Answer:
(a) The common difference is 4
(b) The 25th term is 108
Step-by-step explanation:
Given
[tex]T_7 = 36[/tex]
[tex]T_{14} = 64[/tex]
Solving (a): The common difference
The nth term of an AP is:
[tex]T_n = a + (n -1)d[/tex]
For the 7th term, we have:
[tex]36 = a + (7 -1)d[/tex]
[tex]36 = a + 6d[/tex]
For the 14th term, we have:
[tex]64 =a + (14 -1)d[/tex]
[tex]64 =a + 13d[/tex]
Subtract both equations
[tex]64 - 36 = a - a +13d-6d[/tex]
[tex]28 = 7d[/tex]
Divide by 7
[tex]d = 4[/tex]
Solving (b): The 25th term
First, we calculate the first term (a)
The 7th term of the progression is:
[tex]36 = a + 6d[/tex]
Substitute [tex]d = 4[/tex]
[tex]36 = a + 6 * 4[/tex]
[tex]36 = a + 24[/tex]
Subtract 24
[tex]a = 36 -24[/tex]
[tex]a = 12[/tex]
The 25th term is:
[tex]T_{25} = a + (25 - 1)d[/tex]
[tex]T_{25} = 12 + (25 - 1)*4[/tex]
[tex]T_{25} = 12 + 24*4[/tex]
[tex]T_{25} = 108[/tex]
Graph the inequality: –10 < t < 5
Answer:
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Step-by-step explanation:
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If Z={x:x€ integrates -2<×<2}.List the elements of this set and also express it in description method.
Answer:
Z = {-1, 0, 1}
"The set Z is the set of integer numbers that are larger than -2 and smaller than 2."
Step-by-step explanation:
I guess that here we have:
Z = {x : x ∈ integers / -2 < x < 2}
From this we know that:
Z contains only integer numbers.
Z contains only integer numbers that are larger than -2, and smaller than 2
Let's find these integers:
-1 is larger than -2 and smaller than 2
0 is larger than -2 and smaller than 2
1 is larger than -2 and smaller than 2
So our set is:
Z = {-1, 0, 1}
And in description method (just using words)
"The set Z is the set of integer numbers that are larger than -2 and smaller than 2."
In a theater group of 36 people. 20 can sing and 12 can play instruments. If 5 can play n sing. How many can niether play nor sing
Answer:
9
Step-by-step explanation:
Draw a Venn diagram.
+------------------------------------------------------------+
| N |
| +--------------+ +-----------+ |
| / P /\ S \ |
| / / B \ \ |
| \ \ / / |
| \ \ / / |
| +------------+ +------------+ |
| |
+------------------------------------------------------------+
The Venn diagram is set up as above. The two circles insiode the rectangle look like two hexagons and they overlap.
The overlap is labele B, for people who both play and sing. The left circle is P for people who play, and the right circle is S for people who sing.
Now we begin to fill it in.
5 people both play and sing, so we place a 5 in the overlap section.
+------------------------------------------------------------+
| N |
| +--------------+ +-----------+ |
| / P /\ S \ |
| / / B \ \ |
| \ \ 5 / / |
| \ \ / / |
| +------------+ +------------+ |
| |
+------------------------------------------------------------+
20 people sing. Subtract the 5 who both sing and play, and you have 15 who can only sing.
12 people play. Subtract the 5 who both sing and play, and you have 7 who only sing.
Place the numbers 15 and 7 in the correct places.
+------------------------------------------------------------+
| N |
| +--------------+ +-----------+ |
| / P /\ S \ |
| / / B \ \ |
| \ 7 \ 5 / 15 / |
| \ \ / / |
| +------------+ +------------+ |
| |
+------------------------------------------------------------+
Now add all the people already placed.
15 + 5 + 7 = 27
Subtract that number form the total.
36 - 27 = 9
Place the 9 in the correct area.
