Answer:
the answer is ; Never
Hope this answer correct :)
Answer:
the answer is never
Step-by-step explanation:
1. (a) Find the greatest common divisor of the term 144x3y2and 81xy4
(b) Hence factorise completely this expression 144x3y2-81xy4
Answer:
Step-by-step explanation:
a) 144x³y² = 2 *2*2*2* 3* 3* x³ * y² = 2⁴ * 3² * x³ * y²
81xy⁴ = 3 * 3 * 3 * 3 * x * y⁴ = 3⁴ * x * y³
GCD is that are in both term
Greatest common divisor = 3² * x * y² = 9xy²
b) 144x³y² - 81xy⁴ = 9xy² * 16x²y - 9xy²*9y²
= 9xy²(16x²y - 9y²)
6x-1=11 solve equation
Answer:
x = 2
Step-by-step explanation:
6x-1=11
Add 1 to each side
6x-1+1=11+1
6x = 12
Divide by 6
6x/6 = 12/6
x = 2
Answer:
x = 2Step-by-step explanation:
[tex]6x-1=11 \\\\Collect \: like \:terms\\\\6x = 11+1\\\\Simplify\\\\6x =12\\\\Divide\:both\:sides\:by\:6\\\\\frac{6x}{6} = \frac{12}{6}\\ x = 2[/tex]
Question 12
1 pts
Whitney recently created a new smartphone app. As a result of the initial costs and
fees of producing the app, she did not make any money, or profit, selling the app during
the first two months of the app's release. For the first month, Whitney had a loss of
$324. During the second month of sales, she had a loss of $97. She hopes that in the
third month, she will sell enough apps to break even-that is, she hopes to earn enough
money to cover her losses. What is the amount of money Whitney needs to make in the
third month in order to break even with app sales so far?
Answer:
The amount (revenue) she makes in the third month to break even is $97
Step-by-step explanation:
The given parameters are;
The cost of the app = Initial cost + fees for producing the app
The amount she loss in the first month = Cost of the app - revenue = $324
The amount she loss in the second month = Loss from first month - revenue in second month = $324 - revenue in second month = $97
The amount Whitney has to make in the third month to break even is therefore;
The amount she makes in the third month to break even is given by the equation;
Revenue from third month - Loss from second month = 0
Which gives;
The amount she makes in the third month to break even is given by Revenue from third month - $97 = 0
∴ Revenue from third month = $97
The amount (revenue) she makes in the third month to break even = $97
Two trains leave New York at the same time heading in opposite directions. Train A travels at 4 5 the speed of train one. After seven hours they are 693 miles apart. What was the speed of train A?
Answer:
Speed of train A is 44 miles/hr.
Step-by-step explanation:
Let the speed of train A = [tex]u\ miles/hr[/tex]
Let the speed of train one = [tex]v\ miles/hr[/tex]
Train A travels at [tex]\frac{4}{5}^{th}[/tex] the speed of train one.
i.e.
[tex]u = \dfrac{4}{5}v \\\Rightarrow v =\dfrac{5}{4}u.... (1)[/tex]
Distance traveled = 693 miles
Time taken = 7 hours
They are travelling in opposite directions so the resultant speed will appear to be faster.
Relative speed = [tex]u+v\ miles/hr[/tex]
The trains are 693 miles apart in 7 hours that means they have traveled a total distance of 693 miles in 7 hours with a speed of ([tex]u+v[/tex]) miles/hr.
Using the formula:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
[tex]u+v = \dfrac{693}{7}\\\Rightarrow u+v=99 ...... (2)[/tex]
Putting the value of v using equation (1):
[tex]\dfrac{5}4u+u=99\\\Rightarrow 5u+4u = 99 \times 4\\\Rightarrow 9 u = 99 \times 4\\\Rightarrow u = 11 \times 4 = \bold{44\ miles/hr}[/tex]
Speed of train A is 44 miles/hr.
