Answers
The given ratios expresses the number of time a value is larger or smaller
than another value.
The correct responses are;
3. (B) 12 and 244. (D) 6, 9, 215. [tex]\underline{(E) \ \displaystyle \frac{11}{2}}[/tex]6. [tex]\underline{(E) \ \displaystyle \frac{5}{14}}[/tex]7. (B) [tex]\overline{EF}[/tex] = 6, [tex]\overline{AC}[/tex] = 9·√58. (C) The values are equal9. (A) The value in column A is greaterReasons:
3. Given that the perimeter of the rectangle = 72
The ratio of the lengths of the sides = 1:2
Let a and b represent the sides, we have;
2·a + 2·b = 72
[tex]\displaystyle \frac{a}{b} = \mathbf{\frac{1}{2}}[/tex]
Which gives;
2·a = b
2·a + 2·(2·a) = 72
6·a = 72
a = 72 ÷ 6 = 12
b = 2·a = 2 × 12 = 24
The lengths of the sides are; (B) 12 and 24
4. Extended ratio = 2:3:7
The perimeter = 36
The lengths of the sides are;
[tex]\displaystyle \frac{2}{2 + 3 + 7} \times 36 = \mathbf{6}[/tex]
[tex]\displaystyle \frac{3}{2 + 3 + 7} \times 36 = \mathbf{9}[/tex]
[tex]\displaystyle \frac{7}{2 + 3 + 7} \times 36 = \mathbf{21}[/tex]
The lengths are; (D) 6, 9, 21
5. The given equation is presented as follows;
[tex]\displaystyle \frac{5}{x + 7} = \mathbf{\frac{3}{x + 2}}[/tex]
5 × (x + 2) = 3 × (x + 7)
5·x + 10 = 3·x + 21
5·x - 3·x = 21 - 10
2·x = 11
[tex]\displaystyle x = \mathbf{ \frac{11}{2}}[/tex]
The correct option is; [tex]\displaystyle \underline{(E) \ \frac{11}{2}}[/tex]
6. The width to length ratio is [tex]\displaystyle \mathbf{\frac{2.5}{7.0}}[/tex]
The simplified ratio is therefore;
[tex]\displaystyle \frac{2.5}{7.0} = \frac{2 \times 2.5}{2 \times 7.0} = \mathbf{\frac{5}{14}}[/tex]
The correct option is (E) [tex]\displaystyle \underline{(E) \ \frac{5}{14}}[/tex]
7. The given ratio of the lengths is 3:1
Therefore;
[tex]\overline{BC}[/tex]:[tex]\overline{EF}[/tex] = 3:1
Which gives;
[tex]\displaystyle \mathbf{\frac{\overline{BC}}{\overline{EF}}} = \frac{3}{1}[/tex]
[tex]\overline{BC}[/tex] = 18
Therefore;
[tex]\displaystyle \frac{18}{\overline{EF}} = \frac{3}{1}[/tex]
18 × 1 = 3 × [tex]\overline{EF}[/tex]
[tex]\displaystyle \overline{EF} = \frac{18 \times 1}{3} = 6[/tex]
[tex]\overline{EF}[/tex] = 6
By Pythagorean theorem, we have;
[tex]\overline{DF}[/tex]² = [tex]\mathbf{\overline{DE}}[/tex]² + [tex]\mathbf{\overline{EF}}[/tex]²
Which gives;
[tex]\overline{DF}[/tex]² = 3² + 6² = 45
[tex]\overline{DF}[/tex] = √(45) = 3·√5
Using the given ratio, we have;
[tex]\overline{AC}[/tex] = 3 × [tex]\mathbf{\overline{DF}}[/tex]
Which gives;
[tex]\overline{AC}[/tex] = 3 × 3·√5 = 9·√5
[tex]\overline{AC}[/tex] = 9·√5
The correct option is; (B) [tex]\overline{EF}[/tex] = 6, [tex]\overline{AC}[/tex] = 9·√5
8. EF = 1, AB = 2
CD = 2, CE = 4
Therefore;
[tex]\displaystyle \mathbf{\frac{EF}{AB}} =\frac{1}{2}[/tex]
[tex]\displaystyle \mathbf{\frac{CD}{CE}} =\frac{2}{4} = \frac{1}{2}[/tex]
Which gives;
[tex]\displaystyle \frac{EF}{AB} =\displaystyle \mathbf{\frac{CD}{CE}}[/tex]
(C) The values are equal
