Answer:
Step-by-step explanation:
f(n)= -3n + 2
to find :f(12)
substitute 12 in place of n
f(12)= -3*12 + 2
f(12)=-36 + 2
f(12)= -34
The value of the f(12) is equal to -46 where the expression is
f(n) = -3n + 2.
What is an expression?Any mathematical statement which consist of numbers , variables and arithmetic operations is known as expression. An expression gives some numerical value when we put the value of variables in it.
Here, f(n)= -3n + 2 is the given expression.
So, we can find the value of f(12) by putting n=12 in f(n).
Put n=12 in f(n), we get
f(12)= (-3)×12 + 2
= -48 + 2
= -46
Hence, the value of f(12) is -46.
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A debt payment of $5,500 is due in 27 months. If money is
worth 8.4% p.a. compounded quarterly, what is the equivalent
payment? Now? 15 months? 27 months? 36 months?
Step-by-step explanation:
A=P(1+0.084) ^n;
=5500(1
The payment now is $4561.7450, 15 months later $5061.28, 27 months later $5500.00595 and 36 months later $5853.83.
Interest rate = 8.4/4 =2.1% = 0.021 every 3 months
The debt of $5500 is due in 27 months.
What is the formula to find compound interest?The formula to find the compound interest is [tex]FV=PV(1+r)^{n}[/tex].
Now, [tex]PV=FV(1+r)^{-n}[/tex].
The payment now:
5500*(1.021)^-9 = $4561.7450
So if $5500 is due in 27 months its current value is $4561.7450.
( b) 15 months from now? 5 quarters
FV(15months)= 4561.75*1.021^5
4561.75*1.021^5 = $5061.28
(c) 27 months from now? 9 quarters
FV(15 months)= $5500 that was given in the question
Verification:
FV(27months)=4561.75*1.021^9
4561.75*1.021^9 = $5500.00595
(d) 36 months from now? 12 quarters
FV(36months)=4561.75*1.021^12
4561.75*1.021^12 = $5853.83
Therefore, the payment now is $4561.7450, 15 months later $5061.28, 27 months later $5500.00595 and 36 months later $5853.83.
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If A and B are (-2,-2) and (2,-4). Find the coordinates P such that AP=3/7 AB and P lies on the line segment ab
Answer:
The coordinates of point P are [tex](-\frac{2}{7}, -\frac{20}{7})[/tex].
Step-by-step explanation:
Point P:
The coordinates of point P are (x,y).
AP=3/7 AB
So
[tex]P - A = \frac{3}{7}(B-A)[/tex]
We apply this both for coordinate x and coordinate y.
Coordinate x:
[tex]x - (-2) = \frac{3}{7}(2 - (-2))[/tex]
[tex]x + 2 = \frac{12}{7}[/tex]
[tex]x = \frac{12}{7} - 2 = \frac{12}{7} - \frac{14}{7} = -\frac{2}{7}[/tex]
Coordinate y:
[tex]y - (-2) = \frac{3}{7}(-4 - (-2))[/tex]
[tex]y + 2 = -\frac{6}{7}[/tex]
[tex]y = -\frac{6}{7} - 2 = -\frac{6}{7} - \frac{14}{7} = -\frac{20}{7}[/tex]
The coordinates of point P are [tex](-\frac{2}{7}, -\frac{20}{7})[/tex].
Two similar triangles have a scale factor of 2 : 3. For numbers 7a – 7d, determine whether each statement about the triangles is true or false.
7a. The ratio of their perimeters is 2 : 3. True or False
7b. The ratio of their areas is 4 : 6. True or False
7c. Their perimeters could be 14 cm and 21 cm. True or False
7d. Two corresponding sides could be 6 in and 7 in. True or False
Answer:
Step-by-step explanation:
Two similar triangles have a scale factor of 2 : 3.
7a. The ratio of their perimeters is 2 : 3.
As the sides are 2 : 3, the perimeters which are sums of all sides will also be 2 : 3
True
7b. The ratio of their areas is 4 : 6. True or False
As the sides are 2 : 3, the areas which are the products of two sides will be in the ratio of 2*2 : 3*3 = 4 : 9
False
7c. Their perimeters could be 14 cm and 21 cm. True or False
As the perimeter ratio for 14cm and 21 cm is 14 : 21 = 2 : 3 which complies with 7a. So they could be the perimeters.
