Bob has 49 quarters and 11 dimes.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Let there be x quarters.
Then there are 60 - x dimes so using cents as the unit, we get
25x + 10(60 - x) = 1335
25x + 600 - 10x = 1335
15x = 735
x= 49
and 60 - x = 60 - 49 = 11
Hence, Bob has 49 quarters and 11 dimes.
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Final answer:
By setting up a system of two equations, where q stands for the number of quarters and d for the number of dimes, and solving this linear system, we find that Bob has 49 quarters and 11 dimes.
Explanation:
To solve this problem, we can set it up as a system of equations. Let's call the number of quarters q and the number of dimes d. We have two pieces of information:
The total number of coins is 60: q + d = 60.The total value of the coins is $13.35. Since each quarter is worth $0.25 and each dime is worth $0.10, the value equation is: 0.25q + 0.10d = 13.35Now, we can multiply the second equation by 10 to eliminate decimals:
2.5q + d = 133.5
Using the first equation (q + d = 60), we can express d as d = 60 - q. Substituting this into the second equation:
2.5q + (60 - q) = 133.5
Simplifying, we get:
1.5q = 73.5
Divide both sides by 1.5 to find q:
q = 49
Now, plug q back into the first equation to find d:
d = 60 - 49 = 11
So, Bob has 49 quarters and 11 dimes.
Gigi spent 12% of her birthday money on a new pair of sunglasses. What fraction of her birthday money did she spend in the new sunglasses
Answer:
3/25
Step-by-step explanation:
You know that percent is out of 100, so that's 12/100
Then simplify the fraction to 6/50 then 3/25
Final answer:
Gigi spent 12% of her birthday money on sunglasses, which is equivalent to 3/25 of her birthday money when converted and simplified from a percentage to a fraction.
Explanation:
Gigi spent 12% of her birthday money on a new pair of sunglasses. To find out what fraction of her birthday money this represents, we convert the percentage to a fraction. Percent means 'per hundred,' so 12% can be written as 12 per 100 or, more simply, 12/100. However, this fraction can be simplified further. Both the numerator (12) and the denominator (100) can be divided by their greatest common divisor, which is 4. Dividing both by 4, we get 3/25. Therefore, Gigi spent 3/25 of her birthday money on the new sunglasses.
The bearing of point Y from point X is 070°.
The bearing of point Z from point Y is 125°.
The bearing of point Z from point X is 110°.
Find the bearing of point X from point Z
Answer:
The answer is 290°
Step-by-step explanation:
Final answer:
To find the bearing of point X from point Z, we can use the given bearings of points X, Y, and Z. Start with the bearing of point Z from point X, add the bearing of point Z from point Y, and subtract the bearing of point Y from point X.
Explanation:
To find the bearing of point X from point Z, we can use the given bearings of points X, Y, and Z. Here's how:
Start with the bearing of point Z from point X, which is 110°.Add the bearing of point Z from point Y, which is 125°.Subtract the bearing of point Y from point X, which is 70°.The result is the bearing of point X from point Z. So, the bearing of point X from point Z is 165°.
What is the area of the parallelogram with a base of 1.75 cm and a height of 1.5 cm? 2.75 cm2 3.625 cm2 2.625 cm2 3.25 cm2
Answer:
Step-by-step explanation:
Area of parallelogram=base*height
So 1.75*1.5=2.625cm²
Answer:
2.625
Step-by-step explanation:
Help!
Which answer is correct?
Well, since the graph starts at (0,50), making our y-intercept 50, we can knock off D as an option.
The next step is to find the slope. To do this, find two points and subtract the y values over the x values. (Just make sure that whichever y value you start with - start with the same x value).
So we have >>> (50, 200) and (0,50) from earlier.
200 - 50 / 50 - 0 = 150/50 or 3/1, or 3.
This makes the correct answer A since the equation is represented as y = mx + b, where m is the slope and m has a value of 3.
A 2/3 foot board is cut to 7/16 of its original length. What is its new length?
Answer:
7/24 feet.
