Answer:
y = −1/3x+17/3
Step-by-step explanation:
The line segment has slope -1/3. This means that any line perpendicular to it will have a slope of 3 (negative reciprocal)
Any line that bisects the line segment will pass through its midpoint. The midpoint is (5,4)
Midpoint formula: [tex]( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )[/tex]
So perpendicular bisector of this line is simply a line with slope −1/3 that passes through point (5, 4)
y - 4 = -1/3 (x-5)=
y = −1/3x+17/3
Q2:
Which expression is equivalent to 4(x + 1) – 7(x + 3)?
A
11x + 25
B
11x – 17
C
–3x – 17
D
–3x + 25
Answer:
The expression equivalent to the given equation is -3x - 17
Step-by-step explanation:
4(x + 1) - 7(x + 3)
Distribute 4 to (x + 1) and distribute 7 to (x + 3).
4x + 4 - 7x - 21
Combine like terms.
-3x - 17
Can someone help me solve (a) and (c) pls.
Thanks
Answer:
Area of ABCD = 959.93 units²
Step-by-step explanation:
a). By applying Sine rule in the ΔABD,
[tex]\frac{\text{SinA}}{46}=\frac{\text{Sin}\angle{DBA}}{35}[/tex]
[tex]\frac{\text{Sin110}}{46}=\frac{\text{Sin}\angle{DBA}}{35}[/tex]
Sin∠DBA = [tex]\frac{35\times \text{Sin}(110)}{46}[/tex]
m∠DBA = [tex]\text{Sin}^{-1}(0.714983)[/tex]
m∠DBA = 45.64°
Therefore, m∠ADB = 180° - (110° + 45.64°) = 24.36°
m∠ADB = 24.36°
c). Area of ABCD = Area of ΔABD + Area of ΔBCD
Area of ΔABD = AD×BD×Sin([tex]\frac{24.36}{2}[/tex])
= 35×46Sin(12.18)
= 339.68 units²
Area of ΔBCD = BD×BC×Sin([tex]\frac{59.92}{2}[/tex])°
= 46×27×(0.4994)
= 620.25 units²
Area of ABCD = 339.68 + 620.25
= 959.93 units²
A loan of $8,000 is paid back in two years in monthly payments of $400. The percentage interest on the loan was
(a) 5%
(b) 8 ⅓%
(c) 16 ⅓%
(d) 20%
Answer:
D
Step-by-step explanation:
The number of months in two years is 24 months.
Now, with a repayment plan of $400 per month, the total amount returned will be 400 * 24 = $9,600
Now, $8,000 was borrowed but $9,600 was returned
The amount of interest is 9600-8000 = 1600
So what percentage of 8,000 is 1600?
1600/8000 * 100 = 16/80 * 100 = 1/5 * 100 = 20%
Gym A charges a $25 membership fee and a $25 monthly fee. Gym B charges a $55 membership fee and a $10 monthly fee. After how many months will the total amount of money paid to both yoga clubs be the same? What will the amount be?
Answer: 75
solve:
For gym A
total cost= membership fee+monthly fee
membership fee=25
monthly fee=25
cost of x month=25x
total cost=25+25x
for gym B
membership fee=10
total cost=55+10x
now total cost are same
25+25x=55+10x
15x=30
x=30/15
x=2.
2 months
and amount =25+25*2=75
Answer:
2 months, they will have paid 75 dollars
Step-by-step explanation:
Gym A
25+ 25m where m is the number of months
Gym B
55 + 10m
Set them equal
25+25m = 55+10m
Subtract 10m from each side
25+25m-10m = 55+10m-10m
25+15m = 55
Subtract 25 from each side
25+15m-25 = 55-25
15m = 30
Divide by 15
15m/15 = 30/15
m=2
After 2 months
25+25(2) = 25+50 = 75
The cost is 75 dollars
A father is 38 years old, his sons are 13 and 5 years old, and his daughter is 8 years old. In how many years will the father be the same age as his children put together?
