Step-by-step explanation:
Given:
[tex] (x_1, \: y_1 ) =(2, \:3)\:\:\&\:\: (x_2, \: y_2) =(6, \:10)[/tex]
[tex]l(PQ) = \sqrt{ {(x_1 - x_2)}^{2} + {(y_1 - y_2)}^{2}} \\ \\ = \sqrt{ {(2 - 6)}^{2} + {(3 - 10)}^{2}} \\ \\ = \sqrt{ {( - 4)}^{2} + {( - 7)}^{2}} \\ \\ = \sqrt{16 + 49} \\ \\ = \sqrt{65} \\ \\ \therefore \purple{ \boxed{ l(PQ) = 8.06 \: units}}\\\\[/tex]
Let S be the mid-point of PQ.
[tex]\therefore S = \{\frac{x_1+x_2}{2}, \:\:\frac{y_1+y_2}{2}\} \\\\
= \{\frac{2 +6}{2}, \:\:\frac{3+10}{2}\} \\\\
= \{\frac{8}{2}, \:\:\frac{13}{2}\} \\\\
\therefore S= \{4, \:\:6.5\} \\\\[/tex]
Equation of line PQ is given as:
[tex] \frac{y-y_1}{y_1 - y_2}=\frac{x-x_1}{x_1 - x_2} \\\\
\therefore \frac{y-3}{3 - 10}=\frac{x-2}{2 - 6} \\\\
\therefore \frac{y-3}{-7}=\frac{x-2}{-4} \\\\
\therefore \frac{y-3}{7}=\frac{x-2}{4} \\\\
\therefore 4(y-3)=7(x-2)\\\\
\therefore 4y-12=7x-14\\\\
\therefore 7x-14 - 4y + 12=0\\\\
\red{\boxed {\therefore 7x-4y - 2 =0}} [/tex]
Answer:
length = square root of ((2-6)^2)+((3-10)^2) = square root (of) 16+49
square root of 65 = 8.062257748 = approx 8.1
midpoint = (x1+x2)/2 , (y1+y2)/2
= 2+6 /2 , 3+10 /2
=8/2 , 13/2
= 4, 6.5 (midpoint)
equation= y=mx+c
m(gradient) = (y2-y1)/(x2-x1) or (y1-y2)/(x1-x2)
= so, (3-10)/(2-6) (y1-y2)/(x1-x2)- i normally use this one
= -7/-4 = 1.75
so y=1.75x+c
plug in the values from any one of them (2,3) or (6,10)
to get
for example: 3=1.75*2+c
3=3.5+c
-0.5=c
now we get the equation y=1.75x+(-0.5)
you always have to have a plus( +(-0.5)) since the equation is y=mx+c
Which equation has the solutions x = StartFraction 5 plus-or-minus 2 StartRoot 7 EndRoot Over 3 EndFraction?
3x2 – 5x + 7 = 0
3x2 – 5x – 1 = 0
3x2 – 10x + 6 = 0
3x2 – 10x – 1 = 0
Answer:
3x^2 - 10x - 1 = 0 $OPTION D ON EDGE$
Step-by-step explanation:
Answer:
3x2 – 10x + 6 = 0
Step-by-step explanation:
Givena general quadratic equation
ax²+bx+c = 0
The general formula for finding x is;
x = -b±√b²-4ac/2a
Where a,b and c are the coefficient of x², x and x° respectively
Given the solution in question to be;
x = 5±2√7/3
The quadratic equation that has thw above general solution will be;
3x²-10x+6 = 0
From the equation, a = 3, b= -10 and c = 6
Substituting this value in the general formula to get x we have;
x = -(-10)±√(-10)²-4(3)(6)/2(3)
x = 10±√100-72/6
x = 10±√28/6
x = 10±√7×4/6
x = 10±2√7/6
Dividing through by 2 gave;
x = 2(5±2√7)/6
x = 5±2√7/3 (which gives the solution in question)
How to do 2(x+1.25)=3.5 by dividing both sides first.
