The value of x in A is 7 and the value of y in B is -15
Functions and valuesFunctions are represented as a function of variable. Given the following sets of numbers.
A = [3 x 6 1 -8 5] and;
-5A = [-15 35 -30 -5 40 y]
Equate the individual values to have:
-5A= -15
Divide both sides by -5
-5A/-5 = -15/-5
A = 3
Determine the value of y
-5A = y
-5(3) = y
y = -15
Similarly;
5x = 35
x = 35/5
x = 7
Hence the value of x in A is 7 and the value of y in B is -15
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Answer:
The value of x in A is -7
The value of y in B is -25
Step-by-step explanation:
Everything in the first matrix can be multiplied by -5 to equal everything in the second matrix, since we are dealing with x and y, only the first and third rows matter.
In the first row, we know that 3 times -5 equals -15 and x times -5 equals 35
therefore, -5x=35, with basic algebra we find that X = -7
In the third row, we know that 8 times -5 is 40 and 5 times -5 equals y.
This takes just basic multiplication to find that Y = -25
The idea of a rigid motion is a significant concept in geometry. Explain what a rigid motion is and why it is essential. Using the diagram below, identify the specific rigid motions used for the following shapes.
A rigid motion is a type of motion in which all points on a given object move at the same time, in the same direction, and cover the same distance.
A rigid motion is a type of motion in which all points on a given object move at the same time, in the same direction, and cover the same distance. It is an essential type of motion used in geometry due to the rigid transformation of objects considered in the topic.
Rigid transformation is a method required to change the position, size, orientation, or dimensions of a given shape. This implies that the given shape (object) undergoes the appropriate transformation into its image. Types of rigid transformation are translation, rotation, dilation, and reflection.
Considering the given question, the quadrilateral performed a rigid motion. This was done by first reflecting it about the vertical axis, and now translating it 2 units downwards towards the horizontal axis.
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1) La suma de dos números es 58. Si uno de los números es 12 más que el otro
número,
cuáles son los números?
Answer:
Los números son 23 y 35.
Step-by-step explanation:
Q: The sum of two numbers is 58. If one of the numbers is 12 more than the other number, what are the numbers?
Set the numbers as x and y. Using the given information, we have two equations:
x+y=58
x=y+12
Solving using substitution, we have:
y+y+12=58 -> y=23
Substituting, x=23+12=35
The numbers are 23 and 35.
Consider an urn containing 8 white balls, 7 red balls and 5 black balls.
1)Randomly select 2 balls without replacement. The probability of getting 2 white balls is equal to:
2)Randomly select 5 balls without replacement. the probability of getting 2 white balls is equal to:
3) randomly select 150 balls with replacement. The probability of getting at least 72 white balls is:
Answer + Step-by-step explanation:
1) The probability of getting 2 white balls is equal to:
[tex]=\frac{8}{20} \times \frac{7}{19}\\\\= 0.147368421053[/tex]
2) the probability of getting 2 white balls is equal to:
[tex]=C^{2}_{5}\times (\frac{8}{20} \times \frac{7}{19}) \times (\frac{12}{18} \times \frac{11}{17} \times \frac{10}{16})\\=0.397316821465[/tex]
3) The probability of getting at least 72 white balls is:
[tex]=C^{72}_{150}\times \left( \frac{8}{20} \right)^{72} \times \left( \frac{7}{20} \right)^{78} +C^{73}_{150}\times \left( \frac{8}{20} \right)^{73} \times \left( \frac{7}{20} \right)^{77} + \cdots +C^{149}_{150}\times \left( \frac{8}{20} \right)^{149} \times \left( \frac{7}{20} \right)^{1} +\left( \frac{8}{20} \right)^{150}[/tex]
[tex]=\sum^{150}_{k=72} [C^{k}_{150}\times \left( \frac{8}{15} \right)^{k} \times \left( \frac{7}{15} \right)^{150-k}][/tex]
First of all, we would determine the total number of balls in the urn as follows:
Total number of balls = 8 + 7 + 5
Total number of balls = 20 balls.
