Answer:
a) $1520
b) [tex]S_7 =[/tex] $209195
Step-by-step explanation:
The range of salaries forms an arithmetic sequence with the first term as 25325 and its 7th term as 34445:
a) The raise the person can get each year is the common difference of the progression, d.
The nth term of an arithmetic progression is given generally as:
[tex]a_n = a + (n - 1)d[/tex]
where a = first term = 25325
d = common difference
Therefore, the 7th term (34445) will be:
34445 = 25325 + (7 - 1)d
34445 = 25325 + 6d
=> 6d = 34445 - 25325 = 9120
d = 9120 / 6 = $1520
Therefore, the raise the person gets each year (common difference) is $1520.
b) The total amount the person will earn after 7 years is the sum of the salaries of all 7 yeas.
The sum of an arithmetic progression up to the nth term is given as:
[tex]S_n = \frac{n}{2}(2a + (n - 1)d)\\ \\[/tex]
Therefore, the sum of the person's salary for the 7 years is:
[tex]S_7 = \frac{7}{2}(2 * 25325 + (7 - 1)1520)\\ \\S_7 = 3.5 (50650 + 6(1520))\\\\S_7 = 3.5 (50650 + 9120)\\\\S_7 = 3.5 * 59770\\[/tex]
[tex]S_7 =[/tex] $209195
That is the total amount of salary after 7 years
Multiply (3x-2) (2x+3)
Answer:
6x^2 + 5x + 6
Step-by-step explanation:
Distributive property
Answer:
=6x^2+5x−6
Step-by-step explanation:
Using the foil method, 3x*2x+3x*3+-2*2x+-2*3
what is a width of a rectangle prisim if the volume is 50046 cm 3 the hight is 7 cm and the llength is 13 cm
Answer:
2383.14286
Step-by-step explanation:
The volume of a prism is length times width times height. Since we already know the height and length of the prism, we can divide the volume of the prism by the height and length. This becomes: 50046/3 = 16682. Next we divide by 7: 16682/7 = 2383.14286. Hope this helps!
I'm marking good anwsers as brainliest. When solving this system of equations with substitution one of the following is a step. x+y=6, - 6x+8y = 6 -6(-x + 6) + 8y = 6 x+y = 6 -6x+8 (-x + 6) = 6 8y = 6x + 6
Answer:
(C)[tex]-6x+8(-x+6) = 6[/tex]
Step-by-step explanation:
Given the system of equations
[tex]x+y=6 \\-6x+8y = 6[/tex]
From the first equation:
x+y=6
Making y the subject, we have:
y=-x+6
Substituting y=-x+6 into the second equation, we obtain:
[tex]-6x+8(-x+6) = 6[/tex]
The correct option is C.
NOTE: The goal of substitution is to reduce the number of unknown variables to 1. Therefore, after the substitution, if you still have the two unknown, you might have done something incorrect.
X*2+1=10 then x=? Tell me the value of x
Answer:
4.5Step-by-step explanation:
[tex]x \times 2 + 1 = 10[/tex]
[tex]2x + 1 = 10[/tex]
Move constant to R.H.S and change its sign
[tex]2x = 10 - 1[/tex]
Subtract the numbers
[tex]2x = 9[/tex]
Divide both sides of the equation by 2
[tex] \frac{2x}{2} = \frac{9}{2} [/tex]
Calculate
[tex]x = 4.5[/tex]
Hope this helps..
Best regards!!
I need Help!!! Will give Brainliest ABC≅DEF Find the following: 1. x = 2. CB = 3. FE = 4. y = 5. ED = 6. FD = 7. AB = 8. AC = 9. Area =
Answer:
ABC≅DEF
x = 2
CB = 3
FE = 4
y = 5
ED = 6
FD = 7
AB = 8
AC = 9
In triangle ABC=
Side AC= 9 cm
Side CB= 3 cm
Area= [tex]\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]
=13.5 cm^2
In triangle DEF=
Side FE= 4 cm
Side FD= 7 cm
Area= [tex]\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]
=14 cm^2
Which of the following is not a congruence theorem or postulate A. SSA B. SAS C. AAS D. SSS
Answer:ITS A
Step-by-step explanation:
SAS: side angle side
SSA: is not a congruence theorem
AAS:angle angle side
SSS:side side side
Answer:
The answer is A.