Step-by-step explanation:
That would be 7/16 of 2/3
= 2/3 * 7/16
= 14/48
= 7/24 feet.
The new length of the board after being cut to 7/16 of its original length is 7/24 foot.
Explanation:Yes, the thing you need to understand here is that you've to multiply the length of the board by the fraction given to find the new length. So, in this problem, the original length of the board was 2/3 foot and it was cut to 7/16 of its original length. Hence, to find the new length, you multiply 2/3 foot by 7/16.
This results in 14/48 foot, which when simplified/reduced gives 7/24 foot. Therefore, the new length of the board after it is cut is 7/24 foot.
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PLEASE HELP. IVE RETAKEN THIS 6 TIMES .
In the figure, ∆BAT ≅ ∆CAT. Which statement is true by CPCTC?
3x+2y=8 is this function a quadratic?
Step-by-step explanation:
Let's select values for X, and find the corresponding Y values:
X = -3, Y = 8.5
X = -2, Y = 7
X = -1, Y = 5.5
X = 0, Y = 4
X = 1, Y = 2.5
X = 2, Y = 1
X = 3, Y = -0.5
So our coordinates are:
(-3, 8.5) ; (-2, 7) ; (-1, 5.5) ; (0, 4) ; (1, 2.5) ; (2, 1) and (3, 0.5)
Graph these on a chart to visualize:
(In picture)
We can see that this is a decreasing linear function, not quadratic. Quadratic functions create a symmetrical curve, which this is not.
Jordan drove a3 miles per hour for a5 hours. Howfar did Jordan drive? A a2 miles B a8 miles C a12 miles D a15 miles
Answer: Option D) 15 miles
Step-by-step explanation:
if Jordan drives 3 miles in one hour
Then, 3 miles = 1 hour
while Z miles = 5 hours
cross multiply
3 miles x 5 hours = Z miles x 1 hour
15 = Z
Thus, jordan drove through a distance of 15miles
can someone help with any of these please?
1. A line passes through the points (-1, -6) and (-4, 3) what is the equation in slope intercept form?
2. The slope of the line that contains the points (-5, 13) and (5, -7) is -2, which of the following equations represents this line?
2a) y= -2x - 17
2b) y= -2x - 3
2c) y= -2x + 3
2d) y= -2x + 23
3. What is the equation in slope-intercept form, of the line that contains the points (3, -4) and (5, -6)?
3a) y= -x - 1
3b) y= -x + 1
3c) y= x - 1
3d) y= x + 1
1. X1 Y1. X2, Y2
(-1,-6). ( -4,3)
Formula for slope which is m
Y2 -Y1 divide by X2-X1
3- -6/ -4 - -1= 9/-3= -3
So M = -3
Y=mx+b
-6= -3 (-1) +b
-6= 3+b
-3=-3
-9=b
Answer Y= -3x-9
2. X, Y
(-5,13)
Y=mx+b
13= 10+b
-10=-10
3=b
Answer C y= mx+b
y=-2x+3
3. (X1,Y1). (X2,Y2)
(3,-4). (5,-6)
Formula for m which is slope y2-y1 / x2-X1
-6- -4 / 5-3 = -2/2= -1 so m = -1
X, Y
(3,-4)
Y=mx+b
-4= -1(3)+b
-4= -3+b
+3=+3
-1. = b
Y= m x+b
-4= (-1) 3 +b
-4= -3. + b
+3= +3
-1. = b
Answer A y= -1x-1
Answer:
Answer Y= -3x-9 Answer C y= mx+b y=-2x+3 Answer A y= -1x-1
Step-by-step explanation:
A circle has a radius of 14 feet. What it’s area
Answer:
6.157
Step-by-step explanation:
A=πr^2=π·14^2≈615.75216
Solve the equation:
x – x² – 12x = 0
Answer: x =0;
Step-by-step explanation:
O raised to power of any number is 0
Use the distributive property to write an equivalent expression. 6(x+y+z)
Answer: 6 x + 6y + 6z
Step-by-step explanation: Simply distribute the 6 by multiplying it by each variable in the parenthesis!
