Answer:
For an nth term U(n) = a + (n - 1)d
n = number of terms
a = first term
d = common difference
a = 5
d = 2 - 5 = - 3
U(n) = 5 + (n -1)-3
= 5 - 3n + 3
= 8 - 3n
The formula for the sequence is 8 - 3n
Hope this helps
A senior class at Smith High School has 84 students.
The number of boys in the class is 4 more than the number of girls.
How many boys and girls are there in the class, respectively?
Answer: 44 boys and 40 girls
Step-by-step explanation:
x = number of girls
x + 4 = number of boys
x + x + 4 = 84
2x + 4 = 84
2x = 80
x = 40
84 - 40 = 44
Can somebody help me with this ?? :)
Answer:
B.
Step-by-step explanation:
ABC ≅ XYZ
∠A≅∠X
∠B≅∠Y
∠C≅∠Z
Also, should be
AB =XY
BC=YZ
CA=ZX
By ASA, ∠A≅∠X, AB =XY, ∠B≅∠Y.
Answer B.
What is the sign of the product (–5)(–3)(–8)(–6)? Positive, because the products (–5)(–3) and (–8)(–6) are negative, and the product of two negative numbers is positive Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive Negative, because the products (–5)(–3) and (–8)(–6) are negative, and the product of two negative numbers is negative Negative, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is negative
Answer:
Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive
Step-by-step explanation:
There are an even number of negative factors, so the product is positive:
Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive
Which symbol would make the statement TRUE?
-3/4
-0.75
A. <
B. >
C. =
D. none of the above
Answer: C
Step-by-step explanation: -3/4 is equal to -.75 ,
Classify the following triangle. Check all that apply.
Answer:
Scalene, isosceles,
Step-by-step explanation:
Estimate 6 8 9 ( 1 9 10 ) by rounding to the nearest whole number. The estimate is the actual product because
Answer:
[tex]6\frac{8}{9} (1\frac{9}{10}) = 13[/tex]
Step-by-step explanation:
Given
[tex]6\frac{8}{9} (1\frac{9}{10})[/tex]
Required
Estimate
To do this; we start by converting both fractions to improper fraction
[tex]6\frac{8}{9} (1\frac{9}{10})[/tex]
[tex]\frac{62}{9} (1\frac{9}{10})[/tex]
[tex]\frac{62}{9} (\frac{19}{10})[/tex]
Open Bracket
[tex]\frac{62}{9} * \frac{19}{10}[/tex]
Combine to form a single fraction
[tex]\frac{62 * 19}{9 * 10}[/tex]
Multiply numerators and denominators
[tex]\frac{1178}{90}[/tex]
Convert fraction to decimal
[tex]13.0888888889[/tex]
Approximate to nearest whole number
[tex]13[/tex]
Hence, [tex]6\frac{8}{9} (1\frac{9}{10}) = 13[/tex]
Answer:
First box: 14
Second box: greater than
Third box: both factors were rounded up.
Step-by-step explanation:
I JUST DID IT AND GOT IT RIGHT!
HOPE IT HELPS!
If x/y + y/x = -1 , find the value of x^3 - y^3
Answer:
0
Step-by-step explanation:
Multiplying the first equation by xy, we have ...
x^2 +y^2 = -xy
Factoring the expression of interest, we have ...
x^3 -y^3 = (x -y)(x^2 +xy +y^2)
Substituting for xy using the first expression we found, this is ...
x^3 -y^3 = (x -y)(x^2 -(x^2 +y^2) +y^2) = (x -y)(0) = 0
The value of x^3 -y^3 is 0.
PLEASE PLEASE PLEASE!!!! WILL MARK FIRST-PERSON AS BRANLIEST!!!
Brian has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.17 times as many villagers. The game gave Brian 8 villagers to start with. Help Brian expand his empire by solving for how many villagers he can create with 16 towns. Then explain to Brian how to create an equation to predict the number of villagers for any number of towns. Show your work and use complete sentences.
Answer:
f(n) = 8 x 1.17^(n)
f(16) = 8 x 1.17^(16)
f(16) = 8 x 12.330...
f(16) = 98.64243...
