Answer:
P: (3,0)
Step-by-step explanation:
AB = (9,3)
⅔(9,3) = (6,2)
(-3,-2) + (6,2) = (3,0)
the coordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1 is (3,0).
What is the ratio formula for line segment?P=(mx2+nx1/m+n,my2+ny1/m+n).
The formula can be derived by constructing two similar right triangles, as shown below. Their hypotenuses are along the line segment and are in the ratio m : n m:n m:n.
Here, given that,
Given the point A(-3,-2) and B(6, 1),
Let, (x.y) is the coordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1.
Using the formula we get,
(x,y) = (nx1 + mx2)/(m + n) , (ny1 + my2)/(m + n)
P=(3,0)
hence, the coordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1 is (3,0).
To learn more on ratio formula for line segment click:
https://brainly.com/question/19339816
#SPJ3
A gas can hold 10 L of gas. How many cans could we fill with 7 L of gas?
Answer: It is only one can that can be filled up.
Step-by-step explanation: If 1 gas can can hold 10 L of gas and you only have 7 L then how can you fill up more than 1 gas can with only 7 L? You don't have enough gas to fill up more than 1 gas can. So you are left with only 1 gas can filled but only with 7 L.
Final answer:
To find the average density of a full gasoline can, both the mass of the gasoline (20.0 L multiplied by 0.75 kg/L for 15.0 kg) and the mass of the can (2.50 kg) are added to get a total mass of 17.5 kg. This is divided by the volume of gasoline the can holds (20.0 L) to yield an average density of 0.875 kg/L.
Explanation:
The question centers on calculating the average density of a gasoline can when it is full. To do this, we need to consider the total mass of the can and the gasoline together and the total volume they occupy.
The mass of the gasoline can itself is 2.50 kg. When full, the can holds 20.0 L of gasoline. Assuming the density of gasoline is 0.75 kg/L, we can calculate the mass of the gasoline as:
Mass of gasoline = 20.0 L × 0.75 kg/L = 15.0 kg
Then, we add the mass of the gasoline to the mass of the can to get the total mass:
Total mass = Mass of steel can + Mass of gasoline
Total mass = 2.50 kg + 15.0 kg = 17.5 kg
To find the average density, we use the formula:
Density = Total mass / Total volume
The volume here is the volume of gasoline the can holds since we typically ignore the thickness of the container in such calculations unless otherwise specified. Hence the average density is calculated based on the volume of gasoline only.
Average density = 17.5 kg / 20.0 L
Average density = 0.875 kg/L
This value represents the combined density of the steel can and the gasoline within it.
What as a numerical expression four times the sum of 5 and 6
Answer:
4(5+6) = Distribute
20 + 24 = Add
44
Step-by-step explanation:
Answer:
4 * (5 + 6)
Step-by-step explanation:
Step 1: Convert words into an expression
Four times the sum of 5 and 6
4 * (5 + 6)
Answer: 4 * (5 + 6)
The product of 0.031 and 1,000,000 is __ because the decimal point in 0.031 moves __ places to the right.
Step-by-step explanation:
[tex]0.031 \times 1000000 \\ = 31000 \\ moves \: 4 \: places \: to \: the \: right[/tex]
Use the sum and difference formula to determine the exact value of sin195
Answer:
-0.259 or (√2 - √6) / 4
Step-by-step explanation:
Sin (195) using sum and difference formula.
Let's break the figure for convenience.
It becomes sin ( 135 + 60)
Invoking the sin formula we have
sin (A + B) = sin (A) cos (B) + cos (A) sin(B)
Where A = 135, B = 60
Therefore it becomes
sin(135) cos(60) + cos(135) sin (60)
From reference angle relationship we have:
(sin (45))cos (60) + cos (135) sin (60)
From trigonometric ratios, sin (45) = √2/2
Therefore, the equation becomes,
(√2/2) cos(60) + cos (135)sin (60)
(√2/2) (0.5) + cos (135) sin (60)
= (√2/2) (1/2) + ( - √2/2) ( √3/2)
Simplifying the equation
√2/4 + ( -√2/2) ( √3/2)
= √2/4 - √6/4
= (√2 - √6) / 4
OR
=( 1.414 - 2.449 ) / 4
= -1.035/4
= -0.25875
solve by using distributive property: 12x - 6y = 12 and x = -2y +11
Answer:
x = [tex]\frac{1}{11}[/tex]; y = [tex]\frac{-60}{11}[/tex]
Step-by-step explanation:
x = -2y + 11 so x + 2y = 11 (1)
12x - 6y = 12 so 6x - y = 6 (2)
(1) - 2(2) ↔ (x + 2y) - 2(6x - y) = 11 - 2(6)
↔ - 11x = - 1
↔ x = [tex]\frac{1}{11}[/tex]
(2) ↔ y = 6x - 6 = 6([tex]\frac{1}{11}[/tex]) - 6 = [tex]\frac{6}{11}[/tex] - 6 = [tex]\frac{-60}{11}[/tex]
Brainliest???
joe had 84 heads of cabbage . peter picked one third of the heads of cabbage . How many did peter picked?