Next, we would determine the probability of getting two (2) white balls without replacement:
P(2 white balls) = 8/20 × 7/19
P(2 white balls) = 2/5 × 7/19
P(2 white balls) = 0.1474.
Part 2.When 5 balls are selected without replacement, the probability of getting two (2) white balls would be calculated as follows:
P = [⁵C₂ × (8/20 × 7/19) × (12/18 × 11/17 × 10/16)]
P = [5!/(2! × (5 - 2)!) × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = [5!/(2! × 3!) × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = [20/2 × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = [10 × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = 0.3456.
Part 3.When 150 balls are randomly selected with replacement, the probability of getting at least seventy two (72) white balls would be calculated by applying binomial probability equation. Mathematically, binomial probability is given by this equation:
[tex]P =\; ^nC_r (p)^r (q)^{(n-r)}[/tex]
Substituting the given parameters into the formula, we have;
P = [¹⁵⁰C₇₂ × (8/20)⁷² × (8/20)⁽¹⁵⁰ ⁻ ⁷²⁾]
P = [150!/(72! × (150 - 72)!) × (8/20)⁷² × (8/20)⁽¹⁵⁰ ⁻ ⁷²⁾]
P = [150!/(72! × (78)!) × (4/5)⁷² × (4/5)⁽⁷⁸⁾]
P = 0.7948.
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Distance between two points
What is the length of the line?
Answer: B
Step-by-step explanation:
The horizontal change is 6.
The vertical change is 5.
So, the distance is [tex]\sqrt{6^2 + 5^2}=\sqrt{61}[/tex]
Find the area of the rhombus 12 5
If 7 and 9 are the remainders when 98 and 165
respectively, are divided by a positive integer a, then a =
Answer:
Step-by-step explanation:
98-7=91
165-9=156
(91/156)/13=7/12
Answer = 13
It is divided by a positive integer a, which will equal the number 13.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the data provided by the question,
The number are 98 and 165.
The remainders are 7 and 9.
So, the actual number is,
98 - 7 = 91 and,
165 - 9 = 156
They are divided by the number 13, so the value of a will be equal to 13.
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The Two sets A and B are said to be disjoint sets if A n B=_____
The Two sets, A and B, are said to be disjoint sets if A n B=ϕ
What does it mean for two sets to be disjoint?Disjoint sets are a pair of sets that do not share any elements. For instance, sets A=2,3 and B=4,5 are not connected sets.When two sets don't share elements, they are considered disjoint sets. In other words, the null set will result if we find the intersection of two sets. The process is straightforward; two sets are given in this procedure.When using a disjoint set union, it is possible to add new sets, combine existing sets, and check whether two sets of elements are the same in almost real-time.The Two sets, A and B, are said to be disjoint sets if A n B=ϕ
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What is the answer?im having trouble
Answer:
130
Step-by-step explanation:
let the inside value be,x
x+30°+20°=180°(Being sum of interior angle of triangle)
or,x+50°=180°
or,x=180°-50°
or,x=130°
Now,
let the exterior angle be,a
a=x(VOA)
a=130°
Therefore the value of a is 130°.
83
1 Show that I= {xy²w² dx + x²yw² dy + x²y²w dw} is independent of
the path of integration c and evaluate the integral from A (1, 3, 2) to
B (2, 4, 1).
2 Determine whether dz= 3x²(x² + y2) dx + 2y(x3 + y) dy is an exact
differential. If so, determine z and hence evaluate fedz from A (1, 2)
to B (2, 1).
