Answer:
JK = 24
Step-by-step explanation:
Δ BKJ and Δ BCA are similar triangles and ratios of corresponding sides are equal, that is
[tex]\frac{JK}{AC}[/tex] = [tex]\frac{BK}{BC}[/tex] , substitute values
[tex]\frac{JK}{40}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )
5JK = 120 ( divide both sides by 5 )
JK = 24
the triangles are all similar, because they have proportional sides and equal angles.
if you assume the smallest, equal part of side to be x
the biggest triangle has "5 parts" so BC=5x and BK has 3 parts so BK=3x .
since they're similar, ratio of their corresponding sides is constant or equal.
[tex] {BK\over BC}={JK \over AC}[/tex]
BK/BC=3/5
and AC=40
so JK = 40*3/5=24
I NEED HELP!! which expression is the radical form of x - 9/8
Answer:
Step-by-step explanation:
Please use " ^ " to indicate exponentiation.
Your "x - 9/8" should be x ^(-9/8).
The 8 represents "the eighth root" of x, and the -9 represents the power to which x is to be raised. Finally, the " - " sign shows that this 9th power is in the denominator.
x ^(-9/8) in radical form is ----------------
[tex]1 divided by \sqrt[8]{x^9\\} \\[/tex]
|10-11| = simplify the expression
Answer:
1
Step-by-step explanation:
Let's ignore the absolute value signs for a moment.
We have the expression [tex]10-11[/tex]. We know that if we subtract 10 from 10 we get 0, so if we subtract 11 from 10 we must get -1.
However, there is an absolute value sign. This means that whatever number is inside it has to be converted to a positive number.
-1 as a positive number is +1, or just 1.
Hope this helped!
if a man works 400km in 6 minutes.How long will he work in 9 minutes
Answer:
600 kmStep-by-step explanation:
400 km = x
6 min 9 min
cross multiply:
6x = 400 ( 9)
x = 3600 / 6
x = 600 km
-5/6 + 1 2/9
Can some one help me out?
Answer:
[tex]2 \frac{4}{9} [/tex]
[tex] = \frac{ - 5}{6} + 1 \frac{2}{9} [/tex]
[tex] = \frac{ - 5}{6} + \frac{11}{9} [/tex]
[tex] = \frac{ - 5 \times 2 + 11 \times 1}{9} [/tex]
[tex] = \frac{ - 10 + 9}{9} [/tex]
[tex] = \frac{-1}{9} [/tex]
50 points! I would appreciate an explanation, I actually want to know how to do this. Thanks! :P
Answer:
1.
(a) The Domain is the set of inputs of the function.
Considering that the function takes a period of 3 weeks (21 days), the domain is [0, 21], once we can't evaluate what happens after the 21st day.
[tex]\text{Domain is } [0, 21][/tex]
Otherwise, it could be [tex][0, \infty)[/tex]
Note: We include 0 and 21.
Once the greatest balance was $400, it will not exceed $400, either it doesn't show negative values.
[tex]\text{Range is } [0, 400][/tex]
Note: We include 0 and 400.
(b)
Once the greatest balance was $400, when x=0, it seems that the y-value is half of $400, therefore, approximately $200. It also represents the initial value, the amount of money when she opened the account.
(c)
[tex]f(x)=B(d)[/tex]
[tex]B(12)=0[/tex]
(d)
It is in segment 4.
The balance equal to zero means that the y-value of the graph is zero, therefore in the x-axis.
PLEASE HELP! 20 POINTS 1) A ball is thrown starting at a time of 0 and a height of 2 meters. The height of the ball follows the function H(t)=−4.9t2+25t+2. What is the height of the ball at each second from 0 to 5? (I'll put a picture of the graph.) 2) Which expression could represent the height of a soccer ball as it is in the air after being kicked? (This is part 2 to question 1) A. −16t+9 B. −16t2+4t3 C. 9t2+25t D. −16t2+25t+1
Answer:
a or b
Step-by-step explanation:
it just looks like b or a
H(t) = -4.9t^2 + 25t + 2
Height is a function of time
plug in 0, 1,2,3,4, and 5 to find the height at 0, 1,2,3,4, and 5 seconds.
at t = 0
H(0) = -4.9(0)^2+25(0) + 2 = 2 meters
Repeat for T=1,2,3,4 and 5
Notice the ball peaks around t = 3 seconds and starts to descend.
H(1) = (-4.9)(1^2) + 25(1) + 2 = 22.1 meters
H(2) = (-4.9)(2^2)+25(2)+2=32.4 meters
H(3) = 32.9 meters
H(4) = 23.6 meters
H(5) = 4.5 meters
A bus travels from Station A to Station B, and a truck travels from Station B to Station A on the same road. The speed of the bus is 54 km/h, and the speed of the truck is 48 km/h. After they pass each other, they continue drive to the destinations. Once they reach the destination, they turn around to continue travel along the same road. When they meet again, the bus travels 216 km more than the truck. What is the distance between the two stations in kilometers?
