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Work Shown:
y = (1/2)x + 3/2
2y = x + 3 .... multiply every term by the LCD 2
2y-x = 3 ... subtract x from both sides
-x+2y = 3
x-2y = -3 ... multiply both sides by -1
The last step is done so that the x coefficient is positive
The equation is in the form Ax+By = C with
A = 1B = -2C = -3You could have your answer as -x+2y = 3, since that is also in standard form. But many math textbooks make A > 0.
Brandon has 36000 to invest and wants to earn 5% interest per year. He will put some of the money into an account that earns 4.4% interest per year and the rest into an account that earns 6% interest per year. How much money should he put into each account so that he earns 5% annually
Answer:
The money in an account that earns 4.4% interest per year = 22500
The rest into an account that earns 6% interest per year = 13500
Step-by-step explanation:
Interest = Principal × Rate × Time
Let x = money saved in account A
Let y = money saved in account B
Brandon has 36000 to invest and wants to earn 5% interest per year
x + y = 36000..... Equation 1
x = 36000 - y
He will put some of the money into an account that earns 4.4% interest per year and the rest into an account that earns 6% interest per year.
Hence:
4.4% × x × 1 + 6% × y × 1 = 36000 × 5% × 1
0.044x + 0.06y= 1800....... Equation 2
Substitute 36000-y for x in Equation 2
0.044(36000 - y) + 0.06y = 1800
1584 -0.044y + 0.06y = 1800
-0.044y + 0.06y = 1800 - 1584
0.016y = 216
y = 216/0.016
y = 13500
Note that:
x = 36000 - y
x = 36000 - 13500
x = 2250
Therefore,
The money in an account that earns 4.4% interest per year = 22500
The rest into an account that earns 6% interest per year = 13500
Which function has the greatest rate of change? A) y = 3x - 4 B) 4y - 8x = 1 C) a line passing through points (2,6) and (3,10) D) a line passing through points (5,−2) and (6, 4) ?
Answer:
I think the answer would be C. or A.
Step-by-step explanation:
PLEASE HELP OMG I NEED THIS ASAP
Answer:
45
Step-by-step explanation:
To find area, it's length * width. the length is 5 and the width is 9, so you would do 5*9=45
PLEASE HELP simplify (6 1\4) ^4
Answer:
[tex](\frac{390625}{256 } )[/tex]
Step-by-step explanation:
The exponent decides how much times does the base needs to multiply itself. In the given expression, the exponent is 4. Thus, 6 1/4 needs to multiply itself 4 times.
⇒ [tex](6 \frac{1}{4}) ^4[/tex]Convert 6 1\4 into improper fraction
⇒ [tex](\frac{25}{4} ) ^4[/tex]⇒ [tex](\frac{25}{4})(\frac{25}{4})(\frac{25}{4})(\frac{25}{4})[/tex]⇒ [tex](\frac{25^{4}}{4^{4} } )[/tex]⇒ [tex](\frac{390625}{256 } )[/tex]Thus, the simplified fraction is [tex](\frac{390625}{256 } )[/tex].
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
36.8%
Step-by-step explanation:
formula to find percent increase: (|old-new|)/old *100
|95-130|/95 *100
36.8%
Mrs. Baker drove 450 miles on a trip she took last summer. Her car's gas tank holds 15 gallons of gas and she gets 25 miles to the gallon on long trips. How many tanks of gas did she use on her trip?
Answer:
..........
Step-by-step explanation:
Help please, brainliest if you answer in less than 5 minutes!
Answer:
A and C
Step-by-step explanation:
Lawson: 5x3=15
Rhett: 4x4=16
Wynn: 5x3=15
Solve 23 x 105.
23,000,000
230,000
23,000
2,300,000
Arithmetic and geometric sequences plato/edumentuM
Answer:
A
Step-by-step explanation:
tank 2 goes down by a constant difference : -40
(7X^3+4X^2+3X+2) + (2X^2+X+5)
A Table showing Freezing Temperatures in degrees with 2 columns and 6 rows. The First row, F, has the entries, negative 13, negative 4, 5, 14, 23. The second column, C, has the entries, negative 25, negative 20, negative 15, negative 10, negative 5.
The table shows temperatures below freezing measured in different units. Complete the equation in standard form to represent the relationship between F, a temperature measured in degrees Fahrenheit, and C, a temperature measured in degrees Celsius.
5F +
C =
39°F =
°C rounded to the nearest tenth of a degree
Answer: 39F = 3.9C rounded to the nearest tenth of a degree
Step-by-step explanation:
Want Money. Answer thisss below.
Answer:
2.3
Step-by-step explanation:
Use the figure below to match the type of angles with the correct type of angles.