Answer:
6x+6y+6z
Step-by-step explanation:
Apply distribution
Felicia is solving the expression -5(3x+2)+10x. Gregory is solving the expression -12-4x+?+?x. Both students simplified their answers to get the same expression. What are the values missing from Gregory's expression?
Answer:
see the explanation
Step-by-step explanation:
we have
Felicia
[tex]-5(3x+2)+10x[/tex]
Apply distributive property
[tex]-5(3x)-5(2)+10x[/tex]
[tex]-15x-10+10x[/tex]
Combine like terms
[tex]-5x-10[/tex]
Let
a ----> the missing term with coefficient x in Gregory's expression
b ----> the missing constant term in Gregory's expression
so
[tex]-12-4x+ax+b[/tex]
equate Gregory's expression to Felicia's expression
[tex]-12-4x+ax+b=-5x-10[/tex]
so
[tex]-12+b=-10[/tex] ----->[tex]b=2[/tex]
[tex]-4x+ax=-5x[/tex] ------> [tex]a=-1[/tex]
so
Gregory's expression is
[tex]-12-4x+2-x[/tex]
therefore
The missing terms are 2 and -x
Use the quadratic formula to solve x2 - 5x - 2 = 0.
Answer:
x=-0.37 or 5.37
Step-by-step explanation:
The quadratic formula is;
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
The expression to be solved is
[tex] {x}^{2} - 5x - 2 = 0[/tex]
Comparing this to the general form of the quadratic equation,
[tex] a{x}^{2} + bx + c = 0 [/tex]
a=1, b=-5 and c =-2.
We substitute these values into the quadratic formula
[tex] \implies x = \frac{ - ( - 5)\pm \sqrt{ { (- 5)}^{2} - 4(1)( - 2)} }{2(1)} [/tex]
Simplifying we obtain,
[tex] x = \frac{ 5\pm \sqrt{25 + 8}}{2} [/tex]
[tex] \implies x = \frac{ 5\pm \sqrt{28}}{2} [/tex]
[tex] \implies x = \frac{5 + 2\sqrt{7} }{2}or \frac{5 - 2 \sqrt{7} }{2} [/tex]
[tex]\implies x = \frac{5}{2} + \sqrt{7} or \frac{5 }{2} - \sqrt{7} [/tex]
x=5.37 or -0.37
The solutions to the quadratic equation x² - 5x - 2 = 0 are:
x = (5 + √33) / 2
x = (5 - √33) / 2
To solve the quadratic equation x² - 5x - 2 = 0 using the quadratic formula, we can use the formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a, b, and c represent the coefficients of the quadratic equation.
For the equation x² - 5x - 2 = 0, we can identify the values of a, b, and c:
a = 1
b = -5
c = -2
Substituting these values into the quadratic formula, we have:
x = (-(-5) ± √((-5)² - 4 × 1 × (-2))) / (2 × 1)
Simplifying:
x = (5 ± √(25 + 8)) / 2
x = (5 ± √33) / 2
Therefore, the solutions to the quadratic equation x² - 5x - 2 = 0 are:
x = (5 + √33) / 2
x = (5 - √33) / 2
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(9)/(16) x^(2)+7.5x=-25
Answer:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Exact Form:
x= −20/3
Decimal Form:
x= −6.66...
Mixed Number Form:
x= −6 2/3
Step-by-step explanation:
Trapezoid ABCD and trapezoid JKLM are similar. What side corresponds to side BC? Side LM Side KL Side JK Side KJ
Answer: JK
Step-by-step explanation:
Four CDs and 4 DVDs cost $164. The cost of the 4 CDs is half the cost of the
4 DVDs. What is the cost of each CD?
Answer:
$13.67
Step-by-step explanation:
Let's say that CD= c and DVDs= d. Four CDs and 4 DVDs cost $164, so the equation will be:
i. 4c + 4d= 164
The cost of the 4 CDs is half the cost of the 4 DVDs, to put into an equation it will be:
ii. 4c= 0.5(4d)
4c= 2d
d= 2c
Then we can substitute the second equation (ii) into the first equation (i). The calculation will be:
4c + 4d= 164
4c + 4(2c)= 164
4c+ 8c= 164
12c= 164
c=13.67
The cost for each CD is $13.67
5. Higher Order Thinking Maria has two
$20 bills, three $5 bills, and four $1 bills.