Answer:
The distance between the two train stations is 1728 km
Step-by-step explanation:
The speed of the bus = 54 km/h
The speed of the truck = 48 km/h
When the bus and truck meet again, the distance covered by the bus = 216 km more than he distance traveled by the truck
Let the distance between the two train stations = x
Let the location where they first meet be y from station A we have;
The location where they meet again = y - 216 km
Therefore, we have;
Location where they
The time for the truck and the bus to meet again = t
Therefore, 54 × t - 48 × t = 216 km
6·t = 216 km
t = 36 hours
Therefore, the time for the bus to travel x + 216 km = 36 hours
54 × 36 = 1944 = x + 216
x = 1944 - 216 = 1728 km
The distance between the two train stations = 1728 km.
A radioactive substance decays exponentially. A scientist begins with 350 milligrams of a radioactive substance. After 14 hours, 175 mg of the substance remains. How many milligrams will remain after 20 hours
Answer:
N(t)=N∗.5t/h where n(t) is amount of substance left, N = initial amount, t = current time, and h = half-life time.h = 24 hours t= 45 hours, N = 130mg
therefore, N(t)=130∗.545/24=35.44mg
Step-by-step explanation:
N(t)=N∗.5t/h where n(t) is amount of substance left, N = initial amount, t = current time, and h = half-life time.h = 24 hours t= 45 hours, N = 130mg
therefore, N(t)=130∗.545/24=35.44mg
Answer:
≈ 130 mg
Step-by-step explanation:
This is about the half-life of the substance.
There is a formula for this kind of calculations:
N(t)= N₀*(0.5)^(t/T), where
N(t) = substance left after time period of t,t = time passed,N₀ = initial amount of the substance,T = hal-life time of the given substance.In our case, we have:
N₀ = 350 mg,t= 20 hours,T = 14 hours as half of substance decays during this time period,And the calculation:
N(20)= 350*(0.5)^(20/14)N(20) ≈ 130 mgAnswer: about 130 mg of substance remains after 20 hours
Line R: 2x + 2y = 18 Line M: x + y = 9 Which statement is true about the solution to the set of equations?
Answer:
Step-by-step explanation:
2x + 2y = 18
-2x -2y = -18
0 = 0
infinite solution of equations
SOMEBODY PLEASE HELP ME ON THIS ; DUE TODAY, i’ll mark u the brainliest
Answer: Angle Addition Postulate
Step-by-step explanation:
According to the angle addition postulate, the measure of an angle formed by two angles side by side is the sum of the measures of the two angles. It is used to evaluate the measure of an angle formed by two or more angles .In the given picture, we have ∠MRO and ∠MRS on line SRO.
So, ∠SRO = ∠MRO +∠MRS [By angle addition postulate]
So the postulate that justify the statement " ∠SRO = ∠MRO +∠MRS" is Angle Addition Postulate.
Lilianna uses \dfrac{3}{4} 4 3 start fraction, 3, divided by, 4, end fraction calories per minute just by sitting. She uses 111 more calorie per minute by walking. Lilianna uses a total of 12\dfrac{1}{4}12 4 1 12, start fraction, 1, divided by, 4, end fraction calories walking to the park. Lilianna uses the equation, d\left(\dfrac{3}{4}+1\right)=12\dfrac{1}{4}d( 4 3 +1)=12 4 1 d, left parenthesis, start fraction, 3, divided by, 4, end fraction, plus, 1, right parenthesis, equals, 12, start fraction, 1, divided by, 4, end fraction to represent the situation. What does the variable ddd represent in the equation? Choose 1 answer: Choose 1 answer: (Choice A) A Calories per minute Lilianna uses walking (Choice B) B Number of calories Lilianna would have used sitting (Choice C) C Number of minutes Lilianna walked
The Variable d in the equation represents the time per minute Lilianna spends walking to the park
VariableCalories used by sitting = 3/4Calories used by walking = 1Total calories used walking to the park = 12 1/4The equation:
d(3/4 + 1) = 12 1/4
d(3+4/4) = 12 1/4
d(7/4) = 49/4
d = 49/4 ÷ 7/4
= 49/4 × 4/7
= 49/7
d = 7
Complete question:
Lilianna uses 3/4 calories per minute just by sitting. She uses 1 more calorie per minute by walking. Liliana uses a total of 12 1/4 calories walking to the park. Lilianna uses the equation, d(3/4+1)=12 1/4 to represent the situation. What does the variable d represent in the equation?