Answer:
28
Step-by-step explanation:
Answer:
Peter picked 28.
Step-by-step explanation:
1/3 of 84 is 28 because 84 divided 3 and multiplied by 1 is 28.
What is the length and width of a rectangle given by the trinomial r squared - 6r- 55? Use factoring
Answer:
The length and the width of the rectangle are 11 units and 5 units
Step-by-step explanation:
Let us use the factorization to find the length and the width of the rectangle
∵ The trinomial is r² - 6r - 55
∵ r² = (r)(r)
∵ -55 = (-11)(5)
- Multiply r by -11 and r by 5, then add the products, the sum
must be equal the middle term of the trinomial
∵ (r)(-11) = -11r
∵ (r)(5) = 5r
∵ -11r + 5r = -6r ⇒ the middle term of the trinomial
∴ r² - 6r - 55 = (r - 11)(r + 5)
- Equate each factor by 0 to find the value of r
∵ r - 11 = 0
- Add 11 to both sides
∴ r = 11
OR
∵ r + 5 = 0
- Subtract 5 from both sides
∴ r = -5 ⇒ rejected because no negative dimensions
∴ The length of the rectangle is 11 units
∵ The area of the rectangle is 55 units²
∵ Area of a rectangle = length × width
∴ 55 = 11 × width
- Divide both sides by 11
∴ 5 = width
∴ The width of the rectangle is 5 units
what are the factors of x^2 – 100?
Answer:
(x - 10)(x + 10)
Step-by-step explanation:
x² - 100 is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
Thus
x² - 100
= x² - 10²
= (x - 10)(x + 10)
The expression x² - 100 can be factored using the difference of squares rule in algebra. The factors are (x - 10) and (x + 10).
Explanation:
The question asks for the factors of the polynomial expression x² – 100. This is a special kind of polynomial that can be factored using the difference of squares rule, a powerful tool in algebra which states that any expression in the form a² - b² can be rewritten as (a - b)(a + b).
In our case, a would be x (since x² is the first term) and b will be 10 (since 10² equals 100, the second term).
Applying the difference of squares rule to your expression, we get:
x² – 100 = (x - 10)(x + 10)
The factors of the expression are therefore x - 10 and x + 10.
Learn more about Factoring Polynomials here:https://brainly.com/question/28315959
#SPJ6
simplify [tex]\frac{secx^{2} }{cotx^{2}+1}[/tex]
Answer: [tex]tan(x)^{2}[/tex]
Step-by-step explanation:
We will use the trigonometric identities to solve this problem:
[tex]\frac{sec(x)^{2}}{cot(x)^{2}+1}[/tex] (1)
Let's begin by the following trigonometric identity:
[tex]sec(x)^{2}=tan(x)^{2}+1[/tex] (2)
An substitute it in (1):
[tex]\frac{tan(x)^{2}+1}{cot(x)^{2}+1}[/tex] (3)
Then, taking into account [tex]tan(x)^{2}=\frac{sin(x)^{2}}{cos(x)^{2}}[/tex] and [tex]cot(x)^{2}=\frac{cos(x)^{2}}{sin(x)^{2}}[/tex], we rewrite (3):
[tex]\frac{\frac{sin(x)^{2}}{cos(x)^{2}}+1}{\frac{cos(x)^{2}}{sin(x)^{2}}+1}[/tex] (4)
[tex]\frac{\frac{sin(x)^{2}+cos(x)^{2}}{cos(x)^{2}}}{\frac{cos(x)^{2}+sin(x)^{2}}{sin(x)^{2}}}[/tex] (5)
Then, applying the trigonometric identity [tex]sin(x)^{2}+cos(x)^{2}=1[/tex]
[tex]\frac{1}{cos(x)^{2}}}{\frac{1}{sin(x)^{2}}}[/tex] (6)
Finally
[tex]\frac{sin(x)^{2}}{cos(x)^{2}}}=tan(x)^{2}[/tex] (7)
The formula for the volume of a square pyramid is
V 5 (b2
h) 4 3, where b is the length of one side of the
square base and h is the height of the pyramid. Find the
length of a side of the base of a square pyramid that has
a height of 3 inches and a volume of 25 cubic inches.
