Translated these questions to a equation:
6 more than 9 times a number x is -12
the quotient of a number t and 7, plus 2, is -4
Let u = <6, -9>, v = <1, -4>. Find u - v.
A) <5, -5>
B) <10, -10>
C) <15, 5>
D) <7, -13>
Final answer:
To find the difference between vectors u and v, subtract the components of v from the corresponding components of u, resulting in the vector A) <5, -5>.
Explanation:
The question involves finding the difference of two vectors u and v. To find the vector u - v, you subtract each corresponding component of vector v from vector u.
For the first component, subtract the x-component of v (1) from the x-component of u (6), which equals 5.For the second component, subtract the y-component of v (-4) from the y-component of u (-9), which equals -5.Thus, the vector u - v is A) <5, -5>.
What is the value of 4.05 divide by 1.5?
The value of the expression 4.05 / 1.5 using the division property will be 2.7.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numbers are given below.
4.05 and 1.5
Then the division of the numbers 4.05 and 1.5 will be given by putting a division sign between them. Then we have
⇒ 4.05 / 1.5
⇒ 2.7
The value of the expression 4.05 / 1.5 using the division property will be 2.7.
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Final answer:
The result of dividing 4.05 by 1.5 is 2.7.
Explanation:
The value of 4.05 divided by 1.5 can be calculated by simply performing the division.
When you divide 4.05 by 1.5, you get 2.7.
This is because 4.05 is equivalent to 405 tenths, and when you divide 405 by 15 (since 1.5 is the same as 15 tenths), you end up with 27, or 2.7 when you adjust for the decimal placement.
Ari thinks the perfect milkshake has 3 ounces of caramel for every 5 scoops of ice cream. Freeze Zone makes batches of milkshakes with 6 ounces of caramel and 8 scoops of ice cream. What will Ari think about Freeze Zone's milkshakes?
Answer: Ari thinks amount of caramel is more for perfect milkshake as there is only need for 4.8 ounces of caramel but Freeze Zone is using 6 ounces of caramel.
Step-by-step explanation:
Since we have given that
Ari has 3 ounces of caramel for every 5 scoops of ice-cream .
Freeze Zone makes batches of milkshakes with 6 ounces of caramel and 8 scoops of ice-cream.
According to Ari,
For every 5 scoops of ice-cream, he needs 3 ounces of caramel
For every 1 scoop of ice-cream, he needs
[tex]\frac{3}{5}\text{ ounces of caramel}[/tex]
For every 8 scoops of ice-cream, he needs
[tex]\frac{3}{5}\times 8=\frac{24}{5}=4.8\text{ ounces of caramel}[/tex]
So, Ari thinks amount of caramel is more for perfect milkshake as there is only need for 4.8 ounces of caramel but Freeze Zone is using 6 ounces of caramel.
Ari will think Freeze Zone's milkshakes have the perfect amount of caramel.
Explanation:To determine what Ari will think about Freeze Zone's milkshakes, we need to compare the ratio of caramel to ice cream in Ari's perfect milkshake to the ratio in Freeze Zone's milkshakes.
Ari's perfect milkshake has 3 ounces of caramel for every 5 scoops of ice cream, so the ratio is 3:5.
Freeze Zone's milkshakes have 6 ounces of caramel for every 8 scoops of ice cream, so the ratio is 6:8.
To simplify both ratios, we can divide the numbers by their greatest common divisor. The GCD of 3 and 5 is 1, so the simplified ratio for Ari's perfect milkshake is 3:5. The GCD of 6 and 8 is 2, so the simplified ratio for Freeze Zone's milkshakes is 3:4.
Since both ratios are the same, we can conclude that Ari will think Freeze Zone's milkshakes have the perfect amount of caramel.
Which is a disadvantage of withdrawing more money than is available in a checking account?
A disadvantage of withdrawing more than you have in your account is you will be charged an overdraft fee.
What is an Overdraft Fee?An overdraft fee can be described as the fee your bank charges you when you make a withdrawal from your account beyond what you have in it.
An overdraft fee is one of the disadvantages of withdrawing more money than you have in your account..
