d.
What do you notice about the graph of the quadratic equation and where it crosses the
x-axis? How do these values compare to the solutions of x2 - 6x + 5 = 0? Explain.
Answers
This is consistent with the solutions for the equation x2 - 6x + 5 = 0 being x = 1 and x = 5.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It consists of one or more terms, each of which contains one or more variables. The terms are separated by an equal sign (=) and are usually written in a standard form known as an algebraic equation. Equations can be used to model and solve problems in a wide variety of fields, from physics and chemistry to economics and finance.
The graph of the quadratic equation is a parabola that opens upward and intersects the x-axis at two points. The x-intercepts occur when the equation is equal to zero, so the x-intercepts for the equation x2 - 6x + 5 = 0 are the solutions for x. These solutions are x = 1 and x = 5.
The graph of the quadratic equation also shows that the two solutions of the equation, x = 1 and x = 5, are the x-intercepts of the parabola. This means that when x equals 1 or 5, the equation is equal to zero, so the x-intercepts are the solutions of the equation. This is consistent with the solutions for the equation x2 - 6x + 5 = 0 being x = 1 and x = 5.
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Related Questions
Is the function represented by the table linear?
x
y
10
–6
11
1
12
6
13
12
Answers
The function is not linear because the rate of change in not constant.
What is Linear Function?Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable.
Given:
x y
10 -6
11 1
12 6
13 12
So, the rate of Change
= 10/ (-6)
= -5/2
and, again = 11/1 = 11
As, the rate of change is not constant.
But, in linear function the rate of change is same.
Hence, the function is not linear.
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jenny got a box of 15 stickers . then she used 5 on a thank you card what fraction of the box did she used
Answers
algebra 2-2
solve [tex]\sqrt{x}+3=-6[/tex]
√x+3=-6
Answers
The solution of equation is x=-3
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given
The equation;√x+3=-6
Now,
√x=-6-3
√x=-9
x=-3
Therefore the answer of the given equation will be -3
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What is the reverse of multiplied by 146 
Answers
The Multiplicative Inverse of postive 146 is 0.00684932.
What is Multiplicative Inverse?
The reciprocal of a particular integer is referred to as the multiplicative inverse. It is employed to make mathematical expressions simpler. The word "inverse" denotes an opposing or opposed action, arrangement, position, or direction. A number becomes 1 when it is multiplied by its multiplicative inverse.
When a number is multiplied by the original number, the result is 1, that number is said to be the multiplicative inverse of that number. A-1, or 1/a, stands for the multiplicative inverse of the letter "a". In other terms, two numbers are said to be multiplicative inverses of one another when their product is 1.
The division of 1 by a number yields the multiplicative inverse of that number. The number's reciprocal is another name for it. According to the multiplicative inverse formula, a number's product with its reciprocal is 1.
Given number for the multiplicative inverse is 146;
so, If the Multiplicative Inverse of 146 is x
then , the problem can be written as a function as follows:
146(x) = 1
Thus, to get the answer, we divide 1 by 146 like this:
1 / 146 = 0.00684932
Therefore,the Multiplicative Inverse of postive 146 is 0.00684932.
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Eric bought a canoe for $333.75. The sales tax was 5.25%. What was his total cost?
Answers
Step by step
$333.75 x 5.25% = 17.52 tax
$333.75 + 17.52 tax = $351.27 total cost
Why does 5xy³ have a degree of 4? (Hint: Look at the exponents on the variables.)
by number of forme
Answers
Answer:
The degree is 4 because the term shown has TWO variables, while y has an exponent of 3, x has an exponent of 1, add the exponents of the variables to find the degree
Step-by-step explanation:
If u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), use Formula 5 of this theorem to find d/dt [u (t) x v (t). (3t sin(3 t) - cos(3 t) + 3cos(6 t), 3t- 3 sin(6 t), 3 t sin(3 t) - cos(3 t)
Answers
If u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), the derivative of cross product d/dt [u (t) x v (t)] is (3cos(6t) + 3tsin(3t), 2t - 3sin(6t), 3cos(6t) + 3tsin(3t)).
