If a segment XZ joining two endpoints X[tex](x_1,y_1)[/tex] and Z[tex](x_2,y_2)[/tex] is divided by a point Y(x, y) externally in the ratio of m : n,
Coordinates of the point will be,
x - coordinates → [tex]\frac{mx_2-nx_1}{m-n}[/tex]
y - coordinates → [tex]\frac{my_2-ny_1}{m-n}[/tex]
If the coordinates of the endpoints X and Z are (1, 9) and (5, -11) respectively and the ratio in which a point Y divides the segment is 1 : 5,
(Since, XY : XZ = 1 : 4 therefore, XY : YZ = 1 : 5)
Therefore, coordinates of Y will be,
x- coordinates → [tex]\frac{1(5)-5(1)}{1-4}=0[/tex]
y-coordinates → [tex]\frac{1(-11)-5(9)}{1-5}=\frac{-56}{-4}=14[/tex]
Therefore, coordinates of Y will be [tex](0,14)[/tex].
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Find the value of x .
Answer:
10
Step-by-step explanation:
By using intersecting chord theorem:
NH.HT=MH.HY
(x+20)*8=12*20
x+20=12*20/8
x+20=240/8
x+20=30
x=30-20
x=10
please i need helppp
Answer:
x=50°
Step-by-step explanation:
x+3°+x+20°+x+7°=180°
or,3x+30°=180°
or,3x=150°
or,x=50°
Answer:
50
Step-by-step explanation:
→ First add all the angles together as angles on a straight line add to 180°
x + 3 + x + 20 + x + 7 = 180
→ Simplify
3x + 30 = 180
→ Minus 30 from both sides
3x = 150
→ Divide both sides by 3
x = 50
you buy 4 video tapes for 14.99 each and 3 dvds for 19.99 each find the total cost of the movies
Answer:
119.93
Step-by-step explanation:
I will assume the total of the cost of the movies will be the total.
the total = 4*14.99 + 3*19.99
total = 119.93
please help me with this. thanks a lot
Answer:
Part A)
Approximately 318.1318 meters.
Part B)
Approximately 137.7551 meters.
Step-by-step explanation:
The path of a projectile is given by the equation:
[tex]\displaystyle y = \sqrt{3} x -\frac{49x^2}{9000}[/tex]
Part A)
The range of the projectile will be given by the difference between its starting point and landing point. In other words, its two zeros.
Let y = 0 and solve for x:
[tex]\displaystyle 0 = \sqrt{3}x - \frac{49x^2}{9000}[/tex]
Factor:
[tex]\displaystyle 0 = x\left(\sqrt{3} - \frac{49x}{9000}\right)[/tex]
Zero Product Property:
[tex]\displaystyle x = 0 \text{ or } \sqrt{3} - \frac{49x}{9000} = 0[/tex]
Solve for each case:
[tex]\displaystyle x = 0 \text{ or } x = \frac{9000\sqrt{3}}{49}\approx 318.1318[/tex]
Hence, the range of the projectile is approximately (318.1318 - 0) or 318.1318 meters.
Part B)
Since the equation is a quadratic, the maximum height is given by its vertex. Recall that the vertex of a quadratic is given by:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = -49/9000 and b = √3.
Find the x-coordinate of the vertex:
[tex]\displaystyle x = - \frac{(\sqrt{3})}{2\left(\dfrac{-49}{9000}\right)} = \frac{4500\sqrt{3}}{49}[/tex]
Then the maximum height will be:
[tex]\displaystyle \displaystyle \begin{aligned} y\left(\frac{4500\sqrt{3}}{49}\right) &=\sqrt{3} \left(\frac{4500\sqrt{3}}{49}\right) -\frac{49\left(\dfrac{4500\sqrt{3}}{49}\right)^2}{9000} \\ \\ &= \frac{13500}{49} -\frac{6750}{49}\\ \\ &=\frac{6750}{49}\\ \\ &\approx 137.7551\text{ meters}\end{aligned}[/tex]
The maximum height reached by the projectile will be 137.7551 meters.
please help! this is due my today and i don't understand it
-5c+5c+2c–6c–12c-16 16=c
Step-by-step explanation:
-5c+5c+2c–6c–16=c
-16c - 16=c
-16 = c + 16c
-16 = 17c
-16/17 = c
Simplify 9/12 into simplest form
can you please help me with this
Answer:
so
Step-by-step explanation:
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how do i simplify "-2.5"?
Answer:
By adding
please mark me brainliest
write each fraction number as a decimal write each fraction number as a decimal -7 8/45
[tex]\\ \sf\longmapsto -7\dfrac{8}{45}[/tex]
[tex]\\ \sf\longmapsto \dfrac{45(-7)+8}{45}[/tex]
[tex]\\ \sf\longmapsto \dfrac{315+8}{45}[/tex]
[tex]\\ \sf\longmapsto \dfrac{323}{45}[/tex]
[tex]\\ \sf\longmapsto 7.1[/tex]
What is the value of the expression 2 + 3/4 (1 1/2 + 3.8)
Answer:
5.975
Step-by-step explanation:
Solve the proportion below.
90/x=3/4
x =
O A. 91
B. 120
C. 150
O D. 99
Answer:
B) 120
Step-by-step explanation:
Initial problem: 90/x = 3/4
Cross multiply to get:
90*4 = 3x
360 = 3x
x = 120
Check (optional):
90/120 = 3/4
(simplify):
3/4 = 3/4 so it is correct
If you're confused about any of these steps, just let me know and I'll try to help!
The value of x would be B. 120
To solve the proportion 90/x = 3/4, we can use cross-multiplication. Cross-multiplication involves multiplying the numerator of the first fraction (90) with the denominator of the second fraction (4), and multiplying the numerator of the second fraction (3) with the denominator of the first fraction (x).
So, the equation becomes:
90 * 4 = 3 * x
Simplifying:
360 = 3x
Now we divide both sides of the equation by 3:
360/3 = 3x/3
120 = x
Therefore, x = 120.
The correct answer is option B. 120.
More can be learned about proportions at;
brainly.com/question/24372153
#SPJ6
If f(x) = 9^x , them prove that : f(m+n+p) = f(m) × f(n) × f(p) .
Answer:
f(m+n+p) = 9^(m+n+p)
while f(m) × f(n) × f(p) = 9^m+9^n+9^p = 9^(m+n+p)
so the second property explains why it's a + instead of ×
Is (8, –2) a solution to the equation y = 2?
Answer:
No
Step-by-step explanation:
Any point that aligns on the line of y = 2 is a solution. But (8, -2) falls below that line since the point's y-coordinate is equal to -2, not 2. Hope this helps!
х
(-4+ 8x) +3>
What is the solution to the inequality
-4?
Step-by-step explanation:
if I understand the typed information here, we have
(-4 + 8x) + 3 > -4
so, I am looking at that :
-4 + 8x + 3 > -4
let's first add 4 on both sides
8x + 3 > 0
then subtract -3 on both sides
8x > -3
and finally divide both sides by 8
x > -3/8
since we never multiplied or divided by a negative number, the inequality sign stays the same.
so, this inequality is true for all x > -3/8
What is the answer to
5 - ( - 12 )
Answer: 17
Step-by-step explanation:
since there are two minuses, you change them to a plus and add, ending up with 5+12 to get 17
if 3^2x +1 +8 =27 find x
Pls guys I need now
Step-by-step explanation:
3x²+1+8=27
3x²+9=2
3x²=27-9
3x²=19
x²=19/3
[tex]x = \frac{ \sqrt[]{19} }{ \sqrt{3} } [/tex]
Answer:
[tex]3^{2x} + 1 + 18 = 27\\ 3^{2x} = 18\\2x = log_{3} 18[/tex]
Step-by-step explanation:
if n(A) = 12, n(b) = 9 and n(AuB) = 16 then find the value of n (A-B)
Question has a slight error .we should find n(A[tex]\cap[/tex]B)
n(A)=12n(B)=9.$n(A\cup B)=16$[tex]\boxed{\sf n(A\cup B)=n(A)+n(B)-n(A\cap B)}[/tex]
[tex]\\ \rm\longmapsto n(A\cap B)=n(A)+n(B)-n(A\cup B)[/tex]
[tex]\\ \rm\longmapsto n(A\cap B)=12+9-16[/tex]
[tex]\\ \rm\longmapsto n(A\cap B)=5[/tex]
Pls help with this function
Emergency
Answer:
rational function is the correct answer
6x-2+9y-3y-3x
Help anyone?
Step-by-step explanation:
6x-2+9y-3y-3x
6x-3x-2+9y-3y
3x-2+6y
Therefore its 3x-2+6y.
Need help ASAP will give more points
Answer:
30%
Step-by-step explanation:
14+ 18+ 28 = 60
18/60 × 100 = 30%
Answer:
[tex] \frac{18}{60} = \frac{3}{10} = 30\%[/tex]
Step-by-step explanation:
Total token sample = 14 + 18 + 28 = 60
Frequency of blue:
[tex] = \frac{18}{60} \: [/tex]
[tex] = \frac{18}{60} \times 100\%[/tex]
[tex] = 30\%[/tex]
Which properties did you use in solving the equation? Check all of the boxes that apply.
QESTION
Solve the equation based on the description “one-third of a number, decreased by 6, equals 11.”
ANSWERS
.the addition property of equality
.the multiplication property of equality
.the transitive property
the reflexive property
Answer:
the addition property of equality
.the multiplication property of equality
Step-by-step explanation:
1/3x - 6 =11
Add 6 to each side using the addition property of equality
1/3x-6+6 = 11+6
1/3x = 17
Multiply each side by 3, using the multiplication property of equality
1/3x *3 = 17*3
x = 54
I need help with this question please
Simplify.
18 2+6(4+1) -2
Step-by-step explanation:
18 2+6(4+1)-2
18 8(5)-2
18 40-2
18 38
18×38
multiply it to get your answer
a) make h the subject of the formula
T=26- h/500
b) the outside air temperature T°C,of an aircraft at a height, h feet , given by
T=26- h/500
the outside air temperature of an aircraft is -53°C
1 metre=3³/8 feet
calculate the height in metres of the aircraft
Answer:
11703.7 metres
Step-by-step explanation:
* means multiply
/ means divide
plug in the values
T=26- h/500
-53 = 26- h/500
-53 -26 = h/500
-79 = h/500
-79 * 500 = h
-39500 = h
-39500 is in feet
3³/8 =
39500 / 3.375 =
11703.7037037 metres
The answer if any body knows it
Answer:
[tex]A=\pi(336)[/tex]
[tex]A=1055.575[/tex]
Step-by-step explanation:
1. Approach
One is given a prism. The base of the prism is a quarter of a circle, the prism's length is also given. The easiest method to find the volume of the prism is to find the area of the quarter of the circle, then multiply the result by the length of the prism.
2. Find the area of the quarter circle
The following formula can be used to find the area of a circle,
[tex]A_c=(\pi)(r^2)[/tex]
Since one is trying to find the area of a quarter of a circle, one must multiply this formula by ([tex]\frac{1}{4}[/tex]). Please note that the parameter (r) represents the radius of the circle or the distance from the center of the circle to the circumference or outer edge of the circle. The parameter ([tex]\pi[/tex]) represents the number ([tex]3.1415...[/tex]).
[tex]A_c=\frac{1}{4}(\pi)(r^2)[/tex]
Substitute the given values into the formula and simplify to evaluate,
[tex]A_c=\frac{1}{4}(\pi)(r^2)[/tex]
[tex]A_c=\frac{1}{4}(\pi)((8)^2)[/tex]
[tex]A_c=\frac{1}{4}(\pi)(64)[/tex]
[tex]A_c=(\pi)(16)[/tex]
[tex]A_c\approx 50.2655[/tex]
3. Find the volume of the prism
Now multiply the area of the quarter circle by the length of the prism to find the volume of the prism. Note that the parameter (l) represents the length of the prism,
[tex]A=A_c(l)[/tex]
Substitute and simplify to evaluate,
[tex]A=(\pi)(16)(21)[/tex]
[tex]A=\pi(336)[/tex]
[tex]A=1055.575[/tex]
Which equation has the same solution as x2 + 12x +8= -5?
Answer:
Hope its help you...........
is the expression 5+3x/2 equal to the expression 4x
Answer:
No
Step-by-step explanation:
[5+3x] is an expression that cannot be added because 5 is a natural interger but 3x is an unknown
and therefore it cannot be divided by 2 to get 4
Better example :
if the question will give 4x , then
it should be [5x+3x]/2 = 8x/2 = 4x
it's obvious from the example I gave that 8x can be divided by 2 to give 4x
PLEASE HELP I WIL, GIVE BRAINLIST
Answer:
B There should be lines drawn through the inner vertices as well
Step-by-step explanation:
The answer is B There should be lines drawn throu the inner verticesas well Because
those red lines are from inner vertices
If f(x) = x (ln x), find f'(x).
A. e^(x + 1)
B. 1 + ln x
C. 1 + e^x
D. (ln x)^2 + x
Answer:
[tex]f'(x)=1+\ln x[/tex]
Step-by-step explanation:
[tex]f'(x)[/tex] is notation for the first derivative of [tex]f(x)[/tex].
Recall the product rule:
[tex](f\cdot g)'=f'\cdot g+g'\cdot f[/tex]
Therefore, we have:
[tex]\displaystyle \frac{d}{dx}(x\ln x)=\frac{d}{dx}(x)\cdot \ln(x)+\frac{d}{dx}(\ln x)\cdot x[/tex]
Note that:
[tex]\displaystyle \frac{d}{dx}(x)=1,\\\\\frac{d}{dx}(\ln x)=\frac{1}{x}[/tex]
Simplify:
[tex]\displaystyle \frac{d}{dx}(x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x, \\\\\frac{d}{dx}(x\ln x)= \ln x+1=\boxed{1+\ln x}[/tex]
The derivative is:
[tex] \bold{f(x) \: = \: x \: \times \: (In(x))}[/tex]
[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x \: \times \: In(x))}[/tex]
[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x) \: \times \: In(x) \: + \: x \: \times \: \frac{d}{dx} (In(x))}[/tex]
[tex] \bold{f'(x) \: = \: 1In(x) \: + \: x \: \times \frac{1}{x} }[/tex]
[tex] \bold{f'(x) \: = \: In(x) \: + \: x \: \times \: \frac{1}{x} }[/tex]
[tex] \boxed{ \bold{f'(x) \: = \: In(x) \: + \: 1}}[/tex]
MissSpanishthree times the difference of a number cubed and 10 in algebraic expression
Answer:
3 × x³ - 10
Step-by-step explanation:
three times = 3×
difference = -
number cubed (unknown so we use x) = x³
10 = 10
Hope this helps!
I'm sorry if wrong :(