Answer:
both are linear
a) 6x - y = 7
b) 2x - y = -5
Step-by-step explanation:
ABCDE is a regular pentagon. Find each lettered angle measure.
Answer:
x° = 36°, y° = 36°, z° = 72°
Step-by-step explanation:
Each interior angle of a regular polygon is given by the following formula;
Interior angle = (n - 2)×180°/n
Where;
n = The number of sides on the polygon
For the pentagon, we have;
n = 5, therefore;
Interior angle = (5 - 2)×180°/5 = 108°
ΔDCA is an isosceles triangle, with the segments CD and CA being equal, therefore;
∠ADC = ∠DAC = x°, and ∠ACD = 108°
Therefore
x° = (180° - 108°)/2 = 36°
x° = 36°
∠BAC = 2·x° + y° = 108°
∴ y° = 108° - 2·x° = 108° - 2 × 36° = 36°
y° = 36°
ΔADE is an isosceles triangle, with segments AD and AE equal, therefore, the base angles are z° each
Therefore, in ΔADE, we have;
z° = (180° - 36°)/2 = 72°
z° = 72°
Need help geometric sequences see pic for details
Given:
The recursive formula of a geometric sequence is
[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex]
[tex]a_1=-3[/tex]
To find:
The explicit formula of the given geometric sequence.
Solution:
We know that, first term of geometric sequence is [tex]a_1=-3[/tex].
Recursive formula of a geometric sequence is
[tex]a_n=a_{n-1}\times r[/tex] ...(i)
where, r is common ratio.
We have,
[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]r=\dfrac{1}{8}[/tex]
The explicit formula of a geometric sequence is
[tex]a_n=a_1r^{n-1}[/tex]
Putting [tex]a_1=-3[/tex] and [tex]r=\dfrac{1}{8}[/tex], we get
[tex]a_n=-3\left(\dfrac{1}{8}\right)^{n-1}[/tex]
Therefore, the correct option is D.
Which expressions are equivalent to 6a(5+d) ?
Select each correct answer.
30a+6ad
30ad
30a+(6a⋅d)
(6a⋅5)+(6a⋅d)
11a + d
Answer: A is correct i think
Step-by-step explanation: 6a x 5 = 30a
6a x d = 6ad
Answer:
A
Step-by-step explanation:
Steel is an alloy of iron and carbon (98% iron, 2% carbon). Stainless steel is steel and chromium, (90% steel, 10% carbon). What amount of iron, carbon, and chromium are needed for 500 kg of stainless steel?
500 kg x 90% = 500x 0.9 = 450 kg of Steel is needed.
450 kg x 98% = 450 x 0.98 = 441 kg of iron needed.
450 x 0.02 = 9 kg of carbon is needed for the steel.
50 kg of chromium is needed.
Chromium is 10% carbon, 50x 0.1 = 5 kg of carbon is needed for the chromium.
Total iron = 441 kg
Total carbon = 9 + 5 = 14 kg
Total chromium = 50 kg
in a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b what is the value of b, if c=13, a=12?
Answer:
5
Step-by-step explanation:
a=12 (height)
c=13 (hypotenous)
b=? (base)
By using Pythagoras theorm
We have, hypotenous sq=base sq+height sq
Let b =base SO, base sq=hypotenous Sq-height Sq
=>base Sq =13sq-12sq
Base Sq =169-144
Base Sq =25
Base =5 (shifting the sq)....
Hope it's helpful
Luis is buying flour for his bakery, and he buys 8 sacks of flour for $25.75 each. He also has to pay $36.50 for delivery. How much is Luis paying in total for his flour order? (pls help this is a test)
Y’all know this anything about this?
