What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 54
Step-by-step explanation:
The 2 angles shown are vertical angles, so they are equal.
2x + 2 = 3x - 52
2x - 3x = -52 - 2
-x = -54
x = 54
They are 110° angles
Answer: x = -10
Step-by-step explanation:
1: Add: 2x+2 3x-52 = 5x -50
2: Divide both sides by the same factor: 5x - 50
------------
5 5
3: Level: x= -10
How do you simplify 3/4 + (1/4−16) ?
Answer:
To add fractions, find the LCD and then combine.
3/4 + (1/4−16)= −15
Step-by-step explanation:
6. Tyree planned to build a ramp from his window to the sidewalk so he could skateboard right out his window on his way to school. His window is 5 feet off the ground and the sidewalk is 20 feet from his house. How long will Tyree's ramp need to be to make it from his window to the sidewalk?
The length of the ramp Tyree will need to make from window to the sidewalk is 5√17 feet .
In the question ,
it is given that ,
height of the window is = 5 feet ,
distance of sidewalk from the Tyree's house is = 20 feet ,
We know that the angle between the wall and the floor is 90° ,
So , the system is making a right triangle ,
let the length of the ramp be = "x" ,
So, According to Pythagoras Theorem ,
we get ,
x² = 5² + 20²
x² = 25 + 400
x² = 425
x = √425
x = 5√17 feet .
Therefore , the length of the ramp is 5√17 feet .
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give the equation of the line that goes through the point (5, -2) and has a slope of 0.
When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b). B stands in for the y value of the y-intercept point in the formula.
How to calculated the slope intercept?Determine the equation of the line with a slope of 2/3 and a y intercept of (0, 4).
Solution
Step 1: Replace the provided in the formula.
Provided that the slope, m, is given as 2/3 and the y intercept, (0, 4), b = 4.
y = mx + b
y = 2 3 x + 4
2 /3 x – y = - 4
(Note: You must multiply this by the LCD of 3 to fix this since the conventional form does not support fractional numbers.)
3( 2 /3x – y) = (- 4) (- 4)
3/2x – 3y = - 12
This is the line's determined equation.
Verify is the second step.
Utilizing the formula, plot two points. In this example, y1 = 2 and Y2 = -6. 2x - 3y = - 12 2x – 3y = - 12
Let y = 2 Let y = - 6
2x – 3(2) = - 12 2x – 3(-6) = - 12
2x – 6 = - 12 2x + 18 = - 12
2x = - 6 2x = - 30 \sx = - 3 x = - 15
P1 therefore equals (-3, 2) and P2 equals (-15, -6).
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EACH OF THE GREEN EQUATIONS HAS A
SOLUTION THAT MATCHES THE
SOLUTION OF A BLUE EQUATION.
RECORD THE MATCHING PAIRS OF
EQUATIONS AND THEIR SOLUTIONS IN
THE PURPLE BOX AT THE RIGHT.
A
5(3x-2) = 4(2x + 1)
D
-x + 3 = 2(x + 15)
B
Cards A and
Cards B and
Cards C and
-4x=-(10x+18)
E
-3(x + 4) = 6(-x - 1)
C
f
are true when x =
are true when x=
are true when x =
2.5x = 5(4x+12)
4x-20= -2(-3x+22)
Answer:
The answer should be A.
Step-by-step explanation:
Answer:
Step-by-step explanation:
The system of conics has two solutions.
What are the solutions to this system of conics?
The points of intersection of the system formed by the circle (x - 2)² + (y - 3)² = 16 and the ellipse (x - 2)² / 16 + (y - 3)² / 64 = 1 are (x₁, y₁) = (- 2, 3) and (x₂, y₂) = (6, 3).
How to determine the points of intersection between two conics
Herein we get a system formed by two conics, the former represents a circle and the latter represents an ellipse. There are different methods to solve the system, the use of graphing tools offers a quick though reasonable approach to find that. First, write the equations corresponding to the conics:
Circle
(x - 2)² + (y - 3)² = 16
Ellipse
(x - 2)² / 16 + (y - 3)² / 64 = 1
Second, plot the two graphs of the functions. (Please see the image attached below)
Third, write the points of intersection:
(x₁, y₁) = (- 2, 3), (x₂, y₂) = (6, 3)
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A cylinder fitted with a movable piston contains ideal gas at 27 degrees C, pressure 0.50*10^5 Pa, and volume 1.25 m. What will be the final temperature if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa?
