Final answer:
To find the value of 10 times the big number minus 6 times the small number, we need to solve a system of equations. The solution to the system is x = 2 and y = 11, so the value of 10y - 6x is 98.
Explanation:
To find the value of 10 times the big number minus 6 times the small number, we need to solve the system of equations:
4x + 3y = 41 (equation 1)
2x + y = 15 (equation 2)
We can first solve equation 2 for y by subtracting 2x from both sides: y = 15 - 2x. Now we can substitute this value of y into equation 1:
4x + 3(15 - 2x) = 41
Simplifying, we get: 4x + 45 - 6x = 41
Combining like terms, we have: -2x + 45 = 41
Subtracting 45 from both sides, we get: -2x = -4
Dividing both sides by -2, we get: x = 2
Now we can substitute this value of x back into equation 2 to solve for y:
2(2) + y = 15
Simplifying, we get: 4 + y = 15
Subtracting 4 from both sides, we get: y = 11
Finally, we can calculate 10 times the big number minus 6 times the small number:
10y - 6x = 10(11) - 6(2) = 110 - 12 = 98
What is the multiple zero and multiplicity of f(x) = x3 − 8x2 + 16x?
multiple zero = −4; multiplicity = 2
multiple zero = 2; multiplicity = 4
multiple zero = 4; multiplicity = 2
multiple zero = 2; multiplicity = −4
Answer:
B
Step-by-step explanation:
If you divide x so only x and a number remains, you will get B.
[tex]f(x) = x^{3} - 8x^{2} + 16x[/tex] has multiple zero = 4; multiplicity = 2.
What is multiple zero and multiplicity?" A multiple zero has the multiplicity which represents the number of times linear factor of multiple zero occur in the polynomial .Zero of the polynomial is associated with multiple zero."
According to the question,
Given,
[tex]f(x) = x^{3} - 8x^{2} + 16x[/tex]
Simplify the given polynomial to get the multiple zero and multiplicity,
[tex]f(x) = x^{3} - 4x^{2}- 4x^{2} + 16x[/tex]
[tex]\implies x^{2} (x-4) -4x(x-4)=0\\\\\implies (x^{2} -4x)(x-4) =0\\\\\\\implies (x) (x-4)(x-4)=0\\\\\implies x(x-4)^{2} =0[/tex]
Zero is associated with x =4.
(x-4) occur twice.
Hence, multiple zero = 4 and multiplicity = 2 of the given function.
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There are 6 quarters in a jar .jill adds 2 quarters everyday which linear equation represents the total amount of quarters in the jar after x days
Evaluate the expression for x = 3 and y = 6.
5(x2 + y) + y2
pleaseeeeeeeeee help meeeeeeee
What property of equality is used to transform equation 1 to equation 2?
Equation 1: 35 = 5x
Equation 2: 7 = x
addition Property of Equality
subtraction Property of Equality
multiplication Property of Equality
division Property of Equality
Final answer:
The division Property of Equality is used to transform Equation 1 (35 = 5x) into Equation 2 (7 = x) by dividing both sides of the equation by 5.
Explanation:
The property of equality used to transform Equation 1 (35 = 5x) to Equation 2 (7 = x) is the division Property of Equality.
This property states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal. To get from Equation 1 to Equation 2, both sides of Equation 1 are divided by 5.
Division is similar to multiplication in that it follows the same rules for signs and equality. When dividing both sides by the same number, the numerator and denominator cancel out if they are the same, leaving a value of 1.
For instance, dividing 5x by 5 will lead to x, and dividing 35 by 5 will give 7, hence 7 = x, which is Equation 2.
1/4x+5/3x-4=2-1/12x what is the answer ??????
foil (ab - 9)(ab + 8)
Step 1: (ab-9)(ab+8)
Step 2: ab x ab +8 x ab -9 x ab -9 x 8
Step 3: ab2 +8ab-9ab-72=
Step 4: ab2 -ab-72
solved!!! that how you would solve it everything will continue as normal
Monica has saved $735 for a new guitar and lessons. her guitar costs $475, and guitar lessons are $25 per hour. determine how many hours of lessons she can afford.
What’s angle CR PQ and CQ?
CR = CP = 17
PQ = QR = 15
CQ = x^2 +15^2 = 17^2 = x^2 + 225 = 289
x^2 = 289-225 = 64, sqrt(64) = 8, CQ = 8
The cost for parking at a parking garage is $2.25 plus an additional $1.50 for each hour. What is the total cost to park for 5 hours?
The sum of three numbers is 45 one number is 10 more than the second number it is also twice the third number find the numbers
The numbers cannot be uniquely determined with the given information.
Explanation:Let's solve this problem step by step.
Let's assume the second number is 'x'. Since the first number is 10 more than the second number, then the first number can be represented as 'x + 10'.
Since the first number is also twice the third number, the first number can be represented as '2y', where 'y' is the third number.
Now, we can form an equation using the given information: x + (x + 10) + 2y = 45
Simplifying the equation, we get: 2x + 2y + 10 = 45
Further simplifying, we get: 2x + 2y = 35
Dividing both sides of the equation by 2, we get: x + y = 17.5
Now, we have two variables and one equation, which means we have an infinite number of possible solutions. We need more information to determine the actual values of x and y.
Therefore, the numbers cannot be uniquely determined with the given information.
Forty-eight pounds of sand are used to fill 12 bags.
Miranda uses the five-step problem-solving plan. After completing the Solve step, how many pounds of sand should she find each bag will hold?
If she steals 100 buys 70 worth of stuff owner gives u 30 back how much did owner lose
What is the measure of angle C? 25° 30° 60° 75°
Answer:
75°
Step-by-step explanation:
HELP PLEASE!
Which equation can be used to find the solution of (1/2)^2x = 32 ?
a) 1/2x=5
b) −2x=5
c) 2x = 5
d) −1/2x=5
The answer is b, not c. I just completed the quiz and got the question wrong by answering c. :/
what is the slope-intercept equation of a line that has a slope of -2 and a y-intercept of (0,3)
PLZZZZZZZZZZZZ HELP ME!!!!!!!!!!!!
Use the order of operations to simplify this expression.
4 + 0.8 × 1.5 - 3
4.2
3.3
2.2
7.2
A squirrel climbs 15 feet up a tree. He then runs 8.26 feet down the tree. How much further does the squirrel need to go before reaching the ground?
A)7.36 feet
B)7.26 feet
C)6.74 feet
D)8.11 feet
Answer:
C
Step-by-step explanation:
What is the measure of angle 1
Jimmy had $4.52 to spend. He found something he wanted to buy for $6.21. How much would he need to borrow from his friend to make his purchase?
Answer:
$1.69
Step-by-step explanation:
If he wants to buy something for $6.21 but he only has $4.52, we need to find out the difference between $6.21 and $4.52.
For that, we have to subtract the smallest number from the biggest, that is
$6.21 - $4.52 = $1.69
Therefore, he would need to borrow $1.69 from his friend.
Helppppp plzz quickkk
he hiked 4 km east in 45 minutes
45 minutes = 3/4 of an hour
4 /.75 = 5.33
so the answer would be D. 5.3 km per hour east
BRAINIEST ANSWER! PLEASE! ABOUT AREA AND PERIMETER!
each little square = 1 square inch
the design takes up 21 squares so area is 21 square inches
the perimeter = 6 +2+3+3+3+5 = 22 inches
The first side of a triangle is 2 cm longer than the second side. the third side is 5 cm shorter than twice the second side. the perimeter is 49 cm. find the length of each side.
The sides of the triangles will be 15 cm, 13 cm and 21 cm.
What is a triangle?A closed polygon with three sides, angles and vertex is called triangle.