9. AC = 6, BE = 8
DF = 3, BD = 6
Column A
[tex]\displaystyle \frac{AC}{BE} =\displaystyle \mathbf{\frac{6}{8}} = \frac{3}{4}[/tex]
Column B
[tex]\displaystyle \frac{DF}{BD} =\displaystyle \mathbf{\frac{3}{6}} = \frac{1}{2}[/tex]
[tex]\displaystyle \frac{3}{4} > \mathbf{\frac{1}{2}}[/tex]
Therefore;
Column A is greater than column B
(A) The value in column A is greater
Learn more about ratios here:
https://brainly.com/question/2774839
Related Questions
pls help me not fail
Answers
Answer:
D
Step-by-step explanation:
Using the Cosine rule to find AC
AC² = BC² + AB² - (2 × BC × AB × cosB )
= 18² + 12² - ( 2 × 18 × 12 × cos75° )
= 324 + 144 - 432cos75°
= 468 - 111.8
= 356.2 ( take the square root of both sides )
AC = [tex]\sqrt{356.2}[/tex] ≈ 18.9
-----------------------------------------
Using the Sine rule to find ∠ A
[tex]\frac{18}{sinA}[/tex] = [tex]\frac{18.9}{sin75}[/tex] ( cross- multiply )
18.9 sinA = 18 sin75° ( divide both sides by 18.9 )
sinA = [tex]\frac{18sin75}{18.9}[/tex] , then
∠ A = [tex]sin^{-1}[/tex] ( [tex]\frac{18sin75}{18.9}[/tex] ) ≈ 66.9°
A man invested ksh. 36000 in two companies P and Q . Company P pays a dividend of 11.25% while Q pays a dividend of 10.5%. Is from his total investment, he obtained a return of 10.75%,how much did he invest in each company?
Answers
Answer:
Investment in company P = 12,000
Investment in company Q = 24,000
Step-by-step explanation:
Given that,
Total investment = 36,000
Dividend paid by company P = 11.25%
Dividend paid by company Q = 10.5%
Total return = 10.75%
Now, let investment made in company P be 'a' and company 'Q' be 'b.' So,
A.T.Q.
a + b = 36,000 ...(i)
11.25% of a + 10.5% of b = 10.75% of 36000 ...(ii)
On simplification,
a + b = 36,000
11.25% of a + 10.5% of b = 3870
Now,
11.25% of a + 10.5% of (36000 - a) = 3870
⇒ 0.1125 * a + 0.105 * (36000 - a) = 3870
⇒ 0.1125 a + 3780 - 0.105a = 3870
⇒ 0.1125a - 0.105 a - 3870 - 3780
⇒ 0.0075 a = 90
⇒ a = 90/0.0075
∵ a = 12000
Since, a = P = 12,000
Q = b = (36000 - a)
= 36000 - 12000
= 24,000
Thus,
Investment in company P = 12,000
Investment in company Q = 24,000
Answer:
Amount invested in P = 12,000
Amount invested in Q = 24,000
Step-by-step explanation:
Given:
Amount invested = 36,000 in two companies P and Q
P pays dividend = 11.25%
Q pays dividend = 10.5%
Total return = 10.75%
Find:
Amount invested in each company
Computation:
Total return = 36,000 x 10.75
Total return = 3870
Assume;
Amount invested in P = a
So,
Return in P = a x 11.25%
Return in P = 0.1125a
Return in Q = [36000 - a]10.5%
Return in Q = 3,780 - 0.105a
Total return = Return in P + Return in Q
3,870 = 0.1125a + 3,780 - 0.105a
90 = 0.0075a
a = 12,000
Amount invested in P = 12,000
Amount invested in Q = 36,000 - 12,000
Amount invested in Q = 24,000
The amount oRs.4500 for 5 ye is 8550 8550. Find the interest and the rate of interest
Answers
Answer:
Step-by-step explanation:
We have;
P = 4500
A = 8550
T= 5 years
I= ?