Step-by-step explanation:
Just took the test
Need help ASAP thankyou sorry if u can’t see the picture but u can zoom in :)
Answer:
a)Volume 390ft3. Surface area 450ft2
b)surface area
c)volume
Step-by-step explanation:
2*15*13=390
2*15*2=60+15*13*2=390
Elton is a candle maker. Each 15 \text{ cm}15 cm15, start text, space, c, m, end text long candle he makes burns evenly for 666 hours. If Elton makes a 45 \text{ cm}45 cm45, start text, space, c, m, end text long candle, how long would it burn?
Answer:
18
Step-by-step explanation:
cm 15 -> 14
hours 6 ->?
cm 15 x3->45
hours 6 x3->18
the 45 cm long candle is 3 times as long ,so it would burn for 3 times as long A 45cm long candle would burn for 18 hours
What is the slope of a line that contains the points (4, -2) and (-1, 4)
Answer:
-6/5
Step-by-step explanation:
The slope is (4 - (-2)) / (-1 - 4) = (4 + 2) / (-5) = 6 / -5 = -6/5.
Answer:
-6/5
Step-by-step explanation:
We can find the slope by using the slope formula
m = (y2-y1)/(x2-x1)
= (4 - -2)/(-1 -4)
= (4+2)/ ( -1-4)
=-6/5
Justin weighed 8 lb 12 oz when he was born. At his two-week check-up, he had gained 8 ounces. What was his weight in pounds and ounces?
Answer:
9 lb 4 oz
Step-by-step explanation:
Justin weighed 8 lb 12 oz at birth. He gained 8 ounces by his two-week checkup. So,
8 lb 12 oz + 8 oz = 8 lb 20 oz
But, 16 oz equals one pound. So,
20 oz = 1 lb with 4 oz remaining
Now add them together.
8 lb + 1 lb 4 oz = 9 lb 4 oz
Justin's weight is 9 lb 4 oz.
Hope that helps.
if sade can be 12 years and his mother senior him with 24 years and his dad senior him with 30 yearshow old is the sum of the both parents
Answer:
88
Step-by-step explanation:
mother's age = 12+24
= 36
father's age = 12+40
=52
add the parent age= 36+52
= 88
Are the following angle relationships possible? Explain.
Answer:
no
Step-by-step explanation:
The 5x+30 is the supplementary angle of the interior one:
180 - 5x - 30 = -5x + 150
Then they have to add up to 180:
4x-9 + 2x+3 -5x + 150 = 180
which simplifies to x = 36
So the angles would be 135, 75 and -30, which is impossible!
What is the circumference of a circle with a diameter of 100m. A 100m B 157m C 300 m D 314m
Answer:
C = 314 m
Step-by-step explanation:
The circumference of a circle is given by
C = pi * d
Using 3.14 for pi
C = 3.14 * 100
C = 314 m
Answer:
The answer is option D.
314mStep-by-step explanation:
Circumference of a circle = πd
Where d is the diameter
From the question
d = 100m
Circumference of the circle is
100π
= 314.2
Which is 314m to the nearest whole number
Hope this helps you
How much does a composition notebook weigh?
Answer:
11.2 ounces
Step-by-step explanation:
A ladder is placed 8 feet away from the base of a tree. If the ladder forms a 57° angle
with the ground, how high up the tree will the ladder reaach
Answer:
3.88 feet
Step-by-step explanation:
let the length the ladder reaches be x
[tex] \tan(57) = \frac{x}{8} [/tex]
[tex]x = 8 \tan(57) [/tex]
x = 3.8775938143
Dora bought a bottle of nail polish that was marked down by 20 percent from its original price of $4.50. Including a 9 percent sales tax, what is the final cost of the bottle of nail polish?