Given that, the first side of a triangle is 2 cm longer than the second side. the third side is 5 cm shorter than twice the second side and the perimeter is 49 cm.
Let the second side be x, then the sides will be,
x+2, x and 2x-5
∵ Perimeter = 49 cm
∴ x + 2 + x + 2x - 5 = 49
4x-3 = 49
4x = 52
x = 13
Therefore, side will be =
Side 1 = 15 cm
Side 2 = 13 cm
Side 3 = 21 cm
Hence, the sides of the triangles will be 15 cm, 13 cm and 21 cm.
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A box with a square base and no top is to be made from a square piece of carboard by cutting 3 in. squares from each corner and folding up the sides. the box is to hold 9075 in3. how big a piece of cardboard is needed?
Final answer:
To create a box with a volume of 9075 in3, a 61 in. by 61 in. piece of cardboard is needed after cutting out 3 in. squares from each corner and folding up the sides.
Explanation:
To determine the size of the cardboard needed to construct a box with a volume of 9075 in3 when 3 in. squares are cut from each corner and the sides are folded up, we first need to express the volume of the box in terms of the dimensions of the cardboard. Let x represent the length of one side of the original square piece of cardboard. After cutting out 3 in. squares from each corner, the length and width of the base of the box will be x - 6 inches (since 3 inches are removed from each side), and the height will be 3 inches (the size of the squares cut from the corners).
The volume V of the box can be expressed as V = (x - 6)(x - 6)(3). Given that V = 9075 in3, we can set up the equation 9075 = (x - 6)2 × 3. Solving for x will give us the size of the original cardboard piece.
To solve the equation, divide both sides by 3 to isolate (x - 6)2, which gives 3025 = (x - 6)2. Taking the square root of both sides gives x - 6 = 55, so x = 61. Therefore, a 61 in. by 61 in. piece of cardboard is needed to construct the box.
Amanda was 48 inches She grew n inches last year and is now 56.5 inches write an expression that represents the number of inches Amanda grew
True or false: there are infinitely many bisectors, but only one perpendicular bisector for any segment.
Find the missing angle.
Find the length of the hypotenuse:
to find the hypotenuse on the given triangle
divide the given height ( 3sqrt(2) ) by the sin of the given angle (45)
3sqrt(2) / sin 45 = 6
answer is B. 6
A segment with endpoint a(3,1) and b(-1,1) is rotated 90° about the origin.what are the coordinates of a' and b' ? (geometry 10 a lesson 3 unit 5,if you know the answers to this whole practice pls give them to me pls and tysm)
An internet service provider is implementing a new program based on the number of connected devices in each household. Currently, customers are charged a flat rate of $175 per month. The new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network. Find and graph the number of devices, x, for which the cost of the new plan is less than the current plan.
The current rate is simply equal to $175 per month, let us call this as rate A:
A = 175
The new rate is $94 plus $4.50 per devices, let us call this as rate B:
B = 94 + 4.50 x
where x is the number of devices connected to the network
The inequality equation for us to find x which the new plan is less than current plan is:
94 + 4.50 x < 175
Solving for x:
4.50 x < 81
x < 18
So the number of devices must be less than 18.
- From the graph, we can actually see that the new rate intersects the current rate at number of devices equal to 18. So it should really be below 18 devices.
The number of devices connected should be less than 18 (1 to 17 devices) so that the new charges will be less than the old charge.
Given:
The old monthly charge for internet service per household is $175.
The new charges include a fixed pay of $94 plus $4.50 per connected device.
Let x be the number of connected devices.
So, the new charges can be written mathematically as,
[tex]C=94+4.5x[/tex]
Now, the new charge should be less than the old charge. This condition can be written as,
[tex]C=94+4.5x<175\\4.5x<81\\x<18[/tex]
So, the number of devices connected should be less than 18 (1 to 17 devices) so that the new charges will be less than the old charge.
See the attached graph.
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