R=?
We know,
A= P+I
or, 8550=4500+I
∴I=8550-4500= 4050
Now, I= PTR/100
Or, 4050= (4500*5*R)/100
Or, 4050=45*5*R
Or, R= 4050/225
∴R= 18%
what percentage of 50kg is 65 kg?
Answers
Answer:
130
Step-by-step explanation:
65/50*100= 130
at what rate of interest the sum of Rs 4000 amount to rs 6000 in 4 years
Answers
interest=4000
amount =6000
time =4yr
principal =6000-4000
=2000
interest=principal×time×rate/100
4000= 2000×4×r/100
4000=8000×r/100
r=8000-4000/100
r=2000/100
r=20
Answer:
12.5 %
Step-by-step explanation:
I = PRT
I is the interest, P is the Principle, R is the Rate and T is the time
The interest is 6000- 4000 = 2000
2000 = 4000* R *4
2000 = 16000R
Divide each side by 16000
2000/16000 = R
.125 = R
Changing to percent form
12.5 %
Two of the exterior angles of a triangle are $158^\circ$ and $99^\circ.$ Find the third exterior angle, in degrees.
Answers
Answer:
The third exterior angle is [tex]103^o[/tex]
Step-by-step explanation:
Given
[tex]\theta = 158^o[/tex]
[tex]\alpha = 99^o[/tex]
Required
The third exterior angle [tex](\beta)[/tex]
The exterior angles of a triangle add up to 360 degrees.
So:
[tex]\theta + \alpha + \beta = 360^o[/tex]
Make [tex]\beta[/tex] the subject
[tex]\beta = 360^o - (\theta + \alpha)[/tex]
Substitute known values
[tex]\beta = 360^o - (158^o + 99^o)[/tex]
[tex]\beta = 103^o[/tex]
Given: BE and AD are altitudes (intersecting at H) of triangle ABC, while F,G, and K are midpoints of AH, AB and BC, respectively. Prove: angle FGK is a right angle.
Answers
Solution :
Since [tex]BE[/tex] is an altitude of a triangle [tex]ABC[/tex], it is perpendicular to [tex]AC[/tex] (since the triangle ).
Since [tex]G[/tex] and [tex]K[/tex] are the midpoints, then the line [tex]BG=GA[/tex] and the line [tex]BK=KC[/tex]. The line [tex]KG[/tex] must be parallel to the line [tex]AC[/tex] and is therefore perpendicular to [tex]BE.[/tex]
Now since F and [tex]G[/tex] are the mid points, we get [tex]GA=BG[/tex]. The line [tex]GF[/tex] is parallel to BH and is perpendicular to AC.
Therefore, we have
[tex]KG-GK[/tex] parallel to [tex]AC[/tex]
[tex]AC[/tex] perpendicular to [tex]BE-BH-BJ[/tex]
[tex]BE-BH-BJ[/tex] parallel to [tex]GF[/tex]
Thus [tex]GK[/tex] is perpendicular to [tex]GF[/tex] and also ∠[tex]FGK[/tex] is a right angle.
HELP.... please??????????????
Answers
Answers:
Functions
y = -x+11y = 2x^2-6x+4y = -7Not functions
x = 3x^2+y^2 = 81y^2 = -5x-12=======================================================
Explanation:
A function is possible if and only if any given x input leads to exactly one y output.
For something like x^2+y^2 = 81, we can see that x = 0 leads to either y = 9 or y = -9. So this would not be a function. We would need x to pair with only y value to have it be a function.
We have the same thing going on with y^2 = -5x-12 as well.
For anything of the form x = k, where k is any real number, this is also not a function. We have one single input only and it leads to infinitely many outputs. So in a sense, this is even worse compared to the other examples.
-----------------
In summary, we have these three non-functions:
x = 3x^2+y^2 = 81y^2 = -5x-12Everything else is a function. You can use the vertical line test as a visual way to check.
Line A passes through points (-3,2) and (-23,54) line B is parallel to line A and passes through point (-8,0) what is the equation of line B? please help!!
Answers
Answer:
the correct answer to this question is b
Step-by-step explanation:
got it right
I need help!!
Find the height of this cone using the Pythagorean Theorem.
Answers
Answer:
h = 4sqr(3)
Step-by-step explanation:
r = d/2
d = 8
r = 8/2
r = 4
a = 4
c = 8
b = h = ?
a^2 + h^2 = c^2
4^2 + h^2 = 8^2
16 + h^2 = 64
h^2 = 64 - 16
h^2 = 48
sqrt(h^2) = sqrt(16*3)
h = 4 sqrt3)
Answer:
48
Step-by-step explanation:
Select the best real-world situation that can be represented by 12 + = 13.50. Group of answer choices Mary wants to buy flowers and perfume. She has $13.50 to spend, but has already spent $12 on perfume. How much does she have left to spend on flowers? Rachel earns $12 per hour. How long does it take her to earn $13.50? Jane has $13.50 to spend. How many roses can she buy if they are $12 each? Sarah has $12 in her checking account, but has written a check for $13.50. How much is she overdrawn?
Answers
Answer:
Mary wants to buy flowers and perfume. She has $13.50 to spend, but has already spent $12 on perfume. How much does she have left to spend on flowers?
Step-by-step explanation:
12 + c = 13.50
OpruonnA seems to be the best, hence, Breaking down in real world terms :
13.50 = total cost
Number of variables added to make up total cost = 2 ; this represents the cost of the 2 items purchased ; flowers and perfume
Cost of perfume = 12
Cost of flowers = c
Total cost of items = $13.50
Between which two intergers does -3 7/8 lie?
Answers
Answer:
Step-by-step explanation:
-4 and -3
Answer:
-4 and 3 because I tookt the test and the other guy was right too
12) Gina is making a bookcase and has 92 inches of wood. If she uses 61 inches of wood for the top and bottom, how much wood does she have left for the sides?
Answers
Answer:
92 - 61 = 31
There are 31 inches of woods left.
Answer:
31 inches
Step-by-step explanation:
Simply subtract: 92 - 61 = 31
(Assuming that the bookcase has 3 sides, she has about 10.33 inches of wood for each side.)
PLZZZ HELPPP, IF NOT 100% SURE PLZ DONT ANSWER…BRAINLIEST TO FIRST AND CORRECT ANSWER, THX TO SECOND AND CORRECT ANSWER
Answers
Answer:
2 1/4 cups.
Step-by-step explanation:
If we want to find the total amount of cheese Belle used, we have to add the number of cups of cheddar and parmesan together:
2 + 1/4 = 2 1/4
Therefore, our answer is 2 1/4, specifically, 2 1/4 cups.
4. Which equations have 4 as a possible solution for p? Select all that apply.
A. p²= 8
B.p³= 8
c.p²= 16
D.p²= 64
E.p³=64
Answers
Answer:
A. p2=16
soln:
p=4×4=16
so,
p2=16
someone help me with this
find points a b c
Answers
Answer:
<a=32
<b=40
<c=40
Step-by-step explanation:
to find angle a you have to subtract the 50 minus 180 to find the angle close to the 50 because angles in a straight line add up to 180. the answer will be
180-50=130
after finding the angle in that triangle you must add it to the other angle present which is 18° then subtract by 180 because angles in a straight line add up to 180
130+18+a=180
a=180-148
a=32 and that's how you find a
to find b you must know that the angle at the center is twice the angle at the circumference meaning the large angle C is 90°,now if it's 90° inorder to find the big angle B you must add the 18+90 then subtract 180
18+90+B=180
B=180-108
=72
since the combination of angle a and b will give you 72 you can find angle c by subtracting a from 72
c=72-32
=40
then if you look at angle c and angle b you can tell that they are alternating meaning angle b is also 40
I hope this helps
Using Eulers formula, how many edges does a polyhedron with 6 faces and 6 vertices have? Eulers Formula: F+V=E+2
Answers
Answer:
10
Step-by-step explanation:
E = F + V - 2
E = edges
F = faces = 6
V = vertices = 6
E = 6 + 6 - 2
E = 12 -2
E = 10
Question : A scale model of a tower is made using the scale 1 in=4ft. If the height of the scale
model is 20 in, what is the height of the tower?
Answers
Answer:
80ft
Step-by-step explanation:
1ib=4ft, multiply by 20 both sides and you will get 20in=80ft
Diagnostic
Analytics
When completing an online shopping transaction, a typical shopper takes 7 seconds to
select each product and another 9 seconds to complete the check-out process. If it takes 37
seconds to complete a transaction, how many products are being purchased?
products
Submit
Answers
Answer:
In 26 seconds to complete a transaction, 2 products are being purchased.
Step-by-step explanation:
1 item = 9 seconds
Time taken in all to check out = 8 seconds
Time taken to shop = 26 seconds
Now as check out process takes 8 seconds, so the
Time left to ACTUALLY SHOP = Total Time - Time Used to check out
= 26 seconds = 8 seconds = 18 seconds
Shopping of 1 item = 8 seconds
Shopping of 2 items = 2 x ( Time taken in 1 item) = 2 x 9 = 18 seconds
So, in 18 seconds, 2 clothing item can be selected.
Hence,in 26 seconds to complete a transaction, 2 products are being purchased.
Answer please please I cant think
Answers
Answer: ∠A = 20°; ∠B = 59°; ∠C = 101°
Step-by-step explanation:
According to the problem:
∠A = ∠A∠B = 4 · ∠A - 21°∠C = 5 · ∠A + 1°All interior angles within a triangle adds up to 180°:
∠A + ∠B + ∠C = 180°
[tex]A+(4A-21)+(5A+1)=180\\\\A+4A+5A-21+1=180\\\\10A=180+21-1\\\\10A=200\\\\A=20\°[/tex]
Substitute in the value of ∠A into the other equations:
∠B = 4 · ∠A - 21° = 4(20°) - 21° = 80° - 21° = 59°
∠C = 5 · ∠A + 1° = 5(20°) + 1° = 100° + 1° = 101°
Evaluate the following expression 2x - |4 - 7x| when x = -3
Answers
Answer:
-31
Step-by-step explanation:
2x - abs(4 - 7x)
2x = 2 * - 3 = - 6
4 - 7x = 4 - 7*-3 = 4 + 21 = 25
-6 - abs(25)
-6 - 25 = -31
You should note three things.
1. the absolute value of 25 is 25
2. There is a - sign outside the influence of the 25 so 25 becomes - 25
3. - 6 - 25 = - 31
PLEASE HELP ASAP
A helicopter hovers 500 feet
above a small island. The
figure shows that the angle of
depression from the helicopter
to point P is 48º. How far off
the coast, to the nearest foot, is
the island?
d ft
(Round the answer to the nearest whole number.)
Answers
Answer:
d = 450 ft
Step-by-step explanation:
Hi there!
First, we can find the angle in the triangle at the point of the helicopter, the angle opposite [tex]d[/tex]. Subtract 48° from 90°:
90-48=42
Now, given that this is a right triangle and we have an angle and the side adjacent the angle, we can solve for [tex]d[/tex] by using the tangent ratio:
[tex]tan\theta=\displaystyle \frac{opposite}{adjacent}[/tex]
Replace θ with 42°, "opposite" with [tex]d[/tex], and "adjacent" with 500 ft:
[tex]tan(42)=\displaystyle \frac{d}{500}[/tex]
Multiply both sides by 500 to isolate [tex]d[/tex]:
[tex]500*tan(42)=d\\450=d[/tex]
Therefore, d = 450 ft when rounded to the nearest whole number.