+------------------------------------------------------------+
| N 9 |
| +--------------+ +-----------+ |
| / P /\ S \ |
| / / B \ \ |
| \ 7 \ 5 / 15 / |
| \ \ / / |
| +------------+ +------------+ |
| |
+------------------------------------------------------------+
Answer: 9
A more normal looking Venn diagram looks like this:
Still trying to understand this help
The volume of a cylinder is 1280pi cm cubed. The radius is 8cm. Find the missing length.
Which of the following is most likely the next step in the series?
Answer:
d
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The shape starts with 2 dots, then to 3 dots, and then to 4 dots. This means that the next step must have 5 dots, which option D has.
Which equation is perpendicular
Answer:
option A
Step-by-step explanation:
[tex]y - 9 = \frac{2}{3} (x + 7)\\\\ y - 9= \frac{2}{3} x + \frac{14}{3}\\\\ y = \frac{2}{3} x + \frac{14}{3} + 9\\\\y = \frac{2}{3}x + \frac{14 +27}{3}\\\\y = \frac{2}{3}x + \frac{41}{3}\\\\[/tex]
Therefore, slope of the given line is
[tex]m_ 1 = \ \frac{2}{3}[/tex]
Find the slope of the new line
The product of slope of lines perpendicular to each other = - 1
That is ,
[tex]m_ 1 \times m_2 = - 1\\\\\frac{2}{3} \times m_ 2 = - 1\\\\m_ 2 = - \frac{3}{2}[/tex]
Find the equation of the line.
[tex]Let \the \ given \ points \ be \ ( x_ 2 , y _ 2 ) = ( 2 , 3 ) \\\\(y- y_2) = m_2 (x - x_ 2)\\\\( y - 3 ) = - \frac{3}{2}(x - 2)\\\\y = -\frac{3}{2}x + \frac{3 \times 2}{2} + 3\\\\y = - \frac{3}{2} x +3+3\\\\y = - \frac{3}{2} x +6\\\\[/tex]
Can anyone help me with this question pls ! I would appreciate it !!
-
A great white shark swims 56 feet below sea level and is 97ft from the sail boat
What is the ANGLE OF DEPRESSION from the sail boat to the shark ?? ( round the the nearest WHOLE degree )
Answer:
35
Step-by-step explanation:
We use trignometry here
Assuming that the angle created between the surface of the sea and the 56feet below line is 90 degrees.
So we use the sin rule
sin90/97 = sin x/56
multiply 56 to the other side
56*sin90/97 = sin x
sin90=1
56/97 = sin x
x= sin^-1 (56/97)
x= 35.3
Round and you get 35
PLEASE PLEASE HELP ME WITH THIS GEOMETRY QUESTION!!!
Step-by-step explanation:
Objective: Circle Theorems
The arcs add up to 360 and they are in proportion so
[tex]3x + 3x + 4x + 5x = 360[/tex]
[tex]15x = 360[/tex]
[tex]x = 24[/tex]
So this means that Arc AB and BC measure is 72 each. Arc CD measure is 96 and Arc DA measures is 120.
Angle 1 measure is a inscribed angle of Arc CD.
So it measures
[tex] \frac{96}{2} = 48[/tex]
Angle 2 is a inscribed angle of Arc AB so it measures
[tex] \frac{72}{2} = 36[/tex]
Angle 3 is a inscribed angle of Arc DA.
[tex] \frac{120}{2} = 60[/tex]
Angle 4 is a inscribed angle of Arc BC so it measures
[tex] \frac{72}{2} = 36[/tex]
Angle 5 is formed by tangent line ED. Since D lies on the circumference, it also is tangent to point e so it also measures 90 degrees.
Angle 4 measures 32 so Angle 5 is it complement to Angle 4.
[tex]32 + x = 90[/tex]
[tex]x = 58[/tex]
Angle 6 is formed by two intersecting chrods
so it measures
[tex] \frac{1}{2} (120+ 72) = 96[/tex]
1. A zoo has an Asian elephant that weighs 6 tons. The elephant got sick and lost 1450 pounds. What is the elephants new weight in tons? 2. In a package of balloons, the ratio of purple balloons to green balloons is 3 to 4. What could be the total number of balloons in the package? 3. The ratio of red flowers to yellow flowers in a field is 5 to 7. If there are 392 yellow flowers in the field, how many red flowers are there?