This is right because
8 x 1.17 = 9.36
9.36 x 1.17 = 10.9512
10.9512 x 1.17 = 12.812904
Answer:
8 × (1.17)^t
99 villagers
Step-by-step explanation:
Each town Brian has allows him to create 1.17 times as many villagers as he had in the town before. The initial number of villagers to start with = 8. To predict the number of villagers in any specific town :
Initial number × (Increment)^number of town
Let number of town = t
Increment = 1.17
Initial number (I) = 8
8 × (1.17)^t
Using this formula :
Number of villagers in 16th town:
t = 16
Number of villagers :
8×(1.17)^(16)
8×(1.17)^16
8 × 12.33030
= 98.642
= 99 round up
Suppose you inherited a house that was purchased in 1950 for 20,000. It is now 2015 and the value of the house has increased by approximately 5% each year what is the house worth now round to the nearest dollar
Answer:
I think the house would now costs $85,000
Step-by-step explanation:
First, I multiplied by how many years between 1950 to 2015 and 5 to get 325.
Next, I divided 20,000 by 100 to get 200 to find 1% of 20,000.
Then, I multiplied 325 by 200 to get 65,000
Finally, I added 20,000 to 65,000 to get 85,000
So, I guess/answer is $85,000
If I was wrong, then just say, "Sorry, but that was incorrect."
Answer:
$476798
Step-by-step explanation:
2015-1950= 65 years
Initial price= $20000
Price increase= 5% yearly
Current price= $20000*(1+0.05)^65= $476798
What is the slope of the line in the graph? On a coordinate plane, a line goes through points (negative 2, negative 1) and (0, 1). slope =
Answer:
1
Step-by-step explanation:
The slope is given by
m = (y2-y1)/(x2-x1)
= (1 - -1)/(0- -2)
= (1+1)/(0+2)
2/2
=1
Answer:
1
Step-by-step explanation:
by using rise over run
By selling a watch in Rs 150 and Rs 200 loss and profit are happened
respectively. If the loss and the profit are equal, find its cost price.
Answer:
Rs 175
Step-by-step explanation:
Suppose the cost is x and at Rs150 the loss is 150-x (this should be a negative number).
At Rs200, the profit is 200-x.
So we have an equation: minus 150 minus x is equal to 200 minus x.
To solve the equation, the cost price X is Rs175.
What is a regular Polygon? Name all the types of polygon.(HELP ASAP)
Answer:
A regular polygon is a polygon with sides of equal length. Some examples include, a equilateral triangle, square, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon, regular decagon...
A rectangle has perimeter P, length 1, and width w. Which of the following represents lin terms of Pand w?
O I = P-w
O I = (2P-W)/2
O I = (P-2w)/2
O I = 2P-2w
have any of you read chike and the river
Answer:
Yes, I have it's about a Nigerian boy called Chike who leaves his village, Umuofia, to go and stay with his uncle in the big city of Onitsha.
Which equation is represented by the graph below
Answer:
2nd option.
Step-by-step explanation:
y int at 1/2.
Keeping the properties of exponents in mind, to what power must you raise the expression to get 7 as the result? Hint: Use the property (am)n = amn.
Answer:
2.6
Step-by-step explanation:
(2.6)
[tex] {2.6}^{2} = 6.76[/tex]
Approximately 7
determine domain and range for f(x)=72-12x
Answer:
Domain: All real numbers
Range: All real numbers
Step-by-step explanation:
Domain is all the x-value inputs that can be used in the equation.
Range is all the y-value outputs that can be used in the equation.
Since the equation is linear, any value of x and y would work for both domain and range, so both are (negative infinity, positive infinity).
Attachment Mathswatchhhh!!!!!!!!! answer only no explanation
Answer:
Option A is the correct answer
Step-by-step explanation:
Line is passing through the points (2, 0) and (0, - 3)
Gradient of line = (-3-0)/(0 - 2) = - 3/-2 = 3/2
Answer:
3/2
Step-by-step explanation:
3/2 is the gradient of the line
What is the measure of EAC?
In circle O, AD and BE are diameters. The measure of arc
AB is 55° and the measure of arc CD is 25°.
100°
125°
235°
280°
Answer:
D. 280°
Step-by-step explanation:
The question lacks the required diagram. Find the diagram attached below.