Formula 5 of the cross product theorem states that the derivative of the cross product of two vectors u and v is equal to the cross product of the derivatives of u and v:
d/dt [u(t) x v(t)] = (du/dt) x v(t) + u(t) x (dv/dt)
Where u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), we can find the derivatives as follows:
du/dt = (d(sin 3t)/dt, d(cos 3t)/dt, dt/dt)
= (3 cos 3t, -3 sin 3t, 1)
dv/dt = (dt/dt, d( cos 3t) /dt, d( sin 3t)/dt)
= (1, -3 sin 3t, 3 cos 3t)
Now, we can substitute these derivatives into the formula to find d/dt [u (t) x v (t)]:
d/dt [u(t) x v(t)] = (du/dt) x v(t) + u(t) x (dv/dt) = (3 cos 3t, -3 sin 3t, 1) x (t, cos 3t, sin 3t) + (sin 3t, cos 3t, t) x (1, -3 sin 3t, 3 cos 3t)
= (-3sin²3t - cos3t, t - 3cos3tsin3t, 3cos²3t + 3tsin3t) + (3cos²3t + 3tsin3t, t - 3cos3tsin3t, -3sin²3t - cos3t)
= (3cos²3t + 3tsin3t - 3sin²3t - cos3t, 2t - 6cos3tsin3t, 3cos²3t + 3tsin3t - 3sin²3t - cos3t)
= (3cos(6t) + 3tsin(3t), 2t - 3sin(6t), 3cos(6t) + 3tsin(3t))
The cross product of two vectors is a vector, and the result of the above calculation will be a vector that describes the rate of change of the cross product u(t) x v(t).
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When Mamadou goes bowling, his scores are normally distributed with a mean of 175 and a standard deviation of 13. Using the empirical rule, what percentage of the games that Mamadou bowls does he score between 136 and 214?
Answers
The percentage of games that Mamadou scores between 136 and 214 is given as follows:
99.7%.
What is defined by the Empirical Rule?These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:
68% of the measures within one standard deviation of the mean.95% of the measures within two standard deviation of the mean.99.7% of the measures within three standard deviation of the mean.For this problem, we have that
136 = 175 - 39 = 175 - 3 x 13.214 = 175 + 39 = 175 + 3 x 13.Hence the percentage is of 99.7%, as the measures are within three standard deviations of the mean.
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what is the equation of the line that passes through the point (−1,1)(−1,1) and has a slope of 5?
Answers
Answer:
The equation of a line can be represented in the slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.
Given that the line has a slope of 5 and passes through the point (-1,1) we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1)
The point (-1,1) can be plugged into the equation:
y - 1 = 5(x + 1)
By simplifying and re-arranging the equation, we get:
y = 5x + 6
So the equation of the line that passes through the point (-1,1) and has a slope of 5 is: y = 5x + 6
Answer:
y = 5x+6
Step-by-step explanation:
Using the slope-intercept form of a line
y = mx+b where m is the slope and b is the y-intercept
y = 5x+b
Substitute the point into the line.
1 = 5(-1) +b
1+5 = b
6=b
The equation is
y = 5x+6
Gary used to make bottles of glitter glue.
Bottles Glue Glitter
1 3.8 1.9
4
How much glue and glitter would he need to make 4 bottles?
Gary would need 15.2 oz glue and 3.8 oz of glitter to make 4 bottles.
Gary would need 6.8 oz glue and 4.9 oz of glitter to make 4 bottles.
Gary would need 7.8 oz glue and 5.9 oz of glitter to make 4 bottles.
Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.
Answers
Gary would need 15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Bottles Glue Glitter
1 3.8 1.9
This means,
1 bottle = 3.8 oz of glue and 1.9 oz of glitter
Now,
1 bottle = 3.8 oz of glue
Multiply 4 on both sides.
4 bottle = 4 x 3.8 oz
4 bottle = 15.2 oz
1 bottle = 1.9 oz of glitter
Multiply 4 on both sides.
4 bottle = 7.6 oz
Thus,
15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.
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a cypress beam found in the tomb of sneferu in egypt contained 55% of the amount of carbon-14 found in living cypress wood. estimate the age of the tomb given that carbon-14 has a half-life of 5730 years.
Answers
The estimated age of the tomb of Sneferu is 8,330 years.