We are given:
Parallelogram CDEF∠C = 13x - 10∠D = 5x + 10To Find: ∠E
Concept Used:
Adjacent angles of a Parallelogram are SupplementaryFinding the value of 'x':
Since adjacent angles of a parallelogram are Supplementary:
∠D + ∠C = 180
5x + 10 + 13x - 10 = 180 [replacing the values of angle C and D]
18x = 180
x = 10 [dividing both sides by 18]
__________________________________________________________
Finding Measure of Angle D:
We are given that:
∠D = 5x + 10
∠D = 5(10) + 10 [since x = 10]
∠D = 60°
__________________________________________________________
Finding the measure of ∠E:
∠D and ∠E are Adjacent angles
Since Adjacent angles are Supplementary:
∠D + ∠E = 180
60 + ∠E = 180
∠E = 120° [subtracting 60 from both sides]
Hence, the measure of ∠E = 120°
In ΔDEF, if DE ≅ DF and EF is the hypotenuse, then ΔDEF is
a acute and scalene. c. right and isosceles.
b right and scalene. d. obtuse and isosceles.
Answer:
C. Right and isosceles
Explanation:
Since two sides of the triangle are equal in length ([tex]DE[/tex] and [tex]DF[/tex]), this means that the triangle is an isosceles triangle. Since [tex]EF[/tex] is the hypotenuse of this triangle, it also means that the triangle is a right-angle triangle (the hypotenuse refers to the longest side of a right triangle). Therefore, we can conclude that ΔDEF is right and isosceles.
Hope this helps :)
Answer:
It is C.
Step-by-step explanation:
Hope this helped have an amazing day!
can u pls help me with this question
16
NOT TO
SCALE
The dagen sboas a circle, centre O.
AB is a chord of length 12 cm.
Vis the mid-point of 43 and OM = 45 cm
Calculate the radius of the circle.
7.5cm
lets take point K represent lenght from M to perimeter of circle.
r is radius
KM= r-OM= r-4.5cm
now lets draw line from O to A (OA)
we get triangle.
hypotenuse is OA and it equals r(radius)
ab=12 cm. so another side of the triangle (AM) is 12/2=6cm. and the last side of the triangle is 4.5(OM)
use pythaghorean theorem
squares of sides added = square of hypotenuse
20.25+36=r^2(our hypotenuse is radius)
56.25=r^2
r=√56.25=7.5cm
Answer:
The radius of the circle is 7.5 cm
Step-by-step explanation:
Circles and Lines
The figure provided shows a circle with two prominent features: a chord of length 12 cm and a segment from the center to the midpoint of the chord of length 4.5 cm.
We have attached an image with some additional measures to solve the problem.
Note a right triangle is formed with half the length of the chord (6 cm) and the distance from the center to the chord. We are sure the intersection divides the chord into two equal parts because M is its midpoint.
The radius of the circle is the hypotenuse of the triangle of legs 6 cm and 4.5 cm, thus the radius is:
[tex]r=\sqrt{6^2+4.5^2}[/tex]
[tex]r=\sqrt{36+20.25}[/tex]
[tex]r=\sqrt{56.25}[/tex]
[tex]\boxed{r = 7.5\ cm}[/tex]
The radius of the circle is 7.5 cm
what is the final position of (-7) + (-2) on a number line ?
Answer:
answer is A, source: a calculator
Step-by-step explanation:
if you are adding two negitives, take the signs away and add normal, then add the sign back at the end, ONLY WORKS WITH TWO NEGITIVES AND HAS TO BE ADDITION
Answer:
Step-by-step explanation:
It’s 9 because you make 7 and 2 a positive number
Mr. and Mrs. Brown went to two movies. The first one lasted 3 1/2 hours and the second one lasted 1 1/3 hours . How much longer was the first than the second movie?
Answer:
2 1/6 longer
Step-by-step explanation:
3 1/2-1 1/3
7/2 - 4/3
21/6-8/6
13/6 or 2 1/6
so 2 1/6 longer.
Hope this helps :D
Answer:
2 1/6 hours longer
Step-by-step explanation:
Hope the helps!
There are 1,800 pastries in a bakery shop. 45% of them are pretzels and the rest are croissants. How many croissants are there?