Learn more about variable:
https://brainly.com/question/11885867
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How do I solve this?
Answer:
[tex]\Large \boxed{- \frac{1}{5}}[/tex]
Step-by-step explanation:
[tex]\displaystyle \sqrt[3]{-\frac{1}{125} }[/tex]
Distribute the cube root to the numerator and denominator.
[tex]\displaystyle -\frac{\sqrt[3]{1} }{\sqrt[3]{125} }[/tex]
Solve for the cube root.
[tex]\displaystyle - \frac{1}{5}[/tex]
ASAP PLEASE GIVE CORRECT ANSWER
In a rectangular coordinate system, what is the number of units in the distance from the origin to the point $(-15, 8)$? Enter your answer
distance of a point [tex](x,y)[/tex] from origin is $\sqrt{x^2+y^2}$
so distance is $\sqrt{(-15)^2+(8)^2}=\sqrt{225+64}=\sqrt{289}=17$
Answer:
Distance=17 units
Step-by-step explanation:
Coordinates of the origin: (0, 0)
Coordinates of the point in question: (-15, 8)
Distance formula for any two points [tex](x_1,y_1), (x_2,y_2)[/tex] on the plane:
[tex]distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance=\sqrt{(-15-0)^2+(8-0)^2}\\distance=\sqrt{(15)^2+(8)^2}\\distance=\sqrt{225+64} \\distance=\sqrt{289} \\distance=17[/tex]
A file that is 276 megabytes is being dowloaded. If 16.7% complete how many megabytes have been dowloaded? Round your answer to the nearest tenth
Answer:
30.9 mb
Step-by-step explanation:
Which of the following expressions demonstrates the distributive property?
3 + 4 + 5 = 4 + 3 + 5
-2(5 + 7) = -2(7 + 5)
O 3(-8 + 1) = 3(-8) + 3(1)
6[(7)(-2)] = [(6)(7)](-2)
Answer:
3(-8 + 1) = 3(-8) + 3(1)
Step-by-step explanation:
The distributive property is quite literally when you distribute numbers. This is the only instance of that happening here
The first two are the communitive property of addition, and the last one is the communitive property of multiplication.
Cheers.
Answer:
c
Step-by-step explanation:
Flaming BBQ restaurant makes a dipping sauce with 9 mL of hot sauce for every 6 ounces of barbecue sauce. Which of the following mixtures will taste the same as flaming BBQ's dipping sauce?
Choose 3 answers:
A. 6 mL of hot sauce mixed with 20 oz of barbecue sauce
B. 3 mL of hot sauce mixed with 2 oz of barbecue sauce
C. 45 mL of hot sauce mixed with 30 oz of barbecue sauce
D. 24 mL of hot sauce mixed with 18 oz of barbecue sauce
E. 12 mL of hot sauce mixed with 8 oz of barbecue sauce
pls help me ;-;
Answer:
B, C , and E
Step-by-step explanation:
for 9 ml of hot sauce (x) +6 ounces of BBQ sauce(y)= flaming BBQ(c)
9x+6y=c
B: 3x+2y will give the same taste ( the quantity reduced to one third)
C: 45x+30y will give the same taste ( the quantity multiply by 5)
E:12 x+8y will give the same taste ( the quantity multiplied by 0.75)
figure a is a scale image of figure b. what is the value of x? please answer asap!
Greetings from Brasil...
According to the statement, one figure is scaled in relation to another, so we can apply similarity to polygons.....
So
BIG/small = BIG/small
or
small/BIG = small/BIG
12.5/10 = X/16
OR
10/12.5 = 16/X
12.5/10 = X/16
10X = 12.5 · 16
X = 200/10
X = 20Can I name my Angle VTS as STV? And use it interchangeably in proving?
Answer:
both angles are the same, so you can use it interchangeably in proving.
But i suggest you to mantain only one, because it's easier to understand and it looks better.
A caterer needs to know the volume of the remaining cake to determine how many servings she has. What is the volume of the remaining cake?
Step-by-step explanation:
Hello, there!!!
Let's simply work with it,
Firslty let's assume the whole cake, when you assume the cake in whole. you get,
length (l)= 16 in
breadth (d)= 6 in
and height (h)= 4 in
now, as it is a rectangle shaped cake,
volume of a whole cake (v)= l×b×h
or, v= 16 in × 6 in × 4 in.
Therefore, the volume of whole cake is 384 cubic inch.
now,
let's find the volume of eaten part,
As per the picture, the 1/4th part of cake is eaten so,
length = 8 in
breadth = 3in
and height = 4in.
so, volume of eaten part = l × b × h
v= 8in × 3in × 4in
Therefore , v= 96 cubic inch.
now, lastly finding the volume of remaining part,
v. of remaining part = v.of whole cake - v. of eaten part.
or, v. of remaining part = 384 in^3 - 96 in^3
Therefore, the volume of remaining part is 288in^3.