Answer: 6
Step-by-step explanation:
38+x= 13+5+8+x
38+x=26+x
38-26=2x
12=2x
x=6
A hiker is climbing down a valley. He stops for a water break 4 times. Between each break, he descends 15 meters. How many meters did he descend? Ju Chan answered the question by writing the following: 4(−15) meters = −60 meters. Which word in the problem indicates that a negative number should be used?
Answer:
"descends"
Step-by-step explanation:
(just had the same question).
a) Complete the table of values for y = 3x – 1
X
-2
-1
0
1
2
3
y
I
-4
5
Answer:
x | y
− 2 − 6
− 1 − 3
0 0
1 3
2 6
hope this helps!
The table of values for the equation y = 3x - 1, is attached.
x y
-2 -7
-1 -4
0 -1
1 2
2 5
3 8
What are equations?Equations are relations between two or more variables, used to find the value of an unknown variable from the known value of other variables.
How do we solve the given question?We are given the equation y = 3x - 1. We are asked to complete the table, for the given values of x: -2, -1, 0, 1, 2, 3.
To find the y variable, for the given x's, we substitute each value of x, one at a time in the equation.
Value of y when x = -2 is, y = 3(-2) -1 = - 6 - 1 = -7.Value of y when x = -1 is, y = 3(-1) -1 = - 3 - 1 = -4.Value of y when x = 0 is, y = 3(0) -1 = 0 - 1 = -1.Value of y when x = 1 is, y = 3(1) -1 = 3 - 1 = 2.Value of y when x = 2 is, y = 3(2) -1 = 6 - 1 = 5.Value of y when x = 3 is, y = 3(3) -1 = 9 - 1 = 8.We put all these values of y, for the corresponding value of x in the table. The completed table is attached.
Learn more about equations at
https://brainly.com/question/4344214
#SPJ2
Please help ! ;v; A coordinate plane is shown. A line passes through the point (-4,1) and through the y-axis at 4. What is the y-intercept of the line shown?
Answer:
(0, 4)
Step-by-step explanation:
The y-intercept is where the graph crosses the y-axis when x = 0. Since you are given the graph, you can see that when x = 0, the graph crosses y = 4, so our y-int is (0, 4).
PLS HELP ASAP Event A and event B are independent events. Given that P(B)=13 and P(A∩B)=16, what is P(A)?
Answer:
Step-by-step explanation:
hello,
As A and B are two independent events we can say that P(A∩B)=P(A)P(B)
P(A)=P(A∩B)/P(B)=16/13
thanks
What is the simplified expression fro -3cd-d(2c-4)-4d
Answer:
-5cd
Step-by-step explanation:
-3cd-2cd+4d-4d
-3cd-2cd=-5cd
4d-4d=0
=-5cd
Answer:
-5 cdSolution,
[tex] - 3cd - d(2c - 4) - 4d \\ = - 3cd - 2cd + 4d - 4d \\ = - 5cd[/tex]
Hope this helps...
Good luck on your assignment..
What is the measure of angle D?
Answer:
52
Step-by-step explanation:
Since the sum of interior angles in a quadrilateral is 360°, you have to subrtact all those numbers from 360° in order to get angle D. What I mean is:
360 - (128+126+54)
360 - 308
52
Answer:
52°
Step-by-step explanation:
The trapezoid is a closed figure, meaning all the angles must equal 360°.
1. Set up the equation
128° + 126° + 54° + ∠D = 360°
2. Solve for ∠D
360 - 128- 126- 54 = 52
∠D = 52°
You can also solve this by knowing that in a trapezoid:
∠A + ∠D = 180° and ∠B + ∠C = 180°
1. Set up the equation
128 + ∠D = 180°
2. Solve
180 - 128 = 52
∠D = 52°
helppp
Determine the x-intercept of the line whose equation is given:
y = StartFraction x Over 2 EndFraction minus 3
a.
(6, 0)
b.