Answer:
1. The new weight of elephant is 5.342 tones.
3. The number of red flowers are 280.
Step-by-step explanation:
1. weight of elephant = 6 tons
weight lost = 1450 pounds
As , 1 pound = 0.000454 ton
So, 1450 pounds = 0.658 ton
The new weight of elephant is
= 6 - 0.658 = 5.342 tones
3.
red flower to the yellow flower is 5 : 7
Number of yellow flowers = 392
Let the red flowers are R.
So,
[tex]\frac {5}{7}=\frac{R}{392}\\\\R = 280[/tex]
What is the perimeter of the shape?
2 yd
3 yd
5 yd
4 yd
2 yd
6 yd
Answer:
22 yards
Step-by-step explanation:
P = 5+2+3+4+2+6
P = 22
Convert 10m in cm.
♡
Answer:
1000 cm
Step-by-step explanation:
Recall that 100 cm = 1 m.
This results in the conversion factor 100cm
-------------
1 m
Then 10 m times the conversion factor shown above yields 1000 cm
Help me please! I will give brainliest!
Answer:
i think its B if it's a multiple choice i wouldn't need to do a step by step explanation.
A side of the triangle below has been extended to form an exterior angle of 157°. Find the value of x
Answer:
x=67
Step-by-step explanation:
180-157 = 23
180-90-23 = 67
x = 67
Answer:
Recall ...
Angles on a straight Line Total to 180°
So
The angle at the Tip of the triangle = 180-157
=23°.
Now 23 is a part of the triangle...
Recall also..
Total angles in a triangle also Total to 180°.
Now that's a Right angled Triangle...
There's the 90° Angle present
So Total angle =
90° + x° + 23° =180
x=180° – (23+90)
x=67°.
4 hamburgers cost $10.00 Fries cost $2 each. How much does ONE hamburger with fries cost?
A $14.10
B $12.00
C $4.50
D $3.50
Answer:
4.50
Step-by-step explanation:
divide 10 by 4. this equals 2.5, add the 2 dollars for fries and your answer is 4.5 dollars
Can some one help me with the rest of this chapter! I’ll pay them as-well!
Answers:
a = 475r = -0.5f(3) = 59.4=======================================================
Explanation:
Any exponential function is of the form y = a*b^x
Comparing that to y = 475*(0.5)^x, we see that a = 475 and b = 0.5
Set b equal to 1+r and solve for r
1+r = 0.5
r = 0.5-1
r = -0.5
The negative r value tells us that the growth rate is -50%, in other words, we have a 50% decay rate. The amount drops by 50% each time x goes up by 1. This is the same as saying the amount cuts in half each time x goes up by 1.
-----------------------
Lastly, plug in x = 3 to find f(3)
f(x) = 475(0.5)^x
f(3) = 475(0.5)^3
f(3) = 59.375
f(3) = 59.4
find h r=4 l=9
im lost
The circumference of the top rim of the cone shaped paper cut is 7.87 inches. Find the least amount of paper that can for a cone shaped cup
Answer:
14.55 square inches
Step-by-step explanation:
From the figure it is given that,
The circumference of the top rim of a cone shaped paper cut = 2πr = 7.87 inches
The slant height is l = 3.7 inch
Therefore the least amount of paper which can form a cone shaped cup is the surface area of the cone.
The surface area of the cone is given as :
[tex]$A=\frac{2 \pi r l}{2}$[/tex]
[tex]$A=\frac{(2 \pi r) (l)}{2}$[/tex]
[tex]$A = \frac{(7.87) \times (3.7)}{2}$[/tex]
[tex]$A=\frac{29.119}{2}$[/tex]
A = 14.55 square inches
Amount of paper required = 14.55 square inches
Sendo =e y = x+2. O resultado da soma x + y, é
A) 2
B) 4
C)3
D)6
Answer:
b)4Step-by-step explanation:
A cyclist travels 8 km from home to the park. She leaves home at 10:15 and arrives at the park at 10:30. What is her average speed in km/h?
