Final answer:
To determine 'a' and 'd' for tn = a + (n-1)x, substitute the values of 'n' and 't' into the equations and solve the system of equations.
Explanation:
To determine 'a' and 'd' for tn = a + (n-1)x, we need to find the values of 'a' and 'd' that satisfy both t7 = 3 + 5x and t11 = 3 + 23x.
Step 1: Set up two equations
t7 = 3 + 5x
t11 = 3 + 23x
Step 2: Use the formula tn = a + (n-1)x to substitute the values of 'n' and 't' in the equations.
a + 6d = 3 + 5x (equation 1)
a + 10d = 3 + 23x (equation 2)
Step 3: Solve the system of equations.
Subtract equation 1 from equation 2: (a + 10d) - (a + 6d) = (3 + 23x) - (3 + 5x)
Cancel out the 'a' terms and simplify the 'd' and 'x' terms: 4d = 18x
Divide both sides by 18: d = 4.5x
Substitute the value of 'd' in equation 1 to solve for 'a': a + 6(4.5x) = 3 + 5x
Expand and simplify the equation: a + 27x = 3 + 5x
Subtract 5x from both sides: a + 22x = 3
Subtract 22x from both sides: a = 3 - 22x
So, the values of 'a' and 'd' are a = 3 - 22x and d = 4.5x.
how do I graph y=−2x?
Answer:
Use the slope-intercept form to find the slope and y-intercept.Slope:
2
Y-Intercept:
0
Any line can be graphed using two points. Select two
x
values, and plug them into the equation to find the corresponding
y
values.x
y
0
0
1
2
Graph the line using the slope and the y-intercept, or the points.
Slope:
2
Y-Intercept:
0
x
y
0
0
1
2
Step-by-step explanation:
Mr.Steve drove 92 miles using 4 gallons of gasoline. Find the unit rate of miles driven per gallon.
Answer:23
Step-by-step explanation:
92/4
There is a game at the carnival that costs $20 to play. There are two outcomes: either you win $100 , or you lose.
To play you roll a die. If a six appears you win; all other rolls you lose. What is the mean (or the expected value) of the game?
A. -$1.66
B. -$3.33
C. $1.66
D. $3.33
Answer:
I would say that the answer is a. because I would go with the lowest one knowing that if I roll anything other than six, I lose this game is designed for you to nearly lose, so I would go with the lowest choice which is a. since i have a lower chance at winning.
Step-by-step explanation: please mark this brainliest and I will be glad to help anytime.
Chris plants 40 pumpkin seeds in five equal how many seats does Chris Plant in each row? Make an array to represent the problem?
A theater charges $9.50 for adults and $6 for children. Which expression shows the total cost of buying 3 adult tickets and 2 children’s tickets?
Answer:9.5*3+6*2
Step-by-step explanation:
You multiply each price by the number that they want to buy
Every minute,
2.2
gallons of water flows from a shower. A family of
5
people showers for an average of
9
minutes per person every morning.
Answer:
Step-by-step explanation: If you are trying to figure out how many gallons the whole family uses, the answer is 99 gallons.The reason is is because it says 2.2 gallons a minute and it takes 9 minutes for a shower. So you multiply 9 by 2.2 which would give you 19.8. Then you multiply it by 5 isnce it says 5 people take a shower.
Answer:
99 gallons
Step-by-step explanation:
Let as assume we need to find how many gallons of water does the family use for showering every morning.
It is given that every minute 2.2 gallons of water flows from a shower.
Total number of family members = 5
Average time of shower = 9 minutes per person every morning.
Total time of shower = [tex]9\times 5=45[/tex] minutes
1 minute = 2.2 gallons
45 minute = 2.2 × 45 gallons
45 minute = 99 gallons
Therefore, in every morning 99 gallons of water was used by the family
Is 4/25 terminating or non-terminating?
Answer:
terminating decimal
Step-by-step explanation:
Terminating decimals stop, non terminating decimals go on forever.
4/25
Multiply the top and bottom by 4
4/25*4/4 = 16/100
.16
This is a terminating decimal
how to rewrite
[tex]5 {?}^{ - 2} [/tex]
Answer:
[tex]\frac{1}{25}[/tex]
Step-by-step explanation:
using the rule of exponents
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex], then
[tex]5^{-2}[/tex] = [tex]\frac{1}{5^{2} }[/tex] = [tex]\frac{1}{25}[/tex]
congruent by identifying all congruent corresponding parts
Answer:
Corresponding Parts of Congruent Figures. The word corresponding refers to parts that match between two congruent triangles. You can identify corresponding angles and corresponding sides. First, name the corresponding angles.