PLEASE HELP I PUT THE PROBLEM AS A PICTURE PLEASE ANSWER WILL GIVE 30 POINTS SHOW WORK
Answer:
[tex]\huge\boxed{9}[/tex]
Step-by-step explanation:
[tex]\sf (2^8 * 3^{-5} * 6^0)^{-2 } (\frac{3^{-2}}{2^3} )^4*2^{28}[/tex]
Rule of exponents [tex]a^0 = 1[/tex] , [tex]1/a^m = a^{-m}[/tex]
=> [tex]\sf 2^{8*-2} * 3 ^{-5*-2} * 3 ^{-2}* 2^{-3*4} * 2^{28}[/tex]
=> [tex]\sf 2 ^ {-16} * 3^{10} * 3^{-8} * 2 ^{-12}* 2^{28}[/tex]
Combining same bases
=> [tex]\sf 2 ^ {-16} * 2 ^{-12}* 2^{28}* 3^{10} * 3^{-8}[/tex]
When bases are same , powers are to be added
=> [tex]\sf 2 ^{-16-12+28} * 3^{10-8}[/tex]
=> [tex]\sf 2^{-28+28} * 3^2[/tex]
=> [tex]\sf 2^0 * 3^2[/tex]
=> [tex]\sf 3^2[/tex]
=> 9
A student finds the slope of the line between (8,17,) and (1,4) she writes 17-4/1-8 What mistake did she make?
The first mistake is that she didn't use parenthesis to indicate we're dividing all of one thing (numerator) over all of another expression (denominator)
slope = rise/run = numerator/denominator
So she should write (17-4)/(1-8) to indicate all of "17-4" is divided over all of "1-8"
However, there's another error that your teacher is probably more focused on. Note how 17-4 represents subtracting the y coordinates from left to right. We start with the left point y coordinate 17 and subtract off the right point y coordinate 4
left y - right y = 17 - 4
But then the student swaps the order when they wrote 1-8. Instead it should be 8-1
-----------------
Here's what they should have written (17-4)/(8-1)
This is the same as (4-17)/(1-8)
We can subtract in any order as long as it stays consistent between the numerator and denominator
How many times does 5 go into 1,200??
240 times.
Explanation:
24 times because,
If you divide 5 with 12k that's,
= 1200/5
= 240
Hence proved, 240 times.
Jonathan's parents told him that for every 2 hours of homework or reading he completes, he would be able to play 30 minutes of video games. His friend Lucas's
parents told their son that he could play 1.5 hours for 5 hours of homework or reading time he completes. What is the unit rate for each boy? You must label both unit rates.
Answer:
Jonathan's Unit rate = 4 hr (reading/homework)/(1 hour for video games)
Lucas' Unit rate = 3 hr (reading/homework)/(1 hour for video games)
Step-by-step explanation:
The unit rate is the rate per unit of a quantity, that is the rate at which the denominator has been made a unit or one
The given parameters are;
The number of hours of homework or reading Jonathan needs to do for his parents to allow him to play video games for 30 minutes = 2 hours
The number of hours of homework or reading Lucas needs to do for his parents to allow him to play video games for 30 minutes = 1.5 hours
We note that 30 minutes = 0.5 hours
For Jonathan we have
Unit rate = (Number of hours of reading or homework)/(Number of hours playing video games)
Unit rate = (2 hours)/(0.5 hours) = 4 hours of reading or homework per hour of paying video games
Jonathan's Unit rate = 4 hr (reading/homework)/(1 hour for video games)
For Lucas we have
Unit rate = (Number of hours of reading or homework)/(Number of hours playing video games)
Unit rate = (1.5 hours)/(0.5 hours) = 3 hours of reading or homework per hour of paying video games
Lucas' Unit rate = 3 hr (reading/homework)/(1 hour for video games).
Find the values of a and b so that the following
system of linear equations have infinitely solutions:
(1) (2a - 15x + 3y - 5 = 0, 3x + (6 - 1)y - 2 = 0
plz answer step by step
Answer:
a = 15/2, b = 2/5
Step-by-step explanation:
For a system of two linear equations to have infinitely many solutions, the equations must be equivalent to one another.
Assuming a and b to be constants, and since b is absent from equations, there must be a typo where b was mistaken for a 6.