Answer:
reeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
the graph of y= x is scaled vertically by a factor of 1/5
Answer:
y = 1/5x
Graph Below:
Can someone help me solve this
Answer:
∠ 6 = 38°
Step-by-step explanation:
∠6 and 38° are vertical and congruent, thus
∠ 6 = 38°
Calculate, to the nearest cent, the future value FV of an investment of $10,000 at the stated interest rate after the stated amount of time. 7.5% per year, compounded daily (assume 365 days/year), after 12 years
Answer: 1,000
First, you have to find how much 7.5% is coming out of 10,000. So in this case it's 750. Multiply 750 by 12 years. Thats 9000, you then subtract 9000 and 10,000 to get 1,000.
The future value of a $10,000 investment at a 7.5% annual interest rate compounded daily after 12 years is $22,589.67.
Explanation:To calculate the future value of an investment that is compounded daily, we use the formula: FV = P ((1 + (r/n))^{nt}, where:
P is the principal amount (the initial amount of money)r is the annual interest rate (in decimal form)n is the number of times the interest is compounded per yeart is the time the money is invested for in yearsGiven that the principal amount P is $10,000, the annual interest rate r is 7.5% (or 0.075 in decimal form), the number of times the interest is compounded per year n is 365, and the time t is 12 years, we plug these values into the formula:
FV = $10,000 ((1 + (0.075/365))^{365 * 12}
By calculating this amount, we find that the future value of the investment, to the nearest cent, would be $22,589.67.
g The circumference of a circle is 268.53 m. What is the approximate area of the circle? Use 3.14 for pi.
Answer:
5741.11 m^2
Step-by-step explanation:
The formula for circumference is C=2(pi)r. Solve for r with the given info of the the circumference. r= 268.53/(2*3.14) r=42.76. The formula for area is (pi)r^2. Knowing r, substitute and solve.
The difference of a number and five is negative one. Find the number.
Answer:
The number is 4
Step-by-step explanation:
Write algebraically:
n-5=-1
n=4
The number is 4
To find the number when the difference of a number and five is negative one, substitute the given values into an equation and solve for the unknown variable.
Explanation:To solve the problem, let's assign a variable to the unknown number. Let's call it 'x'. The difference of a number and five can be represented as 'x - 5'. According to the problem, this expression is equal to -1. So, we can write the equation x - 5 = -1. To find x, we need to isolate it on one side of the equation. Adding 5 to both sides, we get x = 4. Therefore, the number is 4.
Learn more about number difference here:https://brainly.com/question/18757471
#SPJ2
Just a test. What is 2+2 equal to?
Answer:
4
Step-by-step explanation:
Answer:
2+2 = 4
Step-by-step explanation:
2 + 2 = 4...
Calvin has $360 less in his savings account than he had 8 weeks ago. Each
week he deposited $15 into his account. What was his average withdrawal
each week?
Answer:
Calvin withdraws $ 60 each week
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Calvin's account balance difference than 8 weeks ago = - $ 360
Weekly amount Calvin deposits = $ 15
Number of weeks to compare = 8
2. What was his average withdrawal each week?
Let's calculate the weekly average withdrawal this way:
Weekly average withdrawal = [Calvin's account balance difference than 8 weeks ago - (Weekly amount Calvin deposits * Number of weeks to compare)]/Number of weeks to compare
Replacing with the values given:
Weekly average withdrawal = [-360 - (15 * 8)]/8
Weekly average withdrawal = -360 - 120 / 8
Weekly average withdrawal = -480 / 8
Weekly average withdrawal = -60
Calvin withdraws $ 60 each week
Isabella has some dimes and some quarters. She has at most 25 coins worth a minimum of $4.45 combined. If Isabella has 17 dimes, determine all possible values for the number of quarters that she could have.
Answer: No Solutions
Step-by-step explanation:
Define Variables:
May choose any letters.