What other bill or bills does she need to
buy a present that costs $69?
Answer:
one $10 bill
Step-by-step explanation:
First you have to add them all together then subtract the sum by $69. That's how you get the answer.
Which statement is true about the factorization of 30x^2 + 40xy + 51y^2
The factorization of 30x^2 + 40xy + 51y^2 over the integers appears not to be possible due to the coefficients and a discriminant that is unlikely to be a perfect square. Advanced methods may be needed to factorize it if at all possible.
Explanation:The factorization of the expression 30x^2 + 40xy + 51y^2 is a task in algebra, which involves breaking down the given quadratic expression into products of its factors. However, this specific expression does not factorize neatly over the integers. When factoring, one would typically look for two binomials that multiply to the quadratic expression, but in this case, due to the coefficients and the lack of a clear common factor or a pattern that matches a known factoring formula, it is likely that the quadratic expression cannot be factored over the rational numbers without resorting to more advanced techniques or numerical methods. To completely verify this, you would use the quadratic formula to find the roots of the corresponding quadratic equation and see if they are rational numbers. If they are not, then exact factoring over the rationals is impossible.
Remember, for a quadratic expression ax^2+bx+c to be factorizable over the rationals, the discriminant, which is b^2-4ac, must be a perfect square. In the case of 30x^2 + 40xy + 51y^2, calculating the discriminant may help determine the factorizability of the expression. If the discriminant is not a perfect square, the expression cannot be factored into rational factors.
What’s the remainder of 84 divided by 25
Answer:
remainder is 9
Step-by-step explanation:
remainder of 84 divided by 25multiples of 25 are:
25 , 50 , 75
84-75 = 9
remainder is 9
Answer:
The remainder is 9
Step-by-step explanation:
Step 1: Find the remainder
84/25
25 goes into 84 3 times.
84 - 3(25)
84 - 75
9
Answer: The remainder is 9
Annie is working furiously to knit scarves and beanies for a craft fair next weekend. Yesterday she completed 3 scarves and 2 beanies, using a total of 22 meters of yarn. The day before, she used 10 meters to knit 1 scarf and 2 beanies. Assuming Annie is using the same pattern and type of yarn for each scarf and beanie, how much yarn does each project require?
Annie uses 6 meters of yarn for each scarf and 2 meters for each beanie, based on creating a system of equations from the given data and solving it.
Explanation:The student is asking to solve a system of equations to find out how much yarn is required for each scarf and beanie that Annie is knitting. To determine the amount of yarn needed for each project, we will use the information given for two separate days. On the first day, 3 scarves and 2 beanies used a total of 22 meters of yarn. On the second day, 1 scarf and 2 beanies used a total of 10 meters of yarn. Let's denote the amount of yarn needed for a scarf by 'S' and for a beanie by 'B'.
We can set up the following system of equations:
3S + 2B = 22 (from the first day's work)1S + 2B = 10 (from the second day's work)Subtract the second equation from the first to eliminate 'B' and solve for 'S':
(3S + 2B) - (1S + 2B) = 22 - 102S = 12S = 6 metersNow, we can substitute 'S' back into the second equation to solve for 'B':
1(6) + 2B = 106 + 2B = 102B = 4B = 2 metersTherefore, each scarf requires 6 meters of yarn and each beanie requires 2 meters of yarn.
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144 oz= lb huhuhuhu
Answer:9
Step-by-step explanation:
Answer:
9 lb
Step-by-step explanation:
pretty sure if not then sorry
Line v has a slope of -5/2
Line w is parallel to line v. What is the slope of line w?
Simplify your answer and write it as a proper fraction, improper fraction, or integer,
Answer:
-5/2
Step-by-step explanation:
Since they are both parallel they have the same rate of change. this means they have the same slope
Final answer:
Since line w is parallel to line v, which has a slope of -5/2, the slope of line w is also -5/2.
