Let the number of toys Teddy has on Monday = x
On Monday Harry has = 75% of x or 0.75x
As given, On Tuesday, after Harry acquired 32 more toys and Teddy acquired 15% more than he had on Monday, Harry had as many toys as Teddy did.
Toys Teddy has = [tex]x+\frac{15x}{100}[/tex]
=[tex]\frac{100x+15x}{100} =\frac{115x}{100}[/tex] = 1.15x .... (i)
Toys Harry has = 0.75x+32 ...... (ii)
As both have equal toys now, so equation (i) equals equation (ii)
[tex]1.15x=0.75x+32[/tex]
[tex]1.15x-0.75x=32[/tex]
[tex]0.4x=32[/tex]
x=80
Hence, Teddy had 80 toys on Monday.
And Harry had 75% of 80 toys = 60 toys on Monday.
what type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue a.find a mixture that will make the same shade of green but a smaller amount
Answer:
Step-by-step explanation:
We are given that a shade of green is prepared using 2 cups of yellow and 3.5 cups of blue.
We want to make the same shade of green, but lesser quantity. We can assume a smaller value for either of the yellow or the blue colors, and find the corresponding value of the other to figure out the answer.
Let us assume that 1 cup of yellow is mixed with x cups of blue to prepare the same shade of the green. Now we can set up the ratios as shown below:
[tex]\frac{1}{x}=\frac{2}{3.5}\\2x=3.5\\x=1.75[/tex]
Therefore, 1 cup of yellow and 1.75 cups of blue color will also make the same shade of green
What does pathagery and theorem solve for? Please help!!!
Answer:
The Pythagorean theorem shows that one leg squared plus the other leg squared is equal to the hypotenuse squared
Step-by-step explanation:
Solve for x and y
3x+y=6
x+y=2
3x+y=6
x+y=2
rewrite x + y = 2 as y = 2-x
Replace Y in the first equation with the re-written equation:
3x + 2-x = 6
Solve for x:
3x + 2-x = 6
subtract x:
2x +2 = 6
Subtract 2 from each side:
2x = 4
Divide both sides by 2:
x = 2
Now you have x, replace x with 2 in the second equation and solve for y:
x + y = 2
2 + y = 2
Subtract y 2 from each side:
y = 0
The answer is: X = 2, Y = 0
50 POINTS PLEASE HELP FAST DUE TODAY: Explain why any of the four operations (+ - × ÷) placed between the two terms 5 and -3√8 will result in an irrational number.
Answer:
Because -3-/8 itself is an irrational number. No matter the operation it wil always be irrational
Step-by-step explanation:
x square plus 3x minus 18 equal 0 by using quadratic formula
Answer:
Step-by-step explanation:
x^2 + 3x - 18 = 0
(x+6)(x-3)=0
x=-6 x=3
i had this on my book so i just wanted to help.
Final answer:
The quadratic equation x^2 + 3x - 18 = 0 can be solved using the quadratic formula, resulting in two solutions, x = 3 and x = -6.
Explanation:
To solve the quadratic equation x^2 + 3x - 18 = 0 using the quadratic formula, we must first identify the coefficients a, b, and c in the standard form ax2 + bx + c = 0. In our equation, a = 1, b = 3, and c = -18. Substituting these values into the quadratic formula gives us:
x = [-b ± √(b^2 - 4ac)] / (2a)
By substituting the values we have:
x = [-(3) ± √((3)^2 - 4(1)(-18))] / (2(1))
Which simplifies to:
x = [-3 ± √(9 + 72)] / 2
x = [-3 ± √(81)] / 2
x = [-3 ± 9] / 2
Therefore, we have two possible solutions for x:
x = (-3 + 9) / 2 = 3
x = (-3 - 9) / 2 = -6
So, the solutions to the equation x2 + 3x - 18 = 0 are x = 3 and x = -6.
Which question shows the quadratic fomula used correctly to solve 7x^2=9+x for x
Answer:
x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac} }{2a}[/tex]
Step-by-step explanation:
We have
7x²=9+x
Subtracting x from both sides, we get
7x²-x=9+x-x
Cancelling out +x and -x from the right side, we get
7x²-x=9
Subtracting 9 from both sides, we get
7x²-x-9=9-9
Cancelling out 9 and -9 from the right side, we have
7x²-x-9 = 0
The above equation is in the form ax²+bx+c=0 where upon comparing we get a= 7 , b = -1 and c= -9
We can solve for x using the below quadratic formula:-
x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac} }{2a}[/tex]
Upon solving we'll get two values for x, one positive an the other negative.