Modified equations:
2a - 15x + 3y - 5 = 0 ...................(1)
3x + (b - 1)y - 2 = 0 .....................(2)
rearrange equations to standard form:
-15x + 3y + 2a-5 = 0 .................(1a)
3x + (b-1)y -2 = 0 ........................(2)
To equalize the coefficient of x, multiply (2) by -5
-15x - 5(b-1) y +10 = 0 ................(2a)
Subtract (2a) from (1a)
3y + 5(b-1)y + 2a-5 -10 = 0 ..............(3)
For the two equations (1a) and (2a) to be identical, coeffients of y and constant term of (3) must equal zero.
3+5(b-1) = 0 .................(4)
3+5b-5 = 0
5b = 2
b = 2/5
2a-5-10 = 0 .....................(5)
a = 15/2
Simplify the following expression 5(y + 3) + 7(y − 5) + 6
Answer:
12y-14
Step-by-step explanation:
we expand first and doing that we get
5y+15+7y-35+6
12y-14
2(6y-7)
Step-by-step explanation:
5(y+3) + 7(y-5) +6
5y+15+7y-35+6
5y+7y+15-35+6
12y-14
y= -14-12
y= +26
MATHEMATICS
Algebra
Simultaneous Equations
1. 5u + 2v=7
2u - 2v=7
2. 3x - 4y=19
4x - 5y=23
Answer:
1. u = 2, v = -1.5
2. y = -7, x = -3
Step-by-step explanation:
1) For the following simultaneous equation, we have;
5·u + 2·v = 7....................(1)
2·u - 2·v = 7......................(2)
Adding equation (1) to equation (2), gives;
5·u + 2·v + 2·u - 2·v = 14
5·u + 2·u + 2·v- 2·v = 14
7·u = 14
u = 14/7 = 2u = 2
u = 2
From equation (1), we have;
5·u + 2·v = 7 substituting u = 2 gives;
5×2 + 2·v = 7
2·v = 7 - 5×2 = 7 - 10 = -3
v = -3/2 = -1.5
v = -1.5
2.
3·x - 4·y = 19....................(1)
4·x - 5·y = 23.......................(2)
Multiplying equation (1) by 4 and equation (2) by 3 gives;
For equation (1)
4 × (3·x - 4·y) = 4 ×19
12·x - 16·y = 76...........................(3)
For equation (2)
3 × (4·x - 5·y) = 3 × 23
12·x - 15·y = 69...........................(4)
Subtracting equation (3) from equation (4) gives;
12·x - 15·y - (12·x - 16·y) = 69 - 76 = -7
12·x - 15·y - 12·x + 16·y = 69 - 76 = -7
12·x - 12·x - 15·y + 16·y = -7
y = -7
Substituting the value of y = -7 in equation (1), we have;
3·x - 4·y = 19 = 3·x - 4×(-7) = 19
3·x - 4×(-7) = 19
3·x + 28 = 19
3·x = 19- 28 = -9
x = -9/3 = -3
x = -3.
A___has a regular polygon base and a vertex over the center of the base.
A. Regular pyramid
B. Prism
C. Pyramid
D. Right Prism
Answer:
A. Regular pyramid
Step-by-step explanation:
If it has a vertex over the centre of the base, it has to be a pyramid.
Also, since the base is a regular polygon, the solid is a regular pyramid.
Answer:
The correct answer is
Step-by-step explanation:
Regular pyramid: A regular pyramid has a regular polygon base and a vertex over the center of the base.
Hope this helps....
Have a nice day!!!!
The net of a rectangular prism is shown below. What is the total surface area of this prism
Answer:
142 cm^2
Step-by-step explanation:
Okay, we can first break this down into 3 different rectangles.
3 x 5 rectangle
16 x 7 rectangle
3 x 5 rectangle.
From here, we just multiply these out and add them. 15 + 15 + 112 = 142. So our answer is 142 cm^2
Answer:
142 cm²
Explanation:
to find the surface area, you need to find the area of all of the boxes within the image above add them all together.
Starting in the middle row and working from left to right it is,
7×3+7×5+7×3+7×5
21+35+21+35=112
Than the bottom and top box is
3×5+5×3
15+15=30
Than you add both of them together,
112+30=142
HELP DOES ANYONE KNOW THIS
Answer:
10x
Step-by-step explanation:
The height on the left is the same as the height on the right:
(2x -y) +(y) = (2x)
2x = 2x . . . . . not particularly helpful
The width across the top is the same as the width across the bottom:
3x = (y) +(4x -2y)
y = x . . . . . . . . add y-3x to both sides
The perimeter is the sum of side lengths. Working clockwise from the top, that is ...
