Answers
Side PQ corresponds to side TS. 9/7 is roughly 1.29, which would make that its scale factor. (I’m dividing because when side lengths are proportional, there is a specific value, the scale factor, that you can multiply or divide by to find the unknown side length of a corresponding side). Side QR corresponds to side UT. 15/10 is 1.5, thus making that the scale factor between these two sides. Finally, we see that side PR corresponds to side US. 12/8 is 1.5, making the scale factor between those two sides 1.5. Although two pairs of corresponding sides have the same scale factor, the same cannot be said for the third pair of corresponding sides. In order for the triangles to be similar, the scale factor should remain constant between each corresponding side, therefore, the triangles are not similar.
For number 6, since you are only given the side lengths, you would not be able to use the AA (Angle-Angle Similarity Theorem), or SAS (Side-Angle-Side Similarity Theorem). The calculations are shown below:
PQ~TS: 9/6= 1.5
QR~UT: 15/10= 1.5
PR~US: 12/8= 1.5
The scale factor for each pair of corresponding sides is congruent, proving that the triangles are proportional, making them similar.
Answer:
need thiss
Step-by-step explanation:
Related Questions
A doctor prescribes 500 milligrams of a therapeutic drug that decays by about 19% each hour.
a) To the nearest minute, what is the half-life of the drug?
b)
Write an exponential model representing the amount of the drug remaining in the patient's
system after t hours. (2 points)
c)
Use your formula to find the amount of drug that would remain in the patient's system after 24
hours. Round your answer to the nearest hundredth of a gram. (2 points)
Answers
Answer:
a) half life is 3h 17 minutes
b) function of residue drug after t hours with initial quantity = 500 mg
f(t) = 500 (0.81^t)
c) drug left in patient's system after 24 hours
= 0.00 grams (to the hundredth of a gram.
Step-by-step explanation:
Given:
Drug initial active weight, A = 500 mg
Residue active weight, f(t) = A 0.81^t
t = time in hours.
a) half life
Half life is T, such that f(T) = 0.5A =>
0.5A = A(0.81^t)
0.81^t = 0.5
t*log(0.81) = log(0.5)
t = log(0.5) / log(0.81) = -0.6931 / -0.2107 = 3.2894 hours
= 3 h 17.36 minutes
b) Equation of function of residue drug as a function of time t in hours
A=500 mg
f(t) = A(0.81^t) substitute A = 500 mg
= 500(0.81^t) mg
c) weight of residue drug after 24 hours to the hundredth of a gram.
t=24 hours
A=500
f(t) = 500(0.81^t) substitute t=24 hours
= 500(0.81^24)
= 3.181 mg
= 0.003181 g
On two investments totaling $13,500, Peter lost 3% on one and earned 5 % on the other. If his net annual receipts were $319, how much was each investment?
Answers
y = amount of 5% gain investment
x + y = 13,500 {the two investments total $13,500}
-0.03x + 0.05y = 319 {3% loss on one and 5% gain on other, receipt is $319}
x = -y + 13,500 {subtracted y from each side of first equation}
-0.03(-y + 13,500) + 0.05y = 319 {substituted (-y + 13,500), in for x, into second equation}
0.03y - 405 + 0.05 = 319 {used distributive property}
0.08y - 405 = 319 {combined like terms}
0.08y = 724 {added 405 to each side}
y = 9050 {divided by 0.08}
x = -y + 13,500 {from equation above}
x = -9050 + 13,500 {substituted 9050 in for y}
x = 4450 {added}
The 3% loss investment was $4450
The 5% gain investment was $9050
What is the slope-intercept form of the equation of the line that passes through the points (−3, 2) and (1, 5)?
y=34x−92
y=34x+72
y=34x−74
y=34x+174
Answers
Answer:
y = 3/4x + 17/4
Step-by-step explanation:
Step 1: Find slope m
m = (5 - 2)/(1 + 3)
m = 3/4
y = 3/4x + b
Step 2: Find b
5 = 3/4(1) + b
5 = 3/4 + b
b = 17/4
Step 3: Rewrite equation
y = 3/4x + 17/4
Answer:
y = 3/4x + 17/9
Step-by-step explanation:
Find the slope:
5 - 2/ 1 - (- 3)
3/ 1 + 4
3/4
Find the y-intercept:
2 = 3/4(-3) + b
2 = -9/4 + b
17/4 = b
Put it in an equation:
y = 3/4x + 17/9
310
Which law would you use to simplify the expression
quotient of powers
power of a quotient
product of powers
power of a product
Answers
power of a quotient
edge 2021
The law used to simplify the expression is quotient of powers.
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, 3¹⁰ / 3⁴, we need to determine the law used to simply the expression,
3¹⁰ / 3⁴
For this case we have an expression formed by a division of powers of the same base in which we must apply a law to simplify said expression.
By the definition we have the property of the power quotient of the same base set:
xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾
So, using the same,
3¹⁰ / 3⁴ = 3⁽¹⁰⁻⁴⁾ = 3⁶
Thus, to simplify the expression we must use the property of the power quotient of the same base.
Hence, the law used to simplify the expression is quotient of powers.
Learn more about expression, click;
https://brainly.com/question/16804733
#SPJ7
The question and pic is on the picture I took a picture of
Answers
Answer:
m<y = 155
Step-by-step explanation:
If m<x = 155, then m<y = 155 (Because vertically opposite angles are congruent)
Answer:
155°
Step-by-step explanation:
The two angles are a pair of vertically opposite angles.
Verticall opposite angles are opposite to each other and are equal.
Angle x = Angle y
155 = 155
In how many ways can we put five identical fruits into three bowls? Note that the bowls may be empty.
Answers
Answer:
20
Step-by-step explanation:
If you have a gerbil, then you are a pet owner. Question 7 options: If you are not a gerbil, then you are not a pet owner. True If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner then you have no pets. If you do not have a gerbil, then you are not a pet owner. False; you could have a dog. If you are not a pet owner, then you do not have a gerbil. True
Answers
Step-by-step explanation:
If you are not a gerbil, then you are not a pet owner. False; if you are not a gerbil, you can be a human who owns pets.
If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner then you have no pets.
If you do not have a gerbil, then you are not a pet owner. False; you could have a dog or a cat.
If you are not a pet owner, then you do not have a gerbil. True, since if you do not own any pets, you will not have any animals, so you will not have a gerbil.
Hope this helps!
Answer:
If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner then you have no pets
Step-by-step explanation:
PLEASE HELP Order these numbers from least to greatest. 2 1/10, 61/10, 3.122, 3.19
Answers
Answer: 2 1/10, 3.122, 3.19, 61/10
Step-by-step explanation:
Let's first turn each number into decimal form: (1/10=.1, 2/10=.2,etc.)
2.1, 6.1, 3.122, 3.19. Obviously, the smallest number is 2.1, because it has a 2 in the ones place. Next, we see a tie in the ones place between 3.122 and 3.19. Then we look at the tenths place and see another tie. Then, at the hundredths place, we see that 3.19 is greater that 3.122. Thus, the order of the numbers is 2.1,3.122,3.19,6.1.
Hope it helps <3
Question 18 (5 points)
Identify the independent and dependent variables in the following situation: The
temperature of the water decreases as a diver descends to the bottom of a lake.
The independent variable is the temperature of the water, and the dependent
variable is the depth below the surface of the lake.
The independent variable is the depth below the surface of the lake, and the
dependent variable is the temperature of the water.
The independent variable is the speed at which the diver descends, and the
dependent variable is the temperature of the water.
The independent variable is the type of boat, and the dependent variable is the
temperature of the water.
Answers
Answer:
The independent variable is the depth below the surface of the lake the dependent is the tempeature of the water
Step-by-step explanation:
Tempeture = depth x
Dan must choose a shirt, a pair of pants, and a cap for today's outfit. He has 2 shirts, 2 pairs of pants, and 3 caps to choose from. How many different outfits can he make?
Answers
Answer:
12 different outfits
Step-by-step explanation:
2 x 2 x 3 = 12 outfits.
Answer:
12
Step-by-step explanation:
He has 2 possibilities for a shirt, 2 possibilities for a pant, and 3 possibilities for a cap. You just multiply them together:
2 * 2 * 3 = 12 outfits
literally a free 50 points, just need the answer, What is the solution to the equation fraction 4 over 5 n minus fraction 1 over 5 equals fraction 2 over 5 n?
