The equation of the line in point-slope form, which passes through the pair of points located at (-4 , 2) and (-3 , 5), is y - 2 = 3(x + 4).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (-4 , 2) and (-3 , 5).
m = (y2 - y1)/(x2 - x1)
m = (5 - 2)/(-3 - -4)
m = 3
Using the point slope form, plug in the values of the slope and Point A to set up the equation.
(y - y1) = m(x - x1)
where m = 3 and (x1 , y1) = (-4 , 2)
(y - 2) = 3(x - -4)
y - 2 = 3(x + 4)
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In the diagram below, m/CIH = 105° and m/BGD = 41°. Find m/AHF.
B.
D
41°
G
E
105
H
F
C
∠AHF is the exterior angle to the triangle GHI, so m∠AHF = 116°.
What is exterior angle?
When one side of a triangle is stretched, an external angle is generated. An external angle of a triangle is a non-straight angle (one that is not merely an extension of a side) that is outside the triangle but next to an interior angle.
From figure, m∠CIH = 105° (given)
so, m∠GIH = (180° - m∠CIH) = (180° - 105°) = 75° (complementary angles)
And m∠BGD = 41°
So, m∠IGH = M∠BGD = 41° (vertically opposite angles)
Now, m∠AHF = m∠GIH + m∠IGH (exterior angle)
= 75° + 41°
= 116°
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A bee flies at 6 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 11 minutes, and then flies directly back to the hive at 4 feet per second. It is away from the hive for a total of 15 minutes. a. What equation can you use to find the distance of the flowerbed from the hive? b. How far is the flowerbed from the hive?
Answer:
576 feet
Step-by-step explanation:
The bee is at the flowerbed for 11 minutes so we can subtract that form the 15 minutes. The bee travels for 4 minutes.
So now we have that it flew to the flowerbed at 6 feet per second and back at 4 feet per second.
We have a total of 4 minutes or 240 seconds. we now have two speeds where one is 50% faster than the other. We then find the two percents that one is 50% greater than the other percent and both add up to 100. 40% +50% of 40% is 60. 60%+40% is 100%
We know it spent 40% of 240 seconds flying to the flowerbed at 6 feet per second.
40% of 240 is 96
96 seconds at 6 feet per second is 576 feet
Show ur work please and thank you I’ll give brainilest
Answer:
7
Step-by-step explanation:
If he made 6 in the first game and 34 total, then we cant subtract 34 from 6 to find how many he made in the 4 remaining games.
34 - 6 = 28
Now simply divide 28 by 4 to figure out how much he made in each game
28 / 4 = 7
Write an equation of a circle with the given center and radius. Check your answers.
center (-4,-6) , radius 7
The equation of the circle with radius 7 and center at (-4 , -6) is (x + 4)^2 + (y + 6)^2 = 49.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (-4 , -6)
r = 7
(x - -4)^2 + (y - -6)^2 = 7^2
(x + 4)^2 + (y + 6)^2 = 49
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ANSWER FAST PLEASE simplify the expression negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths −13.16 −9.89 0.49 20.11
The value of the given expression is -6.93
How to simplify the expression?The expression in the question is given as:
negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths
Rewrite the expression properly
So, we have
-15 - 3.7 + 9.15/5 * 3^2 - 4.7
Evaluate the quotient and the exponent
So, we have
-15 - 3.7 + 1.83 * 9 - 4.7
Evaluate the product
-15 - 3.7 + 16.47 - 4.7
Evaluate the sum and the difference
-6.93
Hence, the value of the given expression is -6.93 (none of the options is correct)
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Answer:
Step-by-step explanation: option b
Please help I don't understand!!
1. Use the graph at right to answer the following questions. (Hint: rate of change = slope).
Calculate the average rate of change from x = 1 to x = 4
2. Use the graph at right to answer the following questions. (Hint: rate of change = slope).
Calculate the average rate of change from x = 2 to x = 5
1. Average rate of change = -1/3
2. Average rate of change = 4/3
How to the Average Rate of Change?Average rate of change = change in y /change in x.
1. Average rate of change from x = 1 to x = 4
When x = 1, y = 5
When x = 4, y = 4
Average rate of change = (4 - 5)/(4 - 1)
Average rate of change = -1/3
2. Average rate of change from x = 2 to x = 5
When x = 2, y = 3
When x = 5, y = 7
Average rate of change = (7 - 3)/(5 - 2)
Average rate of change = 4/3
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Determine the range of f(x) = |x + 5|.
if right ill award u pls need fast pretty pls
Answer:it
Step-by-step explanation:
it should be 10 i think
A rectangular room is
1.4
1.4
times as long as it is wide, and its perimeter is
27
27
meters. Find the dimension of the room.