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After losing 30 pounds, an individual weigh 110 pound more than one-third his previous weight
Point R is located at (11,5).point S is located at (-1,5). what is the distance between point R and point S
Please help me with questions 24
Use Cavalieri’s Principle to calculate the exact volume of an oblique cylinder with a radius of 10 meters and a height of 11 meters
The exact volume of the oblique cylinder with a radius of 10 meters and a height of 11 meters is 110π cubic meters.
To calculate the exact volume of an oblique cylinder using Cavalieri's Principle, follow these steps:
1. Consider a right cylinder with the same base and height as the oblique cylinder. The volume of the right cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
2. Since the oblique cylinder and the right cylinder have the same base and height, their volumes are equal according to Cavalieri's Principle.
3. The formula for the volume of a right cylinder can be applied to the oblique cylinder, giving the volume as V = πr^2h.
4. Substituting the values of the radius (r = 10 meters) and height (h = 11 meters) into the formula gives V = π(10)^2(11) = 110π cubic meters.
5. Therefore, the exact volume of the oblique cylinder with a radius of 10 meters and a height of 11 meters is 110π cubic meters.
how to solve -2x+y=7, 3y=6x+4
HELP ME PLEASE! How is the graph of mc027-1.jpg related to its parent function, mc027-2.jpg?
The graph of [tex]y = \sqrt{-2x[/tex] relates to its parent function as a result of (d) horizontal compression by a factor of 2, and a reflection across the y-axis
What is a function transformation?A function transformation involves changing the form or equation of a function to another through reflection, dilation, translation or rotation
How to determine the function transformationThe parent function is given as:
[tex]y = \sqrt x[/tex]
Compress the function horizontally by a factor of 2, using the following rule
[tex](x,y) \to (2x,y)[/tex]
So, we have:
[tex]y = \sqrt {2x[/tex]
Next, reflect the function over the y-axis, using the following rule
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex]y = \sqrt {-2x[/tex]
Hence, the function transformation is (d)
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A combination lock has a code consisting of 3 numbers, each of which can be 0 to 39, with numbers repeated. Jillian says that there are only 120 possible codes. Is Jillian correct? If not, explain her error.
Answer:
Jillian is not correct
Jillian has summed up the possible number of codes for each digit instead of multiplying it
Step-by-step explanation:
The lock has a code that consists of 3 number
It is given that the number in the lock code can be used between [tex]0[/tex] to [tex]39[/tex]
Thus, out of total [tex]40[/tex] set of numbers (i.e [tex]0-39[/tex]), the numbers can be repeated.
This means for all three code numbers the opportunity of choosing a number is same i.e. between [tex]0-39[/tex]
Now, the first digit of the code can be any number between [tex]0-39[/tex]
Like wise the second and third digit of the code can be any number between [tex]0-39[/tex]
Thus. the possible number of codes with repetition allowed are
[tex]40 * 40* 40\\64000[/tex]
Hence, Jillian is not correct
Jillian has summed up the possible number of codes for each digit instead of multiplying it
Answer:
No, Jillian is not correct. According to the fundamental counting principle, the total number of possible codes would be (40)(40)(40) = 64,000. Jillian multiplied by 3 instead of multiplying the number of possibilities for each digit.
Step-by-step explanation:
Find the sum of the geometric series with a1 = 7, r = 2, And n = 14
The sum of the geometric series with a1 = 7, r = 2, and n = 14 is -327661.
Explanation:The question is asking for the sum of a geometric series. In mathematics, the sum (S) of a geometric series is determined using the formula S = a1 * (1 - r^n) / (1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.
In the provided geometric series, a1 = 7, r = 2, and n = 14. Substituting these values into the formula gives us S = 7 * (1 - 2^14) / (1 - 2). After performing the calculations, the sum of the geometric series is -327661.
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The sum of the first 14 terms of the geometric series with the first term (a1) = 7, common ratio (r) = 2, is 114,691.