Answers
Answer:
n = 1/2
Step-by-step explanation:
So the equation is 4/5n - 1/5 = 2/5n.
So, the first thing that we need to do is get the variable on one side.
So, to do that we need to subtract 4/5n on both sides.
Now our equation is -1/5 = -2/5n
Now the last step is to simplify.
To do that, we need to multiply by the reciprocal of 2/5 on both sides.
That leaves us with 1/2 = n
Answer:
n = 2
Step-by-step explanation:
=> [tex]\frac{4}{5n} - \frac{1}{5} = \frac{2}{5n}[/tex]
Combining like terms
=> [tex]\frac{4}{5n } - \frac{2}{5n} = \frac{1}{5}[/tex]
=> [tex]\frac{4-2}{5n} = \frac{1}{5}[/tex]
=> [tex]\frac{2}{5n}= \frac{1}{5}[/tex]
Cross Multiplying
=> 5n = 2*5
=> 5n = 10
Dividing both sides by 5
=> n = 2
12/ y + 8 = 4/9 Thats the question. Im dyin for help. :)
Answers
Answer:
-1 10/17
Step-by-step explanation:
Answer:
y = 1 10/17
Step-by-step explanation:
The LCD is 9y. Multiply all three terms by 9y:
(9y)(12) (9y)(4)
----------- + 8(9y) = -----------
y 9
This reduces to 108 + 72y = 4y, or 108 = -68y
Dividing both sides by 68, we get y = 1 10/17
x^2 + 20x + 28 = 9 find the graphing/vertex form
Answers
Answer: [tex](x+10)^2+119=0[/tex]
Step-by-step explanation:
For a quadratic equation, the vertex form is given by : [tex]y=a(x-h)^2+k[/tex], where (h, k) is the vertex.
The given quadratic equation: [tex]x^2 + 20x + 28 = 9[/tex]
Subtract 9 from both sides
[tex]=x^2+20x+19=0[/tex]
compare this to [tex]x^2+bx=c[/tex], and add [tex](\frac{b}{2})^2[/tex] both sides
b= 20
[tex]x^2+20+100+19=-100[/tex] [(b/2)²=20/2=10]
[tex]\Rightarrow\ x^2+2(x)(10)+10^2+119=0[/tex]
[tex]\Rightarrow\ (x+10)^2+119=0\ \ \ [\because\ (a+b)^2=a^2+b^2+2ab][/tex]
So, the vertex form : [tex](x+10)^2+119=0[/tex]
plzzzzz answer this question about density mass and volume!!!!!!!!!
Answers
Answer:
13.896 kg
Step-by-step explanation:
You can find the mass of the bar by first finding the volume.
V = BH
where B = area of the base (the trapezium), and
H = height (distance trapezium between bases)
The area of a trapezium is
A = (b1 + b2)h/2
where b1 and b2 are the lengths of the bases of the trapezium (the parallel sides), and
h = the altitude of the trapezium (distance between the bases of the trapezium)
V = (b1 + b2)h/2 * H
V = (12 cm + 6 cm)(5 cm)/2 * 16 cm
V = 720 cm^3
The volume of the bar is 720 cm^3.
Now we use the density and the volume to find the mass.
density = mass/volume
mass = density * volume
mass = 19.3 g/cm^3 * 720 cm^3
mass = 13,896 g
Now we convert grams into kilograms.
1 kg = 1000 g
mass = 13,896 g * (1 kg)/(1000 g)
mass = 13.896 kg
Answer: 1.3896 kg
If similar cubes have a length ratio of 3:2, what is the volume ratio? PLEASE EXPLAIN a) 9 : 4 b) 9 : 6 c) 27 : 8 d) 3 : 2
Answers
Answer: c) 27:8
Step-by-step explanation:
As volume of cube is side^3
volume of cube with side 2a is 8.a^3
volume of cube with side 3a is 27.a^3
ration of volumes is 27:8
250 people went to a "couples only" party at 9pm.70 people left at 11pm, how many couples stayed at the party?
