The eqution of the diagonal of a parallelogram is 3y=5x +k. The two opposite vertices of a parallelogram are the points (1,-2), (-2,1).Find the value of k
Answer:
[tex]k = 1[/tex]
Step-by-step explanation:
Given
[tex]3y = 5x + k[/tex]
Opposite points: [tex](1,-2)[/tex] and [tex](-2,1)[/tex]
Required
Find k
First, calculate the midpoint of the opposite points.
[tex](x,y) = 0.5(x_1 + x_2,y_1 + y_2)[/tex]
This gives:
[tex](x,y) = 0.5(1 -2,-2 + 1)[/tex]
[tex](x,y) = 0.5(-1,-1)[/tex]
Open bracket
[tex](x,y) = (-0.5,-0.5)[/tex]
The equation [tex]3y = 5x + k[/tex] becomes:
[tex]3 * -0.5 = 5 * -0.5 + k[/tex]
[tex]-1.5 = -2.5 + k[/tex]
Solve for k
[tex]k = 2.5-1.5[/tex]
[tex]k = 1[/tex]
Which of the following choices are equivalent to the expression below? Check
all that apply. X^3/5
Answer:
[tex]\text{C. }(x^3)^{1/5},\\\text{F. }\sqrt[5]{x^3}[/tex]
Step-by-step explanation:
Exponent properties state [tex](a^b)^c=a^{(b\cdot c)[/tex]. Therefore, [tex]{x^{(\frac{3}{5})}=(x^3)^\frac{1}{5}[/tex].
Recall that [tex]a^{(\frac{b}{c})}=\sqrt[c]{a^b}[/tex]. Thus, [tex]x^{(\frac{3}{5})}=\sqrt[5]{a^3}[/tex].
There are 4 second-grade classrooms that share 15 packs of paper. How much paper should each classroom get
Answer:
3.75
Step-by-step explanation:
Unit 6 similar triangles homework 5
Answer:
1) x = 12
2) x = 23.1
3) x = 19
4) x = 16
5) x = 8
6) x = 17
Step-by-step explanation:
Comparing the sides of each triangle, we have;
1) [tex]\frac{32}{32 + x}[/tex] = [tex]\frac{24}{33}[/tex]
Cross multiply to get,
(32 + x) * 24 = 32 * 33
768 + 24x =1056
24x = 1056 - 768
24x = 288
x = 12
2) [tex]\frac{14}{34}[/tex] = [tex]\frac{x}{33 + x}[/tex]
cross multiply to have;
34x = 14 (33 + x)
34x = 462 + 14x
20x = 462
x = 23.1
3) [tex]\frac{20}{36}[/tex] = [tex]\frac{30}{x + 35}[/tex]
cross multiply to have;
36 * 30 = 20(x + 35)
1080 = 20x + 700
1080 - 700 = 20x
380 = 20x
x = 19
4) [tex]\frac{22.5}{42.5}[/tex] = [tex]\frac{2x - 5}{3x + 3}[/tex]
cross multiply to have;
42.5(2x - 5) = 22.5(3x + 3)
85x - 212.5 = 67.5x + 67.5
collect like terms
85x - 67.5x = 67.5 + 212.5
17.5x = 280
x = 16
5) [tex]\frac{2x + 4}{2x + 8}[/tex] = [tex]\frac{x + 7}{x + 10}[/tex]
cross multiply to have;
(2x + 8)(x + 7) = (2x + 4)(x + 10)
2[tex]x^{2}[/tex] + 14x + 8x + 56 = 2[tex]x^{2}[/tex] + 20x + 4x + 40
2[tex]x^{2}[/tex] + 22x + 56 = 2[tex]x^{2}[/tex] + 24x + 40
collect like terms to have;
22x - 24x = 40 - 56
-2x = -16
x = 8
6) [tex]\frac{28}{82}[/tex] = [tex]\frac{2x + 8}{7x + 4}[/tex]
cross multiply to have;
82(2x + 8) = 28(7x + 4)
164x + 656 = 196x + 112
164x - 196x = 112 - 656
-32x = -544
x = 17
The value of x in all the options can be determined by using the arithmetic operations. The calculations are given below.
1)
Given :
Two side lengths of a triangle are (x + 32) and 33.
According to the similar triangles property:
[tex]\dfrac{32+x}{32}=\dfrac{33}{24}[/tex]
SImplify the above expression in order to determine the value of 'x'.
768 + 24x = 1056
24x = 288
x = 12
2)
Given :
Two side lengths of a triangle are 34 and (x + 33).
According to the similar triangles property:
[tex]\dfrac{14}{34}=\dfrac{x}{33+x}[/tex]
SImplify the above expression in order to determine the value of 'x'.
34x = 462 + 14x
20x = 462
x = 23.1
3)
Given :
Two side lengths of a triangle are 36 and (x + 35).
According to the similar triangles property:
[tex]\dfrac{20}{36}=\dfrac{30}{35+x}[/tex]
SImplify the above expression in order to determine the value of 'x'.
1080 = 20x + 700
20x = 380
x = 19
4)
Given :
Two side lengths of a triangle are (3x + 3) and 42.5.
According to the similar triangles property:
[tex]\dfrac{22.5}{42.5}=\dfrac{2x-5}{3x+3}[/tex]
SImplify the above expression in order to determine the value of 'x'.
85x - 212.5 = 67.5x + 67.5
17.5x = 280
x = 16
5)
Given :
Two side lengths of a triangle are (2x + 8) and (x + 10).
According to the similar triangles property:
[tex]\dfrac{2x + 4}{2x+8}=\dfrac{x+7}{x+10}[/tex]
SImplify the above expression in order to determine the value of 'x'.
(2x + 8)(x + 7) = (2x + 4)(x + 10)
[tex]2x^2+22x+56=2x^2+24x+40[/tex]
16 = 2x
x = 8
6)
Given :
Two side lengths of a triangle are 82 and (7x + 4).
According to the similar triangles property:
[tex]\dfrac{28}{82}=\dfrac{2x+8}{7x+4}[/tex]
SImplify the above expression in order to determine the value of 'x'.
28(7x + 4) = (2x + 8)82
32x = 544
x = 17
For more information, refer to the link given below:
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HELP MEEEEEEEE PLEASE
Answer:
B. 5/16
Step-by-step explanation:
Multiply each side by the reciprocal of 2/5 to solve for x
(2/5)(1/8)=x
2/16=x
30 in.
10 in.
10 in.
30 in
20 in
Find the area of the arrow above.
square inches
Answer:
1100 Inches Squared
Step-by-step explanation:
Let the triangle on the top right be - (i)
Let the triangle on the top left be - (ii)
Let the bottom rectangle be - (iii)
1) The base of the triangle (i) = 10 + (20/2) (It is the base of the rectangle halfed + the given amount of half base of the triangle)
=> 10 + 10
=> 20 in
Base = 20 in
Height = 30 in
Area = 1/2 * 20 * 30
=> 10 * 30
=> 300 in
Triangle (i) = (ii)
So, the area of triangle (ii)
=> 300 in
Area of rectangle,
Length * Breadth
=> 20 * 30
=> 500 in
Total arrow's area = 300 + 300 + 500 (i + ii + iii)
=> 1100
Therefore the total area of the shape = 1100 in squared.
Hope it helps :)
It takes Jada 20 minutes to walk to school. It takes Andre 80% as long to walk to
school.
How long does it take Andre to walk to school?
Answer:
16
Step-by-step explanation:
assume f is a one to one function of f(x)= 4-6x find f^-1(-32)
Answer:
f^-1(-32)=6
Step-by-step explanation:
Find the inverse of the function f(x)=4-6x:
f(x)=4-6x
y=4-6x
x=4-6y
x-4=-6y
(x-4)/-6=y
-1/6x+2/3=y
y=-1/6x+2/3
f^-1(x)=-1/6x+2/3
Plug in f^-1(-32) for f^-1(x) and simplify:
f^-1(-32)=-1/6(-32)+2/3
f^-1(-32)=16/3+2/3
f^-1(-32)=18/3
f^-1(-32)=6
The surface area of a three-dimensional object is? This is a brainpop question, there is no picture, and tis a straight forward question
Answer:
What it is is basically when you take the area of every side of a three dimensional shape and then add it all together.
don't know if this is what you were looking for but I hope this helps.
find the equation of the line with a slope of 3/4 and passes through (4-2)
Answer:
y = 3/4x - 5
Step-by-step explanation:
An equation of a line can be written in slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept.
Let's plug in what we know.
The slope is 3/4.
y = 3/4x + b
To find b, we want to plug in a value that we know is on this line: in this case, I will use the point (4, -2). Plug in the x and y values into the x and y of the standard equation.
-2 = 3/4(4) + b
To find b, multiply the slope and the input of x(4)
-2 = 3 + b
Now, subtract 3 from both sides to isolate b.
-5 = b
Plug this into your standard equation.
y = 3/4x - 5
This is your equation. It has a slope of 3/4, and passes through (4, -2)
Hope this helps!
The owners of a smoothie shop want the price of each size smoothie to be proportional to the amount of liquid it contains. A small smoothie will be 16 fluid ounces and sell for $3.52
Answer:
?
Step-by-step explanation:
Whats the question?
The proportionality constant if, A small smoothie will be 16 fluid ounces and sell for $3.52 is 22.
What is proportionality?When the corresponding elements of two numerical sequences, frequently experimental data, have a fixed ratio, this is referred to as the coefficient of proportionality, and the two sequences are said to be proportional or directly proportional.
Given:
A small smoothie will be 16 fluid ounces and sell for $3.52,
Convert the price of the smoothie in cents as shown below,
The price of a smoothie = 3.52 × 100 ($1 = 100 cents)
The price of a smoothie = 352 cents
Calculate the proportionality constant as shown below,
The proportional constant = Fluid / price
The proportional constant = 352 / 16
The proportional constant = 22
Thus, The proportional constant is 22.
To know more about proportionality:
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The complete question is: The owners of a smoothie shop want the price of each size smoothie to be proportional to the amount of liquid it contains. A small smoothie will be 16 fluid ounces and sell for $3.52. Find the proportionality constant.
PLEASE I NEED THE ANSWER IN THE NEXT MINUTE
Answer:
Step-by-step explanation:
A
Answer:
96
Step-by-step explanation:
:)
The theater sells two types of tickets: adult tickets for $7 and child tickets for $4. Last night, the theater sold a total of 76 tickets for a total of $469. How many adult tickets did the theater sell last night?
Answer:
55 tickets for adults
Step-by-step explanation:
Start by setting up two equations. One equation will be the total amount of money spent and the other is the total amount of tickets sold. a is the # of adult tickets and c is the # of children tickets sold.
7a+4c=469
a+c=76
Now solve for c in the second equation. Then use that to substitute for c in the first equation.
c=76-a
7a+4(76-a)=469
7a+ 304-4a =469
7a+4a=165
3a=165
a=165/3
a=55
Help! Tysm in advance :)
Line BC is a tangent line to the circle centered at A. If angle BAC is 64 degrees, what is the
measure of angle ACB? Explain/show your reasoning.
Answer:
Here.
Step-by-step explanation:
Step-by-step explanation:
BC is tangent to the circle at point B.
Therefore, by tangent-radius theorem:
Step-by-step explanation:
BC is tangent to the circle at point B.
Therefore, by tangent-radius theorem:
what ratio is the same as 2/3?
a ) 8 / 12
b) 6 / 12
c) 9 / 12
d) 10 / 12
Answer: a) 8/12
Step-by-step explanation:
Both numbers have to be the same for it to be equal: More info below.
The answer is a) because 8 divided by 2 is 4, and 12 divided by 3 is also 4.
It is not b) because 6 divided by 2 is 3, but 12 divided by 3 is 4.
Not c) because 9 divided by 2 is 4.5, and 12 divided by 3 is 4.
Not d) because 10 divided by 2 is 5, and 12 divided by 3 is 4.
Therefore, the answer is a) 8/12.
Hope this helps!
A model rocket is launched with an initial upward velocity of 188 ft/s. The rocket's height h (in feet) after t seconds is given by the following.
h=188t-16t^2
Find all values of for which the rocket's height is 92 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Answer:
0.51 and 11.24 seconds.
Step-by-step explanation:
The height h of a rocket with an initial upward velocity of 188 feet per second after t seconds is modeled by the function:
[tex]h(t)=188t-16t^2[/tex]
And we want to find all values of t for which the rocket's height is 92.