The final temperature is calculated to be 41.8 degrees Celcius if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa
The final temperature can be calculated by using the combined gas law as follows;
[tex]\frac{P_{1}V_{1} }{T_{1} } = \frac{P_{2}V_{2} }{T_{2} }[/tex]
Here [tex]P_{1}[/tex] and [tex]P_{2}[/tex] represent the initial and final pressure respectively,
[tex]V_{1}[/tex] and [tex]V_{2}[/tex] represent the initial and final volume respectively
[tex]T_{1}[/tex] and [tex]T_{2}[/tex] represent the initial and final temperature respectively
Converting [tex]T_{1}[/tex] to kelvin as follows;
[tex]T_{1}[/tex] = 27 degrees Celcius = 27 + 273 = 300 K
Now the final temperature can be determined by substituting the values in this equation of the combined gas law as follows;
(0.50×10^5)(1.25) / 300 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]
208.333333333 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]
208.333333333 ([tex]T_{2}[/tex]) = (0.82×10^5)(0.80)
[tex]T_{2}[/tex] = (0.82×10^5)(0.80) ÷ 208.333333333
[tex]T_{2}[/tex] = 314.8 K
Converting K to degree Celcius as follows;
[tex]T_{2}[/tex] = 314.8 - 273 = 41.8 degree Celcius
Hence 41.8 degrees Celcius is calculated to be the final temperature.
Although a part of your question is incorrect, you might be referring to this question:
A cylinder fitted with a movable piston contains ideal gas at 27 degrees C, pressure 0.50*10^5 Pa, and volume 1.25 m^3. What will be the final temperature if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa?
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find the percentage of the first quantity with
reference to the second quantity: 480 units, 560 units.
Answer:
85.7142857%
Step-by-step explanation:
To find the percentage, take the first quantity and divide by the second quantity
480/560 =.857142857
Then multiply by 100 %
857142857 * 100% = 85.7142857%
pollsters are concerned about declining levels of cooperation among persons contacted in surveys. a pollster contacts 77 people in the 18-21 age bracket and finds that 65 of them respond and 12 refuse to respond. when 294 people in the 22-29 age bracket are contacted, 259 respond and 35 refuse to respond. assume that 1 of the 371 people is randomly selected. find the probability of getting someone in the 22-29 age bracket or someone who agreed to respond.
The probability of getting someone in the 22-29 age group to respond or someone who agreed to respond is 259/371
Let X be the event of contacting the 18-21 age group
Let Y be the event of contacting 22-29 age group
Let A be th event that the pollster responded
Let B be the event that they did not respond
Here,
Probability no. of favorable outcomes/total no. of outcomes/
Hence,
n(A) = 65 + 259
= 324
P(A) = 324/371
Similarly, P(Y) = 294/371
Now,
P(A∩Y) = 259/371
We know that P(C ∪ D) = P(C) + P(D) - P(C∩D)
Therefore, P(A∪Y) = P(A) + P(Y) - P(A ∩ Y)
= 324/371 + 294/371 - 259/371
= 359/371
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Which of the following ratios is used to determine one's debt-to-income? A. 20/28
B. 20/36
C. 28/30
D. 28/36
Answer:
d
Step-by-step explanation:
What is the solution to 1/2 |x| = -3?
Answer: 1/2 |x| = -3?
Step-by-step explanation:
Find the vertex of the following function. Write your answer in the form (x, y).
Use the slash mark (/) as a fraction bar if necessary, but do not enter
decimals.
y = x² - 8x+12
Answer here
SUBMIT
The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).
Define parabola.A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. A plane curve created by a point moving so that its distance from a fixed point equals its distance from a fixed line is known as a parabola. A normal parabola's standard equation is y 2 = 4 an x, where an is the distance from the vertex to the focus.
Given,
Function,
y = x² - 8x + 12
The supplied equation's vertex must be located.
The equation is a parabolic equation when we look at it.
We are aware that a parabolic equation's generic form is
y = x² - 8x + 12
where the parabola's vertex's x and y coordinates are denoted by h and k.
We can determine the following by comparing the aforementioned equation with the parabola's general form:
x = 4, y = 4 and h = -8
The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).
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write the expression in exponential from 7×7×7×7×7×7
Answer:
7^6
Step-by-step explanation:
7 to the power of 6
Answer: [tex]7^{6}[/tex]
Step-by-step explanation:
Exponential form denotes how many times a value is multiplied by itself.
This is 7 times itself 6 times, so it is written as 7 with a 6 in the top right corner.
Marc deposited $175 in a new bank account. After buying some furniture, he was overdrawn by $55. Select all the true statements about Marc's account.
The correct statements regarding Marc's account balance are given as follows:
In this situation, 0 would represent an empty bank account.When Mark was overdrawn, he had a negative balance.The lowest balance in the account was of -$55.How to obtain Mark's account balance?Mark's account balance is the amount of money that he has on his account.
Hence the balance is obtained as follows:
Initially -> $0 -> empty bank account.Deposit of $175.Overdrawn by $55 -> negative balance of -55, as the cost of the furniture bought was 55 more than the $175 that he had deposited, hence the total cost was of $230.Missing InformationThe statements are given by the image shown at the end of the answer.
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Directions: Answer all questions in complete sentences and show all work to receiv
full credit. For all parts, please use $1,502.45 as your bi-weekly net pay.
Part 1: Build a Budget (15 points)
A. (10 points) Using the categories and percentages below, create a monthly budge
using the monthly net pay given.
1. Choose a percent within the given range. Make sure when choosing each
percent, that the sum of all categories equals 100%. For example, you decide
you want to spend 20% of your budget on housing. 20% for housing plus eac
percent from all other categories will equal 100%.
2. Then, using the bi-weekly net pay of $1,502.45, calculate, in dollars, the
maximum amount you can spend in each category monthly. (Calculate your
monthly net pay and multiply by your chosen percentage.)
• Housing 25% - 35%: percent chosen =
●
●
●
Food/Household 10% - 20%: percent chosen =
Savings 5%-10%: percent chosen =
• Transportation 15% - 20%: percent chosen =
Debt 5%-15%: percent chosen =
I
1. The percentages chosen are given as follows:
Housing: 35%.Food/Household: 20%.Savings: 20%.Transportation: 20%.Debt: 5%.2. The maximum amount that can be spent in each category is given as follows:
Housing: $525.86.Food/Household: $300.49.Savings: $150.25.Transportation: $300.49.Debt: $225.37.How to divide the percentages?
The percentages for each of the four applications can be divided in any form, as long as the sum of the five percentages is of 100%.
This is the case for the attributed percentages, as:
35 + 20 + 20 + 20 + 5 = 100.
How to find the maximum amounts?The maximum amounts are found applying the proportions, multiplying the decimal equivalents of the maximum percentages by the bi-weekly net pay of $1,502.45.
Then the amounts in this problem are calculated as follows:
Housing: 0.35 x 1502.45 = $525.86.Food/Household: 0.20 x 1502.45 = $300.49.Savings: 0.10 x 1502.45 = $150.25.Transportation: 0.20 x $1502.45 = $300.49.Debt: 0.15 x 1502.45 = $225.37.More can be learned about proportions at https://brainly.com/question/24372153
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Find x, given
AD = BC = 6m.
The value of x in the trapezium is 60 degrees.
How to find the angle of a trapezium?A trapezium is a quadrilateral . The sum of angles in the trapezium is 360 degrees. The legs of the trapezium ABCD are congruent.
The length AB and CD are parallel to each other.
Let's find the angle x as follows:
Therefore, using trigonometric ratios,
cos x = adjacent / hypotenuse
Where
adjacent side = 3 m
hypotenuse side = 6 m
Hence,
cos x = 3 / 6
cos x = 1 / 2
x = cos ⁻¹ 0.5
x = 60 degrees
Therefore,
x = 60 degrees.
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if a and b are positive numbers, find the maximum value of f(x) = xa(9 − x)b on the interval 0 ≤ x ≤ 9.
So, for f(x)=xa(9-x)b on the interval 0≤x≤9, the maximum value of f(x) is 0, and a and b are positive numbers.
What is function?A function is an expression, rule, or law in mathematics that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences. Functions are broadly classified into four categories. Element-based: one-to-one function, many-to-one function, onto function, one-to-one and onto function, into function
Here,
f(x)=xa(9-x)b
If we put x=0,
f(x)=0
If we put x=9,
f(x)=0
So, the maximum value of f(x) is 0 for f(x)=xa(9-x)b on the interval 0 ≤ x ≤ 9 and a and b are positive numbers.
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solve using the quadratic formula
show all work
These are separate equations
x^2+3x-4=0
2x^2-4x-3=0
The solutions of the equation x² +3x - 4=0 are x=1 and x= -4 .