P = 3x +2x +(4x-2y) +y +y +(2x -y) = 11x -y = 10x
The perimeter is 10x. (or 10y, if you like)
Adding
ing and Multiplying Rati
What type of answer would you expect from the problem below? Expla
answer
DONES
On a distant planet, a ball is thrown upwards from ground level, reaching a maximum height of 12m and hitting the ground again in eight seconds. Determine a quadratic equation in the form ax^2 + bx^2+c = 0 that could be used to calculate when the ball is at a height of 3m. Do not solve the equation.
Answer:
(-3 ÷ 4)x^2 + 6x
Step-by-step explanation:
Data mentioned in the question
Maximum height = 12m
Number of seconds = 8
Height = 3m
Depend on the above information, the quadratic equation is shown below:
As it took 8 seconds to hit the maximum altitude and it reverted to the ground floor, this graph also reflects the motion in parabola after 4 seconds, so that the a must be negative
Now it is given that
a × x ^ 2 + bx + c =0
We can considered that
x = 0
x = 8
As {0.8} are intercepts of x
When x = 0, then it is
a × 0 ^ 2 + b(0) + c = 0 .................... (i)
Hence 0 = 0
Now x = 8, it is
a × 8 ^ 2 + b(8) + c = 0
Hence a(8)^2 + b(8) + c = 0 ..................(ii)
As it can be seen that in the first equation c must be zero
Whereas the second equation is
64a + 8b = 0
i.e.
8a = -b or a = -b ÷ 8
Now according to the quadratic function, it presented
(-b ÷8)x^2 + bx + 0
So, the parabola vertex is (4, 12)
Now place this in the place of a
(-b ÷ 8)(4)^2 + b(4) = 12
And for calculating this b, all terms must be multiplied by 8
That appears
-b(16) + 32b = 96
16b = 96
So, b = 6.
As a = -b ÷8
a = -6 ÷ 8
a = -3 ÷4
So, the equation is
= (-3 ÷ 4)x^2 + 6x
Hence, this is the equation
I am on a farm with pigs and horses. The ratio of pigs to horses is 4:1. The ratio of adult pigs to piglets is 1:5. The ratio of adult horse to foal is 3:1. What fraction of the farm are babies (foals and piglets)?
Answer:
EAT THIS ANDAD Which polynomial has (3x + 2) as a binomial factor?
6x3 + 3x2 + 4x + 2
12x2 + 15x + 8x + 10
18x3 – 12x2 + 9x – 6
21x4 + 7x3 + 6x + 2
Step-by-step explanation:
If the coefficient of determination for a data set containing 24 points is 0.5,
12 of the data points must lie on the regression line for the data set.
A. True
O B. False
SUBMIT
Answer:
False
Step-by-step explanation:
False - one has nothing to do with the other. None of the data points can lie on the regression line,
and you can have the coeff. of determination be 0.5.
Question 10(Multiple Choice Worth 1 points) (06.01 LC) Choose the polynomial that is written in standard form.
2x2 + 3x4 + 10x6
4x4 + 6x3 + 10x4
−3x8 + 9x2 + 10x
−7x6 + x3 + 10x8
Answer:
−3x^8 + 9x^2 + 10x
Step-by-step explanation:
A polynomial is in standard form when the exponents of the variable decrease left to right. The only given expression in that form is ...
−3x^8 + 9x^2 + 10x
solve the equation: csc(4x)-2=0
Step-by-step explanation:
csc(4x) − 2 = 0
csc(4x) = 2
sin(4x) = 1/2
In radians:
4x = π/6 + 2kπ, 5π/6 + 2kπ
x = π/24 + kπ/2, 5π/24 + kπ/2
In degrees:
4x = 30° + 360°k, 150° + 360°k
x = 7.5° + 90°k, 37.5° + 90°k
Consider the plot created from the residuals of a line of best fit for a set of data.