(negative 6, 0)
c.
(0, three-halves)
d.
(Negative three-halves, 0)
Answer:
A
Step-by-step explanation:
If you put your function in a graphing calculator you will get (6,0)
Use the graph to evaluate the function below for specific inputs and outputs.
Answer:
y = G(x) = 6, when x = -4
y = G(x) = -2, when x = 3
Step-by-step explanation:
From the attached graph tracing the first point to the graph and then to x axis.
y = G(x) = 6
as shown on the attachment(by the thick line)
y = G(x) = 6, when x = -4
From the attached graph tracing the second point to the graph and then to x axis.
y = G(x) = -2
as shown on the attachment(by the thin line)
y = G(x) = -2, when x = 3
A drawer contains 60 pairs of socks. Each pair is one of four colors. What is the minimum number of socks that must be drawn, at random, from the drawer to ensure that a pair of matching-color socks is selected?
Answer:
5.
Step-by-step explanation:
If the first 4 picked are of different colours then the fifth sock must be a match. for one of the four.
I have two U.S. coins that total 30 cents. One is not a nickel. What are the two coins?
To solve the given problem, we need to know the types of US coins. The given problem is one of the tricky problems. So lets find out
In the united states, there are six types of coins produced. Penny- 1 cent, nickel- 5 cents, dime- 10 cents, quarter- 25 cents, half dollar- 50 cents and dollar- 100 cents. So u should know these types to slove this know lets move on to the :
Answer and Explanation:
The given problem is a kind of a riddle. It is given that the total of two US coins is
30
cents.
One is not a nickel, But the other one can be a nickel=
5
cents. So, the first one coin is a quarter=
25
cents. Which gives the total
30
cents.
Therefore, the two coins are a nickel and a quarter.
Hope you understood it!!!What does x(x - 2) equal?
Answer:
x^2 - 2x
Step-by-step explanation:
Distribute the x to every term in the parenthesis.
Answer:
x^2 -2x
Step-by-step explanation:
x(x - 2)
Distribute
x*x - 2*x
x^2 -2x
If 3x-5=10x+9, what is 4(x+7)?
Answer: not sure
Step-by-step explanation:
Answer:
Hey there!
3x-5=10x+9
-5=7x+9
-14=7x
x=-2
4(x+7)
4(-2+7)
4(5)
20
Hope this helps :)
help me solve this please
Answer:
Center : (-2, 7)
Radius : 6
Step-by-step explanation:
If you use desmos (graphing website), you're able to plug in the the equation to find the radius and center.
find the value of t perimeter
Answer:
t = 15.2 is the answerStep-by-step explanation:
1. Make an equationnumbers to find perimeter = perimeter
Side + Side + 2 unknown sides = perimeter
12 + 7.8 + 2t = 50.2
2. Simplify like terms19.8 + 2t = 50.2
3. Solve19.8 + 2t = 50.2
-19.8 - 19.8
2t = 30.4
t = 15.24. Check:12 + 7.8 + t + t = 50.2
12 + 7.8 + (15.2) + (15.2) = 50.2
50.2 = 50.2 Correct!Hope this helped,
Kavitha
Answer:
t = 15.2 miles
Step-by-step explanation:
First, let's add the top and bottom numbers together.
7.8 + 12 = 19.8 mi
Next, we subtract that from 50.2 to get the combined value of both t's.
50.2 - 19.8 = 30.4 mi
Finally, we can divide 30.4 by 2 to get the value of t.
30.4 ÷ 2 = 15.2 mi
To check our answer, we can add all the sides up to see if they equal to 50.2. 15.2 + 15.2 = 30.4
30.4 + 12 + 7.8 = 50.2
In the right triangle LMN L and M are complementary angles and sin L is 19/20 what is cos M
Hey there! I'm happy to help!
There is a rule in trigonometry that says that the sine of one angle is equal to the cosine of that angle's complement.
Complementary angles are ones that equal 90 degrees when added.