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Given equation:
x² +3x - 4=0
Standard form of a quadratic equation:
ax² +bx+c=0
On comparing, a=1, b= 3, c= -4
Quadratic formula:
x = [ -b ± √(b² - 4ac ) ] /(2a)
Substitute the values
x = [ -3 ± √(3² - 4*1*(-4) ) ] /(2*1)
x= [ -3 ± √(9 + 16 ) ] /(2)
On simplifying,
x=1 and x= -4
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Three friends are buying food for and end-of-school party. Adrian spends $16 for 2 pounds is sliced turkey. The turkey costs $_____ per pound.
Answer:
$8 per pound
Step-by-step explanation:
16/2 = 8
Answer: $8
Step-by-step explanation:
16 divided by 2 = $8 per pound
A certain small town, whose population consists of 100 families, has 30 families with 1 child, 50 families with 2 children, and 20 families with 3 children. The birth rank of one of these children is 1 if the child is the firstborn, 2 if the child is the secondborn, and 3 if the child is the thirdborn. (a) A random family is chosen (with equal probabilities), and then a random child within that family is chosen (with equal probabilities). Find the PMF, mean, and variance of the child’s birth rank. (b) A random child is chosen in the town (with equal probabilities). Find the PMF, mean, and variance of the child’s birth rank.
a) A random family is chosen and then a random child within that family is chosen the mean is 1.45 and the variance is 0.38.
b) A random child is chosen in the town, the mean is 1.579 and the variance is 0.454.
For part A:
A random family is chosen and then a random child within that family.
P(X=1)= P(X=1 | family with one child). P(family with one child)
+ P(X=1 | family with two children).P(family with two children)
+P(X=1 | family with three children).P(family with three children)
= 1.30/100 + 1/2 . 50/100 + 1/3 . 20/100 = 37/60
P(X=2)=P(X=2 | family with one child). P(family with one child)
+ P(X=2 | family with two children).P(family with two children)
+P(X=2 | family with three children).P(family with three children)
= 0.30/100 + 1/2 . 50/100 + 1/3 . 20/100 = 19/60
P(X=3)=P(X=3 | family with one child). P(family with one child)
+ P(X=3 | family with two children).P(family with two children)
+P(X=3 | family with three children).P(family with three children)
= 0.30/100 + 0 . 50/100 + 1/3 . 20/100 = 4/40
hence, using these probabilities we can find,
E(X) = 1(37/60) + 2(19/60) + 3(4/60) = 1.45,
therefore, Var(x) = 149/60 − [tex]1.45^{2}[/tex] = 457/1200 ≈ 0.38
hence, the mean of the child's birth is 1.45 and the variance of the child's birth ranks 0.38.
For part B,
When a random child is chosen in the town with equal probabilities.
There are 1 x 30 + 2 x 50 + 3 x 20 = 190 children in the town where 100 of them are first born, 70 of them are second born, and 20 of them are third born. Let X be a random variable that marks the birth rank of a child.
Hence,
E(X) = 1(100/190) + 2(70/190) + 3(20/190) ≈ 1.579
and
Var(X) = 2.947 − [tex]1.579^{2}[/tex] ≈ 0.454
For a random child chosen, the mean of the child's birth is 1.579 and the variance of the child's birth ranks 0.454.
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5pages in a book have pictures and if there are 40pages in the book what percent of the book has pictures
Answer:
12.5%
Step-by-step explanation:
First,
take 5 page and divide by total amount in book 40 pages.
5/40 = 0.125.
Second,
To get percent multiply by 100.
0.125*100 = 12.5%
How many kilometers are in 40miles
Answer:
Below
Step-by-step explanation:
I do not know which conversion factor you are to use, but here is one:
1 km = .62137 mi
then 40 miles becomes :
40 miles / ( .62137 mi / km) = 64.4 km
Which values are solutions to the inequality?
3r≤4r−6
Select each correct answer.
Responses
r = 4
r = , 4
r = 5
r, = 5
r = 6
r, = 6
r = 7
Answer:
3r < = 4r - 6
3r - 4r < = -6
-r < = -6
r > = 6........it is 6 and 7
Step-by-step explanation:
Answer:
your answer would be 6, and 7.
Step-by-step explanation:
how do you find the range of a graph
Answer:
look at the y axis. :)
Anne bought a television for 75% off she spent 24 dollars what was the original price
the original price was "x", which oddly enough is the 100%.
now, we know the TV is 75% off, that means the sale price is 100% - 75% = 25%, and we know that's 24 bucks.