Step-by-step explanation:
In geometry, two figures are congruent if they have the same size and shape. To verify congruence, all corresponding sides and angles of two figures must match in size and measure. For instance, given two triangles ABC and DEF, they would be congruent if their corresponding sides and angles were equal.
Explanation:In geometric terms, two figures are congruent if they have the same size and shape. This means all corresponding sides and angles of the two figures are equal. In order to determine if two shapes are congruent, you need to match each part of one shape with a corresponding part on the other and see if they are of the same size and angle.
For instance, if you have two triangles ABC and DEF, these triangles would be congruent (often written as △ABC≅△DEF) if the sides AB=DE, BC=EF, and AC=DF and angles ∠A=∠D, ∠B=∠E and ∠C=∠F. This is the principle of corresponding parts of congruent figures being congruent.
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The internal dimension of a cylindrical container has a base area of 20 cm2 and a height of 10 cm. What is the internal volume of the container?
Answer:
As per the statement:
The internal dimension of a cylindrical container has a base area of 20 cm2 and a height of 10 cm.
Volume(V) of a cylinder is given by:
[tex]V =A \cdot h[/tex]
where
A is the area of the base cylinder and
h is the height of the cylinder
Substitute the value A = 20 cm square and h = 10 cm we have;
[tex]V=20 \cdot 10[/tex]
Simplify:
V = 200 cubic cm
Therefore, the internal volume of the container is 200 cubic cm
Answer:
200 cm³
Step-by-step explanation:
In question we have given the area and height of the internal dimension of a cylindrical container.We have to find volume of the container.
From question statement ,we observe that
Area=20 cm² and Height=10 cm
The formula to find volume is :
Volume= Area×Height
putting the values of area and height in above formula,we get
Volume= 20 cm²×10 cm
Volume= 200 cm³
Hence, The internal volume of the container is 200 cm³.
a factory makes parts for toys in different quantities,as shown in the table. how much would 11 part cost?
Answer can you show use the graph then i would be able to answer it
Find the area and perimeter of the triangle below. Show all work.
Answer:
Area = 20.52 cm^2 and Perimeter = 28.68 cm.
Step-by-step explanation:
Use Pythagoras theorem to find the base of the triangle.
a^2 = 6^2 - 3^2 = 27
a = sqrt27
b^2 = 9^2 - 3^2 = 72
b = sqrt72
Base = sqrt27 + sqrt72
= 13.68
So Area = 0.5 * 13.68 * 3
= 20.52 cm^2 (answer)
Perimeter = 9 + 6 + 13.68
= 28.68 ( answer).
Isabel is making bead necklaces.she wants to use thirty eight beads to make four necklaces.if she wants each necklace to have the same number of beads,how many beads will she have left over?
Answer:
Step-by-step explanation:
Make circles. 4 circles. Then divide the beads to your circles. The one's you have leftover is your remainder. Hope that helps.
Your odometer read 12,3686. You drove your car until the odometer read 16,282 and had used 203 gallons of gasoline. How many miles per gallon has your car been getting? Round answer to the nearest ten (10)
Answer:
80 miles per gallon
hope it helps
Step-by-step explanation:
to find the miles per gallon you would have to divide the miles driven (16,282) by gallons used (203) to find how many miles per gallon wasted
16,282 ÷ 203 = 80.2
80.2 rounded to the nearest 10 = 80 miles per gallon
Classify the sequence (an) =(1,16,31,46,...) as arithmetic, geometric, or neither. If there is not enough information to classify the sequence, choose not enough information.
Answer:
arithmetic
Step-by-step explanation:
It is arithmetic because the terms go up by 15 . That is the common difference is 15.
Answer:
it is an arithmetic sequence
Step-by-step explanation:
general formula of arithmetic progression is
an=a1+(n-1)d
we are given
a1=1
a2=16
we can find d
d=a2-a1=16-1=15
d=a3-a2=31-16=15
d=a4-a3=46-31=15
as we can see that there is a common difference d =15 between successive terms of the this sequence
hence it is a arithmetic sequence
how to answer this questions
The perimeter of a rectangular campsite is 64 cm and its area is 207 cm. Find the length and the breadth of the rectangle.
Answer: w = 9 cm, L = 23 cm
Step-by-step explanation:
P (Perimeter) = 2L(length) + 2w(width)
A (Area) = L (length) x w (width)
Use the formulas above to create a system of equations, then solve using the substitution method.