Answers
Answer:
90
Step-by-step explanation:
Total People = 250
Left the party at 11 pm = 70
Stayed = 250-70
=> 180
Couples that stayed = 180/2
=> 90
Answer:
90 Couples
Step-by-step explanation:
There were 250 total people at the beginning at the party. 70 people left at 11pm.
Subtract 70 from 250:
[tex]250-70=180[/tex]
There were 180 people that stayed.
A couple consists of two people. The question asks how many couples stayed at the party, not people.
Divide 180 by 2:
[tex]\frac{180}{2}= 90[/tex]
There would be 90 couples that stayed at the party.
What is the new cost if a $2.75 toy is marked up by 29%?
Answers
Answer:
$3.55
Step-by-step explanation:
You need to add 29% of $2.75 to $2.75.
That means the price will be 129% of $2.75.
129% of $2.75 =
= 1.29 * $2.75
= $3.55
2.75 x .29 = 0.7975
2.75 + 0.7975 = 3.54
The diagram shows a 5 cm x 5 cm x 5 cm cube.
Calculate the length of the diagonal AB.
Give your answer correct to 1 decimal place.
Answers
Answer:
8.7 cm
Step-by-step explanation:
The question is a 2-two-step Pythagoras theorem. (c^2 = a^2 + b^2)
Consider as such, If I were to draw a diagonal line along the base of the cube what is the length of the diagonal line. To find out that we use the theorem. We can substitute a for 5 and b for 5 as well. So
a^2 +b^2 = c^2
5^2 + 5^2 = c^2
25 + 25 = c^2
√50 = c
Then since the line side of the cube is on a 3d angle we need to do the same process again but now using the imaginary diagonal line that we just calculated and the height (5).
a^2 +b^2 = c^2
√50^2 + 5^2 = c^2
50 + 25 = c^2
√75 = c
c = 8.6602...
when rounded to 1 d.p.
c = 8.7
Line AB is 8.7 cm long.
FIND THE MISSING LENGTH INDICATED
Answers
Answer:
25 units.
Step-by-step explanation:
The first thing we need to do is find the hypotenuse of the triangle with side lengths 12 and 16. 12^2 + 16^2 = 144 + 256 = 400. sqrt(400) = 20. So, the hypotenuse of that triangle is 20 units.
Because the smaller length of the smaller triangle bisects the largest triangle's right angle, the two triangles are similar, with the side length 12 corresponding to the smaller side length of the larger triangle, the side length 16 corresponding to the 20 unit side, and the 20 unit hypotenuse corresponding to x.
Now that we know the triangles are similar, we can construct a proportion...
[tex]\frac{16}{20} =\frac{20}{x}[/tex]
That means that 4/5 = 20/x
1/5 = 5/x
x = 25
Hope this helps!
Fill in the blank with a number to make the expression a perfect square.
Answers
Answer:
16
Step-by-step explanation:
[tex] {w}^{2} - 8w + { {4}^{2} } \\ = {w}^{2} - 8w + \boxed{ 16} \\= (w-4)^2 [/tex]
Answer:
Step-by-step explanation:
a² + 2ab +b² = (a+ b)²
w² - 8w + _?___
a = w
2ab = -8w
2*w*b = -8w
b = -8w/2w
b = 4
8w = 2 * 4*w
w² - 8w + 4² =w² -8w + 16
steve can run 3.5 miles in 30 minutes. if he increases his rate by 1/2 mile per hour, how far will he run in 2 hours?
Answers
Answer:
15 miles
Step-by-step explanation:
Currently, he can run 3.5 * 2 = 7 mph. Adding 1/2 mph to that gives us 7.5 mph, so therefore, in 2 hours he can run 7.5 * 2 = 15 miles.
Answer:
15
Step-by-step explanation:
because its correct just did the thing.
pls hurry the answer is not 36.......Given a * b=ba−ba+ab, find (2*3)×(3*2).
Answers
Answer:
36
Step-by-step explanation:
In the above question, we have been given a rule to follow
Given a * b = ba−ba+ab
We are to find (2*3)×(3*2)
Let simplify each bracket first
a * b = ba−ba+ab
2*3, a = 2, b = 3
2*3 = 3×2 - 3×2 + 2×3
= 6 - 6 + 6
= 6
a * b = ba−ba+ab
3*2, a = 3, b = 2
3*2 = 2×3 - 2×3 + 3×2
= 6 - 6 + 6
= 6
(2*3)×(3*2)
= 6 × 6
= 36
The answer is 36
PLEASE HELP ME ASAP!!!! I DON'T UNDERSTAND THIS!!!!