The age of the tomb can be estimated using the carbon-14 decay equation, which states that the amount of carbon-14 remaining after time t (in years) is equal to the initial amount of carbon-14 multiplied by 0.5^(t/5730).The decay equation for carbon-14 is A = A₀e⁻kt, where A₀ is the original amount of carbon-14, A is the amount of carbon-14 at time t, k is the decay constant, and t is the amount of time that has passed.
We can rearrange the equation to solve for t: t = -ln(A/A₀)/k. In this equation, A is the amount of carbon-14 found in the cypress beam, and A₀ is the amount of carbon-14 found in living cypress wood.
In this case, the initial amount of carbon-14 was 100%, and the remaining amount was 55%. Solving for t, we get t = (ln(55%)/ln(0.5))*5730 = 8,330 years.
Therefore, the estimated age of the tomb of Sneferu is 8,330 years.
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MATHHHHH PLEASEEEEEEE
Answers
Answer:
halfway between 862350 and 862360
Is the following is considered a LINEAR table. True or False.
Answers
The following is considered a LINEAR table is True .
What is mean by LINEAR table?By observing how X and Y vary, you may determine whether a table is linear. A table is linear if Y rises at a steady pace as X increases by 1. Finding the initial difference allows you to determine the constant rate.Look for a consistent rate of change to establish if the function is linear or nonlinear.The rate of change between any two rows in the table may be calculated.Pick another set of rows and figure out how much they have changed at this point.Both change rates are the same.There are several instances of linear equations, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3.To learn more about LINEAR table refer to:
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When does king become the most emotional ? What is the message at this moment?
Answers
King usually becomes the most emotional during moments of reflection or when he is expressing his views on civil rights and justice. King's message of hope, courage, and resilience encourages individuals to stand up for what is right and to never give up in the face of injustice.
In what ways does Dr. King use emotion in his speech?Dr. King utilises passion in his lectures to accentuate his message and to connect with his audience on an emotional level. He frequently speaks about the sorrow and injustice that his people have endured, eliciting an emotional response from his audience. He also inspires his audience to believe in the prospect of a brighter future, which instills hope and motivation. Furthermore, he frequently employs metaphors and analogies to underline his ideas, which may be extremely effective.
When does king become the most emotional?King is generally the most emotional when he is reflecting or expressing his ideas on civil rights and justice. In these times, he sends a message of hope, strength, and endurance. King usually uses compelling metaphors and parables to highlight the necessity of equality and justice. He highlights the power of our actions to effect change and the importance of never losing hope in the face of hardship. He frequently urges for unity among all races and sexes and opposes all types of prejudice. He also discusses the power of love, understanding, and mutual respect in bridging gaps and creating a better society.
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A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 55 pounds each, and the small boxes weigh 15 pounds each. There are 120 boxes in all. If the truck is carrying a total of 3800 pounds in boxes, how many of each type of box is it carrying?
Answers
If a delivery truck is transporting boxes of two sizes: large and small. The number of each type of box it carrying is: Large boxes is 50 and small boxes is 70.
How to find the number of each type of box ?Let L represent the number of Large boxes.
Let S represent the number of Small boxes.
Total number of boxes = 120
L + S = 120
The two equations are:
L + S = 120
55×L + 15×S = 3800
L + S = 120 eliminate L by multiplying this equation by -55
-55×(L + S = 120)
The equations are:
55 ×L + ×15S = 3800
-55×L -55×S = -6600
0 - 40×S = - 2800
S = -2800/(-40)
S = 70
Plug S back into one of our equations.
L + S = 120
L + (70) = 120
L = 120 - 70
L = 50
So ,
L = 50 and S = 70
Therefore the number of each type of box it carrying is: Large boxes is 50 and small boxes is 70.
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Quadrilateral EFGH is a rectangle. If EF=4x−6 and HG=x+3 , find EF .
Answers
We are given that quadrilateral EFGH is a rectangle. If EF=4x−6 and HG=x+3 , then the side EF= -34.
What is a quadrilateral?
A quadrilateral is a four-sided polygon, or a shape with four straight sides. It is a type of closed, two-dimensional shape. The four sides of a quadrilateral can be of equal or varying lengths and angles. Examples of quadrilaterals include squares, rectangles, rhombuses, parallelograms, and trapezoids.