Answer choices:
Vertical Angles
Complementary
Corresponding Angles
Same-Side Interior Angles
Alternate Interior Angles
Alternate Exterior Angles
Same-Side Exterior Angles
Supplementary
Answer:
1 & 3 - Vertical Angles1 & 2 - Supplementary4 & 6 - Alternate Interior Angles3 & 6 - Same-Side Interior Angles1 & 7 - Alternate Exterior Angles2 & 7 - Same-Side Exterior Angles1 & 5 - corresponding angles5 & 8 - Supplementary6 & 8 - Vertical Angles3 & 5 - Alternate Interior Angles4 & 5 - Same-Side Interior Angles1 & 8 - Same-Side Exterior Angles2 & 6 - corresponding angles4 & 8 - corresponding angles3 & 7 - corresponding anglesHope this helps!
How does a dilation affect the side lengths and angle measures of a figure?
After the dilation, the lengths are multiplied by the value of the scale factor while the angles remain same.
What is image dilation?An enlargement or reduction of a figure that preserves shape but not size.All dilations are similar to the original figure.Dilations have a center and a scale factor.Given is to find how dilation affect the side lengths and angle measures of a figure
Assume that the initial length of the figure
After the dilation, the coordinates will become -
(x, y) → (Kx, Ky)
Where {K} is the scale factor by which the image is dilated.
The angles after the dilation remain same.
Therefore, after the dilation, the lengths are multiplied by the value of the scale factor while the angles remain same.
To solve more questions on dilation, visit the link below -
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pls help! i need to know the slope of the graph! will give brainliest to best explanation
Answer:
1200
Step-by-step explanation:
Find A1 in a geometric series for which sn=3045,r=2/5, and an=120
Answer:
a = 1875
Step-by-step explanation:
Sum of geometric series formula:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Geometric series formula:
[tex]a_n=ar^{n-1}[/tex]
Given:
[tex]S_n=3045[/tex][tex]r=\dfrac25=0.4[/tex][tex]a_n=120[/tex][tex]\implies 120=a(0.4)^{n-1}[/tex]
[tex]\implies a=\dfrac{120}{(0.4)^{n-1}}[/tex]
[tex]\implies 3045=\dfrac{a(1-0.4^n)}{1-0.4}[/tex]
[tex]\implies 3045=\dfrac{a(1-0.4^n)}{0.6}[/tex]
[tex]\implies 1827=a(1-0.4^n)[/tex]
[tex]\implies a=\dfrac{1827}{1-0.4^n}[/tex]
Equate equations for a:
[tex]\implies \dfrac{120}{(0.4)^{n-1}}=\dfrac{1827}{1-0.4^n}[/tex]
Apply exponent rule [tex]a^{b-c}=\dfrac{a^b}{a^c}[/tex]
[tex]\implies \dfrac{120}{\frac{0.4^n}{0.4^1}}=\dfrac{1827}{1-0.4^n}[/tex]
[tex]\implies \dfrac{48}{0.4^n}=\dfrac{1827}{1-0.4^n}[/tex]
[tex]\implies 48(1-0.4^n)=1827(0.4^n)[/tex]
[tex]\implies 48-48(0.4^n)=1827(0.4^n)[/tex]
[tex]\implies 48=1875(0.4^n)[/tex]
[tex]\implies 0.4^n=\dfrac{48}{1875}[/tex]
[tex]\implies 0.4^n=0.0256[/tex]
Taking natural logs:
[tex]\implies \ln0.4^n=\ln0.0256[/tex]
[tex]\implies n\ln0.4=\ln0.0256[/tex]
[tex]\implies n=\dfrac{\ln0.0256}{\ln0.4}[/tex]
[tex]\implies n=4[/tex]
Substituting found value for n into one of the equations and solving for a:
[tex]\implies a=\dfrac{120}{(0.4)^{4-1}}[/tex]
[tex]\implies a=\dfrac{120}{0.4^3}[/tex]
[tex]\implies a=\dfrac{120}{0.064}[/tex]
[tex]\implies a=1875[/tex]
I need to stay in math
Answer:
? = 42 degrees
Step-by-step explanation:
The 105 is part of a 180 degree angle so we do 180-105 giving us 75 degrees. and the sum of the internal angles of a triangle should equal 180. so we add 57 + 75 giving us 132. 180-132 will be 48 degrees.
Divide 66 chocolates between arun and vikasin the ratio 7:4
Answer:
hello
7 + 4 = 11
arun = 66 x 7/11 = 42
vikasin = 66 x 4/11 = 24
Step-by-step explanation:
Please help me if you can and thank you :)))
Answer:
$1920
Step-by-step explanation:
12800 X 0.15 = 1920
A company fabricates cast concrete cylindrical columns for a new pavilion.The columns are 3 meters tall and have a radius of 0.6 meters.What is the approximate surface area of a single column?