Answer:
3.92$
Step-by-step explanation:
The first step is to deduct 20% of 4.50 from 4.50.
20% of 4.50 is 0.2 x 4.50 = .90
4.50 - 0.90 = 3.60
That's the new price without the sales tax.
Now we need to add 9% of 3.60 to 3.60 to get the final cost.
9% of 3.60 is .09 x 3.60 = 0.32
3.60 + .32 = $3.92
Hope it helps.. If yes mark me BRAINLIEST
Tysm!
Answer:
$3.92
Step-by-step explanation:
Hello! For this question we need to gather up all the facts before we could answer it!
The original nail polish cost was $4.50
But the bottle was marked down by 20%
Then has a sales tax of 9%
So let's multiply 4.50 x 0.2 = 0.9
With that we need to subtract off of the original price because it is decreasing.
4.50 - 0.9 = 3.60
But that is not the final price because the bottle has a sales tax! We need to multiply the price after the 20% mark down, so, 3.60 x 0.09 = 0.324
And Then because we are dealing with money, we are going to make sure that we are only adding a decimal that goes up to the hundredths place.
Add: 3.60 + 0.32 = 3.92
The Final price of the nail polish that Dora bought would be $3.92. Which is actually a 0.58 cents drop!
I hope this helped!
pls help me with this (ill give brainliest)
Answer:
72.96
Step-by-step explanation:
Let the first circle's radius be r and quarter circle's radius be R
Area of circle = π[tex]r^{2}[/tex]
= 3.14 × 8 × 8
= 200.96 [tex]cm^{2}[/tex]
Area of quarter circle = π[tex]R^{2}[/tex]/4
= 3.14 × 16 × 16
= 803. 84/4
=200.96
Area of shaded portion = (Area of Quarter circle - Area of semi-circle ACD - Area of triangle ABC) + (Area of the circle - Area of semi-circle ACD - Area of triangle ABC)
Area of Semi-circle = Area of the circle divided by 2
= 100.48
Area of triangle = [tex]\frac{bh}{2}[/tex]
= [tex]\frac{16 * 8}{2}[/tex]
= 64
Therefore, The area of shaded portion= (200.96-100.48-64) + (200.96 - 100.48 - 64)
= 36.48 +36.48
=72.96
Use the linear combination method to solve this system of equations. What is the value of x? Negative 2.4 x minus 3.6 y = 1.2. 2.4 x + 1.2 y = 1.2. Negative 1 0 1 -4.8
Answer:
x=1/4
y=1/2
Step-by-step explanation:
Given:
-2.4x+3.6y=1.2
2.4x + 1.2y=1.2
-2.4x+3.6y=1.2
Divide through by 1.2
-2x+3y=1
2.4x + 1.2y=1.2
Divide through by 1.2
2x+y=1
-2x+3y=1 (1)
2x+y=1 (2)
From 2
y=1-2x
Substitute y=1-2x into (1)
-2x+3y=1
-2x+3(1-2x)=1
-2x+3-6x=1
-8x=1-3
-8x=-2
Divide both sides by -8
x=1/4
Substitute x=1/4 into (2)
2x+y=1
2(1/4)+y=1
2/4+y=1
1/2+y=1
y=1-1/2
y=1/2
x=1/4
y=1/2
Answer:
x=1
Step-by-step explanation:
edge 2021
Please helpppp!!!
Solve: x^2 - 4x-5=0
Answer:
[tex]x=-1,5[/tex]
Step-by-step explanation:
[tex]x^2-4x-5=0[/tex]
In order to solve this quadratic, we have many methods. We can factor, complete the square, or use the quadratic formula. I'm going to factor since it's the easiest method.
To factor, find two numbers that when multiplied equal a(c) and when added equal b.
a=1, b=-4, and c=-5.
So we want two numbers that when multiplied equals 1(-5)=-5 and when added equals -4.
-5 and 1 are the possible numbers. Therefore:
[tex]x^2-4x-5=0\\x^2+x-5x-5=0\\x(x+1)-5(x+1)=0\\(x-5)(x+1)=0\\x=5, -1[/tex]
Please help as soon as possible
Your question has been heard loud and clear.
Answer is option d or the fourth option.
thank you
sin theta = x , sec theta =y . find cot theta pls answer fast i need to verify my answer . you can directly write the answer no issues
Answer:
[tex]\huge\boxed{\cot\theta=\dfrac{1}{xy}}[/tex]
Step-by-step explanation:
[tex]\bold{METHOD\ 1}[/tex]
[tex]\sin\theta=x\\\\\sec\theta=y\\\\\cot\theta=?\\\\\text{We know:}\\\\\sec x=\dfrac{1}{\cos x};\ \cot x=\dfrac{\cos x}{\sin x}\\\\\sec\theta=y\to\dfrac{1}{\cos \theta}=y\to\dfrac{\cos\theta}{1}=\dfrac{1}{y}\to\cos\theta=\dfrac{1}{y}\\\\\cot \theta=\dfrac{\frac{1}{y}}{x}=\dfrac{1}{xy}[/tex]
[tex]\bold{METHOD\ 2}[/tex]
[tex]\text{We know}\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\cot x=\dfrac{\cos x}{\sin x}=\dfrac{1}{\tan x}\\\\\sec x=\dfrac{1}{\cos x}\\\\\text{therefore}\\\\(sin x)(\sec x)=(\sin x)\left(\dfrac{1}{\cos x}\right)=\dfrac{\sin x}{\cos x}=\tan x\\\\\dfrac{1}{(\sin x)(\sec x)}=\dfrac{1}{\tan x}=\cot x[/tex]
[tex]\\\sin \theta=x;\ \sec\theta=y\\\\\text{substitute}\\\\\cot\theta=\dfrac{1}{xy}[/tex]
Given the coordinates for the function below, which of the following are
coordinates for its inverse?
Gallons Cost, in
of Gas Dollars
1
2
5
15
20
1.25
2.50
6.25
18.75
25.00
The coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
How to determine the inverse coordinates?The table of values is given as:
Gallons Cost
1 1.25
2 2.50
5 6.25
15 18.75
20 25.00
The inverse of the above table would have the following header
Cost Gallons
When the inverse table is populated, we have:
Cost Gallons
1.25 1
2.50 2
6.25 5
18.75 15
25.00 20
The coordinates are: (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
Hence, the coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)
Read more about coordinates at:
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Write each as a decimal. Round to the thousandths place. 0.2%, 756%, 762%, and 90%. Please answer i need it by tonight >~
Answer:
0.2%=0.200%
756%=756.000%
762%=756.000%
90%=90.000%
( plz mark me as brainliest, that wold be most appreciated! )
A number is 30% of 20% of the number x.
Answer:
6/100x
Step-by-step explanation:
Answer:6/100x
Step-by-step explanation:
You have 0.895 m of ribbon to hang the “Grand Opening” sign. You need 100 cm to hang it correctly. Do you have enough ribbon? If not,how much more do you need?
Answer:
no you need 10.5cm
Step-by-step explanation:
so convert 0.895m to cm by multiplying it by 100 to get 89.5 which is less
so take the required 100-89.5
Subtraction is a mathematical operation. The ribbon is not enough. 10.5 cm of ribbon is more needed.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
It is known that 1 meter is equal to 100cm, therefore, the length of the ribbon will be equal to,
[tex]\rm 1\ m =100\ cm\\\\0.895\ m = 0.895 \times 100 = 89.5\ cm[/tex]
Now, as the ribbon needed is 100 cm, therefore, the length of ribbon that is needed more is
[tex]\rm \text{length of the ribbon needed} = 100\ cm - 89.5\ cm = 10.5\ cm[/tex]
No, the ribbon is not enough. 10.5 cm of ribbon is more needed.
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The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options. $8 $9 $11 $13 $14
Answer:
The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options.
$8 . YES
$9 . HELL NO
$11 . DEFINITLY NOT
$13 . GET OUTTA HERE
$14 . MMM YES
Step-by-step explanation:
Answer:
A and E or 8, 14
Step-by-step explanation:
A village P is 10km from a lorry station,Q on a bearing 065°.another village R is 8km from Q on a bearing 155°.calculate;1.the distance of R from P to the nearest kilometer and 2.the bearing of R from P to the nearest degree.
Answer:
Step-by-step explanation:
find the difference between the two angles first:
155-65=90 degrees
d is the distance d:
d^2=a^2+b^2-2ab cos(90)
d^2=10^2+8^2-2(10)(8)cos(90)
d^2=164
d=√164=12.81
the bearing of R from P to the nearest degree:
180-155=35 degrees
1. Robert and Casey added the following values shown below. Who solved
correctly?
ROBERT
CASEY
5 1/8+ 2 1/3 = 7 1/2
-4 1/2+ 6 3/4= 2 1/4
Answer:
Casey is correct.
Step-by-step explanation:
Robert's 5 1/8 + 2 1/3 = 7 1/2 is wrong because if 5+2 = 7, I would have to change the denominator of both fractions so they are both the same. The denominator would have to be 24. That would make the fractions 3/24 and 8/24. If you added them together, it would not be able to simplify to 1/2.
Casey's -4 1/2 + 6 3/4 = 2 1/4 is correct because —4 - 6 = 2. In order to make the fractions have the same denominator, you would have to multiply -1/2 by 2 on both numerator and denominator wich would equal -2/4. Now add -2/4 and 1/4 and you get 1/4. If my explaining is confusing, I'm sorry!☜(ﾟヮﾟ☜)
Casey is correct and he will get the correct solution.
We have given that,
ROBERT CASEY
5 1/8+ 2 1/3 = 7 1/2 -4 1/2+ 6 3/4= 2 1/4
Robert's 5 1/8 + 2 1/3 = 7 1/2 is wrong because if 5+2 = 7, I would have to change the denominator of both fractions so they are both the same.
What is the equation?A statement that the values of two mathematical expressions are equal.
The denominator would have to be 24.
That would make the fractions 3/24 and 8/24.
If you added them together, it would not be able to simplify to 1/2.
Casey is correct.
-4 1/2 + 6 3/4 = 2 1/4 is correct
because 4 - 6 = 2.
In order to make the fractions have the same denominator, you would have to multiply -1/2 by 2 on both numerator and denominator which would equal -2/4.
Now add -2/4 and 1/4 and you get 1/4.
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Tasha wants to find out if she is going to pass her test. She decides that she will
simulate her test by flipping a coin. This means
a) There is a 50-50 chance she will pass her test.
b) All of the questions are multiple choice.
c) She hasn't studied.
d) There is a 20% chance she will pass.
Answer:
A
Step-by-step explanation:
Since a coin only has two sides, the test must be referring to the fact that she has a 50, 50 shot at passing.
Solve. x2+5x−2=0 Enter your answers, as exact values, in the boxes. x = or x =
Answer:
[tex]x=\frac{-5+\sqrt{33} }{2}[/tex]
[tex]x=\frac{-5-\sqrt{33} }{2}[/tex]
Step-by-step explanation:
Using the quadratic formula in which a=1, b=5 and c=-2
[tex]x_1=\frac{-b+\sqrt{b^{2}-4ac } }{2a} \\x_2=\frac{-b-\sqrt{b^{2}-4ac } }{2a}\\x_1=\frac{-5+\sqrt{5^{2}-4(1)(-2) } }{2(1)}\\x_1=\frac{-5+\sqrt{33} }{21}\\x_2=\frac{-5-\sqrt{25+8 } }{2}\\x_2=\frac{-5-\sqrt{33} }{2}[/tex]