Hope it helps....
maggie’s brother is 3 years younger than twice her age. The sum of their age is 24. How old is Maggie
Answer:
I HOPE IT WILL WORK
Step-by-step explanation:
let age of Maggie =x years
as given that Maggie brother is 3 year less than twice of her age
hence
brother = (2x-3) years
also given that sum of ages =24
hence
x+(2x-3)=24
3 x-3=24
3 x=27
x=9 years Maggie
so his brother=9-3=6 years
pls hit the star and brainlist it if you found it helpfull thanks
find the missing part of the proportion 12/x = 3/7 x= _
Answer:
x = 28
Step-by-step explanation:
12/x = 3/7
Using cross products
3x = 12*7
3x = 84
Divide by 3
x = 28
∠4 and ∠6 can be classified as:
Answer:
same side interior angles
Step-by-step explanation:
<4 and <6 are same side interior angles
Same side interior angles are on the same side of the transversal and inbetween the two lines
un automóvil recorre 90 km con 2 galones de gasolina cuantos kilómetros recorre con 11 galones de gasolina y cuantos galones de gasolina necesita para recorrer 650 km
Answer:
Recorrera 495 km con 11 galones de gasolina
Y necesitara 14.44 galones para recorrer 650 km
Step-by-step explanation:
k g k g
90 2 90 2
x 11 650 x
=(11 x 90)/2 =(650x2)/90
=990/2 =1300/90
=495 km =14.44
Please answer this question now
Answer:
PQ = 17
Step-by-step explanation:
Tangents drawn to a circle from an external point are congruent, thus
TS = TU = 6
VU = VO = 20
PO = PQ = 37 - VO = 37 - 20 = 17
That is PQ = 17
Evaluate each expression. Name the property used in each step.
Answer:
7). 1
8). 3
9). 1
Step-by-step explanation:
7). [tex][3\div (2\times 1)]\frac{2}{3}[/tex]
[tex]=[3\div 2]\frac{2}{3}[/tex]
[tex]=\frac{3}{2}\times \frac{2}{3}[/tex]
[tex]=1[/tex]
8). [tex]2(3\times 2-5)+3\times \frac{1}{3}[/tex]
[tex]=2(6-5)+\frac{3}{3}[/tex]
[tex]=2(6-5)+1[/tex]
[tex]=2+1[/tex]
= 3
9). [tex]6\times \frac{1}{6}+5(12\div 4-3)[/tex]
[tex]=6\times \frac{1}{6}+5(\frac{12}{4}-3 )[/tex]
[tex]=1+5(3-3)[/tex]
= 1
What is -13/20 in decimal form
Answer:
-0.65
Step-by-step explanation:
Step 1: Write out fraction
-13/20
Step 2: Evaluate fraction
-13/20 = -0.65
a symbol used to name one or more parts of a whole or asset or a location on the number line is a
Answer:
Fraction is the answerWhich point would be a solution to the system of linear inequalities shown below? {see image for inequalities}
(-10, -2)
(−5,2)
(10,7)
(10,−2)
Answer:
(10, -2)
Step-by-step explanation:
The inequalities are:
y < x - 7 (1)
y < (1/5)x - 2 (2)
To solve this problem, we have to solve both equations simultaneously and then find the value of x and y that makes the inequality true.
To solve the inequality, subtract inequality (2) from inequality (1) which gives:
0 < (4/5) x - 5
-(4/5)x < -5
Dividing both sides of the equation by -4/5 gives:
-(4/5)x / (-4/5) < -5/ (-4/5)
x > 6.25
Put x > 6.2 in inequality 1
y < 6.25 - 7
y < -0.75
The solution of the inequality is x > 6.25 and y < -0.75
From the list of option, the correct answer is (10, -2) since 10 > 6.25 and -2 < -0.75
You need to prepare 30mL solution of a 1:8 syrup solution. You have on hand 50% syrup solution and a 1:20 soda solution. How many mL of each solution do you need to create the final solution?
Answer:
5 ml of 50% syrup solution will be used to create the final solution
Step by step Explanation:
Let the amount of 50% solution that was used = b
Which means ( 30 - b ) is the amount of 1/200 solution used then we can derive an equation as follows,
set up will then be,
0.5b +0.05(30 -b) = 1/8 (30)
We can simplifiy this as
0.5b+ 1.5 -0.05b = 3.75
Then make b the subject of the formula we have
0.45b = 2.25
b= 2.25/0.45
b = 5 ml
Therefore, 5ml of 50% syrup solution will be used to create the final solution
help with math again please
ANSWER:
It is C
NO EXPLANATION