Answer:
The answer is 13.57m^2
Step-by-step explanation:
On Edmentum I got it right.
Find the product: -4/9 and -3/8
Answer:
1/6
Step-by-step explanation:
-4/9 * (-3/8) =
= 12/72
= 1/6
Answer:
Step-by-step explanation:
-4/9 x -3/8 = (-4)(-3) / 8x9 = 12 / 72 = 6/36 = 1/6
Dante is studying the growth of a particular type of plant. He is testing the effects of four growth factors: lighting, age, temperature, and humidity …. Here are the levels he's
The level from each growth factors is an illustration of combination
There are 90 ways of combining one level from each growth factors
How to determine the number of combination
From the complete question (see attachment), we have the number of levels in each growth factor is:
Lighting = 3Age = 5Temperature = 2Humidity = 3So, the number of combination (n) is:
n = 3 * 5 * 2 * 3
n = 90
Hence, there are 90 ways of combining one level from each growth factors
Read more about combination at:
https://brainly.com/question/11732255
Carter’s bikes look in the image. Thank you in advance.
Answer:$12 + $15h = $72
H=4 Scott rented the bike for 4 hours.
Step-by-step explanation:
Subtract 12 from each side. You then have $15h = $60 now you divide each side by 15 to get 4
Answer:
The solve for h= is 4 hours
The equation is 12+ 15=27
He rented the bike for 4 hours.
help me please thank you
18
RS = BC
19
angle A = angle Q
20
real blueprint
we know 45 9 width
we're looking for 70 n
45 x n = 70x 9
n = 630 : 45 = 14
=> 14 in
#18
Just observe the naming you can answer without seeing the diagram even
∆ABC~∆QRS
RS is at end so it is similar to BCOption D.
#19
<A~<QOption B
#20
Let that be x
Ratio remains same[tex]\\ \tt\hookrightarrow \dfrac{45}{70}=\dfrac{9}{x}[/tex]
[tex]\\ \tt\hookrightarrow \dfrac{9}{14}=\dfrac{9}{x}[/tex]
[tex]\\ \tt\hookrightarrow x=14in[/tex]
Option D
A customer in Indiana buys 4 bags of Gone Bananas treats for $8.99 each. The sales tax in Indiana is 7%. What is the total cost of the order?
4 x 8,99 x 1,07 = £38,48
Was the caste system a fair system based on religious beliefs or was it a social
structure that promoted inequality?
I really need help!!!
Suppose that ∠BNR and ∠RNA are adjacent angles where m∠BNR=12w-19,
m∠RNA= ¼(w+199), and m∠BNA=2(12w-19).
What is the value of W
Answer:
Step-by-step explanation:
Sum of interior adjacent angle is 180 degrees.
Given
m∠BNR=12w-19,
m∠RNA= ¼(w+199)
m∠BNA=2(12w-19).
Substitute
m∠BNR+m∠RNA=
¼(w+199)+12w-19, = 2(12w-19).
W+796+48W-76 = 96W-152
49W-96W = -152+76-796
-47W = 872
W = 872/47
W = 18.55
Which expression is equivalent to (2 cubed) Superscript negative 5?.
The expression which is equivalent to (2³)^-5 is; 1/(2)^15.
Which expression is similar to (2³)^-5?By the law of indices, it follows that exponents as that given in the task content can be evaluated as follows;
(2³)^-5
= (2) ^(3×-5)
= 2 ^(-15)
Hence, the expression can be rewritten as; 1/(2)^15.
Read more on indices;
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Answer:
a
Step-by-step explanation:
i did the test
A colony of spiders has a population of 350. The population is decreasing at a rate of 3% per year. Write an exponential decay function for the quarterly decay rate. What does the y-intercept of its graph mean in this context? Round values to the nearest thousandth. function:__________
The y-intercept is the_________
at time________
Step-by-step explanation:
350 decreasing at 3% per year
the function is
y = mx + c
m is the gradiant (change)
c is the y-intercept (when x = 0)
first m
it is decreasing by 3 %
3% as a decimal = 0.03
m = -0.03
c is
at the start
we start with 350
c = 350
put back into the equation
y = ?x + ?
put answer in comments i will mark
please mark brainest
If you deposit $5000 into an account that pays 3% annual Interest compounded -annually, how much money will you have after 2 years?
Answer:
$5304.5
Step-by-step explanation:
5000 x 1.03²
1.03=3%
x² =2 years