Answer:
speed = 32km/hr
Step-by-step explanation:
Time
10:15 to 10:30 = 1/4 hr
speed = distance/time
speed = 8 / (1/4)
speed = 32km/hr
PLEASE HELP! Find code (answer)
Answer:
so this is what I got (i could be wrong)-- H=8 G=21 F=24 E=2
Step-by-step explanation:
3(7+10) = G + 30
21 + 30 = G+30 (mutilpy-3 times 7 and 10)
minus 30 from both sides
21=G
5(3 + H) = 15 + 45
15 + 5H = 15 + 45 (multipy- 5 times 3 and H)
minus 15 from both sides
5H = 45
divde both sides by 5
H=8
For E all you have to do is list out all the multiples that makeup 22 and 30 and you should find that 2 is the answer
Use Venn diagrams notation to describe the shading of
A
B
Answer:
A ∩ B
Step-by-step explanation:
The shaded part is in common between the two diagrams
We can write this part in this way :
A ∩ B
Here is a pattern made from sticks:
a)
How many sticks would be in pattern number 6?
b)
How many sticks would be in pattern number n?
Help needed I can’t figure this out.
Answer:
maybe like 12
Step-by-step explanation:
I would think 12 because because it is 2 of the square so I think 6 + 6 correct me of I'm wrong.
If f(x) - 4x2-3 and g(x) = x+1, find (f - g)(x).
O A. x - 4x2 - 2
O B. 4x - 3
O C. 4x2 - X-4
O D. 4x2 - X-2
Answer:
4x^2-x-4
Step-by-step explanation:
f(x) = 4x^2-3 and g(x) = x+1,
(f - g)(x)= 4x^2-3 -( x+1)
Distribute the minus sign
=4x^2-3 - x-1
Combine like terms
=4x^2-x-4
Answer:
C
Step-by-step explanation:
4x^2 - 3 - (x+1)
Distribute the -
4x^2 - 3 - x -1
=4x^2-x-4
So c
Can I get some help?
Answer:
ok for this what we need to do is just do the equation
y=2x+3
with the x inserted
y=2*-2+3
y=-1
y=2*0+3
y=3
y=2*1+3
y=5
y=2*3+3
y=9
this is the answer from left to right
y=-1,y=3,y=5,y=9
( 15points)Help!!! I need to finish this less than 10 minutes
PlzzPlease help me bunnies <3
No monkey business plz. Or I will report
Okay! When you are ready, let me know what you need help with. Just comment this answer!
What is the question here?
Which relation is a function?
O A. {(7, 8)(5,0)(-3, 1)(-5, 0)(-3, 2)}
B. {(0, 0)(1, 1)(4, 2)(9, 3)(16,4)}
O C. {(-4, 1)(-2, 2.5)(0, 4)(-4, -1)(-2, -2.5)}
OD. {(1, 0)(2, 1)(3, 2)(1, 3)(2, 4)}
What is the probability that if you combined your mnms, you would choose the following colors in order: Red, green, orange, yellow
Answer:
Step-by-step explanation:
1/1044
6/30 x 5/29 x 3/28 x 7/27 = 1/1044
A girl meets a lion and unicorn in the forest. The lion lies every Monday, Tuesday and Wednesday and the other days he speaks the truth. The unicorn lies on Thursdays, Fridays and Saturdays, and the other days of the week he speaks the truth. "Yesterday I was lying," the lion told the girl. "So was I," said the unicorn. What day is it?
You deposit $70 in a savings account that pays an annual interest rate
of 3%. How much simple interest would you earn in 2.5 years?
Answer:
I=70*.03*2.5
I=70*.075
I=$5.25 is the interest.
Step-by-step explanation: