Answer:
A = 8 and B = 6
Step-by-step explanation:
Since (B = A - 2), we can substitute (A - 2) in for the "B" variable in the first equation to isolate "A".
(A - 5)² + (B - 3)² = 18 -----> Original equation
(A - 5)² + ((A - 2) - 3)² = 18 -----> Plug in B = A - 2
(A - 5)² + (A - 5)² = 18 -----> Subtract
(A² - 10A + 25) + (A² - 10A + 25) = 18 -----> Expand parentheses
2A² - 20A + 50 = 18 ------> Add like terms
2A² - 20A + 32 = 0 -----> Subtract 18 from both sides
2(A² - 10A + 16) = 0 -----> Remove common factor
2(A - 2)(A - 8) = 0 -----> Factor within parentheses
A = 2 -----> Find A - 2 = 0
A = 8 -----> Find A - 8 = 0
Since "A" gave two possible values, we need to plug them into both equations to see which value gives reasonable "B" values.
When A = 2:
B = A - 2 -----> Original equation
B = 2 - 2 -----> Plug in A = 2
B = 0 -----> Subtract
(A - 5)² + (B - 3)² = 18 -----> Original equation
(2 - 5)² + (B - 3)² = 18 ------> Plug in A = 2
(-3)² + (B - 3)² = 18 -----> Subtract within first parentheses
9 + (B - 3)² = 18 -----> Square value within first parentheses
(B - 3)² = 9 -----> Subtract 9 from both sides
B - 3 = 3 -----> Take square root of both sides
B = 6 -----> Add 3 to both sides
When A = 8:
B = A - 2 -----> Original equation
B = 8 - 2 -----> Plug in A = 8
B = 6 -----> Subtract
(A - 5)² + (B - 3)² = 18 -----> Original equation
(8 - 5)² + (B - 3)² = 18 ------> Plug in A = 8
(3)² + (B - 3)² = 18 -----> Subtract within first parentheses
9 + (B - 3)² = 18 -----> Square value within first parentheses
(B - 3)² = 9 -----> Subtract 9 from both sides
B - 3 = 3 -----> Take square root of both sides
B = 6 -----> Add 3 to both sides
As you can see, when A = 2, there are two possible values of "B" depending on the equation. However, when A = 8, both equations give a "B" value of B = 6. Therefore, A = 8 and B = 6 are the answers.
Which two answer choices below would give you a value of 4 times smaller than (20 x 100)? A) (20 x 100) 4 B) 204 x 100 C) 20 - 25 D) 5 x 25
The option (C) 20 – 25, and option (D) 5×25 are 4 times smaller than (20 × 100) option (C) and (D) are correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, —, ×, and ÷.
We have:
= (20 x 100)
= 2000
4 times smaller will be:
=2000/4
= 500
A) (20×100) 4 = 4000
B) 204×100 = 20400
C) 20 – 25 = -5
D) 5×25 = 100
-5 < 500
100 < 500
Thus, the option (C) 20 – 25, and option (D) 5×25 are 4 times smaller than (20 × 100) option (C) and (D) are correct.
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What is the median of the data?
20, 19, 13, 23, 16, 15, 17, 17, 15, 15, 22, 19
18
15
O 17
016
median = the middle number {always remember this}.
To find the median of a set of numbers we arrange that set of numbers either in ascending order (smallest to biggest value) or in descending order ( biggest to smallest value).
so we are given :
20, 19, 13 , 23, 16, 15 , 17, 17, 15 , 15, 22, 19, .
we rearrange in ascending order (I chose ascending order).
Soo...
13, 15, 15, 15, 16, 17, 17 , 19, 19, 20, 22, 23.
so we cancel out (we cancel out left number, right number)
I mean
cancel out 13, cancel out 23
cancel out 15, cancel out 22
cancel out 15, cancel out 20 and so on.....
after that we will be left with 2 numbers which are 17 and 17.
NOTE: ( if we get 2 numbers instead of 1, then we add those 2 numbers and divide by 2)
so...
17 + 17 = 34
34/2 = 17.
the median of the set of numbers is equal to 17.
Hope this helps.