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 24& 25 \end{array} \implies \cfrac{x}{24}~~=~~\cfrac{100}{25} \implies \cfrac{ x }{ 24 } ~~=~~ 4\implies x=96[/tex]
which functions have a zero at x equals 4? check all that apply. and (x )equals negative 2 x squared minus 18 x minus 40 b. c (x )equals 2 x squared minus 11 x plus 12 c. e (x )equals 3 x cubed plus x squared minus 48 x minus 16 d. a (x )equals x squared minus 3 x minus 28 e. b (x )equals x cubed minus 4 x squared minus x plus 4
The function that have a zero at x = 4 are
f(x) = 2x^2 - 11x + 12 f(x) = 3x^3 + x^2 - 48x - 16 f(x) = x^3 - 4x^2 - x + 4The first function is
f(x) = -2x^2 - 18x - 40
Substitute the value of x = 4
f(4) = -2(4)^2 - 18(4) - 40
= -2(16) - 72 - 40
= -32 - 72 - 40
= -144
The result is not zero
The second function is
f(x) = 2x^2 - 11x + 12
f(4) = 2(4)^2 - 11(4) +12
= 32 - 44 + 12
= 0
The result is zero
The third function is
f(x) = 3x^3 + x^2 - 48x - 16
f(4) = 3(4)^3 + 4^2 - 48(4) - 16
= 192 + 16 - 192 - 16
= 0
The result is zero
The fourth function is
f(x) = x^2 - 3x - 28
f(4) = 4^2 - 3(4) - 28
= 16 - 12 - 28
= -24
The fifth function is
f(x) = x^3 - 4x^2 - x + 4
f(4) = 4^3 - 4(4)^2 - 4 + 4
= 64 - 64 - 4 + 4
= 0
Therefore, the function f(x) = 2x^2 - 11x + 12, f(x) = 3x^3 + x^2 - 48x - 16 and f(x) = x^3 - 4x^2 - x + 4 have zero at x equals 4
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lara chooses a number less than 100 she devides it by 3 and subtracts 11 divides by 2 her answer is 10.5 what was the number she started with
Answer: 96
Step-by-step explanation:
The easy way to do this is to start backward. The last step she did before she got 10.5 as her answer was dividing her answer by 2.
So we can just multiply 10.5 by 2 to reverse the last step.
After doing that we get 21. The step Lara did before dividing by 2 was subtracting 11.
So we can just add 11 to 21 to reverse this step.
After doing that we get 32. The step Lara did before subtracting 11 was dividing by 3.
So we can just multiply 32 by 3 to reverse this step.
After doing that we get 96. So the number that Lara started with is 96.
Please help! More points today!
Answer:
138
Step-by-step explanation:
23 x 6 (sides) = 138
In the diagram below, \overline{EF}
EF
is parallel to \overline{BC}
BC
. If DC=27DC=27, EF=27.5EF=27.5, and BC=49.5BC=49.5, find the length of \overline{DF}
DF
. Figures are not necessarily drawn to scale.
)
Applying the AA similarity theorem, the length of DF is: 15 units.
What is the AA Similarity Theorem?When two angles in one triangle are congruent to the corresponding two angles in another triangle, both are said to be similar to one another. This means that, the corresponding sides of these two triangles would be proportional or have the same ratio.
In the image attached bellow, triangle DEF and triangle DBC are similar to each other because they have two pairs of corresponding angles that are congruent which are:
<DFE ≅ <DCB [right angles are equal]
<EDF ≅ <BDC [reflexive property of congruence]
Therefore, their corresponding sides will have equal ratios such as:
DC/DF = BC/EF
Substitute:
27/DF = 49.5/27.5
Cross multiply:
DF = (27.5 * 27) / 49.5
DF = 15
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A veterinarian surveys households in her area to find out how many pets they own. She estimates that households have 1.8 pets on average, with a margin of error of ±0.4 pets. There are 1,200 households in her area.
1. The minimum number (Lower Limit) of pets one can find in the area is 1,680 pets, given the margin of error.
2. The maximum number (Upper Limit) of pets in the area will be 2,640 pets, given the margin of error.
What is the margin of error?The margin of error shows the statistical difference between actual and projected results in a random survey sample.
In other words, the margin of error reveals the level of unpredictability in research outcomes.
The statistical difference can be explained with an upper limit (maximum) and lower limit (minimum) between which the statistical value lies, thereby offering some level of confidence.
Average (mean) number of pets in each household = 1.8 pets
The margin of error = ±0.4 pets
The total number of households in the area = 1,200
Upper limit (maximum) of pets in the area = 2,640 pets (1,200 x 1.8 +0.4)
Lower limit (minimum) of pets in the area = 1,680 pets (1,200 x 1.8 - 0.4)
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Question Completion:What are the minimum and maximum numbers of pets you expect to find in her area?