We see that L and M are complementary angles, so we can apply this rule.
The sine of L is 19/20. We know that the sine of angle L is equal to the cosine of L's complement from our rule, which is M. This means that the cosine of M is equal to 19/20.
Have a wonderful day!
I will mark brainiest if correct Let f(x)=5x−7 and g(x)=x+3. Find f(g(x)) and g(f(x)).
Step-by-step explanation:
f(g(x))= 5(g(x))- 7 = 5(x+3) - 7 = 5x +8
g(f(x)) = f(x) +3 = 5x -7 +3= 5x -4
Some one HELP PLEASE
THE ANSWER IS NOT 40,5 20 -20
Answer:
x = 20
Step-by-step explanation:
If AE is a bisector then it divides the angle in half
BAE = EAC
x+30 = 3x-10
Subtract x from each side
30 = 2x-10
Add 10 to each side
40 = 2x
Divide by 2
40/2 =2x/2
20 =x
The surface area of a cube is 78 cm^2. What is the volume of the cube, rounded to
the nearest tenth of a cm^3?
Answer:
46.87
Step-by-step explanation:
V=*(A^3/2
)/36
V=*(46.87^3/2
)/36
The diagram shows a parallelogram.
4 cm
7 cm
100°
Work out the area of the parallelogram.
Give your answer to 2 significant figures.
Answer:
27.44 square cm
Step-by-step explanation:
If the length of parallelogram is a and b and angle between side a and b is [tex]\alpha[/tex].
Then area of parallelogram = [tex]a*b*sin(\alpha ) = ab sin(\alpha )[/tex]
Given side length 4 cm and 7 cm
angle between them = 100°
value of sin(100°) = 0.98
Thus, area of given parallelogram = 4*7*sin(100°) = 28*0.98 = 27.44
Thus, area of given parallelogram is 27.44 square cm.
A
B
C
D
WHICH ONE??
PLEASE HELP ME !!!
Answer:
Is it B?
Step-by-step explanation:
ab^2 + 2a^2b + 4a + 2b
ab(b+2a) +2(2a+b)
ab(b+2a) +2(b+2a)
(ab+2)(b+2a)
that's why ab+2 is the answer.
what is a other name for the set of all x-values
Answer:
its domain
Step-by-step explanation:
Answer:
i believe it is A- range.
Step-by-step explanation:
i took the quiz
geometry question please help
Answer:
see below
Step-by-step explanation:
Alright, geometric probability.
We need to find
the area of the rectanglethe area of the equilateral triangle the area of the square the area of the part of the circle that does not include the squareand the area of the part of the rectangle that does not include the square, circle, or triangle.To find those, we need to find the areas of:
the outer rectanglethe circlethe equilateral trianglethe squareLet's start off with the easiest figure. The circle.
The circle has a radius of 10. Therefore, its area is is π[tex]r^2[/tex]. 100π is roughly 314.159265.
The circle has an area of around 314.159265.
Half of the diagonal of the square is 10m. That means that the full diagonal of the square is 20 m.
Formula for side of square using diagonal:
a = q / √2
20/√2 = 14.142135623731
The area of a square is a^2
14.142135623731^2= 200
The area of the square is 200 m^2. (28)
Using this, and the area of the circle, we can find the area of the part of the circle that does not include the square.
314.159265 - 200= 114.159265
The area of the part of the circle that does not include the square is 114.159265.
Now, the most important calculation (because it lets us find the total area of the rectangle); the equiangular triangle.
The height of this triangle is 30m. Therefore, the area is 519.6152422706632.
The area of the equiangular triangle is 519.6152422706632.
The side length of the equiangular triangle is 34.64101615137755.
The area of the rectangle= l times w.
l = 34.64101615137755
w= 30
30 times 34.64101615137755= 1039.23048454133
The total area is 1039.23048454133.
Now that we have the denominator of our fraction (total area), lets go back to our questions.
We need to find
the area of the equilateral triangle the area of the square the area of the part of the circle that does not include the squareand the area of the part of the rectangle that does not include the square, circle, or triangle.The area of the equilateral triangle = 519.6152422706632
519.6152422706632/1039.23048454133 = .5
The geometric probability that a point chosen randomly inside the rectangle is inside the equilateral triangle is .5
The area of the square = 200
200/1039.23048454133 = 0.19245008973
The geometric probability that a point chosen randomly inside the rectangle is inside the square is 0.19245008973
The area of the part of the circle that doesn't include the square: 114.159265
114.159265/1039.23048454133= 0.10984980396
The geometric probability that a point chosen randomly inside the rectangle is inside the part of the circle that doesn't include the square is 0.10984980396
The part of the rectangle that doesn't include the square, circle or triangle.
Area of triangle = 519.6152422706632
(The triangle contains the circle and square).
1039.23048454133- 519.6152422706632 = 519.61524227067
519.61524227067 /1039.23048454133 = 0.5
The geometric probability that a point chosen randomly inside the rectangle is inside the part of the circle doesn't include the square, circle, or triangle is 0.5
Hope this helped! Let me know if I made an errors, or if my answers are incorrect.
i mark brainliest for all my questions that are answered right :) thx for helping me
Please! Someone help me! You will get a BRAINLIEST if you get this correct!
Answer:
Yes because 9x2+6x=0 when x=-2/3Answer:
option 4
Step-by-step explanation:
Simplify the equation,
9x² + 6x = 3x ( 3x + 2)
9x² + 3x = 3x*(3x + 1)
9x² + 9x + 2 =9x² + 3x + 6x + 2*1
= 3x(3x + 1) + 2(3x + 1)
= (3x+ 1)(3x +2 )
[tex]\frac{10}{9x^{2}+6x}-\frac{1}{9x\frac{}{}+3x}=\frac{10}{3x(3x+2)}-\frac{1}{3x(3x+1)}\\\\=\frac{10(3x+1)}{3x(3x+1)(3x+2)}-\frac{1(3x+2)}{3x(3x+1)(3x+2))}\\\\=\frac{10(3x+1)-(3x+2)}{3x(3x+1)(3x+2)}\\\\\\\frac{5}{9x^{2}+9x+2}= \frac{10(3x+1)-(3x+2)}{3x(3x+1)(3x+2)}\\\\\frac{5}{(3x+1)(3x+2)}=\frac{10(3x+1)-(3x+2)}{3x(3x+1)(3x+2)}\\[/tex]
Both sides (3x+1)(3x+2) will get cancelled
[tex]5=\frac{10(3x+1)-(3x+2)}{3x}\\[/tex]
Cross multiply,
5(3x) =10(3x+1)-(3x+2)
When x = -2/3, LHS = 5(3x) = [tex]5*3*\frac{-2}{3}[/tex]
= -10
When x= -2/3, RHS = 10(3x+1)-(3x+2)
= [tex]10(3*\frac{-2}{3}+1)-(3*\frac{-2}{3}+2)\\[/tex]
= 10(-2+1) - (-2+2)
= 10 * (-1) -0
= -10
LHS = RHS
So, -2/3 is a solution
HELP ME PLEASE PLEASE IM BEGGING
Answer:
The solution is the triplet: (a, b, c) = (-3, 0, 0)
Step-by-step explanation:
Let's start with the second equation, and solving for "a":
a - b = -3
a = b - 3
Now replace this expression for a in the third equation:
2 a + b = -6
2 (b - 3) +b = -6
2 b - 6 +b = -6
3 b = -6 +6
3 b = 0
b = 0
So if b = 0 then a = 0 - 3 = -3
now we can replace a= -3, and b = 0 in the first equation and solve for c:
2 a - b + c = -6
2 ( -3) - 0 + c = -6
-6+ c = -6
c = -6 + 6
c = 0
Our solution is a = -3, b= 0 , and c = 0 which can be expressed as (-3, 0, 0)