Answers
Answer: 62
Step-by-step explanation:
The surface area of a rectangular prism is 2(wl+hl+hw).
Simply plug in the values to get 62
Answer:
62cm ^2
Step-by-step explanation:
every cube has 6 sides,
2(3*5) + 2(2*3)+ 2(2*5)=
2(15)+2(6)+2(10)=
30+12+20=
62
What are all of the real roots of the following polynomial? f(x) = x4 - x3 - 13x2 + x + 12
Answers
We can find roots by setting f(x) = 0 --> x^4 - x^3 - 13x^2 + x + 12 = 0.
Factoring f(x) to make things easier for us gives us (x - 1)(x + 1)(x - 4)(x + 3), which, equal to 0, gives us the ability to set each set of parentheses = 0.
x - 1 = 0 gives us x = 1.
x + 1 = 0 --> x = -1.
x - 4 = 0 --> x = 4.
x + 3 = 0 --> x = -3.
our roots are x = 1, -1, 4, and -3.
A car begins to depreciate at a rate of 24.9% annually as soon as it is driven off the lot. If a car was purchased for 26,500; how much is it worth after the second year? The equation you used is? What is the value of the car after two years?
Answers
Answer:
13197
Step-by-step explanation:
You have to do 24.9*2 and then find that percent of 26500
$6,000 dollars is invested in two different accounts earning 3% and 5% interest. At the end of one year, the two accounts earned $220 in interest. How much money was invested at 3%? $2,000 $3,000 $4,000
Answers
Answer:
money invested at 3% is $4000
Step-by-step explanation:
let the money invested in 3% account be x
then money invested in 5% account = 6000 - x
we know interest = p*r*t/100
p is the principle amount invested
here t = 1 year
interest on 3% money
interest= x*3*1/100 = 3x/100
interest on 5% money
interest= (6000-x)*5*1/100
Total interest earned on both the account
3x/100 + 5(6000-x)/100 = (3x + 30,000 - 5x)/100 =( 30000-2x)/100
given that total interest earned = $220
thus
( 30000-2x)/100 = 220
=> 30000-2x = 220*100= 22,000
=> -2x = 22,000- 30,000
=> x = -8000/-2 = 4000
Thus, money invested at 3% = x = $4000
Answer:)
$4000
Step-by-step explanation:
write the equation of a line that is perpendicular to x=3 and that passes through the point (0 -4) will mark brainliest asap!!!
Answers
Answer:
y = -4
Step-by-step explanation:
x = 3 is a vertical line.
The perpendicular line passes through (0, -4) (x, y)
y = -4
The line is perpendicular, so the line should be also horizontal.
Answer:
y = -4
Step-by-step explanation:
The line x = 3 is a vertical one; any line perpendicular to x = 3 is a horizontal line (which has a zero slope).
Thus, the desired line is a horizontal one that passes through (0, -4) and is represented by y = -4.
Given the figure below, find the values of x and z.
Answers
Answer:
X= 6°z= 112°Solution,
Finding the value of X,
[tex]11x + 2 = 68[/tex]
( being vertically opposite angles)
[tex]11x = 68 - 2 \\ 11x = 66 \\ x = \frac{66}{11} \\ x = 6[/tex]
Value of X is 6
Now, finding the value of z
[tex]z + 68 = 180[/tex]
(sum of angle in linear pair)
[tex]z = 180 - 68 \\ z = 112[/tex]
Value of z is 112.
Hope this helps....
Good luck on your assignment...
explanation:
the diagram shows a right angled triangle use pythagoras theorem to work out length of side ac
Answers
Answer:
Step-by-step explanation:
Using Pythagoras theorem,
AC^2 = AB^2 + BC^2
AC^2 = 4^2 + 15^2
AC^2 = 16 + 225
AC^2 = 241
AC = √241
The points plotted below satisfy a polynomial. In what ranges of x-values must there be a root of the graph? Check all that apply. I will mark brainliest!
Answers
Answer:
not sure,but I think the answer is 3 to 4