Since quadrilateral EFGH is a rectangle, the opposite sides are congruent and parallel.
Therefore, if EF = 4x - 6 and HG = x + 3, then HG=EF
so, x+3=4x-6
then, x=-9
Therefore, EF=4x-6=4(-9)-6= -34
Hence, EF= -34
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b. What is the probability that the boys will draw matching blocks? Is the game fair? Justify your answer.
Answers
yes it is fair The probability of drawing matching blocks is 1/3
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
The probability of drawing matching blocks is 1/3
The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favorable Outcomes/Number of total outcomes.
four main types of probability exist: classical, empirical, subjective and axiomatic. Probability is synonymous with possibility, so you could say it's the possibility that a particular event will happen.
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A restaurant used 2 1/2 kilograms of potatoes to
make 6 meals. If they used an equal amount of
potatoes on each meal, how much potato did they
use for each meal?
Answers
Based on the information provided, it can be concluded that for each meal the restaurant used 0.4166 kilograms of potato.
How to calculate how many kilograms of potatoes the restaurant used in each meal?To calculate the quantity of potatoes used, you can use the following formula shown below:
Total of potatoes used / number of meals
2 1/2 kilograms of potatoes/ 6 meals
2 1/2 kilograms of potatoes is equivalent to 2.5 (1/2 = 0.5)
2.5 kilograms of potatoes/ 6 meals
0.4166
Therefore for each meal, the restaurant used 0.4166 kilograms of potatoes.
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−2>m/6−7 graph the iniquality how do you do this????
Answers
A graph of the inequality is shown in the image attached below.
How to graph the inequality?In this scenario, we would solve the given inequality by making m the subject of formula as follows;
-2 > m/6 - 7
By collecting like terms, we have the following:
-2 + 7 > m/6
5 > m/6
Cross-multiplying, we have:
30 > m
By re-writing the inequality, we have:
m < 30
Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Also, the circle is open because of the greater than (>) symbol.
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13. You need to make 18 one-cup bags of trial mix for a class trip. The recipe calls for peanuts,
chocolate chips, and raisins in the extend ratio of 5:1:4. How many cups of each item do you
need? You will get some decimal answers.
Answers
The cups of each items needed will be 9 cups of peanuts, 1.8 cups of chocolate and 7.2 cups of raisins.
How to calculate the number of cups of each item that is needed?From the information, 18 0ne-cup bags of tail mix is needed for the class tripThe recipe includes chocolate, chips and raisins in the ratio of 5:1:4
Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number.
5x- peanuts
1x- chocolate chips
4x- raisins
5x + 1x + 4x= 18
10x= 18
x= 18/10
x = 1.8
Chocolate = 1.8 cups
Raisins = 4x
= 4 × 1.8
= 7.2 cups.
Peanut = 5x
= 5 × 1.8
= 9 cups
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Which is greater, 20·34 or 20÷34? Explain.
Answers
Answer:
Step-by-step explanation:
The result of 20 · 34 is 680, and the result of 20 ÷ 34 is approximately 0.588235294117647. Therefore, 20 · 34 is greater than 20 ÷ 34.The symbol "·" is used for multiplication, and the symbol "÷" is used for division. When we multiply 20 and 34, we are finding the total value of 20 items that are each worth 34. While when we divide 20 by 34, we are finding out how many times 34 can fit into 20, which is less than one.In short, Multiplication gives a bigger value than division, that's why 20*34 is greater than 20/34.
Answer:
Step-by-step explanation:
Hello! The way you can figure this question out is by solving each one. Let's start with 20 x 34.
How you can multiply 20 x 34
34
x20
______
00 - 0 x 4, 0 x 3 both equal 0
+ 680 - Put a 0 to the right of the number, 2 x 4 = 8, 3 x 2 = 6
______
680
34 x 20 = 680
Now, divide 20 by 34
20/34 = 10/17
10/17 is less than 1, while 680 is much greater than 1.
680 > 10/17
20 x 34 is greater than 20 divided by 34
Fun fact:
If two numbers are greater than 1, are whole numbers, and they are multiplied and divided, the number produced by each equation will always be greater when multiplied.
I can't figure this out and yet it's just a simply question. Not the best at math so please help me
Answers
[tex]6=\textit{oz of solution at x\%}\\\\ ~~~~~~ x\%~of~6\implies \cfrac{x}{100}(6)\implies \cfrac{6x}{100} \\\\\\ 9=\textit{oz of solution at 0\%}\\\\ ~~~~~~ 0\%~of~9\implies \cfrac{0}{100}(9)\implies 0 \\\\\\ \textit{15 oz of solution at 16\%}\\\\ ~~~~~~ 16\%~of~15\implies \cfrac{16}{100}(15)\implies 2.4 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{lcccl} &\stackrel{oz}{quantity}&\stackrel{\textit{\% of oz that is}}{\textit{acid only}}&\stackrel{\textit{oz of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&6&\frac{x}{100}&\frac{6x}{100}\\ \textit{2nd Sol'n}&9&0&0\\ \cline{2-4}&\\ mixture&15&0.16&2.4 \end{array}~\hfill \begin{cases} 6 + 9 = 15\\\\ \frac{6x}{100}+0=2.4 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 2nd equation}}{\cfrac{6x}{100}=2.4}\implies \cfrac{3x}{50}=\cfrac{24}{10}\implies 30x=1200 \\\\\\ x=\cfrac{1200}{30}\implies \boxed{x=\stackrel{\%}{40}}[/tex]
(x^3+5x^2-24x)/(x+8) Synthetic Division
Answers
The solution of (x³ - 5x² -24x) / (x + 8) using synthetic division is x² - 3x.
What is the solution of (x³ - 5x² -24x) / (x + 8) using synthetic division?The solution of (x³ - 5x² -24x) / (x + 8) using synthetic division is given below:
(x³ + 5x² -24x) / (x + 8)
The divisor is -8
The coefficients are:
1 5 -24
Using synthetic division
the first coefficient is 1
the second coefficient = 1 * (-8) + 5
the second coefficient = -3
the third coefficient = -3 * (-8) + (-24)
the third coefficient = 0
Therefore, the solution = 1(x³/x) -3(x²/x) + 0(x/x)
The solution = x² - 3x
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01
3
✓5
Check
Unit price for the 2.24-pound bag:
$per pound
Unit price for the 3.12-pound bag: $ per pound
The better buy:
O The 2.24-pound bag
O The 3.12-pound bag
O Neither (They have the same unit price)
Answers
The better buy for the shrimp based on the information will be the A. 2.24 pound bag.
How to calculate the unit price?From the information, Josh paid $11.96 for a 2.24 -pound bag of shrimp at one store and the following week, he paid $17.24 for a 3.12 -pound bag at another store.
The unit price when Josh paid $11.96 for a 2.24 -pound bag of shrimp will be:
= $11.96 / 2.24
= $5.34
The unit price when he paid $17.24 for a 3.12 -pound bag at another store will be:
= $17.24 / 3.12
= $5 53
Therefore, A is cheaper.
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Complete question
Josh paid $11.96 for a 2.24 -pound bag of shrimp at one store. The following week, he paid $17.24 for a 3.12 -pound bag at another store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent.
One apple costs S0.55 at the grocery store. Customers receive one free apple for every 8 apples that they buy. Anna paid a total of $8.80 for her apples. How many apples did Anna receive?
Answers
Answer:
She was given 1 free apple and paid for 15 apples.
Step-by-step explanation:
0.55x2=1.1
1.1x8=8.8
8.8/.55=16
16-1=15
And you know she paid for 15 apples and got 1 free.
A function is shown f(x)=-(13)/(5)x+k if f(30)=-1 what is the vallue of k?
Answers
The value of the variable , k is -385/13
What is a function?A function can be described an expression, equation, law or rule explaining the relationship between two variables.
These variables are known as;
Dependent variableIndependent variableFrom the information given, we have the function;
f(x)=-(13)/(5)x+k
Also, for the value of f(30), the function is equivalent to -1
Now, substitute the value of x as 30 and equate the function to -1. we have;
-1 = -13/(5)30 + k
Divide both sides by the cofficient of 30 + k
30 + k = -1 × -5/13
Multiply the values
30 + k = 5/13
Now, collect like terms
k = 5/13 - 30
k = -385 /13
Thus, the value is -385/13
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the length of the diagonal AC and BD of a rhombus ABCD are 6m and 8cm, Find the length of each side of the rhombus
Answers
Length of side of the rhombus is 5cm.
Find the length of each side of the rhombus?A rhombus can be thought of as a special parallelogram since it satisfies the requirements for one (a quadrilateral with two pairs of parallel sides). Another characteristic of a rhombus is that it has four equal sides, just like a square. It is also known as a tilted square for this reason.
step1
Diagonals of a rhombus bisect each other at right angles.
Let point of intersection of diagonals be O
So, OD = 3cm , OA = 4cm
From Right angled triangle △ AOD,
⇒ AD² = OA² + OD² (Pythagoras theorem)
⇒ AD² =4² + 3²
⇒ AD² = 16+9
⇒AD² =25
step2
⇒ AD² =25
⇒ AD=5 cm
AD is side of the rhombus.
So, length of side of the rhombus is 5cm
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Circle the representation that has the less steep slope.
Pls help me with 3 and 4
Answers
The line of linear equation y = 8x - 48 is much steeper than the line of linear equation y = -x - 4-.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The table of input and output values are given for the function.
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[16 - 32]/[8 - 10]
(-16)/(-2)
8
So, the slope point is obtained as m = 8.
The equation becomes - y = 8x + b
To find the value of b substitute the values of x and y in the equation -
32 = 8(10) + b
32 = 80 + b
b = 32 - 80
b = -48
So, the value for b is -48.
Now, the equation becomes -
y = 8x - 48
A graph has been plotted for the equation.
Similarly, the points for a line is given as (-6,2) and (-9,5).
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[5 - 2]/[-9 - (-6)]
(3)/(-9 + 6)
3/-3
-1
So, the slope point is obtained as m = -1.
The equation becomes - y = -x + b
To find the value of b substitute the values of x and y in the equation -
2 = -(-6) + b
2 = 6 + b
b = 2 - 6
b = -4
So, the value for b is -4.
Now, the equation becomes -
y = -x - 4
A graph has been plotted for the equation.
It is known that the larger the slope the steeper the line.
In the graph also it can be seen that the graph of line y = 8x - 48 is much steeper.
Therefore, the slope of line y = 8x - 48 is more steeper.
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The sequence of the other length of the rectangles is represented by the equation: an=8+(n−1)4 a) Determine two side lengths of the tenth rectangle in the sequence. b) You are given the following areas of rectangles: 392in2, 128in2, 576in2, and 968in2 Determine which of the areas is not possible in the given sequence and explain why.
Answers
Answer:
a) The two side lengths of the tenth rectangle in the sequence are 8 + (10 - 1)4 = 32 and 8 + (10 - 2)4 = 28.
b) The area of 576in2 is not possible in the given sequence because it would require a side length of 24, which does not follow the sequence given.
Step-by-step explanation:
The given sequence is represented by the equation an=8+(n−1)4, which means that for each successive rectangle in the sequence, the length of one of the sides will increase by 4. Therefore, in order for the area of a rectangle to be 576in2, the length of one of the sides must be 24, which does not follow the sequence given.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The diameter of a tire is 2. 5 ft. Use this measurement to answer parts a and b. Show all work to receive full credit.
a. Find the circumference of the tire.
b. About how many times will the tire have to rotate to travel 1 mile? (1 mile = 5,280 ft)
Answers
a) The circumference of the tire is 7.85 ft
b) About 673 times the tire will have to rotate to travel 1 mile.
The diameter of a tire is 2. 5 ft.
Let r represents the radius of the tire.
r = diameter/2
r = 2.5 / 2
r = 1.25 ft
a) the circumference of the tire:
We know that the formula for the circumference of circle:
C = 2πr
So, the circumference of the tire would be,
C = 2 × π × r
C = 2 × π × 1.25
C = 7.85 ft
b) Let the tire will have to rotate n times in order to travel 1 mile.
We know that 1 mile = 5,280 ft
So, n = 5280 / 7.85
n = 672.6
n ≈ 673
Thus, the tire will have to rotate 673 times in order to travel 1 mile.
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