Answer:
215 students
Step-by-step explanation:
500 divided by 2 = 250
250 - 35 each= 215
What is the arc length of an arc with radius 14 in and central angle 66^o? Show all calculations that lead to the answer and include units.
Answer:
28pi*66/360
Step-by-step explanation
Used the equation Central angle/360*2pi r
JAERA HAD 13 TOY CARS. SHE BOUGHT 26 CARS FROM THE TOY STORE AND GOT 23 FOR HER BDAY. JAERA GAVE 10 CARS TO HER CAITLYN SHAW AND 38 TO HER COUSIN. HOW MANY TOY CARS DOES SHE HAVE LEFT?
A geometric sequence is given by the recursive rule $a_1=\frac{2}{3},\ a_n=3a_{n-1}$ . Give an explicit rule for the nth term of the sequence $b_1,\ b_2,\ b_3,\ \dots\ ,$ given that $b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots$ .
Answer:
[tex]b_n = \frac{2}{27} (9^n)[/tex]
Step-by-step explanation:
Given
[tex]a_1=\frac{2}{3},\ a_n=3a_{n-1}.[/tex]
Required
An explicit rule for [tex]b_1,\ b_2,\ b_3,\ \dots[/tex]
Where [tex]b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots[/tex]
We have:
[tex]a_1=\frac{2}{3},\ a_n=3a_{n-1}.[/tex]
Calculate a2
[tex]a_2 = 3a_{2-1}[/tex]
[tex]a_2 = 3a_1[/tex]
[tex]a_2 = 3 * \frac{2}{3}[/tex]
[tex]a_2 = 2[/tex]
Calculate a3
[tex]a_3 = 3a_{3-1}[/tex]
[tex]a_3 = 3a_2[/tex]
[tex]a_3 = 3 *2[/tex]
[tex]a_3 = 6[/tex]
Calculate a4
[tex]a_4 = 3a_{4-1}[/tex]
[tex]a_4 = 3a_3[/tex]
[tex]a_4 = 3*6[/tex]
[tex]a_4 = 18[/tex]
Calculate a5
[tex]a_5 = 3a_{5-1}[/tex]
[tex]a_5 = 3a_4[/tex]
[tex]a_5 = 3*18[/tex]
[tex]a_5 = 54[/tex]
So:
[tex]b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots[/tex]
[tex]a_1=\frac{2}{3}[/tex] [tex]a_3 = 6[/tex] [tex]a_5 = 54[/tex]
The above sequence form a geometric sequence.
Calculate common ratio (r)
[tex]r = \frac{b_3}{b_2}[/tex]
[tex]r = \frac{a_5}{a_3}[/tex]
[tex]r = \frac{54}{6}[/tex]
[tex]r = 9[/tex]
So, the explicit formula is:
[tex]b_n = b_1 * r^{n-1[/tex]
[tex]b_1=a_1[/tex], so:
[tex]b_n = a_1 * r^{n-1[/tex]
[tex]a_1=\frac{2}{3}[/tex], so:
[tex]b_n = \frac{2}{3} * 9^{n-1[/tex]
Split:
[tex]b_n = \frac{2}{3} * \frac{9^n}{9}[/tex]
[tex]b_n = \frac{2}{3*9} (9^n)[/tex]
[tex]b_n = \frac{2}{27} (9^n)[/tex]
The explicit rule is: [tex]b_n = \frac{2}{27} (9^n)[/tex]
See image for question.
Please show workings and diagrams.
Answer:
a) 16.4 m, 101°b) 6.22 m, 51 m²Step-by-step explanation:
Find the measure of angle Q:
50° + (180° - 130°) = 100°a) Find PR using the law of cosines:
PR = √(8² + 13² - 28*13*cos 100°) = 16.4 m (rounded)Find ∠P using law of sines:
16.4/sin 100° = 13/ sin Pm∠P = arcsin (13 sin 100° / 16.4) = 51° (rounded)The bearing of R from P is:
50° + 51° = 101°b)
Find the measure of h, the distance from Q to PR:
h/ PQ = sin Ph = PQ sin Ph = 8 sin 51° = 6.22 mFind the area of ΔPQR:
A = 1/2PR*hA = 1/2(16.4)(6.22) = 51 m²you roll a die twice. What is the probability of rolling a 3 and then a 4?