1. Observe that
[tex]\nabla \dfrac{x^2y^2w^2}2 = \langle xy^2w^2, x^2yw^2, x^2y^2w\rangle[/tex]
is a gradient field, so the gradient theorem holds and the integral in question is indeed path-independent. Its value is
[tex]\dfrac{x^2y^2w^2}2\bigg|_{x=1,y=3,w=2}^{x=2,y=4,w=1} = 32 - 18 = \boxed{14}[/tex]
2. [tex]dz[/tex] is an exact differential if we can find a scalar function [tex]z=f(x,y)[/tex] such that
[tex]\dfrac{\partial f}{\partial x} = 3x^2 (x^2+y^2) = 3x^4 + 3x^2y^2[/tex]
[tex]\dfrac{\partial f}{\partial y} = 2y(x^3+y) = 2x^3y + 2y^2[/tex]
Integrating both sides of the first equation with respect to [tex]x[/tex] yields
[tex]f(x,y) = \dfrac35 x^5 + x^3 y^2 + g(y)[/tex]
Differentiating with respect to [tex]y[/tex] gives
[tex]\dfrac{\partial f}{\partial y} = 2x^3y + \dfrac{dg}{dy} = 2x^3y + 2y^2 \\\\ \implies \dfrac{dg}{dy} = 2y^2 \implies g(y) = \dfrac23y^3 + C[/tex]
and we ultimately find
[tex]f(x,y) = \boxed{z = \dfrac35 x^5 + x^3y^2 + \dfrac23 y^3 + C}[/tex]
(We can also use the same method here to determine the scalar function in part (1).)
Then the integral is path-independent, and its value is
[tex]f(2,1) - f(1,2) = \dfrac{418}{15} - \dfrac{149}{15} = \boxed{\dfrac{269}{15}}[/tex]
A participant in a medical study walked 10,388 steps per day. If their
steps are 2.5 feet per step, how many kilometers would they walk in aweek if they took 10,388 steps per day? Round to the nearest kilometer.
Do not include units with your answer.
Answer:
55.4068881439
Step-by-step explanation:
Lets first find the feet they walk per day, multiply the steps by the feet/step:
[tex]10,388*2.5=25970[/tex]
Now lets find the feet/week by multiplying that value by 7:
[tex]25970*7=181790[/tex]
Now lets convert the feet to km:
[tex]181790/3281=55.4068881439[/tex]
Resulting in approximately 55 kilometers
Dominique from "Dominique's Pizza" bakes p pizzas every day. Currently, it costs her $8 dollar sign, 8 per day to use the oven and $1.50 per pizza for the ingredients
Tomorrow, the price for the ingredients will increase from $1.50 per pizza to $2 per pizza. The oven costs will stay the same at $8 per day.
Dominique did some calculations and found that she should bake 8 more pizzas each day in order for the total expenses per pizza (including ingredient and shared oven costs) to remain the same.
Write an equation in terms of p to model the situation.
The equation in term of p that models the above experience is:
2p + 10 = 0.8p + 20.
What is an equation?
Any statement that models or captures the factors of a problem where in an equal sign is present to equate two of the factors or expressions therein is called an equation.
How do we form the above equation?Everyday pizza production is equal to p.Brick oven use fees are $10 per day.Ingredients for brick oven pizza cost $2 per pizza.$20 a day is the cost of using an electric oven.Pizzas baked in an electric oven cost $0.8 per pizza in ingredients.If an electric oven is used, the total cost of making a pizza falls by $1, including the cost of the ingredients.Total cost of baking p pizzas with brick oven = A = p(cost of one pizza) + cost of baking = p(2) + 10 (in dollars).
Total cost of baking p pizzas with electric oven = B = p(cost of one pizza) + cost of baking = p(0.8) + 20 (in dollars).
B = A - 1 (as using electric oven saves $1 per day, as given)
Thus, we get:
2p + 10 = 0.8p + 20
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why kilogram is more appropriate unit than milligram?
Step-by-step explanation:
that question is fundamentally wrong.
"appropriate" completely depends on the situation and circumstances.
if we are dealing with a weight that a human can feel, lift and distinguish from other weights without any special tool, then we are usually using kg. because then we humans can "connect" with the case, and deal with every day numbers.
if we are dealing with tiny little quantities like dosages of substances in a pill or other medication, then milligram is more than "appropriate".
because then, as humans, we are still dealing with numbers we can understand. like tens or hundreds.
if we kept kg in such situations, we would have to deal with numbers like 0.000008 kg vs. 0.000021 kg, where we could not see the magnitude of difference right away.
Find the interquartile range of the following data set.
Number of Points Scored at Ten Basketball Games
48, 26, 31, 50, 38, 40, 42, 34, 44, 36
3
8
6
10
The interquartile range of 48, 26, 31, 50, 38, 40, 42, 34, 44, 36, is: D. 10.
What is the Interquartile Range of a Data Distribution?The interquartile range of a data distribution is determined as: upper quartile (Q3) - lower quartile (Q1).
How to Find the Upper Quartile and Lower Quartile of a Data Distribution?The upper quartile of a data distribution is the center of the second half of a data distribution while the lower quartile is the center of the first half of a data distribution.
Given the data, 48, 26, 31, 50, 38, 40, 42, 34, 44, 36:
Order the data set as, 26, 31, 34, 36, 38, 40, 42, 44, 48, 50
The first half of the data is: 26, 31, 34, 36, 38.
The center is 34.
Lower quartile (Q1) = 34.
The second half of the data is: 40, 42, 44, 48, 50. The center is 44.
Upper quartile (Q3) = 44.
Interquartile range = 44 - 34
Interquartile range = 10
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What is the range of the function f(x) = 2x^2 + 2 over the interval of -2 ≤ x < 5?
Answer:
10 ≤ f(x) < 52
Step-by-step explanation:
the range is the values of f(x) given by the domain - 2 ≤ x < 5
substitute the end points of the interval into f(x)
f(- 2) = 2(- 2)² + 2 = 2(4) + 2 = 8 + 2 = 10
f(5) = 2(5)² + 2 = 2(25) + 2 = 50 + 2 = 52
then range is 10 ≤ f(x) < 52
which theorem can be used to show that LABC is to LDEC
Aspen has 306 green beads and 210 silver beads. For every 5 cm of a belt that Aspen sews,
they use 40 green beads and 24 silver beads.
After how many centimeters of the belt will Aspen have equal numbers of green and silver
beads left?
Answer:
30 cm
Step-by-step explanation:
every 5 cm of a belt, 16 more green beads are used.
there are 96 more green beads than silver, so it will take 6 5 cm belts in order to have equal numbers of green and silver beads left
Answer:
Step-by-step explanation:
After Aspen sews 30 cm of the belt, they have equal numbers of green and silver beads left. ANSWER:30
Slope=-6/5
Y intercept=2
What is the point slope form?
Answer: [tex]\Large\boxed{y-2=-\frac{6}{5} (x-0)}[/tex]
Step-by-step explanation:
Given the requirement of function form
Point-slope form: y - y₁ = m (x - x₁)
m = slope(x₁, y₁) = Any point on the lineGiven information
Slope (m) = -6/5
Y-intercept (x₁, y₁) = 2 = (0, 2)
Substitute values into the required form
y - y₁ = m (x - x₁)
y - (2) = (-6/5) (x - 0)
[tex]\Large\boxed{y-2=-\frac{6}{5} (x-0)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Subtract: 3x to the power 2 - 6x - 4 from 5 + x - 2xto the power 2.
Answer:
[tex]-8x^2 - 4x + 29 \\[/tex]
Step-by-step explanation:
Second expression evaluates to:
[tex](5 + x -2x)^2 = (5 -x)^2 = (-x+5)^2 = x^2 + 2(-x)(5) +5^2 = x^2 -10x + 25[/tex] (1)
For (1) We are using the rule [tex](a+b)^2 = a^2 +2ab + b^2\\\\[/tex]
Here [tex]a = -x, b = 5\\\\[/tex]
First expression evaluates to
[tex](3x)^2 -6x - 4 = 9x^2 -6x -4[/tex] (2)
Subtract (2) from (1)
[tex]x^2 - 10x +25 - (9x^2 -6x -4) = x^2-9x^2 -10x - (-6x) +25 -(-4)\\\\= -8x^2 - 4x + 29 \\[/tex]
PLEASE ANSWER VERY EMERGENT
The theoretical probability of randomly getting a black counter is P = 2/5.
