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
Can someone please help me with problem 6 of this assignment? I included the measurements of the triangle so that you are able to solve it accurately.
Geometry Topic: 6.1 - 6.4 Constructing Parts and Centers
Problem 6 Directions: Remember! Triangle centers may be outside the triangle. Locate the orthocenter of each triangle by finding the intersection of the altitudes.
Answer:
let say the 3 points that make the triangle is A-B-C, you draw a line from A to the line opposite to A, make it perpendicular. If it's not inside of the triangle, you just extend the line to make it work. Then repeat for B and C. Then you extend the perpendicular lines (altitude) and make them intersect. The intersect point is the orthocenter.
Step-by-step explanation:
Then you extend the perpendicular lines (altitude) and make them intersect. The intersect point is the orthocenter.
Answer:
see attached
Step-by-step explanation:
You want to construct the orthocenter of the given triangle.
OrthocenterThe orthocenter of a triangle is the point of intersection of the altitudes. The construction of it requires construction of at least two altitudes of the triangle. This is accomplished using the "perpendicular through an external point" construction.
Perpendicular through an external pointA perpendicular to a line through a point not on the line is constructed in a few simple steps:
Using the external point as a center, draw an arc that intersects the line in 2 places.Using each of those points as a center, draw intersecting arcs with the same radiusThe line through that point of intersection and the original point is perpendicular to the lineThe attachment shows arc FG using C as a center, and arc HI using A as a center. Arcs using those points as center are drawn so they intersect at points V and W.
Lines CV and AW are altitude lines that intersect at the orthocenter: point Z.
__
Additional comment
The vertices of the original triangle have been labeled A, B, C counterclockwise from upper left.
It may appear that point Z is a reflection of point C in line AB, but it is not.
Why does 5xy³ have a degree of 4? (Hint: Look at the exponents on the variables.)
by number of forme
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:
−2>m/6−7 graph the iniquality how do you do this????
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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Is the function represented by the table linear?
x
y
10
–6
11
1
12
6
13
12
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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When does king become the most emotional ? What is the message at this moment?
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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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.
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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How do you solve this type of problem?
It's a fact that the sum of the angles of a triangle add up to 180º.
So, 55º + 85º + (3x+4)º = 180º.
That's the equation you need to solve:
55 + 85 + 3x+4 = 180 (combine like terms)
144 + 3x = 180 (subtract 144 from both sides)
3x = 36 (divide both sides by 3)
x = 12 (you've got x)
Quadrilateral EFGH is a rectangle. If EF=4x−6 and HG=x+3 , find EF .
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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algebra 2-2
solve [tex]\sqrt{x}+3=-6[/tex]
√x+3=-6
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 answer? thanks
The solution for the expression given above would be = 31/40. That is option B.
What is a fraction?A fraction is defined as the part of a whole value which is written in the form of a numerator and a denominator.
The given fractions from the question;
2/5 + 3/8
Find the lowest common multiple of the figures below ( denominator) = 40
= 16 + 15/40
= 31/40
Therefore the correct fraction for the given expression = 31/40.
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Eric bought a canoe for $333.75. The sales tax was 5.25%. What was his total cost?
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?
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.
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)
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.
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)
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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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.
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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jenny got a box of 15 stickers . then she used 5 on a thank you card what fraction of the box did she used
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?
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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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
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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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?
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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factor the expression 15x - 10xy
Answer: 5x(3-2y)
Step-by-step explanation:
Step 1:
Find the greatest common factor (GCF):
Both values have 5x as the GCF.
Step 2:
Take out the GCF:
15x/5x=3
-10xy/5x=-2y
Step 3:
Write it out:
5x(3-2y)
Check:
Apply Distributive Property:
5x*3=15x
5x*-2y=-10xy
15x-10xy=15x-10xy
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.
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.
I can't figure this out and yet it's just a simply question. Not the best at math so please help me
[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]
if one addend of x is c, what is the other addend?
If one addend of x is c, the other addend is x-c.
How to find the other addend?An addend is a term that is added to another term to form a sum. In the equation x = c + (x-c) , c and (x-c) are the two addends that make up the sum x.
The reason why x-c is the other addend is that the sum of the two addends (c and x-c) must equal x.
In other words x = c + (x-c) can be simplified to x = c + x - c which is x = x
Therefore, If one addend of x is c, the other addend is x-c.
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The amount of sand left in a 600 mL vase can be modeled by the equation s = – 1 5 t + 600, where s is the amount of sand left in the vase and t is time in minutes since the sand started leaking out. The vase is full of sand. Sand leaks out of the vase until the vase is empty. Determine the domain and range of this scenario
As per the given equation, the domain is [0, 3000] and the range is [0, 600].
In the term domain is defined as the set of values that we are allowed to plug into our function where as the range of a function is the set of values that the function assumes.
Here we know that the amount of sand left in a 600 mL vase can be modeled by the equation that is written as,
=> s = – 1/5 t + 600
here s refers the amount of sand left in the vase and t refers time in minutes since the sand started leaking out
Here we also know that the vase is full of sand and sand leaks out of the vase until the vase is empty.
Then in order to find the domain we have to put the value of s as 0, then we get the domain as,
=> 0 = -1/5t + 600
=>1/5t = 600
=> t = 3000
Then the domain is [0, 3000].
Similarly, in order to find the value of range we have to put the value of t as zero, then we get
=> s = -1/5(0) + 600
=> s = 600
Then the range is [0, 600]
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(x^3+5x^2-24x)/(x+8) Synthetic Division
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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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.
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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Shane bought a package of 12 bagels. He gave b of them to his friends. Write an expression that shows the number of bagels Shane has left.
The expression that shows the number of bagels Shane has left is 12-b.
What is an expression?Expression in math is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given;
Shane bought a package of 12 bagels
He gave b of them to his friends
Now;
Shane bought 12 bagels
Expression= 12
Shane gave b
Expression=12-b
Therefore, the expression will be 12-b.
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A function is shown f(x)=-(13)/(5)x+k if f(30)=-1 what is the vallue of k?
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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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?
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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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)
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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