Answer:
1/2
Step-by-step explanation:
2(x+1.25)=3.5
2x+2.5=3.5
2x=3.5-2.5
2x=1
x=1/2
Given that (3,-8) is on the graph of f(x), find the
corresponding point for the function
f(x+4).
If I remember correctly, the x-coordinate 3 goes 4 left and the new ordered pair is (-1,-8). Don't take my word for it unless I'm actually right.
enter the explicit rule for the geometric sequence.
3/2, 3/4, 3/8, 3/16, 3/32, . . .
an=
A park has a 333 meter (\text{m})(m)left parenthesis, start text, m, end text, right parenthesis tall tether ball pole and a 6.8\,\text{m}6.8m6, point, 8, start text, m, end text tall flagpole. The lengths of their shadows are proportional to their heights.
Which of the following could be the lengths of the shadows?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
Tether ball pole shadow: 1.35\,\text{m}1.35m1, point, 35, start text, m, end text
Flagpole shadow: 3.4\,\text{m}3.4m3, point, 4, start text, m, end text
(Choice B)
B
Tether ball pole shadow: 1.8\,\text{m}1.8m1, point, 8, start text, m, end text
Flagpole shadow: 4.08\,\text{m}4.08m4, point, 08, start text, m, end text
(Choice C)
C
Tether ball pole shadow: 3.75\,\text{m}3.75m3, point, 75, start text, m, end text
Flagpole shadow: 8.35\,\text{m}8.35m8, point, 35, start text, m, end text
(Choice D)
D
Tether ball pole shadow: 0.6\,\text{m}0.6m0, point, 6, start text, m, end text
Flagpole shadow: 1.36\,\text{m}1.36m1, point, 36, start text, m, end text
(Choice E, Checked)
E
Tether ball pole shadow: 2\,\text{m}2m2, start text, m, end text
Flagpole shadow: 4.8\,\text{m}4.8m
Answer:
b and d
Step-by-step explanation:
The following D Tether ball pole shadow: 0.6\,\text{m}0.6m0, point, 6, start text, m, end text Flagpole shadow: 1.36\,\text{m}1.36m1, point, 36, start text, m, end text and E Tether ball pole shadow: 2\,\text{m}2m2, start text, m, end text Flagpole shadow: 4.8\,\text{m}4.8m could be the lengths of the shadows. Correct Option is 4 and 5.
Let's assume "x" is the length of the tether ball pole shadow, and "y" is the length of the flagpole shadow.
According to the information given, the proportional relationship can be expressed as:
Tether ball pole height / Tether ball pole shadow length = Flagpole height / Flagpole shadow length
The height of the tether ball pole is 333 meters, and the height of the flagpole is 6.8 meters.
So, we have the following equation:
333 meters / x = 6.8 meters / y
Now, let's solve for "y" in each choice and check which choices satisfy the proportional relationship:
Choice A:
333 / 1.35 = 6.8 / 3.4
246.67 ≈ 2
Choice B:
333 / 1.8 = 6.8 / 4.08
185 ≈ 1.67
Choice C:
333 / 3.75 = 6.8 / 8.35
88.8 ≈ 0.81
Choice D:
333 / 0.6 = 6.8 / 1.36
555 ≈ 5
Choice E:
333 / 2 = 6.8 / 4.8
166.5 ≈ 1.42
The two choices that satisfy the proportional relationship are:
(Choice D) Tether ball pole shadow: 0.6 m, Flagpole shadow: 1.36 m
(Choice E) Tether ball pole shadow: 2 m, Flagpole shadow: 4.8 m
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If the function f(x) = (2x - 3)^3is transformed to g(x) = (-2x - 3)^3, which type of transformation occurred?
A. vertical shift
B. horizontal reflection
C. horizontal shift
D.vertical reflection
PLS HELP! WILL MAKR BRAINLIEST AND GIVE 20 POINTS!!!!
Answer:
See attached table for the answers.
Step-by-step explanation:
Because 1/4 inches is 2 feet, 1 inch is 8 feet, making the conversion factor x8.
Answer:
The scale factor is 1/4 inch to 2 feet but can be simplified to 8 feet per inch.
1. Lobby drawing length is 2 inches.
2. Principal's Office actual length is 10 feet.
3. The library's drawing length is 2.5 inches.
4. The science lab's actual length is 12 feet.
5. The cafeteria's drawing length is 6 inches.
6. The music room's actual length is 32 feet.
8. The gym's actual length is 104 feet.
9. The auditorium's drawing length is 7 inches.
10. The teachers' lounge's actual length is 14 feet.
I hope this helped you. If you would mark brainliest that would be appreciated.
the amount in a savings account increased from $200 to $216. what was the percent increase?
Answer:
7.41%
Step-by-step explanation:
16/216 =
16 ÷ 216 =
0.074074074074074 =
0.074074074074074 × 100/100 =
0.074074074074074 × 100% =
(0.074074074074074 × 100)% ≈
7.407407407407% ≈
7.41%;
I NEED HELP ASAP The base of a triangle is 21 in. The height is 14 in. What is the area of the triangle?
A) 35 in2
B) 98 in2
C) 147 in2
D) 294 in2
Answer:
C 147in2
Step-by-step explanation:
Formula: [tex]\frac{bh}{2}[/tex]
b=base
h=height
21*14=294
294/2=147
The width of a rectangular painting is 3in. More than twice the height. A frame that is 2.5 in. Wide goes around the painting
Question:
A width of a rectangular painting is 3 in. More than twice the height. A frame that is 2.5 in. Wide goes around the painting
a. write an expression for the combined area of the painting and frame.
b. use the expression to find the combined area when the height of the painting is 12 in.
c. use the expression to find the combined area when the height of the the painting is 15 in.
Answer:
a) (h + 5)(2h + 8) is the expression for the combined area of the painting and frame
b) The combined area when h = 12 is 544 square inches
c) The combined area when h = 15 is 760 square inches
Solution:
Given that,
A frame that is 2.5 inches wide goes around the painting
The frame will go around all 4 sides of the painting.
That means that the length of each side of the painting will increase by 2.5 inches
Therefore,
The height of painting and frame is:
h = h + 2.5 + 2.5
h = h + 5
(2.5 inches on the top and the bottom)
Also given that,
Width of a rectangular painting is 3 inches more than twice the height
w = 3 + 2h
Now the width of painting and frame is:
w = 3 + 2h + 2.5 + 2.5
(Again, 2.5 inches on the top and the bottom)
w = 2h + 8
Thus the combined area of the painting and frame is:
[tex]Combined\ area = (h+5)(2h+8)[/tex]
B) Substitute h = 12 inches
[tex]Combined\ area = (12+5)(2(12)+8)\\\\Combined\ area = 17 \times (24+8) = 17 \times 32\\\\Combined\ area = 544[/tex]
Thus the combined area when h = 12 is 544 square inches
C) Substitute h = 15 inches
[tex]Combined\ area = (15+5)(2(15)+8)\\\\Combined\ area = 20 \times (30+8) = 20 \times 38\\\\Combined\ area = 760[/tex]
Thus combined area when h = 15 is 760 square inches
True or false 4.62 < 4.67
True, 4.62 is less than 4.67
You start driving north for 7 miles, turn right, and drive east for another 24 miles. At the end of driving, what is your straight line distance from your starting point?
Answer:
[tex]AC = 25\ miles[/tex]
Step-by-step explanation:
Given:
Distance for north side = 7 miles.
Distance for east side = 24 miles.
We need to find the displacement.
Solution:
Figure shows Point A is starting point and AB = 7 miles is North side distance and BC = 24 miles is east side distance and AC is shown as displacement.
Using Pythagoras theorem to find displacement (AC).
[tex](AC)^{2}=(AB)^{2}+(BC)^{2}[/tex]
Substitute AB = 7 and BC = 24 in above equation.