Which data set matches the box and whisker plot? A. 12.5, 15, 17, 23, 23, 24, 26, 29, 31, 32, 33 B. 11, 13, 16, 19, 23, 23, 24, 29, 31, 33, 34 C. 11, 12, 15, 18, 24, 24, 25, 27, 30, 32, 34 D. 10.5, 12, 15, 17, 23, 23, 24, 26, 29, 34
Answer:
c
Step-by-step explanation:
4,839 sq. yd. 8 sq. ft.139 sq. in.+ 7 sq. ft. 124 sq. in
The Mathematics problem involves adding areas in different units and converting them appropriately. After conversion and addition, the correct answer from the options provided is 1 acre, 7 square feet, and 119 square inches: (a) 1a 7 sqft 119 sqin.
The subject of this question is Mathematics, specifically dealing with area measurements in different units and their conversions. The student needs to solve an addition problem that involves square yards, square feet, and square inches. To solve this problem, we must first understand that there are 9 square feet in one square yard, and we use this knowledge to convert all measurements to the same unit before summing them up.
To answer the student's question, we must add the areas given in the problem:
4,839 sq yd 8 sq ft 139 sq in7 sq ft 124 sq inFirst, we convert square yards to square feet using the conversion 1 sq yd = 9 sq ft:
4,839 sq yd = 4,839 × 9 sq ft = 43,551 sq ft
Now we add the square feet:
43,551 sq ft + 8 sq ft + 7 sq ft = 43,566 sq ft
Lastly, we add the square inches:
139 sq in + 124 sq in = 263 sq in
Since there are 144 square inches in one square foot, we must convert the excess square inches into square feet and square inches:
263 sq in = 1 sq ft (144 sq in) + 119 sq in
Adding the converted square inches to the total square feet:
43,566 sq ft + 1 sq ft = 43,567 sq ft 119 sq in
Next, we convert the total square feet to acres, understanding that 1 acre = 4,840 sq yd or approximately = 43,560 sq ft.
43,567 sq ft ÷ 43,560 sq ft per acre ≈ 1 acre 7 sq ft 119 sq in
Thus, the correct answer is (a) 1a 7 sqft 119 sqin.
Complete question is here:
Solve the following problem 4,839 sq yd 8 sq ft 139 sq in + 7 sq ft 124 sq in Select one of four
a)1a 7 sqft 119 sqin
b)4a 10 sqft 145 sqin
c)3a B sqft 130 sqin
d)2a 9 sqft 150 sqin
The question asks for the addition of different area units, which requires unit conversion. Square yards are converted to square feet and then to square inches, ensuring all areas are in the same units before adding them together.
Explanation:The question involves adding areas measured in different units (square yards, square feet, and square inches) and converting between these units. To perform the calculation correctly, we need to convert all areas to the same unit. One square yard is equivalent to 9 square feet, and one square foot is equivalent to 144 square inches. Thus, to add the areas given in the question, we should first convert the 8 sq. ft. 139 sq. in. to sq. in. by multiplying 8 by 144 and then adding 139. After that, we would need to convert this total area into square yards if required. For the second part, we convert 7 sq. ft. 124 sq. in. to square inches similarly. Once both areas are in square inches, they can be added together. Additionally, it's important to remember that there is no direct conversion between square inches and square yards, so a two-step conversion is needed via square feet.
9ab over 27b = simplify
9ab
___
27b
Answer:
1A/3 OR 1/3A
Step-by-step explanation:
PLEASE HELP QUICK!!!!!!!!!!!!!!! 100 POINTS Please explain how to do this step by step. I'm super confused.
Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown:
A support structure is shown in which a right triangle PQR is formed with the right angle at Q. The length of PQ is shown as 14 feet, and the length of QR is shown as 6 feet..
Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer, stating the theorem you used. Show all your work. (5 points)
Part B: The length of rod PR is adjusted to 16 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work. (5 points)
Answer:
A: 15.23 ft, B: 7.75 ft
Step-by-step explanation:
A:
√(14² + 6²)
√(196 + 36)
√232 = 15.23
B:
√(16² - 14²)
√(256 - 196)
√60 = 7.75
NOTES:
Since Q is a right angle then PQ and QR are the legs and PR is the hypotenuse. Use the Pythagorean Theorem to solve.
********************************************************************************
Part A Answer: PR = 15.23
Step-by-step explanation:
PQ² + QR² = PR²
6² + 14² = PR²
36 + 196 = PR²
232 = PR²
15.23 = PR
************************************************************************************
Part B Answer: PR = 7.75
Step-by-step explanation:
PQ² + QR² = PR²
PQ² + 14² = 16²
PQ² + 196 = 256
PQ² = 60
PQ = 7.75
Find the circumference of each circle. Use 3.14 for the value of π . Round answer to the nearest tenth.
Answer:
[tex]C=9.4\pi[/tex] meters
Step-by-step explanation:
Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex].
We start by substituting 4.7m for r in the second circumference formula.
[tex]C=2\pi r\\C=2\pi (4.7)\\C=9.4\pi [/tex]. We input this value of r into the area formula.
Answer:
its C.
Step-by-step explanation:
Find dy, dx if f(x) = (x + 8)3x. 3xln(x + 8) the product of the quantity 3 times the natural log of the quantity x plus 8 plus 3 times x divided by the quantity x plus 8, and the quantity x plus 8 raised to the 3x power 3 times the natural log of the quantity x plus 8 plus 3 times x divided by the quantity x plus 8 3x(x + 8)(3x − 1)
Answer:
[tex]\displaystyle \frac{dy}{dx} = 3(x + 8)^{3x} \bigg[ \ln (x+ 8) + \frac{x}{x + 8} \bigg][/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x) = (x + 8)^{3x}[/tex]
Step 2: Differentiate
Exponential Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \frac{d}{dx} \bigg[ 3x \ln (x + 8) \bigg][/tex]Derivative Rule [Product Rule]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ \frac{d}{dx}(3x) \ln (x + 8) + 3x \frac{d}{dx}[ \ln (x + 8)] \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \frac{d}{dx}(x) \ln (x + 8) + 3x \frac{d}{dx}[ \ln (x + 8)] \bigg][/tex]Derivative Rule [Basic Power Rule]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \ln (x + 8) + 3x \frac{d}{dx}[ \ln (x + 8)] \bigg][/tex]Logarithmic Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \ln (x + 8) + \frac{3x}{x + 8} \frac{d}{dx} (x + 8) \bigg][/tex]Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \ln (x + 8) + \frac{3x}{x + 8} \Big[ \frac{d}{dx}(x) + \frac{d}{dx}(8) \Big] \bigg][/tex]Derivative Rule [Basic Power Rule]: [tex]\displaystyle \frac{dy}{dx} = (x + 8)^{3x} \bigg[ 3 \ln (x + 8) + \frac{3x}{x + 8} \bigg][/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = 3(x + 8)^{3x} \bigg[ \ln (x+ 8) + \frac{x}{x + 8} \bigg][/tex]∴ we have found the derivative of the given function.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Which equations contain the point (0.5, –6.75). Check all that apply.
2x + 4y = –26
y = x – 7.5
2y = x + 13
y = 0.5x – 7
Answer:
(A) 2x + 4y = –26
(D) y = 0.5x – 7
The equations satisfying the points (0.5, –6.75) will be 2x + 4y = –26 and y = 0.5x – 7. The correct options are A and D.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given point is (0.5, –6.75). Check whether all the equations satisfy the point or not.
A) 2x + 4y = –26
2 x 0.5 + 4 x -6.75 = -26
1 - 27 = -26
-26 = -26
Satisfying
B) y = x – 7.5
-6.75 = 0.5 - 7.5
-6.75 ≠ -7
C) 2y = x + 13
2 x -6.75 = 0.5 + 13
-13.5 ≠ 13.5
y = 0.5x – 7
-6.75 = 0.5 x 0.5 -7
-6.75 = -6.
Satisfying.
Therefore, the equations satisfying the points (0.5, –6.75) will be 2x + 4y = –26 and y = 0.5x – 7. The correct options are A and D.
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Triangle ABC is dilated by a scale factor of 4 to form triangle A′B′C′.
The coordinates of vertex A′ are?
The coordinates of vertex B′ are?
The coordinates of vertex C′ are?
Answer:
The correct answers would be
vertex A' (-8,4)
vertex B' (-12,12)
vertex C' (-4,12)
Step-by-step explanation:
I'm not 100% sure but I took this test a couple days ago and didn't do terribly:).