How to get the theoretical probability?
In this case, we have 8 black counters and 12 white counters, so there is a total of 20 counters.
We assume that all the counters have the same probability of being randomly selected, then the probability of randomly selecting a black counter is just given by the quotient between the number of black counters and the total number of counters.
There are 8 black counters and 20 in total, then the probability is given by:
P = 8/20
Now we can simplify that fraction to get:
P = 2/5
The theoretical probability of randomly getting a black counter is P = 2/5.
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use a graphing device to find all solution of the question rounded to two decimal places.
x^3-x=log(x+1)
0.00.1.14
Answer:
Step-by-step explanation:
....
if g(x)=-2f(x), whats the right graphing
Answer:
IT HAS A SLOPE OF -2
Y INTERCEPT IS 0,0
Step-by-step explanation:
In the given figure,
XZ¯= 14 and YZ¯= 3. Find the measure of XY¯.
Answer: 11
Step-by-step explanation:
XY + YZ = XZ
XY + 3 = 14
XY = 11
The probability of buying a movie ticket with a popcorn coupon is 0.629 and without a popcorn coupon is 0.371. If you buy 29 movie tickets, we want to know the probability that more than 16 of the tickets have popcorn coupons.
Consider tickets with popcorn coupons as successes in the binomial distribution. Do not include p= in your answer.
Answer:
Step-by-step explanation:
The probability and the parameter
Step-by-step explanation:
The formula for probability in a binomial distribution is where p is the probability of success (ticket with popcorn coupon), n is the number of trials (tickets bought) and x the number of successes desired. In this case p=0.629 (probability of buying a movie ticket with coupon), n=29, and x=17,18,19, ...29.
The probability of more than 16 is equal to the sum of the probability of x=17, 17,18,19, ...29.
What is foreshortening?
a.
a technique used to create light and shadow
b.
a technique used to create depth in an image
c.
a technique that draws attention to the foreground
d.
a technique of shading with black pencil
Please select the best answer from the choices provided
A
B
C
D
Answer:
c
Step-by-step explanation:
Foreshortening is a technique used in perspective to create the illusion of an object receding strongly into the distance or background.
Foreshortening is a technique used to create the illusion of depth and three-dimensionality in a two-dimensional image.
Option B is the correct answer.
What is foreshortening?Foreshortening is a technique used in art to create the illusion of depth and three-dimensionality in a two-dimensional image.
It involves distorting the shapes of objects or figures to make them appear closer or farther away from the viewer, often by shortening the lengths of their features or changing the angle from which they are viewed.
Foreshortening is often used in drawing, painting, and other visual arts to create a sense of perspective and realism.
We have,
Foreshortening is a technique used to create the illusion of depth and three-dimensionality in a two-dimensional image.
It involves distorting the shapes of objects and figures to make them appear closer or farther away from the viewer, often by shortening the lengths of their features or changing the angle from which they are viewed.
Foreshortening can be used in drawing, painting, and other visual arts to create a sense of perspective and realism.
Thus,
Foreshortening is a technique used to create the illusion of depth and three-dimensionality in a two-dimensional image.
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Find the volume of the figure
h=9.5', r=1.8'
Answer:
Volume=96.7
Step-by-step explanation:
V=πr^2h=
V=π·1.8^2·9.5=
96.69822
Pls help me with these questions
Step-by-step explanation:
6 and 7 was already answered so I'll do 5 and 8.
5. The point the curve crosses the x axis is the x intercept, to find the x intercept of a rational function, we set y=0, and solve for x.