Explanation:
When two lines are parallel, they have the same slope. In this case, the slope of line w will be the same as the slope of line v.
Therefore, the slope of line w is -5/2.
The question asks about the slope of two parallel lines. By definition, parallel lines have the same slope. Given that line v has a slope of -5/2, and line w is parallel to line v, the slope of line w must also be -5/2. Therefore, line w, being parallel to line v, has a slope of -5/2.
On a field trip there are 18 chaperones supervising 81 children. If the children are broken into groups how many adults are needed for a group of 27 kids
Answer:
6
Step-by-step explanation:
you first divide 81 by 18 and get 4.5, that is the number of children per adult.
next you'll divide 27 by 4.5 and 6.
that's the answer.
Final answer:
With an initially provided ratio of 18 adults for 81 children, the simplified ratio is 1 adult for every 4.5 children. Hence, for a group of 27 kids, 6 adults are needed to maintain the same supervision ratio.
Explanation:
To determine the number of adults needed for a group of 27 kids on a field trip when there are 18 chaperones supervising 81 children, we can calculate the adult-to-child ratio. We start with the given total ratio of 18 adults for 81 children. This simplifies to 1 adult for every 4.5 children, as 81 divided by 18 equals 4.5. Therefore, for a group of 27 children, we divide 27 by 4.5 to find the number of adults needed.
27 kids
/ 4.5 kids/adult = 6 adults
Thus, 6 adults are needed for a group of 27 kids to maintain the same supervision ratio.
What is the least common denominator of the equation StartFraction 2 Over 9 EndFraction x + two-thirds x = 7?
3
Answer:
9 is the least common denominator for the given equationStep-by-step explanation:
Given equation is StartFraction 2 Over 9 EndFraction x + two-thirds x = 7.
It can be written as [tex]\frac{2}{9}x+\frac{2}{3}x=7[/tex]
To find the least common denominator for the given equation :That is to find the Least common Multiple of the denominators.
[tex]\frac{2}{9}x+\frac{2}{3}x=7[/tex]
[tex]\frac{2x+2x(3)}{9}=7[/tex] ( here LCM of 9 and 3 is 9 so we take 9 as LCM )
Therefore 9 is the least common denominator for the given equationAnswer: the answer is 9
Step-by-step explanation: I took the test and its right
if f(x)=2(x)^2+5sqrt(x+2) complete the following statement f(2)=
Solution:
Given that,
[tex]f(x) = 2x^2 + 5\sqrt{x + 2}[/tex]
We have to find f(2)
To find f(2), plug in x = 2 in given f(x) and solve to get the answer
Plug in x = 2 in f(x)
[tex]f(2) = 2(2)^2 + 5 \sqrt{2+2}\\\\f(2) = 2 \times 4 + 5\sqrt{4}\\\\Simplify\\\\f(2) = 8 + 5 \times 2\\\\f(2) = 8 + 10\\\\f(2) = 18[/tex]
Thus the value of f(2) is 18
what is the degree of 23x4
Answer:
92
Step-by-step explanation:
Answer:
92
Step-by-step explanation:
23 x 4 = 92
What are the first 5 common multiples of 4 and 14?
Answer:
28, 56, 84, 112, and 140
Step-by-step explanation:
4: 28,32,36,40,44,48,52,56,60,64,68,72,76,80,84, ...
14: 28,42,56,70,84,98,112,126,140
b) Find the median queuing time
please help!!!!
Answer:
11 minutes.
Step-by-step explanation:
To find the median queing time from the cumulative frequency curve, we find
[tex] \frac{1}{2} \sum \: f[/tex]
and trace it on the cumulative frequency curve.
From the graph, that total frequency is 100.
Half of this 50.
We trace the 50th item.
First locate 50 on the vertical axis and trace to the horizontal axis.
This corresponds to 11.
Note that each box is 0.5 units on the queing time axis.
(8y3 – y + 7) – (6y3 + 3y - 3)
Answer:
2 • (y3 - 2y + 5)
Step-by-step explanation:
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