True
7d. Two corresponding sides could be 6 in and 7 in. True or False
As the corresponding sides of 6in and 7in, the ratio is 6 : 7 and is different from 2 : 3. So they cannot be corresponding sides.
False
Answer:
Step-by-step explanation:
7a. perimeter=3 sides added so the ratio is the same
The ratio of their perimeters is 2 : 3.
True
7b. area= sidexside so the ratio is 2x2:3x3 = 4:9
The ratio of their areas is 4 : 6.
False
7c. 14:21 =2:3
Their perimeters could be 14 cm and 21 cm.
True
7d. 6:7 <> 2:3
Two corresponding sides could be 6 in and 7 in.
False
Find the measure of the arc DC
Answer:
The measure of arc DC is 50°. Circle O is shown. Line segments A C and E B are diameters. Line segment O D is a radii. Point D is between points E and C. Angle B O D is 90 degrees. What is the measure of Arc E B C? 40° 90° 140° 220°
Step-by-step explanation:
What is the angle e in the triangle below? (Hint: Use an inverse trigonometric
function.)
A. 22.00
B. 45.30
C. 0.38
D. 68.00
Answer:
A
Step-by-step explanation:
sin θ=3/8
θ=sin ^{-1}(3/8)
≈22.02 °
Answer:
About 22 degrees
Step-by-step explanation:
Since we are given the opposite side measurement to the angle we wish to find and the hypotenuse measurement, we will want to use sine.
sin(theta)=3/8
theta=arcsin(3/8)
theta=22.024 approximately
Brainliest! How can I solve this?
What equation is equivalent to (1/3)^x = 27^x+2?
Answer:
Step-by-step explanation:
B
Write in slope-intercept form an equation of the line that passes through the points (-3, 2) and (1, -10).
Please help test tomorrow everything you need is in the photo below
Answer:
yes
Step-by-step explanation:
Please help with this!
Answer:
pls help me tooo answer that
On a set of blueprints, the length of a building is 16 inches. The actual building is 85 1/3 feet long. Which of the following is the correct scale?
1:64
1:5
1:32
1:12
Answer:
1 : 64
Step-by-step explanation:
We require the dimensions to be the same units
1 foot = 12 inches , then
85 [tex]\frac{1}{3}[/tex] feet = [tex]\frac{256}{3}[/tex] × 12 = 256 × 4 = 1024 inches
Scale is then
16 in : 1024 in ( divide both parts by 16 )
= 1 : 64
the distance from the earth to the sun is( 1.496 x 10^11 ) m and the distance between earth and moon is 3.84 x 10^8 m. during solar eclipse, moon comes in between earth and sun, at the time what is the distance between moon and sun?
Answer:
1.49216 x 10^11 m.
Step-by-step explanation:
That would be the following difference:
1.496 x 10^11 - 3.84 x 10^8
= 1.49216 x 10^11 m.
What is the area of the rectangle above
A.48 square cm
B.28 square cm
C.14 square cm
D. 24 square cm
Answer:
24
Step-by-step explanation:
Area = width * length
Given width = 2cm
Given length = 12cm
Area = 2 * 12 = 24
can someone help please
In a recent survey,5 out of every 11 dentists recommend fluoride. If there are 690 dentists surveyed, how many are recommend fluoride?
Answer:
314
Step-by-step explanation:
How do I solve this
If the measure of arc CB is 8/3 pi units, what is the measure of angle CAB
Answer:
120° = CAB
arc lenght = CÁB/ 360 × 2(pi)(4)
a/2pi(4) = CAB/360
8/3(pi)/2(pi)(4) × 360 = CÁB
120 = CAB
Answer:
120°
Step-by-step explanation:
that is the procedure above
URGENT PLS HELP!!!
divide £4500 in the ratio 3:7
Answer:
£1350 & £3150
Step-by-step explanation:
[tex]3x+7x=4500\\10x=4500\\x=450\\\\3(450)=1350\\7(450)=3150[/tex]
Surface area.. please answer
[tex] \boxed{ \mathfrak{\huge \: \underline{ \underline{A nswer} }: }}[/tex]
Given terms :
[tex]\hookrightarrow \: length = 8 \: in[/tex]
[tex]\hookrightarrow \: width = 2 \: in[/tex]
[tex] \hookrightarrow \: height = 12 \: in[/tex]
we know,
[tex] \large\boxed{ \mathrm{surface \: \: area \: (a) = 2(lw + wh + lh)}}[/tex]
[tex]\hookrightarrow \mathrm{\: a = 2 \times \bigg [(8 \times 2) + (2 \times 12) + (8 \times 12) \biggr]}[/tex]
[tex]\hookrightarrow a = 2 \times \biggr[16 + 24 + 96 \biggr][/tex]
[tex]\hookrightarrow \: a = \bigg [\: 2 \times 136\bigg ][/tex]
[tex]\hookrightarrow \large \boxed{ \mathrm{a = 272 \: \: in {}^{3} }}[/tex]
____________________________________
[tex] \mathrm{✌TeeNForeveR✌}[/tex]
Lisa and Susan are driving to college together. They look at a map to find out how far they have to drive. On the map, Lisa measures the distance to be 4.5 inches. How many miles do they have to drive if the map scale is 1 in. = 40 mi?
