Answer:
Correct option: First one -> 16 mm
Step-by-step explanation:
The equilateral triangle has its three sides with the same length.
So if the perimeter is 96 mm, we have:
[tex]Perimeter = 3*side[/tex]
[tex]3*side = 96[/tex]
[tex]side = 32 mm[/tex]
The segment MA is the height of the equilateral triangle, and its length can be calculated with the equation:
[tex]height = \frac{side * \sqrt{3}}{2}[/tex]
[tex]height = 16\sqrt{3}[/tex]
Using the Pythagoras' theorem in the triangle ACM, we have:
[tex]side^2 = MC^2 + height^2[/tex]
[tex]1024 = MC^2 + 768[/tex]
[tex]MC^2 = 256[/tex]
[tex]MC = 16\ mm[/tex]
Correct option: First one
Answer:
(A) 16mm
Step-by-step explanation:
1. £500 is deposited in a bank paying 2% simple interest per annum. How much interest will have been paid after 2 years?
2. £500 is deposited in a bank paying 1% simple interest per annum. How much interest will have been paid after 5 years?
3. £1500 is deposited in a bank paying 6.25% simple interest per annum. How much interest will have been paid after 3 years?
4.£3600 is deposited in a bank paying 4% simple interest per annum. How much interest will have been paid after 4 years?
5.£4300 is deposited in a bank paying 5.75% simple interest per annum. How much interest will have been paid after 6 years?
6.£4000 is deposited in a bank paying 9.5% simple interest per annum. How much interest will have been paid after 8 years?
7.£3600 is deposited in a bank paying 14.75% simple interest per annum. How much interest will have been paid after 14 years?
can someone answer number 10 and show the work? I really need it please
Answer:
D
Step-by-step explanation:
f(x)=(3/5)x-10
f(5)=(3/5)(5)-10=
3-10=
-7
Hope this helps!
The proportion of brown M&M's in a milk chocolate packet is approximately 14% (Madison, 2013). Suppose a package of M&M's typically contains 52 M&M's
Answer:
About 7 brown M&M's.
Step-by-step explanation:
To find 14% of 52, multiply 0.14 * 52. This equals 7.28, round to 7.
In the △ABC, the height AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC.
btw i need two answers for bc not just one
Answer:
AB = 30 inch
BC = 14 inch or BC = 50 inch
Step-by-step explanation:
Make a drawing. Please see the attachment. All measurements are in inches.
Consider the two triangles:
∆ ABC and ∆ AB'C
1. Looking only at ∆ ABC. Since this is not a rectangular triangle, let's first consider ∆ ANC, so we can calculate NC.
AN is the height and there fore is perpendicular to NC and thus also to BC.
In ∆ ANC
AN² + NC² = AC²
We want to calculate NC, so:
NC² = AC² - AN²
Given: AC = 40 and AN = 24
NC² = 40² + 24²
NC² = 1600 + 576
NC² = 1024
NC = +-SQRT(1024)
NC = 32
NC = NB + BC
We want to know BC
BC = NC - NB
Given: NB = BN = 18 and we just calculated NC to be 32 so...
BC = 32 - 18
BC = 14
2. Looking only at ∆ AB'C
AN is the height and there fore is perpendicular to B'C. Let's consider ∆ AB'N, so we can calculate AB'.
AN is the height and there fore is perpendicular to B'N, which means it has an angle of 90° in ∆ AB'N.
In ∆ AB'N
c² = a² + b²
AB'² = AN² + B'N²
Given: AN = 24 and B'N = 18
AB'² = 24² + 18²
AB'² = 576 + 324
AB'² = 900
AB' = +-SQRT(900)
AB' = 30
In ∆ AB'C
with AB' = 30 and AC = 40
c² = a² + b²
B'C² = AB'² + AC²
B'C² = 30² + 40²
B'C² = 900 + 1600
B'C² = 2500
B'C = +-SQRT(2500)
B'C = 50
Now we have our answers.
Extra:
Please look at the picture again, but now concentrate on the indicated 50 and - 50...
I am trying to explain something about the meaning of the outcome of mathematical calculations like:
c² = 2500
c = +- SQRT(2500)
c = 50 or c = - 50
Depending on where you want to start from, you can "move" 50 inch in one direction or 50 inch in the opposite direction, hence the -50 inch. Please let me explain why I am making a fuss...
1). Let's consider ∆ AB'C. Going from B' to C, you "move" -50 inch form B' towards C. This 50 inch is what we calculated earlier, but the we neglected to explain why we discarded the minus value of the SQRT... We just stated it to be only the positive value! Normally we give no meaning to the negative variant of it... Well, is this true in this case?
2). Let's consider ∆ ABC'. Going from B to C', you "move" 50 inch form B towards C'. Please understand that the direction is opposite that of - 50 inch in 1).