Explanation:Given the first term of the geometric series (a1) = 7, the common ratio (r) = 2, and the number of terms (n) = 14, we would like to find the sum of this series. Using the formula for the sum of a geometric series, S = a1 * (1 - r^n) / (1 - r), substituting the given values, we get:
S = 7 * (1 - 2^14) / (1 - 2)
This simplifies to S = 7 * ( -16383) / -1, which results in S = 114,691. So, the sum of the first 14 terms of this geometric series is 114,691.
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Each blade on a windmill is in the shape of a triangle with a base of 7 ft and height of 4 ft if there are four blades on the windmill, what is the total area of the blades.
Solution :
As per the problem we have
Each blade on a windmill is in the shape of a triangle with a base of 7 ft and height of 4 ft.
There are four blades on the windmill.
we have been asked to find the total area of the blades.
Area of one blade[tex] =\frac{1}{2}*base*height=\frac{1}{2}*7*4 =14 \ ft^2\\ [/tex]
Total are of blades[tex] =4*\text{Area of one blade}\\ [/tex]
Total are of blades[tex] =4*14=56 \ ft^2\\ [/tex]
△ABC is reflected to form △A′B′C′ . The vertices of △ABC are A(3, 1) , B(1, 5) , and C(6, 9) . The vertices of △A′B′C′ are A′(−1, −3) , B′(−5, −1) , and C′(−9, −6) . Which reflection results in the transformation of △ABC to △A′B′C′ ?
Answer:
that would be a reflection across the y axis resulting in a -x
Step-by-step explanation:
The scale on a map is 1 cm for every 400 km. If Maine and Japan are 22 cm apart on the map, what is the distance between Maine and Japan?
how many radians are in a semicircle? a.2π, b.π, c.π/2, d.3π/2
A semicircle, which is half of a full circle, consists of half the total amount of radians in a full circle. Since a full circle has 2π radians, a semicircle contains π radians. Therefore, the correct answer is b.π.
Explanation:To answer your question, let's review the structure of a circle.It is divided by its radius into 360 degrees or by its diameter into a full rotation of 2π radians. Therefore, a semicircle, which is half of a circle, must consist of half the total amount of radians in a full circle.
In a full circle, there are 2π radians. Hence, in a semicircle, which is exactly half of the full circle, there would be 2π/2. This simplifies to π radians.
So, the correct answer to your question 'How many radians are in a semicircle?' is b.π.
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In an office, the number of chairs, c , is equal to five more than twice the number of desks, d. Which equation matches the information?
Final answer:
The algebraic equation that represents the relationship between the number of chairs, c, and the number of desks, d, in an office, where the number of chairs is five more than twice the number of desks, is c = 2d + 5.
Explanation:
The student's question pertains to creating an algebraic equation based on a given word problem describing the relationship between the number of chairs (c) and desks (d) in an office. The problem states that 'the number of chairs, c, is equal to five more than twice the number of desks, d'.
To formulate the equation that illustrates this relationship, we apply the information provided:
Identify the number of chairs as c.Determine that c is 'five more than' something, which suggests addition.Recognize that 'twice the number of desks' means 2 times d, or 2d.Combine the above to conclude that the 'five more than' is added to the 'twice the number of desks', which gives us the equation c = 2d + 5.1/6 of 3 yards=______feet
I know I just ask one but u get 17 points so plz help I'm stuck
In this question, first we have to see how many feets are in 1 yard .
And there are 3 feets in 1 yard.
So in 3 yards, there are 9 feets
Therefore we will get
[tex] \frac{1}{6}*3 yards= \frac{1}{6} * 9 feet = 1.5 feet [/tex]
Therefore the answer of the given question is 1.5 feet.
Final answer:
To find the equivalent feet for 1/6 of 3 yards, multiply 1/6 by 3 feet per yard to get 1.5 feet.
Explanation:
1/6 of 3 yards=_____feet
Step 1: 1 yard is equal to 3 feet.
Step 2: To find the equivalent feet for 1/6 of 3 yards, calculate 1/6 x 3 = 0.5 x 3 = 1.5 feet.
Sherri uses her credit card to pay for new transmission that ended up totaling $1,050.25. She can pay off up to $400 a month. The card has an annual rate of 18.5%. How much will she pay in interest?