[tex]0 = \frac{x - 4}{x} [/tex]
Set the numerator equal to 0.
[tex]x - 4 = 0[/tex]
[tex]x = 4[/tex]
So the x intercept is (4,0).
Next, to find gradient, we take the derivative of the function.
[tex] \frac{x - 4}{x} [/tex]
We could use product rule, but for simplicity, serperate the function
[tex] \frac{x}{x} - \frac{4}{x} [/tex]
[tex]1 - \frac{4}{x} [/tex]
Next using exponents rules,
[tex]1 - 4 {x}^{ - 1} [/tex]
Now we take the derivative,
Derivative of a constant is zero.
Derivative of a power function,
[tex]n \times x {}^{n - 1} [/tex]
We move the exponent to the front, then we subtract the exponent by 1.
So, we get
[tex]4 {x}^{ - 2} [/tex]
Now, we plug in. 4,
[tex]4(4) {}^{ - 2} [/tex]
[tex]4 \times \frac{1}{16} = \frac{1}{4} [/tex]
The slope or gradient at the x intercept is 1/4
8. The derivative of ax^2+bx, with respect to x is
[tex]2ax + b[/tex]
When x=2, we have a gradient of 8.
[tex]2a(2) + b = 8[/tex]
[tex]4a + b = 8[/tex]
When x=-1, we have a gradient of -10.
[tex]2a( - 1) + b = - 10[/tex]
[tex] - 2a + b = - 10[/tex]
We have two system of equations,
[tex]4a + b = 8[/tex]
[tex] - 2a + b = - 10[/tex]
Let subtract the system to eliminate b.
[tex]6a = 18[/tex]
[tex]a = 3[/tex]
Plug 3 for a, back in to solve for b.
[tex]4(3) + b = 8[/tex]
[tex]12 + b = 8[/tex]
[tex]b = - 4[/tex]
So a is 3
b is -4
The perimeter of a football field is 1040 feet. The length of the field is 120 feet less than 3 times the width. What are the dimensions of the field?
Answer:
length: 360 ftwidth: 160 ftStep-by-step explanation:
The perimeter formula and the given relation between length and width can be used to write and solve an equation for the field dimensions.
SetupLet w represent the width of the field. Then (3w-120) is the length of the field, and its perimeter is ...
P = 2(L +W)
1040 = 2((3w-120) +w)
SolutionDividing by 2 and simplifying, we have ...
520 = 4w -120
130 = w -30 . . . . . . divide by 4
160 = w . . . . . . . . . add 30
3w-120 = 3(160) -120 = 360 . . . the field's length
The dimensions of the field are 160 feet long by 360 feet wide.
216 students enrolled in a freshman-level chemistry class. By the end of the semester, 5 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.
Answer:
The no. of student failed is 36.
Step-by-step explanation:
Given, the number of student enrolled= 216
Let us suppose number of student failed = x
Given,
no. of student passed is 5 times no. of student failed.
Then, no. of student passed = 5x
x +5x = 216
6x = 216
x = 216/6
x = 36
Thus, the no. of student failed is 36.
Tamika builds a wooden skateboard ramp. The ramp measures 63 centimeters, and the length of its horizontal base is 60
centimeters, as shown.
63 cm
60 cm
Answer:
the height would be around 19.2 cm
Step-by-step explanation:
hyp length = 63
base = 60
length = sqrt(63^2 - 60^2) = sqrt(369)
A map uses a scale of 1
cm = 5½ miles. In actual
distance, the entrances to
two parks are 24 miles
apart. How far apart are
they on the map?
Answer:
3.36 cm
Step-by-step explanation:
24 - 5 1/2 = 18.5
To find the distance on the map, we can set up a proportion:
1 cm / 5.5 miles = x cm / 18.5 miles
5.5 times 37/11 equals to 18.5; 1 times 37/11 is approximately equals to 3.36 cm (rounded to the nearest hundredths).