Which of these ordered pairs could you remove to make this relation a function? {(-2,1), (-1, -5), (-1,5), (0, -7), (2, 1)}
A. (-2, 1)
B. (-1, 5)
C. (0, -7)
D. (2, 1)
Your answer would be B. (-1,5).
In order for the order pairs to be a function. All of the x coordinates must be different from each other, they can't be the same. There can't be any repeats of the x coordinates. But for the y coordinates, it's okay for them to be the same. The reason why you would eliminate (-1,5) is because there are 2 -1 x coordinates, and that would not make the ordered pairs a function. When you remove them, none of the x coordinates are the same anymore, so it would now be a function.
Hope this helps out :)
Answer:
B. (-1,5).Step-by-step explanation:
Which of these ordered pairs could you remove to make this relation a function? {(-2,1), (-1, -5), (-1,5), (0, -7), (2, 1)}
B. (-1, 5)
to make 5 dinner rolls 1/3. How much flour is need to make 1 diner roll
A construction worker has a rope that is 6 m long. She needs to cut it into pieces that are each 3/7 m long. How many such pieces can she cut without having any rope leftover?
Answer:
14 pieces
Step-by-step explanation:
We will divide 6 m into 3/7 m pieces
6 ÷ 3/7
Use copy dot flip
6 * 7/3 =
42/3
14
She will have 14 pieces
Determine ‘a’ and ‘d’ for t7= 3 + 5x and t11= 3 + 23x (formula is tn= a + (n-1) x d)
(25 POINTS!!)
Final answer:
To determine 'a' and 'd' for tn = a + (n-1)x, substitute the values of 'n' and 't' into the equations and solve the system of equations.
Explanation:
To determine 'a' and 'd' for tn = a + (n-1)x, we need to find the values of 'a' and 'd' that satisfy both t7 = 3 + 5x and t11 = 3 + 23x.
Step 1: Set up two equations
t7 = 3 + 5x
t11 = 3 + 23x
Step 2: Use the formula tn = a + (n-1)x to substitute the values of 'n' and 't' in the equations.
a + 6d = 3 + 5x (equation 1)
a + 10d = 3 + 23x (equation 2)
Step 3: Solve the system of equations.
Subtract equation 1 from equation 2: (a + 10d) - (a + 6d) = (3 + 23x) - (3 + 5x)
Cancel out the 'a' terms and simplify the 'd' and 'x' terms: 4d = 18x
Divide both sides by 18: d = 4.5x
Substitute the value of 'd' in equation 1 to solve for 'a': a + 6(4.5x) = 3 + 5x
Expand and simplify the equation: a + 27x = 3 + 5x
Subtract 5x from both sides: a + 22x = 3
Subtract 22x from both sides: a = 3 - 22x
So, the values of 'a' and 'd' are a = 3 - 22x and d = 4.5x.
State whether each question below represents a proportional relationship. How can you tell?
a. y= x+ 2.3
b. y=6\13x
c. 7-y=2x
Among the given equations, only 'y = 6/13x' shows a proportional relationship because the ratio between x and y remains constant. The other two equations-'y = x + 2.3' and '7 - y = 2x' are not showing proportional relationships because the ratio between the variables doesn't remain constant.
Explanation:A proportional relationship is one where the ratio between two variables remains constant. This relationship can be represented by the equation y = kx, where k is the constant of proportionality.
a) The equation y = x + 2.3 is not a proportional relationship because it involves an added constant. If x is zero, y is not zero, thus it's not proportional.
b) The equation y = 6/13x is a proportional relationship, because there is a direct proportion between x and y. If x is multiplied by a certain factor, y will be multiplied by the same factor, thus maintaining the ratio.
c) The equation 7 - y = 2x rearranges to y = 7 - 2x, which is not a proportional relationship. Again, if x is zero, y is not zero, thus it's not proportional.