P = 2L + 2w
64 = 2L + 2w
32 = L + w
32 - w = L ←←← use this to substitute for L in the Area equation
A = L · w
207 = (32 - w)w
207 = 32w - w²
w² - 32w + 207 = 0
(w - 23)(w - 9) = 0
w - 23 = 0 w - 9 = 0
w₁ = 23 w₂ = 9
Now, solve for L:
L₁ = 32 - w₁ L₂ = 32 - w₂
= 32 - 23 = 32 - 9
= 9 = 23
We have 2 sets of solutions (w₁ , L₁) and (w₂ , L₂)
(23, 9) and (9, 23)
Notice that they are the same values but in reverse order. These are the dimensions of the rectangle. We generally consider width (w) to have the smaller value. So, w = 9 and L = 23
Jack is 5 times younger than her mother. In 6 years, Jack will be three times younger than her mother. How old is each now?
Answer:
Jack is 6 and Mom is 30
Step-by-step explanation:
J = Jacks age
M = Mom's age
5J = M
In 6 years, so add 6 to the age
3(J+6) = (M+6)
We have a system of 2 equations and 2 unknowns
Lets simplify the 2nd equation
3(J+6) = (M+6)
3J + 18 = M+6
Substituting M =5J
3J + 18 = 5J +6
Subtract 3J from each side
3J-3J + 18 = 5J-3J +6
18 = 2J+6
Subtract 6 from each side
18-6 = 2J+6-6
12 = 2J
Divide each side by 2
12/2 = 2J/2
6=J
Jack is 6
We still need to find Mom's age
M = 5J
= 5*6
=30
Mom is 30
The coordinate points below show part of the data collected by the cell phone company, where x is age in years and y is texting speed in words per minute.
(12, 16), (13, 18), (13, 10), (14, 16), (15, 9), (15, 8), (16, 17), (17, 23)
If this data was plotted on a scatterplot, would there be a relationship between the variables? If yes, explain the relationship.
Yes, there is a relationship. As age increases, texting speed also increases.
Yes, there is a relationship. As age increases, texting speed decreases.
Yes, there is a relationship. As texting speed decreases, age also decreases.
No, there is no clear relationship between age and texting speed.
Answer:
Correct choice is D
Step-by-step explanation:
Plot points (12, 16), (13, 18), (13, 10), (14, 16), (15, 9), (15, 8), (16, 17), (17, 23) on the coordinate plane. On this coordinate plane x represents age in years and y represents texting speed in words per minute.
Option A is false. Consider points A(12,16) and C(13,10). For these points x-coordinates increases, but y-coordinates decreases. Therefore, as age increases, texting speed doesn't increase.
Option B is false. Consider points A(12,16) and B(13,18). For these points both x-coordinates and y-coordinates increases. Therefore, as age increases, texting speed increases too.
Option C is false. Consider points C(13,10) and F(15,8). For these points y-coordinates decreases, but x-coordinates increases. Therefore, as texting speed decreases, age increases.
Option D is true, there is no clear relationship between age and texting speed.
Answer:
The Answer is D. No, there is no clear relationship between age and texting speed.
Step-by-step explanation:
Which equation does not represent a linear function?
a. y = 2
b. y = x^2 + 9
c. y = x
d. y = -8x + 1
My sister needs help! She’s in 3rd grade
Dylan opened a credit card account with $650.00 of available credit. Now that he has made some purchases, Dylan’s account only has $455.00 of available credit. What is the percentage decrease of the amount of available credit in Dylan’s account?
Answer:
32.5%
Step-by-step explanation:
The percentage decrease of available credit in Dylan's account is 30%. This was found by subtracting the new available credit from the original, dividing the difference by the original available credit, and multiplying by 100.
To calculate the percentage decrease of the available credit in Dylan's account, we need to first determine the amount of credit that has been used. The original available credit was $650.00, and it has decreased to $455.00 after some purchases. The difference between the two amounts is $650.00 - $455.00 = $195.00. This value represents the decrease in available credit.
Next, we calculate the percentage decrease by dividing the decrease by the original amount and multiplying by 100. So, the percentage decrease = ($195.00 / $650.00) × 100 = 30%.
an equation and the steps to solve it are shown below: 3x-1/5(10x+5)=6
[tex]3x-\dfrac{1}{5}(10x+5)=6\qquad\text{use distributive property}\\\\3x-\left(\dfrac{1}{5}\right)(10x)-\left(\dfrac{1}{5}\right)(5)=6\\\\3x-2x-1=6\qquad\text{add 1 to both sides}\\\\\boxed{x=7}[/tex]
Blockbuster is a store that used to rent videotapes to customers. They charged a $20 membership fee to open a new account. Then, they charged $3 per movie. Your parents had a goft card for $50. How many movies, m could they afford??? What’s the equation plzzz I will give you 100 points
Hello There,
The answer is:
10 movies
Hope this helps have a great day :)
Lee likes to water ski on his brother's boat and plans to ski for two days in a row. The boat takes two gallons of gas each hour to run. if the price of gas is $5 per gallon, how much money will he spend on gas just ski for 6 hours each day?