Group of answer choices
Answer: There are 990 croissants
Step-by-step explanation:
If 45% of them are pretzels then 55% of the pastries hs to be croissants.
Multiply 55% by the total number of pastries to find the number of croissants.
55% * 1,800 = 990
Count by 5’s starting with 99
104, 109, 114, 119, 124, 129, 134, 139, 144, 149
hehe
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
(a)
Evaluate each of the following:
(i)
10! X 20!
17! X 9!
Answer:
[tex]10!\:\times \:20!=\:8.82851\:\times\:10^{24}[/tex]
[tex]17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}[/tex]
Step-by-step explanation:
1)
Given the expression
[tex]10!\times \:20![/tex]
[tex]\mathrm{Apply\:factorial\:rule}:\quad \:n!=1\times 2\times 3\times \ldots \times \:n[/tex]
[tex]10!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10[/tex]
[tex]20!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:18\times \:19\times \:20[/tex]
Now, multiplying the result
[tex]10!\times \:20!= 1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:18\times \:19\times \:20[/tex]
so
[tex]10!\:\times \:20!=\:8.82851\:\times\:10^{24}[/tex]
Thus, we conclude that:
[tex]10!\:\times \:20!=\:8.82851\:\times\:10^{24}[/tex]
2)
Given the expression
[tex]17!\:\times \:9![/tex]
[tex]\mathrm{Apply\:factorial\:rule}:\quad \:n!=1\times 2\times 3\times \ldots \times \:n[/tex]
[tex]17!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17[/tex]
[tex]9!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9[/tex]
Now, multiplying the result
[tex]17!\:\times \:9!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9[/tex]
so
[tex]17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}[/tex]
Thus, we conclude that:
[tex]17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}[/tex]
Write the data from greatest to least: 0.8, 0.79, 0.08, 0.81, 0.09, 0.9, 0.89
Answer:
0.9, 0.89, 0.81, 0.8, 0.79, 0.09, 0.08
Step-by-step explanation:
Answer: 0.09 , 0.89 , 0.81, 0.08, 0.79 , 0.9, 0.8
Step-by-step explanation:
First find the greatest
0.09, 0.89,0.81, 0.08, 0,79
Then the least
0.9 .0.8
Now put it all together
0.09, 0.89. 0.81 , 0.08, 0.79 , 0.9, and lastly 0.8
A car is traveling at a rate of 48 miles per hour. If the car continues to travel at this same rate, how many hours will it take the car to travel 612 miles?
Answer:
12.75
Step-by-step explanation:
If you make a proportion: 48/1=612/x
1(612)= 612
612/48
12.75 hours
At a speed of 48 miles per hour, the car will take approximately 12.75 hours to go 612 miles.
What is the distance?A mathematical number known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.
A car is traveling at a rate of 48 miles per hour.
To determine the number of hours it will take the car to travel 612 miles at a rate of 48 miles per hour, you can divide the distance traveled by the rate at which the car is traveling:
⇒ distance ÷ rate
⇒ 612 miles / 48 miles/hour
Apply the division operation, and we get
⇒ 12.75 hours
Therefore, it will take the car about 12.75 hours to travel 612 miles at a rate of 48 miles per hour.
Learn more about the distance here:
brainly.com/question/13269893
#SPJ2
HELP!!! STATS!!!
A random sample of 100 felony trials showed a sample mean waiting time between arrest and trial = 173 days with a population standard deviation of waiting times = 28 days. Find a 99% confidence interval for the population mean waiting time.
Stats question, I'm really stck please help me!
Answer:
The 99% confidence interval is [tex] 165.776 < \mu < 180.224 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is [tex]\= x = 173 \ days[/tex]
The population standard deviation is [tex]\sigma = 28 \ days[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.58 * \frac{28 }{\sqrt{100} }[/tex]
=> [tex]E = 7.224 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 173 -7.224 < \mu < 173 + 7.224 [/tex]
=> [tex] 165.776 < \mu < 180.224 [/tex]
What is the value of the expression below when x=5?