The length is : meters and the width is meters. Enter the dimensions as decimals rounded to at least one decimal place.
The length of the rectangle is 7.875 meters and the width of the rectangle is 5.625 meters.
Perimeter of a rectangleLength of the rectangle = 1.4xWidth of the rectangle = xPerimeter of the rectangle = 27 metersPerimeter of a rectangle = 2(length + width)
27 = 2(1.4x + x)
27 = 2(2.4x)
27 = 4.8x
divide both sides by 4.8x = 27/4.8
x = 5.625
Therefore,
Length of the rectangle = 1.4x
= 1.4(5.625)
= 7.875 meters
Width of the rectangle = x
= 5.625 meters
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For the geometric sequence 3,12,48,192, . . . . . , find the indicated term.20 th term
The 20th term of the given geometric sequence, 3, 12, 48, 192, . . . , is 8.246337208 x 10^11.
A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.
a(n) = a r^(n-1)
Where:
a(n) = nth term
r = ratio
Given the geometric sequence 3, 12, 48, 192, . . .
Find the ratio,
r = a(n)/a(n-1)
r = a(2)/a(1)
r = 12/3
r = 4
Notice that the ratio between two succeeding terms is always 4.
Use the formula to find the 20th term of the geometric sequence.
a(20) = a r^(20-1)
a(20) = 3[4^(20-1)]
a(20) = 3(4^19)
a(20) = 8.246337208 x 10^11
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In the pressure equation, P represents the pressure on the object in pascals (Pa), F represents the force applied on the object in newtons (N), and A represents the area, in square meters, of the object over which the pressure is applied.
The pressure inside the container is 81.625 pascals
Calculating pressureFrom the question, we are to determine the pressure applied inside the container
From the Pressure equation, we have that
P = F/A
Where P is the pressure
F is the force
and A is the area
From the given information,
F = 1306 N
A = 16 m²
P = 1306/16
P = 81.625 pascals
Hence, the pressure inside the container is 81.625 pascals
Here is the complete question:
In the pressure equation, P represents the pressure on the object in pascals (Pa), F represents the force applied on the object in newtons (N), and A represents the area, in square meters, of the object over which the pressure is applied. What is the pressure applied inside a container having an inner area of 16 square meters over which a force of 1,306 newtons is applied?
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215,36,6 find the seventh term
Pls help
Answer: 216, 36, 6, 1, 1/6, ...
Step-by-step explanation:
216, 36, 6, ...
[tex]b_1=216\\b_2=36\\b_3=6\\\displaystyle\\q=\frac{b_2}{b_1} \\\\q=\frac{36}{216} \\\\q=\frac{1}{6} \\\\q=\frac{b_3}{b_2} \\\\q=\frac{6}{36} \\\\q=\frac{1}{6} \\\\Hence,\\\\b_n=b_1q^{n-1}\\\\b_5=216*(\frac{1}{6})^{5-1}\\\\b_5=216*(\frac{1}{6} )^4\\\\b_5=216*\frac{1}{6^4}\\\\b_5=6^3 *\frac{1}{6^4} \\\\b_5=\frac{6^3}{6^4} \\\\b_5=6^{3-4}\\\\b_5=6^{-1}\\\\b_5=\frac{1}{6}[/tex]
which is the value of (1.8 x 10^8) (8.3 x 10^-3)
Answer:
О C 1.494*10⁻⁶
Step-by-step explanation:
1.8*10⁸ = 180000000
8.3*10⁻³ = 0.0083
180000000 * 0.0083 = 1494000
= 1.494*10⁶
d. Could the triangle have 110 cans? 140 cans? Explain.
NO, for such a triangle to exist is impossible.
We are given two angles of 110° and 140°.
We have to find whether Triangle with given angles (110° and 140°) is possible or not.
We will utilize the basic knowledge of triangles and their angles to solve this problem. As we know, the sum of all triangle angles is 180°.
If
let the third angle be x
110° + 140° + x = 180
according to the angle sum property of triangles
then,
x = 180° - 250°
which is not possible.
And if we add 110 and 140, we will get 250° as a resultant, which is much greater than the sum of the three angles.
Therefore, a triangle with 110° and 140° as two of its angles is not possible.
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Can smn help me with this problem?
A drawer has 20 red socks a d 20 blue socks. How many ways can we make groups of matching and unmatching pairs?
Using the Fundamental Counting Theorem, the number of pairs are given as follows:
Matching: 760Unmatching: 400.What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For matching pairs, we have that:
There are 2 options(blue/red).For the first option, there are 20 socks, and for the second, 19 socks.Hence the number of pairs is:
N = 2 x 20 x 19 = 760.
For the non-matching pair, we have that there are 20 red and 20 blue to choose, hence the number of pairs is:
N = 20 x 20 = 400.
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the stage wich is 35 feet wide in real life is 5 inches wide in the drawing . what is the scale of the drawing
Answer: 20 feet
Step-by-step explanation:
The scale is 3 inches to is to 2 feet
As a ratio, it would be:
The question is what is the actual length of the stage if the drawing is 30 inches. All we need to do is find a ratio proportional to the scale ratio:
Now to find the missing number, cross multiply the fractions first:
Then solve for x:
The answer is 20 feet
expression to the correct point.
-5
d
f
-4
Point
de
-3
-√8
I
32
-TT
+
match each
-2
f
-1
Expression
Answer:
2x6x6+7+j
34+67897790+b,xyy
Solve for x.
I need help with this geometry problem
Miranda purchased a coat for $101.50 that was regularly priced at $145, not including tax. what percentage did miranda save by purchasing a coat on sale?
If Miranda purchased a coat for $101.50 that was regularly priced at $145, not including tax then the percentage Miranda saved by purchasing the coat on sale is equal to 30%.
Percentage in mathematics can be described as a number expressed as a fraction of 100. The symbol % is used to indicate a percent.
The percentage Miranda saved by purchasing the coat on sale can be calculated as follows,
First, subtract the regular price from the price at which she purchased
145 - 101.50 = 43.5
Now, divide this number by the regular price of the coat,
43.5 ÷ 145 = 0.3
Now, the percentage Miranda saved can be calculated by multiplying the result by 100,
0.3 × 100 = 30%
Hence, the percentage Miranda saved by purchasing the coat on sale is calculated to be 30%.
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Complete the square. x² +14 x+ ____
The complete expression of the given quadratic function is:
x² + 14x + 49
What is an algebraic expression?An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
To solve this problem we must complete square in the expression, it is necessary to note that perfect square trinomial has the form of:
(a + b)² = a² + 2ab + b²
x² + 14x + ?
where:
x² = a²14x = 2abb = ?Substitute and find b
14x = 2xb
2b = 14
b = 7
Let's complete the square
x² + 14x + 7²
x² + 14x + 49
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Your teacher invested 5000 in three funds. After a year they had 5450 . The growth fund had a return rate of 12% , the income fund had a return rate of 8% , and the money market fund had, a return rate of 5 \% . Your teacher invested twice as much in the income fund as in the money market fund. How much money was invested in each fund?
Using a system of equations, the amounts invested in each fund are given as follows:
Growth: $2,000.Income: $2,000.Market: $2,000.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: amount invested into the growth fund.Variable y: amount invested into the income fund.Variable z: amount invested into the market fund.The teacher invested 5000, hence:
x + y + z = 5000.
After a year, the amount was of $5,450, hence, considering the return rates:
1.12x + 1.08y + 1.05z = 5450.
The teacher invested twice as much in the income fund as in the money market fund, hence:
y = 2z.
Then, replacing y = 2z in the first two equations:
x + 3z = 5000 -> x = 5000 - 3z.1.12x + 3.21z = 5450.Replacing the first equation into the second.
1.12(5000 - 3z) + 3.21z = 5450.
0.15z = 150
z = 150/0.15
z = 1000.
Hence:
y = 2z = 2000.x = 5000 - 3z = 2000.The amounts invested in each fund are given as follows:
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Please help
Me asap!
Answer:
36 degrees
Step-by-step explanation:
this a complementary angle. This means that both sides add up to 90 degrees. 90-54=36
Answer:
36°
Step-by-step explanation:
These angles are complimentary, meaning they add to 90°. You know this by the little square marking.
a + 54° = 90°
a = 36°
if a cube has a volume 27 cubic centimeters what is the length of each edge?use the volume formula ,V=[tex]s^{3}[/tex]
Answer:
s = 3 cm
Step-by-step explanation:
the volume (V) of a cube is calculated as
V = s³ ( s is the side length )
here V = 27 cm³ , then
s³ = 27 ( take cube root of both sides )
[tex]\sqrt[3]{s^3}[/tex] = [tex]\sqrt[3]{27}[/tex]
s = 3
the length of each edge of the cube is 3 cm
a school organises a concert for charity the graph and table shows information about the 100 tickets sold
how much money was raised with the 100 tickets sold?
Help ASAP Im ALmost DONE!!
Determine the range of f(x) = |x| + 3.