It is important to understand that a negative sign means the 180° in the direction of the other way.
In general. When calculating a square side by using the SQRT, you carefully need to consider if you can discard the -
minus value of your calculated outcome.
Not always, but usually there is some sort of meaning to the negative part of the SQRT, you just need to be willing to understand what it possibly could mean.
I hope this has made some sense to you :-).
What is 9^-53 × 9^37
Answer: 9⁵³ ₓ 9³⁷ = 9⁹⁰
Explanation: 53 + 37 = 90
So our answer: 9⁹⁰
The difference of six times a number and seven results in 35.
Identify the steps necessary to solve the equation.
A.) Subtract 7, and then divide by 6.
B.) Divide by 6, and then subtract 7.
C.) Divide by 6, and then add 7.
D.) Add 7, and then divide by 6.
this is multiple choice
The difference of six times and seven results in 35.
Difference - subtract
Times - multiply
Result - answer
The subtraction of six multiplied by a number and (subtracting) seven gets you the answer of 35.
6x - 7 = 35
The answer would be...
B. Divide by 6, and then subtract by 7.
what is 222 times 5
no explanation please
Answer:
1110
Step-by-step explanation:
Hey there!
222 multiplied by 5 is 1110.
You can also use a calculator to find that out haha!
Have a wonderful day!
1:750 scale model of the Sydney Opera House after a trip to Australia. The length of the model is 24.4 centimetrers. Find the actual length x (in meters) of the Sydney Opera House.
Answer:
183 meters
Step-by-step explanation:
A 1:750 scale model means that each cm on the model corresponds to 750 cm of the actual Sydney Opera House. If the model is 24.4 centimeters long, the actual Opera House has a length of:
[tex]x = 24.4*750\\x=18,300\ cm\\x=183\ m[/tex]
The actual length of the Sydney Opera House is 183 m.
Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?
Answer:
B - The correct answer is graph B
Step-by-step explanation:
Answer:
the correct choice is graph B. (see attachment below)
7. A box of facial tissue is 22 cm by 10.5 cm by 8 cm.
How much cardboard is on the outside surface?
(Pls!! show work)
Answer:
632.2 cm^2
Step-by-step explanation:
for this, you have to find the surface area:
area of side x 2: 22x10.5x2 = 46.2cm^2
area of top and bottom: 22 x 8 x 2 = 418 cm^2
area of front + back = 8 x 10.5 x 2 = 168 cm^2
sum = surface area = 632.2 cm^2
Please mark brainiest
LAT QUESTION AND LAST TRY!!! WILL GIVE BRANLIEST!!!! AT LEAST TAKE A LOOK, SHARE YO SMARTNESSS!!!!!!!! PLS
12. ___________________ lines cross at a right angle.
A) Parallel
B) Slanted
C) Intersecting
Answer:
The answer is A, parallel.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
took the test
help me pleaseeee due in one minute
Answer:
The anwer is 1/2
[tex]P=N_Y/Total=3/6=1/2[/tex]
Calculate the surface area and the volume of the cylinder.
Pls!! Show how you got the surface area and volume
Find the slope-intercept equation of the line containing (1.-4) and having slope m = 3
Answer:
y=3x-7
Step-by-step explanation:
kinda stuck on this question. please help?
Answer:
The answer is b
Step-by-step explanation:
I know this because a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression and since 9 is being multiplied by x that would mean 9 is a coefficient in this expression.
A runner moves west with an initial velocity of 4 m/s. She accelerates 3 m/s2 for 30 seconds. The runner’s final velocity is m/s.
Answer:94m/s
Step-by-step explanation:
Using the formula:
v=u+at
Where v= final velocity (the unknown)
u= initial velocity (4m/s)
a= acceleration (3m/s)
t= time (30seconds)
v=4+(3*30)
= 4+90
= 94m/s
A person places $72300 in an investment account earning an annual rate of 7.1%, compounded continuously. Using the formula V = Pe^rt, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 19 years.
Answer:
Step-by-step explanation:
Our P is 72300; our r is .071, e is Euler's number (a constant) and t is 19 years. Filling in:
[tex]V=72300e^{(.071)(19)}[/tex] and
[tex]V=72300e^{1.349[/tex] and
V = 72300(3.853570033) so
V = $278,613.11
Mike built a sand castle that measured 484 centimetres by 386 centimetres, and dug a moat around it.Afterward, he decided to change the castle size, making it 725 centimetres by 314 centimetres.How much longer will the newer moat be than the older one?