\text{Let }d=
Let d=
\,\,\text{the number of dimes}
the number of dimes
\text{Let }q=
Let q=
\,\,\text{the number of quarters}
the number of quarters
\text{\textquotedblleft at most 25 coins"}\rightarrow \text{25 or fewer coins}
“at most 25 coins"→25 or fewer coins
Use a \le≤ symbol
Therefore the total number of coins, d+qd+q, must be less than or equal to 25:25:
d+q\le 25
d+q≤25
\text{\textquotedblleft a minimum of \$4.45"}\rightarrow \text{\$4.45 or more}
“a minimum of $4.45"→$4.45 or more
Use a \ge≥ symbol
One dime is worth $0.10, so dd dimes are worth 0.10d.0.10d. One quarter is worth $0.25, so qq quarters are worth 0.25q.0.25q. The total 0.10d+0.25q0.10d+0.25q must be greater than or equal to \$4.45:$4.45:
0.10d+0.25q\ge 4.45
0.10d+0.25q≥4.45
\text{Plug in }\color{green}{17}\text{ for }d\text{ and solve each inequality:}
Plug in 17 for d and solve each inequality:
Isabella has 17 dimes
\begin{aligned}d+q\le 25\hspace{10px}\text{and}\hspace{10px}&0.10d+0.25q\ge 4.45 \\ \color{green}{17}+q\le 25\hspace{10px}\text{and}\hspace{10px}&0.10\left(\color{green}{17}\right)+0.25q\ge 4.45 \\ q\le 8\hspace{10px}\text{and}\hspace{10px}&1.70+0.25q\ge 4.45 \\ \hspace{10px}&0.25q\ge 2.75 \\ \hspace{10px}&q\ge 11 \\ \end{aligned}
d+q≤25and
17+q≤25and
q≤8and
0.10d+0.25q≥4.45
0.10(17)+0.25q≥4.45
1.70+0.25q≥4.45
0.25q≥2.75
q≥11
\text{It is not possible to have }q\le 8\text{ AND to have }q\ge 11\text{.}
It is not possible to have q≤8 AND to have q≥11.
\text{Therefore there is NO SOLUTION}
Therefore there is NO SOLUTION
Isabella has to have a minimum of 11 but could have as many as 19 quarters to meet the criteria given in the question.
Explanation:Isabella has 17 dimes which equates to $1.70 ($.10 x 17 = $1.70). We know she has to have a minimum of $4.45, so let's subtract the value of the dimes from this total ($4.45 - $1.70), resulting in $2.75. This remaining value must come from the quarters Isabella has. Since quarters are worth $0.25 each, we divide $2.75 by $0.25 to discover Isabella must have at least 11 quarters to reach the target dollar amount.
However, since Isabella could have 'at most 25 coins', we realize that she could also have potentially more quarters. We've established she has 17 dimes, so subtract that from the total of 25, resulting in 8. This means she could have in total between 11 (minimum requirement to reach the dollar amount) and 19 (maximum limitation placed by the coin total) quarters.
Learn more about Number of Quartershttps://brainly.com/question/32591052
#SPJ2
last question promise
Answer:
80°
Step-by-step explanation:
A triangle = 180° total.
Because it is a parallelogram, 40° is also the measure of BCE.
180° - 60° - 40° = 80°
BEC = 80°
Train B travels 140 miles which is 40% of the total distance it will travel. What is the total number of miles train B will travel?
Answer:
350 Miles
Step-by-step explanation:
140/40 = x/100
x = 350
350 Miles
I WILL GIVE BRAINLIEST
Part A:
A garden is in the shape of a circle with a radius of 10 feet. Edging is placed around the garden
How much edging, in feet, is needed to go around the garden? Round to the nearest whole number?
Part B:
Another garden is in the shape of a semicircle with a radius of 25 feet. Edging is placed around this garden.
How much edging, in feet, is needed to go around this garden? Round to the nearest whole number.
Answer:
Part A = 64 feet
Part B = 79 feet
Step-by-step explanation:
Part A
10 × 2 = 20 = Diameter
Formula is C = π × diameter
20 × π = 62.8318530718 feet = 64 feet
Part B
25 × 2 = 50
Same formula
50 × π = 157.079632679 feet
157.079632679 ÷ 2 = 78.5398163395 feet = 79 feet
divide by 2 because it is a semi circle
Hope his helped :)
For the circular garden with a radius of 10 feet, 63 feet of edging is required. For the semicircular garden with a radius of 25 feet, 129 feet of edging is needed. These figures are obtained by calculating the circumference of a circle and a semicircle, then rounding to the nearest whole number.
Explanation:To find out how much edging is needed for the gardens, we need to calculate the circumference of the circles.
Part A
The formula for the circumference of a circle (which is the distance around the edge) is 2πr, where π (pi) is approximately 3.14, and r is the radius. For a circle with a radius of 10 feet, the circumference is:
2 × 3.14 × 10 feet = 62.8 feet
Rounded to the nearest whole number, we need 63 feet of edging for the garden.
Part B
For a semicircle with a radius of 25 feet, the circumference is half that of a whole circle, plus the diameter (which is 2 × radius). So, first calculate the circumference of the whole circle and then divide by 2 and add the diameter:
(2 × 3.14 × 25 feet) / 2 + 2 × 25 feet = 78.5 feet + 50 feet = 128.5 feet
Rounded to the nearest whole number, we need 129 feet of edging for the semicircular garden.