Answer:
790
Step-by-step explanation:
You put 5 instead of x and you calculat
6*5^3 +8*5= 750+40=790
Which point on the number line could represent-25? А вс D 54 -3 -2 -1 0 1 2 3 4 5 А OB ОС OD. I will mark 1 answer brainlist
Answer:
B
Step-by-step explanation:
The number, -2¼, if it is to be represented on a directed line, would be about -2¼ places below point zero.
Therefore, the point that would represent -2¼ on a number line is B, as shown in the diagram.
Help please.....its due today
What is the sum of 2x-5y+x+y
Answer:
3x - 4y
Step-by-step explanation:
2x + -5y + x + y
Group Like terms:
2x + x + -5y + y
2x + x = 3x
-5y + y = -4y
3x - 4y
Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
\begin{cases} y=-7x+3 \\\\ y=-x-3 \end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
y=−7x+3
y=−x−3
Answer:
(1,-4)
Step-by-step explanation:
Given:
y = −7x+3
y = −x−3
Computation:
y = −7x+3......eq1
y = −x−3.......eq2
Eq 1 - 2
-6x + 6 = 0
x = 1
So,
y = −7x+3
y = −7(1)+3
y = -4
So,
(1,-4)
-4x+5y-3-11x-y
Does -3 have a like term?
Answer:
nope ❎ ❎ ❎ ❎ ❎ ❎ ❎ ❎
Acardboard popcom container is shaped like a cone that is 11 inches high and has a radius of 2.5 inches What is the volume of the container? Use 3 14 for pi Round your answer to the nearest hundredth
Answer:
71.99 in³
Step-by-step explanation:
The formula to apply is that of volume of a cone where;
V=π*r²*h/3 --------where V is the volume of the container, r is the radius of the container and h is the height of the container
Given that : π=3.14 , r is 2.5 inches , h= 11 inches then apply values to the container as;
V= 3.14 * 2.5²* 11/3
V= 3.14 * 6.25 * 3.67
V= 71.9948
V= 71.99 in³
Answer:
Volume of Cone= 71.9583
Step-by-step explanation:
Volume of Cone= (1/3)πr²h
Volume of Cone= (1/3)×3.14×(2.5)²×11
Volume of Cone= 71.9583
In a random sample of 300 people in a town, 193 were female. What is the sample portion of female
Answer: 0.643
Step-by-step explanation:
There are 300 people and 193 were female.
The sample portion that is female is therefore;
= 193/300
= 0.643
good monke good monke dog
Answer:
very inspirational thanks
Step-by-step explanation:
Answer:
monke
Step-by-step explanation:
How many solutions does this equation have?
-3n = -4n + 7
Answer:
just one: 7 you isolate the numbers by doing -3n + 4n = 7, and u get n = 7
Answer:
2
Step-by-step explanation:
my soulstinos were Solution 1)
3
n
+
7
=
−
1
3
n
+
7
−
7
=
−
1
−
7
3
n
+
0
=
−
8
3
n
=
−
8
3
n
3
=
−
8
3
3
n
3
=
−
8
3
n
=
−
8
3
Solution 2)
3
n
+
7
=
1
3
n
+
7
−
7
=
1
−
7
3
n
+
0
=
−
6
3
n
=
−
6
3
n
3
=
−
6
3
3
n
3
=
−
2
n
=
−
2
The solution is:
n
=
−
8
3
and
n
=
−
2
Find the slope of the line graphed below.
Answer:
-3/2 I believe is the answer,
Step-by-step explanation:
Notice that the (left to right) line is going down, indicating it is negative.
Now do rise over run. Rise Is up and down, so 3, and run is left and right so 2, -3/2 is your answer, Correct me if I am wrong
Solve the following equations | 3x + 3/7 | = 2 1/3
Answer:
X∈[tex]\frac{5}{63}, -\frac{23}{63}[/tex]
Step-by-step explanation: