[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \:x = - \dfrac{ 9}{20} [/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:2(3x + 1) + 3(5x + 2) = x - 1[/tex]
[tex]\qquad❖ \: \sf \:6x + 2 + 15x + 6 = x - 1[/tex]
[tex]\qquad❖ \: \sf \:(6x + 15x - x) + (2 + 6 + 1) = 0[/tex]
[tex]\qquad❖ \: \sf \:20x + 9 = 0[/tex]
[tex]\qquad❖ \: \sf \:20x = - 9[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \:x =- \cfrac{ 9}{20} [/tex]
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
x = –9/20Step-by-step explanation:
________________________________
→ 2(3x + 1) + 3(5x + 2) = x – 1
→ 6x + 2 + 15x + 6 = x – 1
→ 21x + 8 = x – 1
→ 21x – x = – 1 – 8
→ 20x = – 9
→ x = –9/20
________________________________
Hope it helps you :')Which is equivalent to 3/8^1/4x
The CORRECT answer is Option C.
.
.
Mark BRAINLIEST!
PLEASE I NEED HELP SO BADLY
Answer:
[tex]3y^{2} -3y-5[/tex]
A local pizza parlor has the following list of toppings available for selection. The parlor is running a special to encourage patrons to try new combinations of toppings. They list all possible three-topping pizzas (3 distinct toppings) on individual cards and give away a free pizza every hour to a lucky winner. Find the probability that the first winner randomly selects the card for the pizza topped with ham, artichoke hearts, and pepperoni.
The probability that the first winner randomly selects the card for the pizza topped with ham, artichoke hearts, and pepperoni is 1/560 given that there are 16 toppings to choose from. This can be obtained by finding the total number of all possible three-topping pizzas (3 distinct toppings) using combination formula and finding the probability.
What is the required probability?Given that there are 16 toppings,
the total number of all possible three-topping pizzas,
ⁿCₓ = [tex]\frac{n!}{x!(n-x)!}[/tex] = 16!/[3!(16-3)!] = 16!/[3!(13)!] = 14×15×16/3×2 =560
Probability of choosing pizza topped with ham, artichoke hearts, and pepperoni,
P(ham, artichoke hearts, pepperoni) = 1/560
Hence the probability that the first winner randomly selects the card for the pizza topped with ham, artichoke hearts, and pepperoni is 1/560 given that there are 16 toppings to choose from.
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Write down the equation of the straight line which passes through (0, -3) and parallel to the straight line y = -2x+1
Answer:
y = -2x - 3
Step-by-step explanation:
Equation of line:Parallel lines have same slope.
y = -2x + 1
Compare with the equation of line in slope intercept form y = mx + b
Here m is the slope and b is the y -intercept
m = -2
m = -2 ; line passes through (0 , -3)
Equation of line in slope intercept form:
[tex]\sf \boxed{\bf y - y_1=m(x-x_1)}[/tex]
y - [-3] = -2(x - 0)
y +3 = -2x
y = -2x - 3
Vinny worked 8 hours and was paid a total of $66. At this rate, how long
would it take Vinny to earn $165?
a. 40.5 hours
b. 20 hours
c. 15 hours
d. 2½ hours
Answer:
b, 20 hours
Step-by-step explanation:
First, find out how many times 66 (what Vinny made) goes into 165. (what Vinny wants to make) the answer is 2.5. Then, multiply 8 by 2.5 as well. You get 20. The answer is b, 20.
I hope this helps!
10 Points + BRANIEST
Answer:
Step-by-step explanation:
So, we’re probably looking at a n9-m0 cusp, since adding 0 to a number gives a sum lower than adding 9 to a slightly smaller number, something that isn’t true elsewhere in the cycle.
We need a n9 where the sum n+9 is divisible by 3. 9 is divisible by 3 already, so n must be divisible by 3 as well. So, it’s 0, 3, 6, or 9.
Taking as the most likely 3 (because a 39 year old is more likely than a 9 year old, 69 year old, or 99 year old to have a child who doesn’t already know their father’s age) we’ll try 39, 40. 3+9=12, 4+0=4, 12/3=4, this is a possible solution.
Do the others work?
0+9=9, 1+0=1, 9/4=/=1
6+9=15, 7+0=7, 15/4=/=7
9+9=18, 1+0+0=1, 18/4=/=1
1+2+9=12, 1+3+0=4, 12/3=4
there are at least two possibles. the father was correct, the father cannot determine his age from what she has been told, she must guess. From what she knows of him, is it more likely that he’s 39, or 129, or even older?
Identify the scale of measurement for the following variable: The weight of a group of dieters. Group of answer choices nominal ratio ordinal interval
Ratio scale of measurement for the following variable, The weight of a group of dieters.
What scale of measurement is the variable of weight?Ratio measurement scale of ratio variables include height, weight, and distance. The ratio scale allows for the addition, subtraction, division, and multiplication of data. Additionally, ratio scales have a "real zero," which sets them apart from interval scales. The ratio scale is used to determine weight. The ratio is identical to the interval scale, with the exception that 0 on the scale denotes the absence of anything. serval scales can depict values lower than zero and do not hold a true zero. For instance, you can gauge temperatures as low as -10 degrees Celsius. Contrarily, ratio variables are always greater than zero. Height and weight are measured starting at 0 and never below it. Because they are numbers as we typically think of them, ratio scales are the simplest to comprehend. On a ratio scale, the distance between consecutive numbers is equal, and a score of zero indicates that there is no presence of the thing being measured. The majority of ratio scales are counts of items.
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Help with this!! Thank you
Answer:
Step-by-step explanation:
1) The equation of circle having center at origin:
x² + y² = r²
Where 'r' is the radius.
diameter = 36
r = 36 ÷ 2 = 18
Equation of circle :
x² + y² = 18²
x² + y² = 324
Option d.
2) Find the discriminant D.
If D > 0, then the quadratic equation has two distinct real roots.
If D= 0, then the quadratic equation has two identical real roots.
If D < 0, then the quadratic equation has no real roots.
D = b² - 4ac
x² - 6x + 9 = 0
a = 1 ; b = -6 ; c = 9
D = (-6)² - 4*1*9
= 36 - 36
D = 0
As D = 0, the quadratic equation has two identical real roots
Option a.
3) The axis of symmetry of a parabola is the vertical line passing through the vertex. It will be middle of the x-intercepts.
X- intercepts are -8 , 2
( -8 + 2 ) ÷ 2 = -6 ÷ 2 = -3
x = - 3
Option d.
Please help me! due today:(
Step-by-step explanation:
(π * r²) will give you are of entire circle
the multiply by 60/360 , to give the shaded part
Answer:
A ≈ 25.7 cm²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{60}{360}[/tex]
= π × 7² × [tex]\frac{1}{6}[/tex]
= [tex]\frac{49\pi }{6}[/tex]
≈ 25.7 cm² ( to the nearest tenth )
A 4-column table with 3 rows. The first column has no label with entries students, teachers, total. The second column is labeled wear glasses with entries 32, 4, 36. The third column is labeled do not wear glasses with entries 97, 2, 99. The fourth column is labeled total with entries 129, 6, 135.
Which statements are correct about the two-way frequency table? Check all that apply.
The correct statements about the two-way frequency table are:
Option C, and Option E.
According to the statement
we have to check that the given statement is applicable or not on the given conditions.
So, For this purpose
The two-way frequency table is
In Mathematics and statistics, A two-way frequency table is a tabular method for displaying relative data for two categories of variables. (See the attached).
the given options are:
Option A the row categories are "wears glasses"
Option B and "do not wear glasses."
Option C two teachers do not wear glasses.
Option D thirty-six students wear glasses.
Option E a total of 6 teachers were polled.
So, The correct statements about the two-way frequency table are:
Option C, and Option E.
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Answer: the corret answer is A, C and E
i need help in expanded form and simplify the problem
Answer:
[tex]\frac{1}{7w^{2} }[/tex]
Step-by-step explanation:
The expression can be simplified only if you take the same quantity out of both the top and bottom.
You can simplify the numbers by taking a factor of 3 out of the expression.
The numerator changes to 1 (because 3 / 3 = 1) and the denominator changes to 7 (because 21 / 3 = 7).
The variables can be eliminated through subtraction. The numerator variable is completely removed because you can subtract w³ from w⁵. This makes the denominator w² (because w⁵ - w³ = w²).
calculate the area of the shaded part to the nearest whole unit. (show your work)
The area of the shaded part in figure A and B are 2m² and 49 m² respectively.
Area of the shaded partTo determine the area, we must know the shape of the shaded part.
After identifying the shape, we move further to know the formula for such shape
From the figures given in A, we can see that the shaded region is in form of a triangle
a. The area of a right angle is given as;
The base multiplied by the half the height and vice versa
It is written mathematically as;
Area = 1/ 2 × base × height
Where
base = 2m
height = 2m
Substitute into the formula
Area = 1/ 2 × 2 × 2
Area = 2m²
For figure B, the shaded part is a rectangle
The formula for area of a rectangle is given as;
the width multiplied by the length
Area = width × length
Where width = 7m
length = 7m
Area = 7 × 7
Area = 49m ²
Thus, the area of the shaded part in figure A and B are 2m² and 49 m² respectively.
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out
Miranda decided to buy a $50,000 term life insurance policy from Palmetto Insurance Company to cover
her until she is 55. She is currently 50 years old and in good health. The probability of death in a given
year is provided by the Social Security Actuarial Life Table.
= Age
50
51
52
53
54
P(Death at a Given Age) 0.0032 0.0035 0.0038 0.0041 0.0044
1. Fill in the expected cost to Palmetto Insurance Company for each year Miranda has the policy.
Age at
Death
Expected
Cost
50
Check
$
Z=
51
$
x
52
$
x
53
$
x
54
$
x
2. The insurance company wants to make a profit of $500. How much would they need to charge for the
policy? $
x
Finish
The expected cost to Palmetto Insurance Company for each year Miranda has the policy is illustrated.
How to illustrate the information?Term policy amount = $50000
x (age) 50 51 52 53 54
p (death) 0.0032 0.0035 0.0038 0.0041 0.0044
1. Expected cost to Palmetto Insurance Company for each year Miranda has the policy
= P(death for a given year)*term policy amount
Thus, when x = 50
Expected cost = P(x) * 50000 = 0.0032*50000 = $160
Thus, when x = 50
Expected cost = P(x) * 50000 = 0.0032*50000 = $160
Thus, when x = 51
Expected cost = P(x) * 50000 = 0.0035*50000 = $175
Thus, when x = 52
Expected cost = P(x) * 50000 = 0.0038*50000 = $190
Thus, when x = 53
Expected cost = P(x) * 50000 = 0.0041*50000 = $205
Thus, when x = 54
Expected cost = P(x) * 50000 = 0.0044*50000 = $220
Thus, the table will become
x (age) 50 51 52 53 54
p (death) 0.0032 0.0035 0.0038 0.0041 0.0044
Expected cost 160 175 190 205 220
2) For company to make $500 profit
They should charge $500 more than their expected cost
= $(500 + 160 + 175 + 190 + 205 + 220)
= $1450
Thus, they need to charge $1450 overall or (1450/5 = $290 per year)
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The padlock for your gym locker uses a 3 number sequence to open the lock. If
the numbers go from 1 to 22, how many different sequences are there on the dial
without repeating a number?
Answer:
9,240
Step-by-step explanation:
For the first number, there are 22 numbers available to choose from. For the second number, there are 21 numbers available, since the first number cannot be the same as the second number. And for the last number, there are 20 remaining numbers to choose from. So, there are 22*21*20=9240 possible sequences.
What is the equation of a circle whose center at (-5, -2) and radius is 2?
The equation of a circle whose centre ([tex]-5,-2[/tex]) and radius [tex]2[/tex] is [tex]x^{2}+y^{2}+10x+4y+25=0[/tex]
What is equation of a circle?
A circle is a closed curve drawn from a fixed point called centre of the circle. The distance between the centre of the circle and the arc of the circle is called the radius of the circle.
The equation of a circle with centre [tex](h, k)[/tex] radius [tex]r[/tex] is
[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]
Given center = [tex](-5,-2)[/tex] and Radius = [tex]2[/tex]
Put the Given value in the equation:
= [tex](x-(-5))^{2} +(y-(-2))^{2} = 2^{2}[/tex]
= [tex](x+5)^{2} +(y+2)^{2}=2^{2}[/tex]
= [tex](x^{2} +10x+25)+(y^{2}+4y+4)= 4[/tex]
= [tex]x^{2} +y^{2}+10x+ 4y+ 29 = 4[/tex]
= [tex]x^{2} +y^{2}+10x +4y+ 29-4=0[/tex]
= [tex]x^{2} +y^{2}+10x+4y+25=0[/tex]
So, the equation of the circle whose centre is [tex](-5,-2)[/tex] and Radius [tex]2[/tex] is
[tex]x^{2}+y^{2}+10x+4y+25=0[/tex]
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What is the circumference of a circle (to the nearest whole number) whose radius is 5?
Answer:
31
Step-by-step explanation:
C= 2πr We will used 3.14 for pi and the radius is 5
C = 2(3.14)(5)
C =31.4 Then round to the nearest whole number which would be 31. 31.4 is closer to 31 than 32
The numerator in the fixed asset turnover ratio is:_______
The numerator in the fixed asset turnover ratio is sales.
To determine the fixed Asset Turnover ratio, the subsequent components are used: fixed Asset Turnover = sales / common fixed property.
The fixed asset turnover ratio exhibits how green an employer is at generating sales from its current fixed assets. A higher ratio implies that control is the usage of its fixed property extra efficiently.
Within the retail region, an asset turnover ratio of 2.5 or greater can be considered good, even as a business enterprise in the software region is much more likely to intention an asset turnover ratio it is among zero.25 and 0.5.
We can now calculate the constant asset turnover ratio by dividing the internet revenue for the yr through the average constant asset balance, which is equal to the sum of the modern-day and earlier duration balance divided through two.
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I need help someone with graphs
Answer:
B.) The graph of g(x) is shifted 4 units up
Step-by-step explanation:
In a linear function in slope-intercept form, b, or 4 in this case, represents the y-intercept which technically acts as a vertical shift
Problem
Solve for x in the image below.
18
Solution
We can start with the pythagorean theorem:
(leg 1)² + (leg 2)² = (hypotenuse)²
Answer:
20.1246118
Step-by-step explanation:
hypotenus^2 - (leg1)^2 = (leg2) ^2
27^2-18^2 = (leg2)^2
729-324 = (leg2)^2
405 = (leg2)^2
20.1246118 = leg 2
rewrite each expression without using absolute value notation |x-y| if x>y
Answer: x-y
Step-by-step explanation:
If x>y, then [tex]x-y > 0[/tex].
So, [tex]|x-y|=x-y[/tex]
The solution of the expression |x-y| if x>y without using absolute value notation is (x - y).
A collection of constants, variables or numbers connected using one or more arithmetic operator is called an expression
Example = 4y, 3x+4
The absolute value of any number or expression is always positive.
An expression that is either less than or greater than is called as inequality.
Given expression, |x-y| and the given inequality is x>y.
When x is greater than y, the difference between x and y is already positive.
So, the expression will be (x-y).
So, if x > y, then |x - y| = (x - y).
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Hi! I need help on this khan academy equation. If you can, please explain how to do other problems like this too. ): Thank you if you answer <3
Answer:
C
Step-by-step explanation:
x + 2y = 6
isolate x through
x = 6-2y . . . (iii)
Substitute equation (iii) in equation (i)
7x - y = 7
7(6 - 2y) - y = 7
42 - 14y - y = 7
42 - 15y = 7
Collecting Like terms
-15y = 7 - 42
-15y = -35
-15y = -35
-15 -15
y = 7
3
y =
[tex]2\frac{1}{3} [/tex]
Substitute y in equation (iii)
x = 6 - 2y
x = 6 - 2 × 7
3
x = 6 - 14
3
x =
[tex]1\frac{2}{3} [/tex]
Answer:
c is the right answer
Step-by-step explanation:
Travis traveled 135 miles in 5 hours. what is his unit rate of speed in miles per hour?
s= d/t
s= 135/5
s= 27 mph
pls mark as brainliest thanks!
A circle has a central angle measuring StartFraction 7 pi Over 6 EndFraction radians that intersects an arc of length 18 cm. What is the length of the radius of the circle
The length of the radius of the circle is 4.9cm.
What is circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.
The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.
Calculation for the length of the radius of the circle-
In order to overcome this issue, we must first translate the angle from radians to degrees.
The central angle of circle is 7/6π rads = 210 degrees.
Length of the arc is 18 cm.
The formula of length of an arc is given as-
[tex]l_{a r c}=\frac{\theta}{360} * 2 \pi r[/tex]
Let's change the values and find the solution.
[tex]\begin{aligned}&18=\frac{210}{360} * 2 \pi r \\&18=3.663 r \\&r=\frac{18}{3.663} \\&r=4.9 \mathrm{~cm}\end{aligned}[/tex]
Therefore, the length of the radius of the circle is 4.9 cm.
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write 75 as a product of prime use index notation when giving your answer
The formula for finding the kinetic energy, E, of an object is given below, where m represents the mass and v represents the speed of
the object.
Solve the formula for v
The formula for the velocity, v is √2E/m
What is kinetic energy?Kinetic energy is half the mass multiplied by the square of the speed of the object
It is written thus;
Kinetic energy = 1/ 2 × m × v²
To solve for 'v' mean that we should make 'v' the subject of formula
E = 1/ 2 mv²
E = [tex]\frac{mv^2}{2}[/tex]
cross multiply
[tex]2E = mv^2[/tex]
To make 'v' the subject, we have
[tex]v = \sqrt{\frac{2E}{m} }[/tex]
Thus, the formula for the velocity, v is √2E/m
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Anna and Damien are doing inventory at their pet store. Anna has counted 3 cages with 3 rabbits in each. Damien counted 4 cages with 2 rabbits in each. Which expression will help Anna and Damien count the rabbits at their store?
The expression that help Anna and Damien count the rabbits at their store is (3 * 3) + (4 * 2)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Anna has counted 3 cages with 3 rabbits in each. Damien counted 4 cages with 2 rabbits in each. Hence:
Total rabbits = (3 * 3) + (4 * 2)
The expression that help Anna and Damien count the rabbits at their store is (3 * 3) + (4 * 2)
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PLEASE HELP ASAP
List these numbers from SMALLEST TO LARGEST
29.94
28.15
27.068
28.08
28.3
Answer:
Step-by-step explanation:
27.068
28.08
28.15
29.94
which of the following expresses the possible number of positive real solutions for the polynomial equation shown below
The polynomial equation x³ - 4x² - 7x + 28 = 0, has solutions -√7, √7, and 4, among which √7 and 4 are positive real solutions. Hence we have two positive real solutions. Hence, option D is the right choice.
In the question, we are asked for the number of positive real solutions for the polynomial equation, x³ - 4x² - 7x + 28 = 0.
To find the solutions, we do as follows:
x³ - 4x² - 7x + 28 = 0,
or, (x³ - 7x) - (4x² + 28) = 0 {Grouping},
or, x(x² - 7) - 4(x² - 7) = 0 {Taking common},
or, (x - 4)(x² - 7) = 0 {Grouping},
or, (x - 4)(x + √7)(x - √7) = 0 {Using the formula: [tex]a^2 - b^2 = (a+b)(a-b)[/tex]}.
By the zero-product rule, the solutions are:
x - 4 = 0, or, x = 4,
x + √7 = 0, or, x = -√7,
x - √7 = 0, or, x = √7.
Thus, the positive real solutions are 4, and √7. Hence, there are two positive real solutions.
Thus, the polynomial equation x³ - 4x² - 7x + 28 = 0, has solutions -√7, √7, and 4, among which √7 and 4 are positive real solutions. Hence we have two positive real solutions. Hence, option D is the right choice.
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The complete question is:
"Which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?
x³-4x²-7x+28=0
a. two or zero
b. three or one
c. one
d. two"
Answer:
Two or zero.
Step-by-step explanation:
PLEASE HELP IM STUCK
Sonji bought a combination lock that opens with four-digit number created using the digits 0 through 9. The same
digit cannot be used more than once in the combination.
If Sonji wants the last digit to be a 7 and the order of the digits matters, how many ways can the remaining digits be
chosen?
O 84
• 504
• 3,024
• 60,480
Answer:
Step-by-step explanation:
This is what I am thinking. - ,- ,- , - I number goes in each space. There are 10 numbers to choose from and I cannot use a digit more than once. I only have 1 choice for last slot and that is the number 7. I have 9 numbers left . I could put any one of the 9 numbers in the first spot, then there are only 8 numbers to choose from, so I will put 8 in the second spot. I now have only 7 numbers that are left for the third spot.
If I multiple this together 9x8x7x1 = 504