A. 10 miles
B. 220 miles
C. 1/10 miles
D. 180 miles
Answer:
d 180 miles
Step-by-step explanation:
4.5×40= 180 miles
The actual distance to college Lisa and Susan going together is 180 miles.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, The map scale is 1 in. = 40 mi.
Lisa and Susan are driving to college together, On the map, Lisa measures the distance to be 4.5 inches.
Therefore,
The actual distance to college is,
= (4.5×40) miles.
= 180 miles.
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Can someone please help me find the measure of angle ABO?
Answer:
m<ABO = 22 deg
Step-by-step explanation:
A tangent intersects a circle at the point of tangency making a right angle with the radius drawn to that point. That means that <BAO is a right angle and measures 90 deg. That makes the other two angles of the triangle complementary with a sum of 90 deg.
m<O + m<B = 90
68 + m<B = 90
m<B = 22
Answer: m<ABO = 22 deg
the eqashion -4 x <-2
Answer:
8
Step-by-step explanation:
Write the linear function for the graph shown in
slope-intercept form.
Answer:
upper left graph: y = 3/4x-3
lower right graph: x = 3
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
Step-by-step explanation:
circumference of circle=2πr
=2*π*9
=18π m
[tex]{ \bf{ \underbrace{Given :}}}[/tex]
Radius of the circle = 9 m.
[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]
The circumference of the circle.
[tex]{ \bf{ \underbrace{Solution :}}}[/tex]
A. C = 18 π ✅
[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:18\:π\:m.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2Πr }[/tex]
[tex] = 2 \: \pi \times 9 \: m \\ = 18 \: \pi \: m[/tex]
Therefore, the circumference of the circle is 18 π m.
[tex]\large\mathfrak{{\pmb{\underline{\blue{Happy\:learning }}{\blue{!}}}}}[/tex]
please I really need the help:(
Answer:
41
Step-by-step explanation:
The formula for solving for sin is opposite side/hypotenuse.
The opposite side of <A is BC (28 units) and the hypotenuse is AB (53 units).
sin A = 28/53
A = sin^-1(28/53) --> To remove the sin, you have to multiply the inverse of sin on both sides.
A ≈ 41
Hope this helped! <3
Michals basketball team practiced for 2hours 40 minutes yesterday and 3 hours 15 minutes today how much longer did the team practice today than yesterday
Answer:
35 minutes
Step-by-step explanation:
The is calculated using the Subtraction operation
The number of minutes longer the team practiced today than yesterday =
Number of minutes they practiced today - Number of minutes they practiced yesterday
Number of minutes they practiced today = 3 hours 15 minutes
Number of minutes they practiced yesterday = 2hours 40 minutes
The number of minutes longer the team practiced today than yesterday =
3 hours 15 minutes - 2hours 40 minutes
= 35 minutes
Therefore, the team practiced 35 minutes longer today than yesterday
Find the equation of a line with slope - 5 passing through the point A(-3, 6).
Answer:
y=5x-9
Step-by-step explanation:
-5(-3)+b=6
15+b=6
B=-9
what is the distance between a and b
a 45
b 20
c 25
d 60
\ 4 people are going to a dinner party. Each person at the party will eat 56 pound of salad. If you can only buy whole pounds of salad, how many pounds should you buy?
Answer:
224 pounds
step by step :
one person eat 56 pound and we have four person so we must say that :
56 × 4 = 224 pounds
need help asapppp!!! plz i will give brainliest to the person with the correct answer
Answer:
Multiply x by 4 and make x negative if it's positive or make x positive if it's negative.
Step-by-step explanation:
Multiplying x by a number greater than 1 will stretch the parabola.
Changing x from positive to negative and vice versa reflects the parabola over the x-axis.