I hope this helps!
Please help me solve this I’m really struggling
Answers
Answer:
Step-by-step explanation:
I graphed this on my calculator to get the region of feasibility. You should learn how to use your calculator to help you do things like this. You should know by now how to graph by hand, which is tedious, so now it's time to use your calculator to sweat the small stuff and learn to do some useful things.
When you graph this inequality on your calculator, you can see the points of intersection which in turn translate to the vertices of the feasible region. They are located at:
(-14, -6), (-9, -11), (6, 4)
You could then use those vertices to maximize the profit equation or production equation or whatever it is this system pertains to.
can any of yalls help with this one
Answers
Answer:
it's the last option
Step-by-step explanation:
mark me brainliest
Oak wilt is a fungal disease that infects oak trees. Scientists have discovered that a single tree in a small forest is infected with oak wilt. They determined that they can use this exponential model to predict the number of trees in the forest that will be infected after t years.
f(t) = e^0.4t
The scientists believe the forest will be seriously damaged when 21 or more of the forest’s 200 oak trees are infected by oat wilt. According to their model, how many years will it take for 21 of the trees to become infected?
Type the correct answer in the box. Use numerals instead of words. Round your answer to the nearest tenth.
Answers
To solve this question, we need to solve an exponential equation, which we do applying the natural logarithm to both sides of the equation, getting that it will take 7.6 years for for 21 of the trees to become infected.
Model:
The exponential model for the number of infected trees after t years is given by:
[tex]f(t) = e^{0.4t}[/tex]
How many years will it take for 21 of the trees to become infected?
This is t for which:
[tex]f(t) = 21[/tex]
Thus
[tex]e^{0.4t} = 21[/tex]
Applying the natural logarithm to both sides:
[tex]\ln{e^{0.4t}} = \ln{21}[/tex]
[tex]0.4t = \ln{21}[/tex]
[tex]t = \frac{\ln{21}}{0.4}[/tex]
[tex]t = 7.6[/tex]
It will take 7.6 years for for 21 of the trees to become infected.
For another example of a problem in which an exponential equation is solved, you can check brainly.com/question/24290183.
Find a if ZB = 25°, ZC = 48°, AC = 5.
Answers
Answer:
11.3
Step-by-step explanation:
a = AC × sin(A)/sin(B)
Now <A =180-25-48 = 107
a = 5×sin(107)/sin(25)
a ≈ 11.3
Answered by GAUTHMATH
ewdhcbejklwbfchkwefedq3dq3d
Answers
Answer:
Not any question Lol ?
step by steo explanation
oh ik let me ask by speaking your language
nsjwkskxkcnnejskalzlmxmdneja ?
the table of values below represents a liner function and show the amount of money in the savings account since she began her part-time job what is her monthly rate of savings
Answers
Answer:
she saves $24 dollars every month. 36 + 24 =60 +24 =84 +24 =108 +24 =132 :)
using the graph, determine the coordinates of the roots of the parabola
Answers
Answer:
(-8, 0) and (-2, 0)
Step-by-step explanation:
The root of a parabola are the places at which the parabola intersects the x-axis. As one can see, on the graph these points are the following: (-8, 0) and (-2, 0). Thus, the roots of the parabola are (-8, 0) and (-2, 0).
Answer:
-8 and -2
Step-by-step explanation:
Hello!
The roots of the parabola are the points where the graph intersects the x-axis. The x-axis is the equation y = 0.
There are two roots for this parabola, as the vertex is lower than y=0, and it opens up.
The two points of intersection are:
(-8,0)(-2,0)Therefore, the roots of the parabola are -8 and -2.
find x...............................
Answers
Answer:
sqrt(2) =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin 45 = x/2
2 sin 45 =x
2 ( sqrt(2)/2) =x
sqrt(2) =x
im sorry.. im not entirely sure but i just cross-multiplied so x/45 = 2/90 and so yeah I got 1