From the diagram,
arc EAC = arc EAB + arc BC ... (1)
Note that arc EAB is the angle on the straight line EB and since sum of angle on a straight line is 180°, arc EAB = 180°
Next is to get the arc BC. It can be seen from the diagram that arc BC + arc CD + arc DE = 180°
Given arc CD = 25°, arc DE = arc AB = 55° (since the diameter AD and BE are the same). On substituting this values we will have:
arc BC + 25°+55° = 180°
arc BC = 180° - 80°
arc BC = 100°
Remember from initial equation 1 that arc EAC = arc EAB + arc BC
arc EAC = 180°+100°
arc EAC = 280°
The measure of EAC is therefore 280°
Answer:
280
Step-by-step explanation:
AB is a vertical angle of ED. This means that they are congruent.
ED + CD = ?
55 + 25 = 80
360 - 80 = 280
Lizbeth has 38 coins consisting of nickels, dimes, and quarters. The total value of the coins is $6.40. The number of quarters if three more than three times the number of dimes. How many of each type of coin does Lizbeth have? PLEASE EASY 25 POINTS.
Answer:
21 quarters, 6 dimes, and 11 nickels
Step-by-step explanation:
# of Quarters = x.
# of Dimes = y.
# of Nickels = z.
(i)x = 3y+3.
(ii) 0.25x + 0.1y + 0.05z = 6.4
(iii) x + y + z = 38.
Multiplying (iii) by -0.05, and adding it to (ii),
we then get:
0.2x + 0.05y = 4.5.
Now plug in (i) into this.
0.65y + 0.6 = 4.5.
0.65y = 3.9
y = 6.
Since y = 6, we can subsitute this into our equation.
0.2x + 0.3 = 4.5
0.2x = 4.2
x = 21.
Since x = 21, y =6, then z = 11.
A cup of hot coffee will, over time, cool down to room temperature. The principle of physics governing the process is Newton's Law of Cooling. The temperature (in degrees Fahrenheit) of a cup of coffee can be modeled by the following equation: f(t)=80+120e^(-0.08t) Here the time t is measured in minutes after the coffee was poured into the cup. A. Explain, using the structure of the expression 80+120e^(-0.08t), why the coffee temperature decreases as time elapses (8 points). B. What is the temperature of the coffee at the beginning of the experiment (7 points)? C. Drinking coffee at 175 degrees can possibly burn your tongue. After waiting for 2 minutes, Leo became impatient and decided to drink the coffee. Will he be alright (7 points)? D. The ideal temperature to drink coffee is between 120 to 140 degrees, as many of the more subtle flavors of coffee are revealed. When is the best time for Leo to drink coffee (8 points)?
Answer:
A. Because the coefficient of time is negative .
The value of t decreases as time passes .
The temperature of the coffee decreases as time passes and the coffee will evemtually cool down to room temperature
B. At the beginning , t=0
Hence Temperature will be 80 + 120 = 200º
c. He wont be alright . High temperature , less time to cool down . So he wont be alright . Coffee might still be hot .
D. Assuming the temp is 130º
80 + 120ᵅ⁻⁰·⁰⁰⁸ˣ = 130
120ᵅ⁻⁰·⁰⁰⁸ˣ =130-80
120ᵅ⁻⁰·⁰⁰⁸ˣ =50
a-0.008x =(50/120)
0.008x = ln(0.416)
x = 10.962 =11mins
so he has to wait 11 mins to drink.
Step-by-step explanation:
f(t)=80+120e^(-0.08t)
-----------------------
A) Temperature decreases over time as the coefficient of time is negative (-0.08)B. t=0 ⇒ f(0)= 80 + 120*1 = 200 degC. t=2 ⇒ f(2)= 80+120*e^(-0.08*2) ≈ 182 degCoffee is still hot. He won't be alright. He needs to wait more
D. f(x)= 12080+120e^(-0.08x)= 120120e^(-0.08x)=40e^(-0.08x)=1/3-0.08x= ln(1/3)-0.08x= -1.0986x= -1.0986/-0.08x ≈ 14 minbest time is ≈ 14 min
What is the value of n in the equation 1/2 (n-4) -3 = 3 - (2n+3)
Answer:
n = 2
Step-by-step explanation:
Expand the brackets.
1/2n - 2 - 3 = 3 - 2n - 3
Add or subtract terms.
1/2n - 5 = -2n
Add 5 and 2n on both sides.