HELP PLEASE
In the figure MN←→−∥OP←→ and ∠OST=73°.
Find the measure of ∠MTS and ∠STN .
Answer:
B
Step-by-step explanation:
STN is the alt exterior angle of angle 73 which means that it is congruent. STN is the vertical angle is MTQ which means that it is also equal to 73. Then you can use linear pair to find MTS. 180 - 73 which is 107.
Answer:
A
Step-by-step explanation:
What angle is complementary to angle 2
Answer:
angle 1
Step-by-step explanation:
[tex] \angle \: 1 \: is \: complementary \: to \: \angle \: 2 \\ [/tex]
What’s the explicit formula for -4, -16, -64, -256
Answer:
[tex]a_{n}[/tex] = - 4[tex](4)^{n-1}[/tex]
Step-by-step explanation:
Note the common ratio r between consecutive terms in the sequence, that is
- 16 ÷ - 4 = - 64 ÷ - 16 = - 256 ÷ - 64 = 4
This indicates the sequence is geometric with n th term ( explicit formula )
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
Here a = - 4 and r = 4, thus
[tex]a_{n}[/tex] = - 4 [tex](4)^{n-1}[/tex] ← explicit formula
What is the value of log Subscript 27 Baseline 9?
Answer:
23
Step-by-step explanation:
log27(9) can be interpreted as " 27 to what power is equal to 9 . Since 2723=32=9,log27(9)=23
Answer:
2/3
Step-by-step explanation:
-3(2w+5)+7w=5(w-11) what is w?
Answer:
w = 10
Step-by-step explanation
Answer:
53 = w OR 10.6=w
5
Step-by-step explanation:
-3(2w+5)+7w=5(w-11)
-6w-15+7w=5w-55
+6w +6w
-15+13=5w-55
+15 +15
13=5w-40
+40 +40
53=5w
5 5
53 = w OR 10.6=w
5
Hope that helps!! PLEASE GIVE ME BRAINLIEST!!!
#1. Simplify the expression 5+8(3+x)
#2. Simplify the expression x+3+5x
#3. Simplify the expression 5(z+4)+5(2-z)
Answer:
Step-by-step explanation:
5+8(3+x)=5+24+8x=29+8x
x+3+5x=3+6x
5(z+4)+5(2-z)=5z+20+10-5z=30
Which angle is complementary to
Answer:
angle AOC is what i think it is but please dont go on my word wait to see what other people say first sorry
What’s the answer cause I need it bad
Answer: [tex](-9,-3)[/tex]
Step-by-step explanation:
Given the following system of equations:
[tex]\left \{ {{2x=-78-20y} \atop {-x=-51-20y}} \right.[/tex]
In order to solve the System of equations, you can use the Substitution method. The steps are:
1. You can solve for "x" from the second equation:
[tex]-x=-51-20y\\\\x=51+20y[/tex]
2. Substitute the equation obtained into the first original equation:
[tex]2x=-78-20y\\\\2(51+20y)=-78-20y[/tex]
3. Now you must solve for "y":
[tex]102+40y=-78-20y\\\\40y+20y=-78-102\\\\60y=-180\\\\y=\frac{-180}{60}\\\\y=-3[/tex]
4. Substitute the value of "y" into the equation [tex]x=51+20y[/tex] and evaluate:
[tex]x=51+20(-3)\\\\x=51-60\\\\x=-9[/tex]
Then, the solution is:
[tex](-9,-3)[/tex]
Ten increased by 6 times a number
is the same as 4 less than 4 times
the number. Find the number.
Answer: the number is -7
-angie:) pls mark me brainnliest!
Step-by-step explanation:
Explanation:
The easiest way to solve this equation is to write an equation and solve for the unknown number. This is the equation:
10
+
6
x
=
4
x
−
4
Subtract each side by 4x.
10
+
2
x
=
−
4
Subtract both sides by 10.
2
x
=
−
14
Divide by 2 on each side to isolate
x
.
x
=
−
7
So you have your answer: the number is
−
7
. To double-check your answer, you can plug this number back into the equation and see if it comes out to be true:
10
+
6
(
−
7
)
=
4
(
−
7
)
−
4
10
−
42
=
−
28
−
4
−
32
=
−
32
This equation is true, so you know
−
7
has to be the unknown number .
Answer:
-7
Step-by-step explanation:
10+6x=4x-4
-4x -4x
10+2x=-4
-10 -10
2x=-14
/2 /2
x=-7