Answer:
the newer moat is 169 cm longer than the older one
Step-by-step explanation:
in order to find the difference in length of the two castles, we will first find the perimeters of the two castles then calculate the difference in the perimeters:
old castle:
dimension = 484cm by 386cm
perimeter = 484 + 386 = 870 cm
new castle:
dimension = 725cm by 314cm
perimeter = 725 + 314 = 1039 cm
difference = 1039 - 870 = 169 cm
The total length of the moats used is equals to the perimeter of the sand castles, therefore, the newer moat is 169 cm longer than the older one.
Answer:
Look I know I'm about 2 1/2 years late but the answer is not 169 or whatever the person above me said, it's 660 I answered this before.
(Brainliest will be given) Determine which of the following descriptions is accurate.
Answer:
B the size of the circle is a function of the height of the rectangle
Step-by-step explanation:
Please tell me if it is right and give me thanks and brainleist only if right
Subtract 4x4 + 2x² +5 from the sum of 2x4 - 4x2–3 and 3x4 - 3x² +9.
Answer:
x^4-9x²+1
Work:
Which expression represents the number of feet that are in x yards?
A)
12x
B)
36x
C)
3x
D)
x
3
pLS Help will mark brainlyiest
Answer:
C) 3x
Step-by-step explanation:
There are three feet in a yard. Yards are represented by x in this problem and therefore the answer is 3x.
The solutions of a quadratic equation is 8 and 2. What is the quadratic equation?
(i need help now)
Answer:
x² - 10x + 16 = 0
Step-by-step explanation:
Given the solutions x = 8 and x = 2 , then the factors are
(x - 8) and (x - 2) and the equation is
(x - 8)(x - 2) = 0 ← expand left side using FOIL
x² - 10x + 16 = 0
Please answer correctly !!!!!!!! Will
Mark brainliest !!!!!!!!!!!
Answer: Z²+ 9Z + 8
Step-by-step explanation:
You take the two z's and times them to get Z² then you do the Z times 1 to get 1Z then you do the Z times 8 to get 8Z then you take the 8 times 1 and get 8 so then you add the like terms. You add 1Z and 8Z and you get 9Z. The you put it in standard form to get Z²+9Z+8
jill mixes two types of concentrations od hci (hydrochloric acid) 0.375 liters of 25% hydrochloric acid and 0.625 liters of 65% hydrochloric acid. what is the hcl concentration in the mixed solution?
Answer:
The concentration of HCl in the mixture is 1L of 50% HCl
Step-by-step explanation:
Here, we want to know the percentage of HCl present which refers to the its concentration.
Firstly, the total volume we have is 0.375 + 0.625 = 1 L
we can calculate the percentage as follows;
The percentage of the 25% present is 37.5%
while the percentage of the 75% present is 62.5%
When we say the percentage present, we are referring to the amounts of the total liters which is 1 present.
So the concentration of the final mixture will be;
(37.5% of 25) + (62.5% of 65)
= 9.375% + 40.625%
Adding both gives = 50%
So the concentration we have is 1L of 50% HCl
solve tan x - cot x = -2cos 2x cosec 2x
Answer:
Step-by-step explanation:
tan x-cot x
[tex]=\frac{sin~x}{cos~x} -\frac{cos~x}{sin ~x} \\=\frac{sin^2x-cos^2 x}{sin ~x~cos~x} \\=\frac{-2(cos^2x-sin^2x)}{2 sin ~x~cos~x} \\=\frac{-2 cos~2x}{sin~2x} \\=-2 cos ~2x~cosec~2x[/tex]
What is the product of 7/9 and 1/4
Answer:
7/36
Step-by-step explanation:
7/9* 1/4
Multiply the numerator
7*1 = 7
9*4 = 36
Put the numerator over the denominator
7/36
Answer:
Brunliest plzStep-by-step explanation:
7/9 x 1/4 = 7/36
find the circumference
Answer:
25.12
Step-by-step explanation:
C = 2*3.14*4
C = 8*3.14
C = 25.12
Answer:
C =25.12 cm
Step-by-step explanation:
The circumference is given by
C = 2* pi *r
C = 2 * 3.14 * 4
C =25.12 cm
How much money did bianca have?
Answer:
The answer is A. Bianca had $8.
Step-by-step explanation:
I really hope this helps.
How many numbers are in the list 1,4,7...........,2005, 2008? URGENT!
Answer:
670 numbers
Step-by-step explanation:
T1=1*3-2
T2=2*3-2
T3=3*3-2
...............
Tn=n*3-2
n*3-2=2008
n*3=2010
n=2010:3
n=670 (numbers)
Answer:
2005-1=2004 so there is 2004 numbers
every 3 numbers 1 is chosen
2004/3=670
670 numbers are in between
Hope this helps
Step-by-step explanation:
Please please help!!!!
Which ordered pair is a solution of this
equation?
3x - 7y = 28
Click on the correct answer
A.
(-4,1)
B.
(0,-4)
C.
(-4,0)
D.
(1,-4)