Answer:
120 dollars
Step-by-step explanation:
6 hours per day, for 2 days, leads to a total of 12 hours (2*6 = 12)
If it takes 2 gallons of gas to run the boat for 1 hour, then it will take 24 gallons to run for 12 hours. We can see this if we have the ratio below
2 gallons: 1 hour
12*(2 gallons): 12*(1 hour) .... multiply both sides by 12
24 gallons: 12 hours
Now multiply this gallon count (24) by the cost per gallon ($5) and we get to 5*24 = 120
What is the slope-intercept form of the function that contains the point (8, 12) and has a slope of −2? y = x +
Answer:
y = -2x+28
Step-by-step explanation:
We have the slope and a point, so we can use the point slope form to make a line
y-y1 = m(x-x1)
y-12 = -2(x-8)
Distribute the -2
y-12 = -2x+16
Add 12 to each side
y-12+12 = -2x+16+12
y = -2x+28
This is the slope intercept form of the line
cheese production in a country is currently growing at a rate of 4% per year. the equation y=8.3(1.04)^× models the cheese production in the country from 2003 to 2009. In this equation l, y is the amount of cheese produced in billions of pounds and x represents the number of years after 2003.
a. Estimate the total cheese production in the country in 2006
b. assuming this equation continues to be valid in the future use the equation to predict the total amount of cheese produced in the country in 2017.
Answer:
a. 9.34 billions of pounds.
b. 14.37 billions of pounds.
Step-by-step explanation:
We have been given that cheese production in a country is currently growing at a rate of 4% per year. the equation [tex]y=8.3*(1.04)^{x}[/tex] models the cheese production in the country from 2003 to 2009. In this equation l, y is the amount of cheese produced in billions of pounds and x represents the number of years after 2003.
a. To find the total cheese production in the country in 2006 we will substitute x= 3 in our given equation as 2006-2003=3.
[tex]y=8.3*(1.04)^{3}[/tex]
[tex]y=8.3*1.124864[/tex]
[tex]y=9.3363712[/tex]
Therefore, the cheese production in year 2006 will be 9.34 billions of pounds.
b. To find the total cheese production in the country in 2017 we will substitute x= 14 in our given equation as 2017-2003=14.
[tex]y=8.3*(1.04)^{14}[/tex]
[tex]y=8.3*1.7316764476028035[/tex]
[tex]y=14.37291451510326905[/tex]
Therefore, the cheese production in year 2017 will be 14.37 billions of pounds.
Answer:
Given the equation: [tex]y = 8.3(1.04)^x[/tex] ......[1]
where
y is the amount of cheese produced in billions of pounds and
x represents the number of years after 2003
Since, this equation models the cheese production in the country from 2003 to 2009.
(a)
we have to find the total cheese production in the country in 2006.
Substitute x = 3 years(i.e, 2003 -2006) in [1] to solve for y;
[tex]y = 8.3(1.04)^{3}[/tex]
Simplify:
y = $9.3363712
Therefore, the total cheese production in the country in 2006 is, $9.34.
(b)
we use the equation to predict the total amount of cheese produced in the country in 2017.
We have x = 14 years.
Substitute in [1] we get;
[tex]y = 8.3(1.04)^{14}[/tex]
Simplify:
y = $14.3729145151
Therefore, the estimate total amount of cheese produced in the country in 2017 is, $14.37
Write an equation in slope-intercept form for the line that passes through (-3,2) and is perpendicular to the line y=3/2+4
Answer: the equation is slope-intercept form y = -2/3x
Plz tell me the error and what the correct answer is and explain
Answer:
3
Step-by-step explanation:
x÷4 is the expression
Evaluate when x=12
12÷4
12/4
3
He subtracted instead of dividing.
12-4 = 8 12/4 =3
A basketball player made 44 out of 100 attempted free throws. What percent of free throws was made?
Answer:
How much is 44 out of 100 written as a percentage? Convert fraction (ratio) 44 / 100 Answer: 44%
Step-by-step explanation:
44% of the total free throws are made.
What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have a basketball player made 44 out of 100 attempted free throws.
Assume the percent of free throws be [x]%. We can write -
[x] = (44/100) x 100
[x] = 44%
Therefore, 44% of the total free throws are made.
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