[tex](AC)^{2}=(7)^{2}+(24)^{2}[/tex]
[tex](AC)^{2}=49+576[/tex]
[tex](AC)^{2}=625[/tex]
[tex]AC = \sqrt{625}[/tex]
[tex]AC = 25\ miles[/tex]
Therefore, displacement of the car [tex]AC = 25\ miles[/tex]
RS and ST are 2 sides of a regular 12-sided polygon.
RT is a diagonal of the polygon.
Work out the size of angle STR.
You must show your working.
Answer:
15°
Step-by-step explanation:
The exterior angle at vertex S is 360°/12 = 30°. That angle has a measure that is equal to the sum of the congruent angles at R and T of ΔRST. In other words, ...
∠T = 30°/2 = 15°
The size of angle STR is 15°.
The sides of a regular polygon are congruent.
The size of STR is 15 degrees
The polygon is 12-sided.
This means that:
[tex]\mathbf{n =12}[/tex]
The sum of angles in a regular hexagon is 360.
So, the angle at vertex S is:
[tex]\mathbf{\theta = \frac{360}{n}}[/tex]
This gives
[tex]\mathbf{\theta = \frac{360}{12}}[/tex]
[tex]\mathbf{\theta = 30^o}[/tex]
The external angle of a triangle equals the sum of the opposite internal angles.
This means that:
[tex]\mathbf{\theta = \angle STR + \angle SRT}[/tex]
Where:
[tex]\mathbf{ \angle STR = \angle SRT}[/tex]
So, we have:
[tex]\mathbf{\theta = \angle STR + \angle STR}[/tex]
[tex]\mathbf{\theta = 2\angle STR}[/tex]
Substitute [tex]\mathbf{\theta = 30^o}[/tex]
[tex]\mathbf{30^o = 2\angle STR}[/tex]
Divide both sides by 2
[tex]\mathbf{15^o = \angle STR}[/tex]
Rewrite as:
[tex]\mathbf{\angle STR = 15^o }[/tex]
Hence, the size of STR is 15 degrees
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what is 3.40425532 reduced
in rectangle PQRS, shown below, the diagonal PR is 15 meters. if the sine of angle SPR is 7/10, what is the value of RS?
Answer:sin =perpendicular/hypotenuse
Step-by-step explanation:
Sin angle is given use tan theta or cos theta to find the RS
Which number line represents the solutions to x + 4 = 2?
A
+
-7
-6
+
-5
+
-4
+
-3
-2
+
-1
0
1
2
+
3
+
4
+
5
+
6
+
7
A
+
-7
+
-6
+
-5
+
-4
+
-3
+
-2
+
-1
+
0
+
1
+
3
2
+
5
4
+
6
+
+
7
+
I
+
+
+
+
-7
+
-6
+
-5
+ + + +
-4 -3 -2 -1
+
1
2
+
3
+
4
+
5
6
+
7
to to
+
+
-7
-6
-5
-4
-3
-2 -1
1
2
3
+ +
4
5
6
7
Answer:
-2
Step-by-step explanation:
The solution of the expression x + 4 = 2 is shown in image.
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
Expression is,
⇒ x + 4 = 2
Now, We can simplify as;
⇒ x + 4 = 2
Subtract 4 both side,
⇒ x + 4 - 4 = 2 - 4
⇒ x = - 2
Thus, The solution of the expression is,
\⇒ x = - 2
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A line passes through the origin and through points A(−2, b−14) and B(14−b, 72). What is the greatest possible value of b?
Answer:
The greatest possible value for b is 26.
Step-by-step explanation:
Given that the line passes through the Origin O(0, 0); A(-2, b - 14) &
B(14 - b, 72).
Let us assume the points are in the order: AOB.
Since the line passes through all these points the slope of the line segment AO = The slope of the line segment AB.
Slope of a line with two points: [tex]$ \frac{y_2 - y_1}{x_2 - x_1} $[/tex] where [tex]$ (x_1, y_1) $[/tex] and [tex]$ (x_2, y_2) $[/tex] are the points given.
[tex]$ (x_1, y_1) = (0,0) $[/tex]
[tex]$ (x_2, y_2) = (-2, b - 14) $[/tex]
Therefore, the slope of the line segment AO = [tex]$ \frac{b - 14}{-2} $[/tex]
Similarly, for the slope of the line segment OB.