Does the residual plot show that the line of best fit is appropriate for the data?
Yes, the points have no pattern.
No, the points are evenly distributed about the x-axis.
No, the points are in a linear pattern.
Yes, the points are in a curved pattern.
Answer:
No, the points are in a linear pattern.
Step-by-step explanation:
Residual plot is a graph that shows the residuals on the vertices. The y-axis has residual values and x-axis has independent variables. The horizontal axis shows the independent variables to determine the best fit for a set. The graph given is in a linear pattern. The random pattern shows that linear model is good fit.
Answer:
C: No, the points are in a linear pattern
Step-by-step explanation:
edg2021
I have been seeing this question with multiple different answers, and no one is sure about anything! All I can say for sure is that IT IS NOT A! So C makes the most sense. B is simply not true, and neither is D, its not curved or evenly distribute.
7 less than the quotient of a number 5 and w in a algebraic expression.
Answer:
5/w -7
Step-by-step explanation:
quotient means division
5/w
less than means it comes after
5/w -7
Answer:
5/w-7
Step-by-step explanation:
First, let's write out "the quotient of a number 5 and w"
The quotient is the result from dividing two numbers. Therefore, we must divide 5 and w.
5/w
Now, let's add on "7 less than". Since it is "less than" it will come after the division. "Less" means subtract. So, subtract 7 from 5/w.
5/w-7
7 less than the quotient of a number 5 and w as an expression is: 5/w-7
Plz help with this question! What is 1/3 * 3/5 * 5/7 ... * 97/99
Answer:
Step-by-step explanation:
(1/3)*(3/5)*(5/7)*.......*(93/95) * (95/97) * (97/99)
The denominator of each fraction will cancel out the numerator of the next fraction.
Take a close look
Therefore the result is 1/99
HOPE IT HELPS!!
The product of the geometric series is 1/99.
The product is a geometric series with first term 1/3 and common ratio 2/3. The number of terms is 49. The sum of the series is 1/99.
Here's the explanation:
A geometric series is a series where each term is multiplied by a constant value to get the next term. The constant value is called the common ratio.
In this case, the first term is 1/3 and the common ratio is 2/3. This means that each term is multiplied by 2/3 to get the next term.
The number of terms in the series is 49. This means that there are 49 terms in the series, starting with 1/3 and ending with 97/99.
The sum of the series is 1/99. This can be found using the formula for the sum of a geometric series:
S = a × (1 - [tex]r^{n}[/tex]) / 1 - r
where a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 1/3, r = 2/3, and n = 49. Substituting these values into the formula, we get:
S = (1/3) × (1 - (2/3)49) / 1 - (2/3) = 1/99
Therefore, the product is 1/99.
Learn more about geometric series here: brainly.com/question/30264021
#SPJ2
need help right now please
its 4
x=4
[tex]4^{2}[/tex]-2x4
16-8
=8
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your equation step-by-step.
[tex]x^2 - 2x = 8[/tex]
Step 1: Subtract 8 from both sides.
[tex]x^2 - 2x - 8 = 8 - 8\\x^2 - 2x - 8 = 0[/tex]
Step 2: Factor left side of equation.
[tex]( x+2) ( x - 4) = 0[/tex]
Step 3: Set factors equal to 0.
[tex]x + 2 = 0[/tex] or [tex]x - 4 = 0[/tex]
[tex]x = -2[/tex] or [tex]x = 4[/tex]
Answer : -2 , 4
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
What adds to be the bottom numbers but also multiplies to be the top?
39 at the bottom and 25 on the right above 39
Answer:
well i cant answr it if i oont have more inforomartion
Step-by-step explanation:
Answer:
Step-by-step explanation:
if we add 11,36,61,... to the bottom we get bottom as a multiple of numerator.
En la figura adjunta se muestra un estuche de brocas de acero que sirven para perforar paredes de cemento. Las brocas están numeradas de menor a mayor tamaño y las dimensiones están dadas en pulgadas.
En la figura, por falta de espacio, se dan solo las dimensiones de las brocas 1 y 12. Se sabe que las demás brocas son de 9/16 de pulgadas, 3/16 de pulgada, 7/16 de pulgada, 5/16 pulgada, 11/16 pulgada, 1/4 pulgada, 3/8 pulgada, 1/2 pulgada, 5/8 pulgada y 1/8 de pulgada.