So, we can set h(t) = 92 and solve for t:
[tex]92=188t-16t^2[/tex]
We can divide everything by four:
[tex]23=47t-4t^2[/tex]
Rearrange the equation:
[tex]4t^2-47t+23=0[/tex]
We can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 4, b = -47, and c = 23. Substitute:
[tex]\displaystyle x=\frac{-(-47)\pm\sqrt{(-47)^2-4(4)(23)}}{2(4)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{47\pm\sqrt{1841}}{8}[/tex]
Hence, our two solutions are:
[tex]\displaystyle x=\frac{47+\sqrt{1841}}{8}\approx 11.24\text{ or } x=\frac{47-\sqrt{1841}}{8}\approx0.51[/tex]
So, the rocket reaches a height of 92 feet after 0.51 seconds and again after 11.24 seconds.
Find the area please :)
Answer:
it's area is 1/2 b×h
1/2×7×3.8
13.3
Answer:
13.3 ft^2
Step-by-step explanation:
area = base x h / 2
A = 7 x 3.8 / 2
A = 26.6 / 2
A = 13.3 ft^2
What is the surface area of the pyramid?
Answer:
56 inches squared
Step-by-step explanation:
(4x6) ÷ 2 = 12
12 x 4 = 48
4 x 4 = 16
48 + 16 = 56
Ava buys a book for $8.58. She pays with a $10 bill. How much change will she get? (1) $2.28 (2) $4.66 (3) $1.42 (4) $3.52
Answer:
$1.42
Step-by-step explanation:
Ava buys a book for $8.58
She pays with a $10 bill
Hence her change would be
= 10-8.58
= 1.42
Ava change is $1.42
find each missing measure given: m
Help ASAP
Answer:
28 degrees
Step-by-step explanation:
147 - 119 = 28
Answer:
Step-by-step explanation:
Since we already know that PQR is 147 degrees, we just need to subtract PQR to QR, and you will get, (147 - 119), PQ as 28 degrees!
The segments shown below could form a triangle.
help please :)
Answer:
The answer is false! :)
Raj works in a bakery. He has 9 pounds of flour. He needs 14 ounces of flour to make one cake. How many cakes can Raj make? Use the
Answer:
3
Step-by-step explanation:
m
In a local car lot, 1/6
of the cars have standard transmissions. Find the
probability that 3 of 4 randomly-selected cars have standard transmissions.
Answer: [tex]\dfrac{5}{324}[/tex]
Step-by-step explanation:
Given
Probability that car has a standard transmission is [tex]\frac{1}{6}[/tex]
So, the probability that the car does not have transmission is
[tex]1-\dfrac{1}{6}=\dfrac{5}{6}[/tex]
Probability of that 3 out of 4 randomly selected cars have standard transmissions is given by selecting 3 cars with standard deviation and then multiply by their respective probabilities
[tex]\Rightarrow P=^4C_3\cdot \left(\dfrac{1}{6}\right)^3\cdot \left(\dfrac{5}{6}\right)\\\\\Rightarrow P=4\times\dfrac{5}{6^4}\\\\\Rightarrow P=\dfrac{20}{1296}\\\\\Rightarrow P=\dfrac{5}{324}[/tex]
I=$26.24, P=$500, T=18 months the annual interest rate is
If you place a 37-foot ladder against the top of a 15-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.
Answer:
33.8
Step-by-step explanation:
a²+b²=c²
15²+b²=37²
225+b²=1369
-225 -225
b²=1144
√1144
b=33.8
The distance from the bottom of the ladder to the bottom of the building would be 33.8 foot.
What is Pythagoras' Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
If you place a 37-foot ladder against the top of a 15-foot building.
Let BC be the distance from the bottom of the ladder to the bottom of the building.
[tex]|AC|^2 = |AB|^2 + |BC|^2 \\15^2+BC^2=37^2\\225 + BC^2=1369\\BC^2 = 1369 - 225\\\\BC^2 = 1144\\\\BC = 33.8[/tex]
Learn more about Pythagoras' theorem here:
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What is the exact value of tan(300°)?
Answer:
The exact value of tan 300° is ⏩ - √3
Hope it will help :)❤
Calculate the population
data set;
mean for the following
40, 50, 55, 78,58,60,73, 35, 43, 48.
Answer:
I think it’s 11.8
Step-by-step explanation:
Given the passage, what determination can you make about the setting? How does the setting affect Jonathan’s behavior?
Answer: the area is affected by crime. He is protective of his money. Both right on edge
Step-by-step explanation:
Answer: a b
Step-by-step explanation:
need help un geomtry
Answer:
x = 138
Step-by-step explanation:
The 2 arcs above the diameter form a semicircle = 180°
x + 42 = 180 ( subtract 42 from both sides )
x = 138