The two points are [tex]$ (x_1, y_1) = (0, 0) $[/tex] and [tex]$ (x_2, y_2) = (14 - b, 72) $[/tex].
The slope is: [tex]$ \frac{72}{14 - b } $[/tex]
Since, the slopes are equal we can equate:
[tex]$ \frac{b - 14}{-2} = \frac{72}{14 - b} $[/tex]
[tex]$ \implies \frac{b - 14}{-2} = \frac{72}{-(b - 14)} $[/tex]
[tex]$ \implies (b - 14)^2 = 72 \times 2 = 144 $[/tex]
[tex]$ \implies (b - 14)^2 = 12^2 $[/tex]
Taking square root on both sides we get:
[tex]$ \implies (b - 14) = \pm 12 $[/tex]
[tex]$ \implies b = 2 \hspace{2mm} or \hspace{2mm} 26 $[/tex]
Therefore, the maximum value of b = 26.
Hence, the answer.
spinner at the right is spun 12 times. It lands on blue 1 time.
What is the experimental probability of the spinner landing on blue?
Answer:
1/12
Step-by-step explanation:
Which expression represents the phrase the sum of twice a number and 7
Answer:
2n+7
Step-by-step explanation:
Add the following numbers and use the checking method (add down and then add up) to make sure your answer is correct. (Copy carefully on scratch paper to work the problem.)
471
+
582
To add 471 and 582, line up the numbers by place value and add each column, carrying over as needed. The sum is 1053. You check by reversing the order of the numbers and adding again; the sum should remain the same.
Explanation:To add the following numbers and use the checking method (add down and then add up), perform the following steps:
Write down the numbers vertically aligned by their place values: 471 + 582 Add the ones place values (1+2) to get 3. Add the tens place values (7+8) to get 15, write down 5 and carry over 1. Add the hundreds place values (4+5) along with the carried over 1 to get 10, write down 0 and carry over 1. Write the carried over 1 in the next left column to get the final sum: 1053 To check, add the sum upwards: 582 + 471 You should arrive at the same sum: 1053.
If you obtain the same result by both adding down and adding up, your answer is verified as correct.
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Sarai is mixing a solution. She pours all the liquid from a full small beaker into a larger beaker. The liquid fills the large beaker to 15% of its capacity. If the small beaker holds 300 mL, how much does the large beaker hold?
Answer:
2000 ml
Step-by-step explanation:
Given: Sarai pours all the liquid from a full small beaker into a larger beaker.
The liquid fills the large beaker to 15% of its capacity.
The small beaker holds 300 ml.
Lets assume capacity of large beaker to hold be "x".
As given, Sarai pours all the liquid from a full small beaker into a larger beaker
∴ [tex]15\% \times x= 300\ ml[/tex]
⇒ [tex]0.15x= 300[/tex]
Dividing both side by 0.15
⇒[tex]x= \frac{300}{0.15}[/tex]
∴ [tex]x= 2000\ ml[/tex]
Hence, the large beaker can hold 2000 ml of liquid.
A snowboard is on sale for $476. If the
original price was $560, what is the
percent discount?
Answer:
15%
Step-by-step explanation:
we call the original price 100% and to find the discount amount :
Multiply 100 by $476 then divide by $560
100 × $476 ÷ $560 = 85
$476 is 85% of the original price therefore the amount of discount as in percentage is 100 - 85 = 15%
What is the value of x?
Answer: x = 15
Step-by-step explanation: The first thing to note is that what we have here are two similar triangles. First we have triangle ABC and secondly we have triangle EDC. Line BD is a transversal that cuts line AE at point C. Hence we can deduce that angle ACB is equal in measurement to angle ECD (opposite angles). Next we also observe that the other two angles are right angles, that is, 90° in size. Therefore we can conclude that the other two angles (angle ABC and angle EDC) are also of the same measurement.
We can now establish the ratio of the similar sides.
Line AB = Line ED
Line AC = Line EC
AB/ED = AC/EC
24/40 = 2x/3x + 5
3/5 = 2x/3x + 5 {the left hand side has been reduced to it's simplest form}
Next we cross multiply and that gives us
3(3x + 5) = 5(2x)
9x + 15 = 10x
Subtract 9x from both sides of the equation
15 = 10x - 9x
15 = x
Bonds are a(n) _______________ instrument.
Answer:
indebtedness
Step-by-step explanation:
what does 6x +2(5x -6)
Answer:
Step-by-step explanation:
Is you simplify, you get 16x-12
6x+2(5x-6)
6x+10x-12
16x-12
Answer:
Assuming you just want it simplified, the answer would be 16x - 12
Step-by-step explanation:
6x + 2(5x - 6)
6x + 10x - 12
16x - 12
How many times smaller is 2 × 10-3 than 4 × 10-2? PLEASE HELP
A.
20
B.
200
C.
2,000
D.
0.2
Step-by-step explanation:
Let x be the smaller than 4 ×[tex]10^{-2}[/tex].
To find, the number of times smaller is 2 × [tex]10^{-3}[/tex] than 4 × [tex]10^{-2}[/tex] = ?
∴ x = [tex]\dfrac{4\times 10^{-2}}{2\times 10^{-3}}[/tex]
= 2 × [tex]10^{-2}[/tex] × [tex]10^{3}[/tex]
Using the identity,
[tex]a^{m}=\dfrac{1}{a^{-m}}[/tex]
= 2 × [tex]10^{-2+3}[/tex]
Using the identity,
[tex]a^{m} \timesa^{n}=a^{m+n}[/tex]
= 2 × [tex]10^{1}[/tex]
= 2 × 10
= 20
Thus, the required "option A) 20" is correct.
1 > 5 (b - 14) + 16 help me please
Answer:
b < 11
Step-by-step explanation:
Given
1 > 5(b - 14) + 16 ← distribute and simplify right side
1 > 5b - 70 + 16
1 > 5b - 54 ( add 54 to both sides )
55 > 5b ( divide both sides by 5 )
11 > b, thus
b < 11
identify the terms, coefficients, and constants in the expression.
1. 3 + c + e
2. 5m + 9
3. 3p2 + 7
Answer:
1. 3 is a constant term of the expression.
2. 9 is constant term of the expression.
3.7 is a constant term of the expression.
Step-by-step explanation:
1. 3+c+e
Here 3 is a constant term of the expression.
c and e are the variables.
The coefficient of c is 1.
The coefficient of e is 1.
It is a trinomial expression.
2.
5m +9
9 is constant term of the expression.
m is a variable of the expression.
The coefficient of m is 5.
It is a binomial expression.
3.
3p²+7
7 is a constant term of the expression.
p is the variable.
The coefficient of p² is 3.
It is a binomial expression.
The perimeter of a rectangle must be less than 172 feet. If the length is known to be 53 feet, find the range of possible widths for the rectangle. (Note: The formula for the perimeter of a rectangle is P=2l+2w , where l is the length and w is the width).
Express your answer in interval notation. Use decimal form for numerical values.
Answer:
1 - 32.5
Step-by-step explanation:
If the perimider is less then 172, that the limit is 171. 171 - (53)2 = 65. divide that by the two sides that are the width it equals 32.5
Perimeter is the sum of the length of the sides used to make the given figure. The range of the width of the rectangle is (0,33).
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Given that the perimeter of a rectangle must be less than 172 feet. Also, given that the length of the rectangle is 53 feet. Therefore, we can write inequality of the width of the rectangle as,
2(Length) + 2(Width) < Perimeter
2(53 feet) + 2(Width) < 172 feet
106 feet + 2(Width) < 172 feet
2(Width) < 172 feet - 106 feet
2(Width) < 66 feet
Width < 66feet / 2
Width < 33 feet
Hence, the range of the width of the rectangle is (0,33).
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Given the equation y=-1/3x-7, what are the slope and the y-intercept?
Answer: slope is -1/3 and the y intercept is -7
Step-by-step explanation: