8x+8y-8x-5y=264\\3y=264[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3}=\frac{264}{3}\\y=88[/tex]
Putting y=88 in Eqn 1;
[tex]x+88=140\\x=140-88\\x=52[/tex]
The number of adults was 52 and number of children was 88.
Keywords: linear equations, subtraction
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Mr.marichal has quarters ,dimes,and pennies in a jar.he has twice as many quarters as oennies.he also has 5 more dimes than pennies.the total value of the coins is $6.60.how many of each type of coin does he have
He has 20 quarters, 15 dimes and 10 pennies.
Step-by-step explanation:
Let,
Quarters = x
Dimes = y
Pennies = z
We know that,
A quarter is 25 cents, dime is 10 cents and penny is 1 cent.
Total amount = $6.60 = 6.60*100 = 660 cents
According to given statement;
25x+10y+z=660 Eqn 1
x=2z Eqn 2
y=z+5 Eqn 3
Putting these values of x and y in Eqn 1
[tex]25(2z)+10(z+5)+z=660\\50z+10z+50+z=660\\61z=660-50\\61z=610\\[/tex]
Dividing both sides by 61;
[tex]\frac{61z}{61}=\frac{610}{61}\\z=10[/tex]
Putting z=10 in Eqn 2
[tex]x=2(10)\\x=20[/tex]
Putting z=10 in Eqn 3
[tex]y=10+5\\y=15[/tex]
He has 20 quarters, 15 dimes and 10 pennies.
Keywords: linear equations, substitution method
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5) V108
How do I simplify this
Answer:
[tex]\large\boxed{\sqrt{108}=6\sqrt3}[/tex]
Step-by-step explanation:
[tex]\sqrt{108}=\sqrt{4\cdot27}=\sqrt{4\cdot9\cdot3}\\\\\text{use}\ \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt4\cdot\sqrt9\cdot\sqrt3=2\cdot3\cdot\sqrt3=6\sqrt3\\==========================\\\\\sqrt{108}=\sqrt{36\cdot3}=\sqrt{36}\cdot\sqrt3=6\sqrt3\\\\==========================\\\\\begin{array}{c|c}108&2\\54&2\\27&3\\9&3\\3&3\\1\end{array}\qquad108=2^2\cdot3^2\cdot3\\\\\sqrt{108}=\sqrt{2^2\cdot3^2\cdot3}=\sqrt{2^2}\cdot\sqrt{3^2}\cdot\sqrt3\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=2\cdot3\cdot\sqrt3[/tex]
The coordinates of point S are (8.4). What are the
M 17, 3) is the midpoint of RS
coordinates of R?
Answer:
Co-ordinates of point R is (26,2)
Step-by-step explanation:
Given point:
Endpoint S(8,4)
Mid-point M of segment RS (17,3)
Let endpoint [tex]R[/tex] have co-ordinates [tex](x_2,y_2)[/tex]
Using midpoint formula:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are co-ordinates of the endpoint of the segment.
Plugging in values to find the midpoint of segment KN.
[tex]M=(\frac{8+x_2}{2},\frac{4+y_2}{2})[/tex]
We know [tex]M(17,3)[/tex]
So, we have
[tex](17,3)=(\frac{8+x_2}{2},\frac{4+y_2}{2})[/tex]
Solving for [tex]x_2[/tex]
[tex]\frac{8+x_2}{2}=17[/tex]
Multiplying both sides by 2.
[tex]\frac{8+x_2}{2}\times 2=17\times 2[/tex]
[tex]8+x_2=34[/tex]
Subtracting both sides by 8.
[tex]8+x_2-8=34-8[/tex]
∴ [tex]x_2=26[/tex]
Solving for [tex]y_2[/tex]
[tex]\frac{4+y_2}{2}=3[/tex]
Multiplying both sides by 2.
[tex]\frac{4+y_2}{2}\times 2=3\times 2[/tex]
[tex]4+y_2=6[/tex]
Subtracting both sides by 4.
[tex]4+y_2-4=6-4[/tex]
∴ [tex]y_2=2[/tex]
Thus co-ordinates of point R is (26,2) (Answer)
$4000 into a account with 4.8 percent interest assuming no withdrawals are made how much will be n account after 9 years
Answer:
$5728
Step-by-step explanation:
$4000 is deposited into an account with 4.8% interest.
We assume that there are no withdrawals from the account.
Then we are asked the determine the amount will be there in the account after 9 years.
From the formula of simple interest, the final amount in the account after 9 years will be [tex]4000(1 + \frac{4.8 \times 9}{100}) = 5728[/tex] dollars. (Answer)
133/13 as a mixed number
Answer:
10 3/13
Step-by-step explanation:
Answer:
[tex]\large\boxed{\dfrac{133}{3}=10\dfrac{3}{13}}[/tex]
Step-by-step explanation:
[tex]\dfrac{133}{13}=\dfrac{130+3}{13}=\dfrac{130}{3}+\dfrac{3}{13}=10+\dfrac{3}{13}=10\dfrac{3}{13}[/tex]
At the electronics store, television screens are sized by the lengths of their diagonals. The television that Mrs. Mallory wants to buy has a 25 inch diagonal. The width of the screen is 15 inches. What is the height of the screen?