Identifica la medida de las brocas 2 a la 11 en pulgadas y ordénalas de menor a mayor tamaño.
Answer:
1/16 2/16 3/16 4/16 5/16 6/16 7/16 8/16 9/16 10/16 11/16 12/16
Step-by-step explanation:
Para la identificación de las brocas tenemos dos consideraciones:
1.- Fracciones de igual denominador son mas grandes en orden creciente según vayan creciendo los numeradores, de tal forma que entre
9/16 3/16 7/16 5/16 11/16 el orden es como sigue ( de menor a mayor)
3/16 5/16 7/16 9/16 11/16
2.- Las fracciones con denominadores distintos pueden llevarse a denominador común /16 amplificando la fracción es decir por ejemplo
1/4 = 1*4/4*4 = 4/16
Con ese procedimiento las convertimos todas al caso señalado en el punto anterior y ordenamos
1/4 = 4/16
3/8 = 6/16
1/2 = 8/16
5/8 = 10/16
1/8 = 2/16
Entonces hay diez brocas la primera será 1/16 y la número 12 12/16
Y finalmente el orden es:
1/16 2/16 3/16 4/16 5/16 6/16 7/16 8/16 9/16 10/16 11/16 12/16
Patrick deposited $6,875 into a savings account 17 years ago. The account has an interest rate of 4.9% and the balance is currently $15,734.11. How often does the interest compound
Answer:
Quaterly
Step-by-step explanation:
3. Solve 2log4y - log4 (5y - 12) = 1/2
Answer:
y = 4 or y = 6
Step-by-step explanation:
2log4y - log4 (5y - 12) = 1/2
2log_4(y) - log_4(5y-12) = log_4(2) apply law of logarithms
log_4(y^2) + log_4(1/(5y-12)) = log_4(/2) apply law of logarithms
log_4(y^2/(5y-12)) = log_4(2) remove logarithm
y^2/(5y-12) = 2 cross multiply
y^2 = 10y-24 rearrange and factor
y^2 - 10y + 24 = 0
(y-4)(y-6) = 0
y= 4 or y=6
Chen is baking muffins and banana bread for a brunch buffet. He needs 3 and one-fifth cups of flour to make the muffins and 3 and two-thirds cups of flour to make the banana bread. Which is the best estimate of the number of cups of flour that Chen needs to bake both recipes?
Options :
A. 6 cups of flour
B.7 cups of flour
C.8 cups of flour
D.9 cups of flour
Answer:
B.7 cups of flour
Step-by-step explanation:
Given the following :
Cups of flour required to make muffins = 3 1/5
Cups of flour required to make banana = 3 2/3
Number of cups of flour required to make both recipe :
(cups of flour required to make muffins + cups of flour required to make bread)
(3 1/5 + 3 2/3) = 3+3+(1/5 + 2/3)
= 6 + (1/5 + 2/3) = (3 + 10)/15 = 6 + (13/15)
6 13/15 = 6.8666666
The best estimate is to round to the nearest whole number = 7
Answer: The answer is 7
Step-by-step explanation:
I got it right in my quiz! Hope this helps (:
Gisele has $5.90 in quarters and nickels. If Gisele has 16 more nickels than quarters, how many quarters does she have? [I don't want the answer I just want to know how to set the problem up please]
Answer: There are 17 quarters.
Step-by-step explanation:
Let x = Number of quarters and Number of nickels =x+16
∵ 1 nickel = $0.05, 1 quarter = $0.25
value of x quarters = 0.25 x
value of x+16 nickels = 0.05(x+16)
Then, as per given,
[tex]0.05(x+16)+0.25 x= 5.90 \\\\\Rightarrow\ 0.05x+0.8+0.25x=5.90\\\\\Rightarrow\ 0.30x=5.9-0.8\\\\\Rightarrow\ 0.30x=5.1\\\\\Rightarrow\ x=\dfrac{5.1}{0.30}=\dfrac{51}{3}\\\\\Rightarrow\ x=17[/tex]
Hence, there are 17 quarters.