Answer:
1/36
Step-by-step explanation:
P(rolling a 3) and P(rolling a 4)
= 1/6 and 1/6
=(1/6)(1/6)
=1/36
Joaquin walked exactly 3 _ 4 of a mile. According to the line plot, what is the difference between the distance Joaquin walked and the least distance any of the other students walked to school?
Answer:
The difference is [tex]\frac{3}{8}[/tex] mile
Step-by-step explanation:
The question is incomplete, as the line plot is not attached.
I will answer this question with the attached line plot.
From the question:
[tex]Joaquin = \frac{3}{4}[/tex]
From the attached line plot:
[tex]Least = \frac{3}{8}[/tex]
The difference (D) is:
[tex]D = Joaquin - Least[/tex]
[tex]D = \frac{3}{4} - \frac{3}{8}[/tex]
Take LCM
[tex]D = \frac{6 - 3}{8}[/tex]
[tex]D = \frac{3}{8}[/tex]
Hence: The difference is [tex]\frac{3}{8}[/tex] mile
help pls, fast to, thx
Answer:
∠b = 64°
Step-by-step explanation:
We know that a complete rotation is 360°, so:
∠b + 57° + 239° = 360°
∠b = 360° - 57° - 239°
∠b = 64°
what are angles? how do i solve them?
https://courses.lumenlearning.com/prealgebra/chapter/using-properties-of-angles-to-solve-problems/#:~:text=We%20measure%20angles%20in%20degrees,they%20are%20called%20supplementary%20angles.
Answer: do you mean how to find the degree?
Step-by-step explanation:
Count the number of sides in the polygon.
Find the total measure of all of the interior angles in the polygon
Divide the total measure of all of a regular polygon's angles by the number of its angles.
Subtract the sum of the known angles from the total measure of the angles for an irregular polygon.
it really depends
Sarah biked 13 miles south from her house to the library. Then she turned and biked 10 miles
east to the grocery store. Finally, she returned home using a straight path. What was the total
distance she traveled?
Answer:
16.40
Step-by-step explanation:
use Pythagorean theorem
its the last answer thanks :)
Answer:
(7,0)
Step-by-step explanation:
Franco earns $8 per hour at his after-school job. Last week, he received a paycheck of more than $168. If he worked for h hours that week, find all the inequalities that represent this situation.
a.) 8 x h > 168
b.) 8 > 22 x h
c.) 8 x h < 168
d.) h > 21
e.) h < 21
Answer: A and D
Step-by-step explanation:
if he earns $8 an hour and he got $168 and h= the hours then
h=8 x 21 = 168
Answer:
The other person is correct.
Step-by-step explanation:
Find the measures of angle A, B, C and D.
Answer: b = 48 c = 26 d = 106 a = 26
Step-by-step explanation:
A clairinet case is shaped like a rectangular prisim the case is 8 inches tall 3 inches wide and has a volume of 312 cubic inches what is the lenght of the clairnet case
Answer:
13 inches
Step-by-step explanation:
A clarinet case is shaped like a rectangular prism the case is 8 inches tall 3 inches wide and has a volume of 312 cubic inches what is the length of the clarinet case
The volume of a rectangular prism = Length × Width × Height
Length of the rectangular prism = Volume/ Width × Height
= 312 in³/ 3 in × 8 in
= 312 in³/24 in²
= 13 in
Length = 13 inches
Plz help !! 7th grade math !
will mark brainliest if correct
Answer:
2
Step-by-step explanation:
2 is non-linear because it is not a straight line
Sierra has enough fencing to make three chicken coops shown each has the same perimeter which has the greatest area?