Good luck ✅.
Can someone please help me with b and C questions
Answer:
(b) 33919
(c) 8 ¹/₃
Step-by-step explanation:
⇒ 317 × 107 = (300 + 10 + 7)(100 + 7)
= 300(100 + 7) + 10(100 + 7) + 7(100 + 7)
= 30000 + 2100 + 1000 + 70 + 700 + 49
= 30000 + 2000 + 100 + 1000 + 70 + 700 + 40 + 9
= 30000 + 2000 + 1000+ 700 + 100 + 70 + 40 + 9
= 30000 + 3000 + 800 + 110 + 9
= 30000 + 3000 + 800 + 100 + 10 + 9
= 30000 + 3000 + 900 + 10 + 9
= 33919
[tex]\begin{aligned} 5\frac{2}{3}+3\frac{1}{2}-\frac{5}{6}&=\dfrac{5 \times3+2}{3}+\dfrac{3 \times 2+1}{2}-\dfrac{5}{6}\\\\&=\dfrac{17}{3}+\dfrac{7}{2}-\dfrac{5}{6}\\\\& =\dfrac{17 \times 2}{3\times 2}+\dfrac{7\times 3}{2\times 3}-\dfrac{5}{6}\\\\ & = \dfrac{34}{6}+\dfrac{21}{6}-\dfrac{5}{6}\\\\ & = \dfrac{34+21-5}{6}\\\\ & = \dfrac{50}{6}\\\\&=8\frac{1}{3}\end{aligned}[/tex]
The speed of light in a vacuum is 29,980,000,000
centimeters per second. In scientific notation, this
number is written as
A. 2.998 x 10⁹.
B. 2.998 x10¹0.
C.
29.98 x 10⁹.
D. 29.98 x10¹0.
Answer:
[tex]\huge\boxed{\sf 2.998 \times 10^{10}}[/tex]
Step-by-step explanation:
Given number:
29,980,000,000
Rules:
Move the decimal point after the first non-zero digit. (after 2)Here, we will move the decimal point 10 places to the left to move it after the first non-zero digit.Since we move the decimal point 10 places, we will write the number as a multiple of 10¹⁰ (10 being the exponent).The number will become:
2.998 × 10¹⁰
[tex]\rule[225]{225}{2}[/tex]
Answer:
B. 2.998 x 10¹⁰
Step-by-step explanation:
Given :
29,980,000,000Steps in solving :
Take the zeros after the last non-zero digit as a power of 10.Take the non-zero part (in the part) and put a decimal point after between the thousands and hundreds place, and shift the remaining powers of 10 to the previously grouped part.Adjust further if needed to match an answer.Solving :
29,980,000,0002,998 x 10⁷2.998 x 10³ x 10⁷2.998 x 10¹⁰Find the volume of the solid :)
answer key
78.4
Step-by-step explanation:
Multiply 7 x 4 =28
Then Multiply 28 x 2.8 = 78.4
That's how you get your answer ∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞ hope that helps out
Put this equation into slope-
intercept form.
5x – 4y = 12
Ou buy tomato sauce for $0.37 per ounce. one portion of potato gnocchi requires 3.5 ounces of tomato sauce. how much does the sauce for one portion cost? round to the nearest cent.
Answer:
$1.30
Step-by-step explanation:
As with costs anywhere, you find the total cost by multiplying the unit cost by the number of units. Here, a unit is 1 ounce of tomato sauce. 3.5 units are used in the recipe. The unit cost is given as $0.37 per ounce.
__
cost of sauce = (cost per ounce) × (number of ounces)
= ($0.37) × 3.5 = $1.295
This rounds up to $1.30.
The sauce for one portion costs $1.30.
How many days were less than 84°?
Answer:
it has to be 7 days because the other degrees are higher than 84.
Step-by-step explanation:
80 - 82 = 7 days
What are the solutions to the equation x2 − 1 = 399? a. b. c. d.
The given equation is a quadratic equation with a degree of 2 and leading coefficient of 1. The solution to the given quadratic equation are -20 and 20
Solution to the system of equationsThe given equation is a quadratic equation with a degree of 2 and leading coefficient of 1.
Given the expression
x^2 - 1 = 399
Add 1 to both sides
x^2 = 399 + 1
x^2. = 400
Take the square root of both sides
x = ±√400
x = ±20
Hence the solution to the given quadratic equation are -20 and 20
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Please help BRAINLIEST FOR RIGHT ANSWER
Answer:
x = 17
Step-by-step explanation:
4x + 7 = 75 (as the 2 angles are interior alternate angles)
4x = 75 - 7 = 68
x = 68/4 = 17
Answer:
x = 17
Step-by-step explanation:
4x + 7 = 75 (as the 2 angles are interior alternate angles)
4x = 75 - 7 = 68
x = 68/4 = 17
Find the equation of the linear function represented by the table below in slope-
intercept form.
Answer:
y=3x+7
Step-by-step explanation:
take two points, (1,13) (2,19)
subtract using slope formula
19-13 2-1= 6/1 -> 6-> 3
find your y intercept (b) by using the first term in the 7 row (7)
Answer:
y = 3x +
Step-by-step explanation:
The equation of the line is given by:
----------------------------
The equation of a line, in slope-intercept formula, has the following format:
In which
m is the slope, that is, how much y changes when x changes by 1.
b is the y-intercept, that is, the value of y when x = 0.
----------------------------
Given two points (x,y), the slope is the change in y divided by the change in x.
We have points (-1, -1) and (3,11). Thus:
Then
----------------------------
Point (-1,-1) means that when , and we use this to find b.
Thus
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What two operations would you use to solve the equation b/2+5=-7
-multiplication
-addition
-subtraction
-division
what is the essence of calculus?
*friendship
Differential Calculus, or Differentiation
If we have a function of one variable, ie of the form [tex]y=f(x)[/tex], then in its most basic form differentiation is the study of how a small change in one variable [tex]x[/tex] affects the other variable [tex]y[/tex].
As an real life example, consider the average speed of a moving car:
average speed = distance travelled/ time taken
Obviously, this is an average by definition, but if there existed a formal mathematical link between distance and time, could we build a function that would tell us the instantaneous velocity at every given moment? The study of differential calculus gives strategies for calculating the ratio of a little change in distance to a small change in time, and then calculating the real instantaneous speed by making the small change infinitely small.
Similarly if we wanted to find the gradient of the tangent to a curve at some particular point [tex]A[/tex] we would estimate the gradient by using a chord to a nearby point [tex]B[/tex]. As we move this nearby point [tex]B[/tex] closer to the tangent point [tex]A[/tex] the slope of the chord approaches the slope of the tangent with more and more accuracy. Again differential calculus provides techniques for us to make the point [tex]B[/tex] infinitesimally close to the point [tex]A[/tex] o that we can calculate the actual gradient of the tangent.
Integral Calculus, or Integration
Suppose we wanted to calculate the area under a curve, [tex]y=f(x)[/tex], bounded the [tex]x[/tex] =axis, and two points [tex]a[/tex] and [tex]b.[/tex] We could start by splitting the interval [tex][a,b][/tex] into [tex]n[/tex] regular strips, and estimating the area under the curve using trapezia (this is the essence of the trapezium rule which provides an estimate of such an area). If we increase [tex]n[/tex] then generally we would hope for a better approximation. The study of integration provides techniques for us to take an infinitely large number of infinitesimally small strips to gain an exact solution.
The Fundamental Theorem of Calculus
Given the above two notions, it would appear that there is no connection between them at first., The Fundamental Theorem of Calculus, on the other hand, is a theorem that connects the rate of change of the area function (which determines the area under a curve) to the function itself. In other words, the area function's derivative equals the function itself.
Visual for Fundamental Theorem of Calculus for integrals:
[tex]\int\limits^b_af {(x)} \, dx =F(b)-F(a).[/tex]
where F is an antiderivative of [tex]f[/tex]
Physics, Chemistry, all engineering sciences, statistics, economics, finance, biology, computer science, linguistics, to name but a few, are all areas that would be a desert without the use of calculus.