Sherri will pay approximately $30.69 in interest on her credit card debt of $1,050.25 with an 18.5% annual interest rate, assuming she makes payments of $400 per month and the interest compounds monthly.
To calculate how much interest Sherri will pay on her credit card debt, we need to know how the interest compounds. Typically, credit card interest is compounded daily, but since we do not have the compound frequency, we'll use a simplified approach to estimate the interest assuming the interest is compounded monthly.
The annual interest rate is 18.5%, which translates to a monthly rate of 18.5%/12 = 1.54%. Since Sherri can pay $400 a month, we can calculate the time it will take for her to pay off the principal without considering interest. This gives us $1,050.25 / $400 < 3 months.
Since the debt would be paid off in less than three months, we can estimate the interest for each month and sum it up:
First month interest: $1,050.25 < 0.0154 = $16.17Second month principal: $1,050.25 - $400 + $16.17 = $666.42Second month interest: $666.42 < 0.0154 = $10.26Third month principal: $666.42 - $400 + $10.26 = $276.68Third month interest: $276.68 < 0.0154 = $4.26Adding up these interest payments gives us approximately:
$16.17 + $10.26 + $4.26 = $30.69 in interest.
Please note, this is an estimation that assumes a linear payment model. Actual interest charges could be higher due to daily compounding.
Ruben has two congruent wooden dowels. He cuts one dowel in two in order to have three pieces to make a triangle. Explain why, despite having three sides, Ruben will not be able to make a triangle with his three pieces.
Answer:
The dowels are congruent, so they have the same length. If one is cut, the sum of the lengths of the two cut pieces will equal the length of the longer piece. If the pieces are to make a triangle, the sum of the lengths of the two cut pieces must be greater than the length of the third piece.
Step-by-step explanation:
Elijah is going to spin a spinner that goes to 4 180 times.He predicts that 60 of those spins will result in the spinner landing on the section labeled 3. Based on the theoretical probability, which best describes Elijah’s prediction?
Answer:
A. Elijah’s prediction is exact because 180 divided by 3 = 60.
Step-by-step explanation:
A bucket is put under a leaking ceiling. the amount of water in the bucket doubles every minute. after 8 minutes, the bucket is full. after how many minutes is the bucket half full? show work
What is the slope of a line that is parallel to to the one shown? (-3, 2) (0, -2)
A bond is a small, interest-bearing loan made by an individual to a corporate or government entity.
Please select the best answer from the choices provided
T
F
Answer: TRUE
Step-by-step explanation:
A rectangular prism has a length of 4 1/2 millimeters, a width of 4 1/2 millimeters, and a height of 6 millimeters.
Sally has a storage container for the prism that has a volume of 143 cubic millimeters.
What is the difference between the volume of the prism and the volume of the storage container?
Help Please?
Answer:
21 1/2
Step-by-step explanation:
Which expression represents the sixth term in the binomial expansion of (5y+3)^10
Answer:
bb
Step-by-step explanation:
A bathtub is filling with water at a rate of 60 liters per minute.How many liters of water are in the bathtub after t minutes?
Answer:
[tex]60t\text{ Liters}[/tex]
Step-by-step explanation:
We have been given that a bathtub is filling with water at a rate of 60 liters per minute. We are asked to find the water filled in the bathtub after t minutes.
To find the number of liters of water filled in tub after t minutes we will multiply rate of water filling by time.
[tex]\frac{60\text{ Liters}}{\text{Minute}}\times t\text{ minutes}[/tex]
[tex]60\text{ Liters}\times t[/tex]
[tex]60\times t\text{ Liters}[/tex]
[tex]60t\text{ Liters}[/tex]
Therefore, there were [tex]60t\text{ Liters}[/tex] of water in the bathtub after t minutes.
Rearrange the formula A = P + Prt for t.
The measure of angle E, the angle of elevation from point A to point B, is 5(x-2). The measure of angle D, the angle of depression from point B to point A, is (x+14). Find the measure of each angle.
Answer:
measure of angle E equals 20 degrees, measure of angle D equals 20 degrees