Answer:
Top left triangle has the greatest area
Step-by-step explanation:
Area of a triangle:
area = base × height / 2
a = bh/2
Top Left Triangle:
a = 6 × 5.2 / 2
a = 31.2 / 2
a = 15.6
Top Right Triangle:
a = 8 × 2.9 / 2
a = 23.2 / 2
a = 11.6
Bottom Left Triangle:
a = 2 × 7.9 / 2
a = 15.8 / 2
a = 7.9
Compare areas:
15.6 > 11.6 > 7.9
Dr. McCoy, a veterinarian, noticed that she only had about 12 ounces of cat treats left. So, she bought a new 3-pound jar. If she uses about 6 ounces of cat treats every week, in how many weeks will she run out?
DUE SOON
The angle measurements in the diagram are represented by the following expressions.
ZA = 82 – 10
ZB = 3x + 90°
Answer:
8x-10 B=3x+90
Factorise this pleasee
x2+ 11x+ 18
Answer:
[tex](x +9)(x+2)[/tex]
Step-by-step explanation:
Given the problem,
[tex]x^2 + 11x + 18[/tex]
Factor the problem. Find factors of (18) such that when added the result is (11).
[tex](x +9)(x+2)[/tex]
Test by distributing, multiply each term in one parenthesis by every term in the other parenthesis,
[tex](x+9)(x+2)\\\\x^2 + 2x + 9x + 18\\\\x^2 + 11x + 18[/tex]
Answer:
(x+9)(x+2) is your answer
Step-by-step explanation:
x2+ 11x+ 18
x²+9x+2x+18
x(x+9)+2(x+9)
(x+9)(x+2)
RHOMBUS The diagonals of rhombus ABCD intersect at E. Given that
mZBAC = 53° and DE = 8, find the indicated measure.
B
А.
53°
mZAED
m2 DAC
m ZADC
AE
DB
8
E
с
AC
D
11. Name the four isosceles triangles in rhombus ABCD.
12. Name three properties of AC and BD.
Answer:
Question 11:
[tex]\angle DAC = 53^\circ[/tex]
[tex]\angle AED = 90^\circ[/tex]
[tex]\angle ADC = 74[/tex]
[tex]DB = 16[/tex]
[tex]AE = 6.03[/tex]
[tex]AC = 12.06[/tex]
Question 12:
[tex]\triangle ABD[/tex], [tex]\triangle BAC[/tex], [tex]\triangle CDA[/tex] and [tex]\triangle DAB[/tex]
Question 13:
AC and BD are perpendicular lines, and they are diagonals
Step-by-step explanation:
Question 11
Given
[tex]\angle BAC = 53^\circ[/tex]
[tex]DE = 8[/tex]
See attachment for Rhombus
Required
Determine the indicated sides
Solving (a): [tex]\angle DAC[/tex]
Diagonal CA divides [tex]\angle DAB[/tex] into 2 equal angles
i.e
[tex]\angle DAC = \angle BAC[/tex]
So:
[tex]\angle DAC = 53^\circ[/tex]
Solving (b): [tex]\angle AED[/tex]
The angles at E is 90 degrees because diagonals AC and BD meet at a perpendicular.