Leibnitz and Newton worked to define the velocity of a planet moving on a curved trajectory. That was not possible without calculus, and both had to invent differential calculus. Differential calculus allows to compare quantities along a curve, and thus their time rate of change.
All of classical physics can be summarized in this operation. Given second derivative (which is Force/mass), find the position as a function of time. This process is called integration. Half of calculus is made with integration, the other half with derivation. All of classical physics rests on these two parts of the calculus.
Quantum mechanics, quantum field theory, electromagnetism, fluid mechanics all use integration and derivation and much more. I rest my case. I hope this helps you gauge the place that calculus occupies in science.
Answer:
so what i think is that *friendshipStep-by-step explanation:
As inflation increases, it causes the money you earn today to have __________.
more value in the future
less value in the future
more purchasing power in the future
no purchasing power effect in the future
Answer:
less valuable
Step-by-step explanation:
it will be reduced when time goes by
Rand will deprecate
Why is 10^15/10^4 equal to 10^11
An expression is defined as a set of numbers, variables, and mathematical operations. The value of the expression 10¹⁵/10⁴ equals 10¹¹.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression 10¹⁵/10⁴ can be simplified as,
[tex]\dfrac{10^{15}}{10^4}\\\\= 10^{15} \cdot 10^{-4}\\\\= 10^{15-4}\\\\=10^{11}[/tex]
Hence, the value of the expression 10¹⁵/10⁴ equals 10¹¹.
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What is the sum of the angles in the image? 154° 106° 144° 164°
Answer:
154
Step-by-step explanation:
130 + 24 = 154
a. Does the height of the water increase by the same
amount each minute? Explain how you know.
minutes
height
0
150
SO
1
150.5
2
151
b. Does the height of the water increase by the same
factor each minute? Explain how you know.
3
151.5
From the table we can conclude that after 2 minutes the height of the water is increased by 4.
Example: In minute 2 it was 8 inches, in minute 4 it was 12 inches. (12-8=4)
This means that if the height of the water is increased by 4 inches for 2 minutes, then for 1 minute is increased 4/2=2 inches.
The following statement best describes how the slope relates to the height of the water in the pool:
The height of the water increases 2 inches per minute.
Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less.
Starting from a full tank, can Diego’s family drive the car for 25 days without the warning light coming on?
Select the correct choice.
A.) YES
B.) NO
Which of the following is a true proportion of the figure based on the triangle proportionality theorem?
A. j / k = j / i
B. i / j = h / k
C. h / i = h / k
D. k / i = j / i
Based on the triangle proportionality theorem, the true proportion regarding the figure is: B. i/j = h/k
What is the Triangle Proportionality Theorem?The triangle proportionality theorem states that when two sides of a triangle is intersected by a line that is parallel to the third side of a triangle, the two sides intersected are therefore divided in the same ratio.
TU is parallel to QR. Therefore, based on the triangle proportionality theorem, TU will divide QS and RS in the following ratio: B. i/j = h/k
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Which of the following best describes a triangle with one right angle and two congruent sides
Answer:
isosceles triangle
Help me please help me
Answer:
3/10
Step-by-step explanation:
Decimals and fractions are similar 4/5 is 0.8 and 1/2 is 0.5 The F has to be 0.3 to make a 4/5. 0.3 in fraction is 3/10
What is the probability of drawing a spade from a standard deck of cards or a
7?
The probability of drawing a spade is 13/52 = 1/4
Because every hand has 13 cards and there is 52 cards in a deck
The probability of drawing a 7 is 4/52 or 1/13
Because there are seven 7 cards in a deck and 52 cards.
The side lengths of the equilateral triangle pictured are each 12 cm. What is the circumference of the larger circle? Round your answer to the nearest 100th.
Vertical angles are congruent. Find the measure of angle x. X 38 o x = = [?]
Answer:
x=38 degrees
Step-by-step explanation:
Vertical angles are congruent. In the image, angle x is vertical to the angle that is given. Therefore, x=38 degrees
PLEASE HELP!!! 31 POINTS
What is the volume of this rectangular prism?
26 cubic feet
35 cubic feet
50 cubic feet
105 cubic feet
Work Shown:
Volume = length*width*height
Volume = 3*7*5
Volume = 105 cubic feet
length × breadth × height
7 × 3 × 5
105 cubic feet
hope it helps...!!!
evaluate the following if x = 2, y = -1 and z = 5.
a) xz + 1 b) 4x + y c) x - 2yz d) x(y + z) e) x² - 3z
simplify the following:
a) 2 x 4n b) 3x X 2y c) 8a ÷ 2 d) [tex]\frac{4^{2}y }{12x}[/tex]
simplify by collecting like terms:
a) 2b + 4b + b b) 6x + 3 - 2x c) 4p - 3q - p + 5q d) 3mn + 2m - 6mn +n
expand and simplify the following:
a) 2(x + 7) b) -3(2x + 5) c) 2x(3x - 4) d) -2a(5 - 4a) e) 4(x +2) + 5 f) 3(x - 2) - 1
Answer: please mark as brainliest
Step-by-step explanation: a) xz+1 = 2 x 5 + 1 = 11
b) 4x+y = 4 x 2 + (-1) = 7
c) 2 - 2 x -1 x 5= 12
d) 2(-1 + 5) = 2 x 4= 8
e) 2sq - 3 x 5= 4 - 15= -11
Pls help]ppppppppp me
Answer:
a. (2x - 3)(x - 4)
b. 17 m, 6 m
c. 46 m
Step-by-step explanation:
a.
2x² - 11x + 12 = (2x - 3)(x - 4)
b.
2x - 3 = 2(10) - 3 = 17
x - 4 = 10 - 4 = 6
c.
P = 2L + 2W = 2(17) + 2(6) = 46
Please help with question with explanations. Ty.
Answer:
last option is correct answer
Step-by-step explanation:
[tex]perimeter = 2(l + w) \\ = 2( \frac{5x + 10}{2x + 5} + \frac{x - 2}{2x + 5} ) \\ = 2( \frac{5x + 10 + x - 2}{2x + 5} ) \\ = 2( \frac{6x + 8}{2x + 5} ) \\ = \frac{12x + 16}{2x + 16} [/tex]
Please Help me Its a math problem see image attached
Answer:
C. - 3Step-by-step explanation:
Average rate of change within an interval is the slope of the endpoints.
The endpoints are:
(- 1, 6) and (0, 3)The slope is
(3 - 6)/(0 - (-1)) = - 3/1 = - 3Correct choice is C
Answer: -3
--
To find the Average rate of change within an interval use the slope of the endpoints.
(- 1, 6) and (0, 3)
The slope is
[tex]\frac{3-6}{0-(-1)}=\frac{-3}{1}=-3[/tex]
Hope this helps!
Which equation represents the transformed function below? on a coordinate plane, a parent function starts at (0, negative 1) and then curves up into quadrant 1 and approaches y = 1. a transformed function starts at (0, 4) and then curves up into quadrant 1 and approaches y = 6. _____ = parent function; y = log x - - - - - = transformed function y = log x 5 y = log x minus 5 y = log (x 5) y = log (x minus 5)
The parent function which starts at (0, -1) and then curves up into quadrant 1 is logx and the transformed function which starts at (0, 4) and then curves up into quadrant 1 is logx+5.
What is transformation of a function?Transformation of a function is shifting the function from its original place in the graph.
Types of transformation-
Horizontal shift- Let the parent function is f(x). Thus by replacing parent function with f(x-b) shifts the graph b units right and by replacing parent function with f(x+b) shifts the graph b units left.Vertical shift- Let the parent function is f(x). Thus by replacing parent function with f(x)-c shifts the graph c units down and by replacing parent function with f(x)+c shifts the graph c units up.On a coordinate plane, a parent function starts at (0, -1) and then curves up into quadrant 1 and approaches y = 1. Thus, the function of this curve is,
y=logx
A transformed function starts at (0, 4) and then curves up into quadrant 1 and approaches y = 6.
y=logx +5
Thus, the parent function which starts at (0, -1) and then curves up into quadrant 1 is logx and the transformed function which starts at (0, 4) and then curves up into quadrant 1 is logx+5.
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Answer:
yeah its a
Step-by-step explanation:
yw