1/2n + 2n = 5
5/2n = 5
Multiply both sides by 2/5.
n = 5 × 2/5
n = 10/5
n = 2
Can I get the awnser to this?
Answer: 17.8 yds
Step-by-step explanation:
The length of the arc of the ENTIRE circle is the circumference (C = 2πr).
We only want a 60° section of that circumference which is 60°/360° = 1/6 of the circumference.
The formula for length of an arc is: [tex]s=2\pi r\bigg(\dfrac{\theta}{360^o}\bigg)[/tex]
Given r = 17, θ = 60°
[tex]s=2\pi (17)\bigg(\dfrac{60^o}{360^o}\bigg)\\\\\\.\quad =2\pi(17) \bigg(\dfrac{1}{6}\bigg)\\\\\\.\quad =\dfrac{17 \pi}{3}\\\\\\.\quad =\large\boxed{17.8}[/tex]
The diagram shows the cross-section ABCD of a sculpture in the shape of
a prism
with perpendicular height 9 cm.
AB = 14 cm, CD = 8cm, AD = 12cm and BC = 10cm
The height of the prism is also 9 cm.
What is the volume of the sculpture in cm3?
Answer:
891 cm³
Step-by-step explanation:
The volume (V) of the prism is calculated as
V = Ah ( A is the area of cross- section and h is the height (
The cross- section is a trapezium with area (A) calculated as
A = [tex]\frac{1}{2}[/tex] h ( a + b)
where h is the perpendicular height and a, b the parallel bases
Here h = 9, a = AB = 14 and b = CD = 8 , thus
A = [tex]\frac{1}{2}[/tex] × 9 × (14 + 8) = 4.5 × 22 = 99 cm² , thus
V = 99 × 9 = 891 cm³
An acute angles measure is:
Answer:
Acute angles measure less than 90 degrees. Right angles measure 90 degrees. Obtuse angles measure more than 90 degrees.
BD and AC are chords that intersect at point Y. What is the length of line segment AY? 2 units 3 units 4 units 6 units
i need it now please
Answer:
4 units
Step-by-step explanation:
The complete question is
BD and AC are chords that intersect at point Y. A circle is shown. Chords B D and A C intersect at point Y. The length of B Y is 3, the length of Y D is 8, the length of A Y is x, and the length of Y C is 6. What is the length of line segment AY?
The picture of the question in the attached figure
we know that
The Intersecting Chord Theorem states that: When two chords intersect each other inside a circle,the products of their segments are equal.
do
In this problem
substitute the given values
solve for x
therefore
The length of segment AY is 4 units
What is the decimal multiplier to increase by 17%?
To increase by 17% would be 0.17 more than the original number. Therefore, the decimal multiplier to increase by 0.17 would be 1.17.
Which of the following lists orders the sides of ABRV from largest to smallest?
Side B- (4x+7)
Side R- (3x-40)
Side V- (x+13)
A. VB, BR, RV
B. RV,BR,VB
C. BR,RV,VB
D. RV,VB.BR
Answer:
C. br,rv, vb
Step-by-step explanation:
this is beacause it is from the largest to the smallest
Answer:
C. BR,RV,VB
Step-by-step explanation:
This is because it is from the largest to the smallest.
Drilon got 63 out of 72 correct in his test. What fraction of the marks did he get correct?
Answer:
Fraction = [tex]\frac{7}{8}[/tex]
Step-by-step explanation:
Total Marks = 72
Obtained Marks = 63
Fraction = [tex]\frac{Obtained Marks}{Total Marks}[/tex]
Fraction = [tex]\frac{63}{72}[/tex]
In simplified form
Fraction = [tex]\frac{7}{8}[/tex]
A small plane and a large plane are 6.8km from each other, at the same altitude (height). From an observation tower, the two airplanes are separated by an angle of 58°. The large plane is 5.2km from the observation tower. a. Draw a diagram to represent this situation. b. How far is the small plane from the observation tower, to the nearest tenth of a kilometer?
Answer:
7.9km
Step-by-step explanation:
(a)See attached for the diagram representing this situation.
(b)
In Triangle ABC
[tex]\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ[/tex]
Next, we determine the value of Angle B.
[tex]\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ[/tex]
Finally, we find b.
[tex]\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)[/tex]
The distance between the small plane and the observation tower is 7.9km.