So:
[tex]\angle AED = 90^\circ[/tex]
Solving (c): [tex]\angle ADC[/tex]
First, we calculate [tex]\angle ADE[/tex], considering [tex]\triangle ADE[/tex]:
[tex]\angle ADE + \angle AED + \angle DAC = 180[/tex]
[tex]\angle ADE + 90 + 53 = 180[/tex]
[tex]\angle ADE + 143 = 180[/tex]
[tex]\angle ADE = -143 + 180[/tex]
[tex]\angle ADE = 37[/tex]
To calculate [tex]\angle ADC[/tex], we have:
[tex]\angle ADC = 2*\angle ADE[/tex]
[tex]\angle ADC = 2* 37[/tex]
[tex]\angle ADC = 74[/tex]
Solving (d): [tex]DB[/tex]
From the rhombus
[tex]DB = DE +EB[/tex]
Where
[tex]DE =EB[/tex]
So:
[tex]DB = 8 + 8[/tex]
[tex]DB = 16[/tex]
Solving (e): [tex]AE[/tex]
To do this we consider [tex]\triangle ADE[/tex]
Using the tan formula
[tex]tan(\angle ADE) = \frac{AE}{DE}[/tex]
[tex]\angle ADE = 37[/tex] and [tex]DE = 8[/tex]
So:
[tex]\tan(37) = \frac{AE}{8}[/tex]
[tex]AE = 8 * \tan(37)[/tex]
[tex]AE = 6.03[/tex]
Solving (f): [tex]AC[/tex]
This is calculated as:
[tex]AC = AE + EC[/tex]
Where
[tex]AE = EC[/tex]
[tex]AC = 6.03 +6.03[/tex]
[tex]AC = 12.06[/tex]
Question 12: Isosceles Triangle
In the rhombus, all 4 sides are equal;
So, the isosceles triangle are:
[tex]\triangle ABD[/tex], [tex]\triangle BAC[/tex], [tex]\triangle CDA[/tex] and [tex]\triangle DAB[/tex]
Question 13:
AC and BD are perpendicular lines, and they are diagonals
How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 5% antifreeze?
Answer:
95% of a gallon of water, .95, or 19/20 as a fraction
Step-by-step explanation:
How can you tell if a pattern is quadratic or linear?
Answer: By finding the differences between the y-values, we can determine the degree of the model for the data.
If the first difference is the same value, the model will be linear.
If the second difference is the same value, the model will be quadratic.
Step-by-step explanation:
What is X-4<5 Helpppp I dont understand
Answer:
x<9
Step-by-step explanation:
isolate the x by adding 4 on both sides. then add 4+5 to get 9.
i hope this helps :)
45% of c is 72. Find the value of c.. PLEASE IT IS DUE IN 5 MINUTES
Answer:
160
Step-by-step explanation:
72x100/45. Hope this helps
Are the fractions 3/8 and 9/27 equivalent? If yes, explain how you know they are equivalent. If they are not equivalent, what is a fraction that would be equivalent to 3/8.
Answer:
Step-by-step explanation:
The factors are 9 and 27 are 1,3,9,27
With that, 9/27 is undoubtedly reducible to 1/3
Before now,we were told that when a number divides itself,the result is zero...now,⅜÷⅓ should give us 1 but 3/8×3/1 = 9/8 and 9/8≠1 hence,they aren't same!
Find the x and y value of this triangle using the Pythagorean Theorem.
Someone please help giving branliest away to the first answer
Answer:
cos60⁰=3/y
y×cos60⁰=3
y=3/cos60⁰
y=3/0.5
y=6
y²=x²+3²
6²=x²+3²
36=x²+9
x²=36-9
x²=27
x=square root of 27
x=5.19
The table and the graph below each show a different relationship between the same two variables, x and y:
How much more would the value of y be on the graph than its value in the table when x = 12?
150
300
450
600
y=360
Step-by-step explanation:
y goes up by 30 everytime and would start at 30 if X =1, so X x 30= y. 12 x 30= 360=y
Answer:
300 or B
Step-by-step explanation: give the other person brainliest
Write the equation for the line in point-slope form that passes through the point (- 4, - 6) with a slope of 34
Answer:
34 minus -6 minus= -6
Step-by-step explanation:
When an equation in one variable is solved using a system of equations, the solution is always the
of each intersection.
Answer:
When an equation in one variable is solved using a system of equations, the solution is always the x-coordinate of each intersection.
Step-by-step explanation:
Answer:
1st part: X Coordinate
2nd part: A and C
Step-by-step explanation:
Please help. I will give brainliest to correct answer.
Answer:
The area of a square with side length of 2 inches is 4 square inches.
The area of a circle with radius 1.2 inches is:
[tex]\pi \times (1.2) ^{2} \\ = 3.14 \times 1.44 \\ = 4.5216 \: square \: inches[/tex]
That is approximately 4.5 square inches.
Hence, the area of the square (4) is less than {<} that of the circle (4.5)!