{y | −∞ < y < ∞}
{y | −3 ≤ y < ∞}
{y | 0 ≤ y < ∞}
{y | 3 ≤ y < ∞}
A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain and the outputs are called the range.
The range for the function f(x) = |x| + 3 is {y | 3 ≤ y < ∞}.
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain and the outputs are called the range.
We have,
f(x) = |x| + 3
We need to find the range of f(x).
We can have x values of any real numbers.
For x = 0,
f(0) = 0 + 3 = 3
For x = 1,
f(1) = 1 + 3 = 4
For x = 2,
f(2) = 2 + 3 = 5
For x = 3
f(-3) = |-3| + 3 = 6
For x = -1,
f(-1) = |-1| + 3 = 1 + 3 = 4
For x = -2,
f(-2) = |-2| + 3 = 2 + 3 = 5
For x = -3,
f(-3) = |-3| + 3 = 3 + 3 = 6
We see that,
If we take x = 0, 1, 2, 3, 4, .... the f(x) values increases from 3, 4, 5, 6 and so on.
If we take x = 0 , -1, -2, -3, ..... the f(x) values increases from 3, 4, 5, 6 and so on.
This means that f(x) values are from 3 to infinity for x ∈ R
[ R = real numbers ]
Thus the range for the function f(x) = |x| + 3 is {y | 3 ≤ y < ∞}.
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Answer:
Step-by-step explanation: i think C is the answer
.............................................
Answer:
The value would be 100
Step-by-step explanation:
if a box contains 200 tissues and we take 3/5 of these tissues, work out how many tissues we take
Answer:
120 tissues
Step-by-step explanation:
3/5 x 200 tissues
X（´∀｀ ）
Answer:
We take 120 tissues
Step-by-step explanation:
[tex]\frac{200}{1} *\frac{3}{5} = \\\\\frac{600}{5} = 120[/tex]
Simplify (1+1/3)^2-2/9
The simplified form of the expression (( 1 + 1/3 )² - 2/9) is 14/9.
What is the simplified form of the given expression?Given the expression in the question;
( 1 + 1/3 )² - 2/9
Add the two terms inside the parenthesis
( (3+1)/3 )² - 2/9
( 4/3 )² - 2/9
Apply product rule to 4/3
4²/3² - 2/9
Raise 4 and 3 to the power of 2
16/9 - 2/9
Combine the numerators over common denominator
( 16 - 2 ) / 9
14/9
Therefore, the simplified form of the expression (( 1 + 1/3 )² - 2/9) is 14/9.
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FIND x
log(x)+ log (x+3)=1
Determine whether each sequence is arithmetic. If so, identify the common difference. 100,10,1,0.1, ...........
The given sequence 100,10,1,0.1, ........... does not form an AP as the common difference is not same.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between two mathematical orders is a fixed number (AP). Arithmetic Sequence is another name for it.
We'd come across a few key concepts in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be referred to in terms of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows:Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the stated sequence is; 100,10,1,0.1, ...........
The series comprises of four defined terms.
Consider the initial term be 'a₁' = 100.
Consider the second term be 'a₂' = 10.
Consider the third term be 'a₃' = 1.
And, consider the fourth term is 'a₄' = 0.1.
The AP must have the equal common difference. So,
d₁ = a₃ - a₂
Substitute the values.
d₁ = 1 - 10
d₁ = -9
Thus, the computed common difference is -9.
or d₂ = a₄ - a₃ (Substitute the values)
d₂ = 0.1 - 1
d₂ = -0.9.
As, for the result it is clear that the value of both common difference is not same. That is,
d₁ ≠ d₂.
Therefore, the given sequence doesn't not form an arithmetic sequence.
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The total height of the cubes stacked on top of each other is 2f + 3g^2.
The cubes have a combined volume that is the same as a rectangular prism of the same height. What is the area of the base of the rectangular prism? (Recall: V = Bh)
A: 2f + 3g^2
B: 8f^3 + 27g
C: 2f - 6fg^2 + 3g^2
D: 4f^2 - 6fg + 9g^4
(And pls be fast)
The area of the base of the rectangular prism will be D. 4f² - 6fg + 9g⁴.
How to illustrate the information?it should be noted that from the information given, the cubes have a combined volume that is the same as a rectangular prism of the same height.
The total height of the cubes stacked on top of each other is 2f + 3g²
Therefore, the area will be:
= (2f)² - 2(3fg) + (3g²)²
= 4f² - 6fg + 9g⁴
Therefore, the area of the base of the rectangular prism will be 4f² - 6fg + 9g⁴.
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