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a cylinder has diameter of 10 cm and a height of 20 cm what is the volume of the cylinder
Answer:
V = 1570.796327 cm^3
Step-by-step explanation:
V= pi *r^2h
diameter = 2 * radius
10 = 2r
r = 5
substitute in what we know
V = pi *( 5^2) * 20
V = pi * 25 * 20
V = pi *500
V = 1570.796327 cm^3
Answer:
Step-by-step explanation:
Surface Area of circle on top of cylinder:
= πr²
= π(d÷2)²
= π(10÷2)²
= π(5)²
= 25π
Volume of Cylinder:
= 25π × h
= 25π × 20
= 500π
= 1570.8 cm³ (to 1 decimal place)
y = 15x
y = 25 + 12.5x
Substitute y = 15x to the equation y = 25 + 12.5x:
15x = 25 + 12.5x subtract 12.5x from both sides
2.5x = 25 divide both sides by 2.5
x = 10
Substitute the value of x to the equation y = 15x:
y = (15)(10)
y = 150
Answer: x = 10 and y = 150Janelle babysat for 6 hours at an hourly rate.After she got paid she spent $12 at Walmart. She came home with $36. How much money did she make per hour?
By adding Janelle's spending to what she came home with and dividing by the hours worked, we find that she earned $8 per hour babysitting.
To find out how much Janelle made per hour babysitting, we need to add the money she spent at Walmart to the money she came home with.
This gives us the total amount she earned.
Since she spent $12 at Walmart and came home with $36, we add these two amounts together to get $48.
Janelle babysat for 6 hours, so to find out her hourly wage, we divide the total amount she earned ($48) by the number of hours she worked (6 hours).
= $48 / 6 hours = $8 per hour
Thus, Janelle earned $8 per hour for her babysitting.
Solve for a. m=a/9-H
Answer:
9(m+H) = a
Step-by-step explanation:
m=a/9-H
The first step is to add H to each side.
m+H = a/9 -H+H
m+H = a/9
Now multiply both side by 9
9(m+H) = a/9*9
9(m+H) = a
A small airplane takes off from point A and continues to climb upward in a straight line, as shown in the diagram. What is the plane’s distance from point A when it reaches point C?
A. 6,900 feet
B. 7,000 feet
C. 11,636 feet
D. 12,600 feet
E. 13,400 feet
Answer:
The distance from A to C is 12600 ft
Step-by-step explanation:
We can use similar triangles to help us solve the problem.
5600 ft AC
------------- = --------------
5200 ft 5200 + 6500
5600 ft AC
------------- = --------------
5200 ft 11700
We can solve using cross products
11700* 5600 = AC *5200
65520000=5200 AC
Divide each side 5200
65520000/5200 = AC
12600 =AC
Answer:
12600
Step-by-step explanation:
equation is equal to .66...?
a)1/3
b)1/5
c)2/3
d)2/4
REBECA HAD 9/10 OF A YARDOF RIBBON. THEN SHE GAVE 7/20 OF A YARD OF FRIEND. HOW MUCH DOES SHE HAVE LEFT?
Answer:
She has 11/20 yds left
Step-by-step explanation:
We take what she had and subtract what she gave away
9/10 - 7/20
We need to get a common denominator of 20
9/10 *2/2 - 7/20
18/20 - 7/20
11/20
She has 11/20 yds left
Making sure I’m doing this write... please give a walkthrough explanation! :)
144= -12(x+5)
(I’m solving for x)
Start by distributing:
-12(x+5) = (-12 * x) + (-12 * 5) = -12x - 60
144 = -12x - 60
Add 60 to both sides to start isolating your variable:
204 = -12x
Solve for x by dividing both sides by -12:
x = -17
Step-by-step explanation:
multiply -12 with x and 5, after you get the answer. subtract 60 on the left and right, after getting 84 divide it by -12 and the final answer will be -7
the school fit 72 students onto 3 buses. find the unit rate for number of students per bus.
Can someone help me with my math
−36+x<8
Answer:
x<44
Step-by-step explanation:
Answer:
x<-28
Step-by-step explanation:
Y=-4x y=x^2-12 solve the system of equations
Answer:
(-6, 24) and (2, -8)
(-6, 24) and (2, -8) is the answer.
What's the easiest way to remedy a system of equations?
There are three strategies used to resolve structures of equations: graphing, substitution, and elimination. To solve a gadget via graphing, you honestly graph the given equations and locate the factor(s) in which they all intersect. The coordinate of this point will provide you with the values of the variables that you are fixing.
How do you remedy a gadget of equations without graphing?To remedy a machine of linear equations without graphing, you may use the substitution technique. This method works by way of solving one of the linear equations for one of the variables, then substituting this price for the same variable in the different linear equation and solving for the other variable.
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