Group of answer choices
10 inches
15 inches
20 inches
25 inches
Answer:
Pretty sure the answer is 20 :)
Answer:
20 inches
Step-by-step explanation:
From the question, diagonal of the television screen is given to be 25 inch and the width of the television set is given to be 15 inches and we are asked to find the height of the screen.
We can solve this question using the Pythagoras theorem.
The Pythagoras theorem states that in a right-angle triangle;
opposite² + adjacent² = hypotenuse²
From the question, the width is given to be 15 inches, the with is our adjacent. Also the diagonal is given to be 25 inches, the diagonal is our hypotenuse. And we were ask to find the height, the height is our opposite.
so;
opposite = ?
adjacent = 15
hypotenuse = 25
Let opposite = x
we can now substitute into our theorem;
opposite² + adjacent² = hypotenuse²
x² + 15² = 25²
x² = 25² - 15²
x² = 625 - 225
x² = 400
x = √400
x = 20
opposite = 20 inches
Since opposite is the height of the screen, then the height of the screen is 20 inches.
Therefore the height of the screen is 20 inches.
Write an equation in slope intercept form for the line with slope -2/3 and y-intercept -5
Answer:
[tex]y = - \frac{2}{3} x - 5[/tex]
Step-by-step explanation:
slope intercept form is y =mx+b
m is the slope
b is the y intercept
if you have any questions feel free to ask :)
Twenty pounds of strawberries are being shared equally by a group of friends.the equation 20 divided by 5=4 represents the division of strawberries
Answer:
a. 4 represents the amount of pounds of strawberries each friend got.
b. 4 represents the number of friends who were sharing the strawberries.
Step-by-step explanation:
The complete exercise is: "Twenty pounds of strawberries are being shared equally by a group of friends. The equation [tex]20\div5=4[/tex] represents the division of strawberries. a. If the 5 represents the number of people, what does the 4 represent?b. If the 5 represents the pounds of strawberries per person, what does the 4 represent?"You need to analize the information given in the exercise.
You know that the total amount of pounds of strawberries that are shared equally is:
[tex]Total=20\ lb[/tex]
a. Then if the group of people is formed by 5 friends, you need to divide the total pounds of strawberries that by 5 in order to calculate the amount of pounds of strawberries each one of them got.
If in the equation [tex]20\div5=4[/tex], 5 represents the number of people, then 4 represents the amount of pounds of strawberries each friend got.
b. If each person got 5 pounds of strawberries, you can calculate the number of friends who was sharing them by dividing the total pounds of strawberries by 5.
So, if in the equation [tex]20\div5=4[/tex], 5 represents the pounds of strawberries per person, then 4 represents the number of friends who were sharing the strawberries.
The mathematics problem given, namely 20 divided by 5 equals 4, represents the principle of equally distributing 20 strawberries among 5 friends. Each friend gets 4 strawberries.
Explanation:The subject of your question is mathematics. The equation 20 divided by 5 equals 4 represents how twenty pounds of strawberries can be equally divided among a group of five friends. This is a division problem, an essential operation in arithmetic.
The principle it is demonstrating is how to distribute something equally among a group. In this case, if we have 20 strawberries and need to distribute them evenly among 5 friends, each friend will receive 4 strawberries. This is represented mathematically as 20 (total strawberries) divided by 5 (number of friends) equals 4 (strawberries per friend). So, your equation is correct.
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what is the y-intercept of y= -3x
Answer:
c
Step-by-step explanation:
The slope-intercept form is y=mx+b, where m is the slope and
b is the y-intercept.
y=mx+b
m=−3
b=0
y=-3x+0
The required y-intercept of the given y = -3 is (0, 0)
Slope-intercept form of the line:
If the line have m slope and b as y-intercept then the equation of the line will be y = mx + b
How to find intercept?Here we have given that the equation of the line
y = -3x
Make this equation like general form of slope-intercept form
y = -3x + 0
Therefore comparing with general form we have
Slope m = -3
y-intercept = b = 0
The coordinate will be (0, 0)
Therefore the correct option is (c)
This is the conclusion to the answer.
Learn more about slope intercept form of the line here-
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You need to purchase a new cell phone plan. Company A offers 700 minutes of talk time per month but they charge 15 cents for every minute you go over the 700 included minutes. Company A will charge you $40 per month for this plan. Company B offers 500 minutes of talk time per month, but they charge only 5 cents per minute for exceeding the 500 minutes. Company B charges $50 per month for this plan. At what number of minutes per month would both plans charge the same amount?
Answer:
900 minutes
Step-by-step explanation:
Plan A: 700 free minutes + 15 cents per minute over 700 ($40)
Plan B: 500 free minutes + 5 cents per minute over 500 ($50)
The charges for x minutes (assumed x>700) for plan A will be
40+0.15(x-700)
The charges for x minutes (assumed x>500) for plan B will be
50+0.05(x-500)
To find the value of x where both charges are the same, we equate
40+0.15(x-700)=50+0.05(x-500)
Operating
40+0.15x-105=50+0.05x-25
Simplifying
0.10x=90
x=900 minutes
Both plans would charge the same amount when 900 minutes per month are used