Answer:
[tex]y = 5[/tex]
Step-by-step explanation:
Subtract the 4 from 9
Consider U = {x|x is a positive integer greater than 1}.
Which is an empty set?
{x|x ∈ U andOne-half is prime}
{x|x ∈ U and 2x is prime}
{x|x ∈ U andOne-half can be written as a fraction}
{x|x ∈ U and 2x can be written as a fraction}
Answer:
It's B
Step-by-step explanation:
I just took the test and got it right. :D
Using the definition of an empty set, we can see that the empty set in the options is:
{x|x ∈ U and 2x is prime}
Which is an empty set?
First, we know that:
U = {x|x is a positive integer greater than 1}.
So we can write:
U = {2, 3, ...}
Now, take in mind that if:
x ∈ U
Then x is a natural number larger than 1.
Now, if we multiply a natural number different than 1 by 2, we get:
2x
because x is a natural number larger than 1, 2x can't be a prime number (because it is divisible by 2 and by x).
Then the set that is empty is:
{x|x ∈ U and 2x is prime}
Because there is no element x in U that meets the condition that 2x must be prime.
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What value of x is in the solution set of 2x – 3 > 11 – 5x?
–3
0
2
4
Answer:
x = 4
Step-by-step explanation:
Solve the inequality
2x - 3 > 11 - 5x ( add 5x to both sides )
7x - 3 > 11 ( add 3 to both sides )
7x > 14 ( divide both sides by 7 )
x > 2
The only value of x greater than 2 is 4, thus
x = 4 is in the solution set
The value of x that is a solution set to the inequality is: D. 4.
How to Find the Solution Set of an Inequality?Given the an inequality such as, 2x – 3 > 11 – 5x, solve to isolate x.
2x – 3 > 11 – 5x
2x + 5x > 11 + 3
7x > 14
Divide both sides by 7
x > 14/7
x > 2
All set of the solution must be greater than 2. 4 is the only value of x that is greater than 2, so the answer is: D. 4.
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Mary has a collection of nickels and quarters for a total of $4.90. If she has 42 coins in total, how many of each kind are there?
Answer:
14 quarters and 28 nickels
Step-by-step explanation:
System of Equations where x = number of quarters and y = number of nickels
(1) equation with value of each coin
0.25(x)+0.05(y) = 4.90
(2) total number of coins
x + y = 42
Solve system of equations using either substitution or elimination
(elimination multiplying equation 2 by -0.5)
.25(x) + 0.05(y) = 4.90
-0.05(x) - 0.05(y) = 42 * (-0.05)
(3) Resulting equation
.20(x) = 2.8
x = 14
plug x into equation 2
14 + y = 42
y = 28
There are 14 quarters and 28 nickels in Mary's collection.
7.90 for 40 ounces of laundry soap unit rate
Answer:
$0.20 for 1 ounce of laundry soap
Step-by-step explanation:
7.90/40=0.1975
money can't be written like that so we have to round to the nearest hundredths
= $0.20
n is a positive intiger. Explain why 2n+1 must be an odd number.
2n + 1 will be an odd number.
Odd and EvenIf the number is divisible by 2 then the number will be an even number. Similarly, the number is not divisible by 2 then the number will be an odd number.
Given
2n+1 is a number where n is a positive integer.
To findThe 2n + 1 is an odd number.
How to find that 2n + 1 is an odd number?We know that if the integer is multiplied by 2 then it becomes the even number.
So the 2n is an even number.
We know that the sum of an even number and an odd number is an odd number. That is
Even + odd = odd
so 2n + 1 will be an odd number.
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The expression 2n + 1 represents an odd number for any positive integer n.
Explanation:The expression 2n + 1 represents an odd number for any positive integer n. This can be shown through an algebraic proof.
Let's assume that n is any positive integer. When we multiply 2 by any integer, we always get an even number because an even number multiplied by 2 is always even. Adding 1 to an even number results in an odd number. Therefore, 2n is always an even number, and by adding 1 to it, we get an odd number (2n + 1).
For example, if we take n = 1, then 2n + 1 = 2(1) + 1 = 3, which is an odd number. Similarly, if we take n = 2, then 2n + 1 = 2(2) + 1 = 5, which is also an odd number.
the first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. together they charged a total of $1300. what was the rate charged per hour by each mechanic if the sum of the two rates was $105 per hour?
Answer:
1st mechanic charges $55 per hour
2nd mechanic charges $50 per hour
Step-by-step explanation:
Suppose rate charged per hour for first meachnic is "x"
rate charged per hour for 2nd mechanic is "y"
So,
1st mechanic 10 hrs, 2nd mechanic 15 hrs, total charge 1300, so we can write:
10x + 15y = 1300
Also, total hourly rate of both is 105, so we can write:
x + y = 105
or
x = 105 - y
We can substitute this into 1st equation and solve for y:
[tex]10x + 15y = 1300\\10(105-y) + 15y = 1300\\1050-10y+15y=1300\\5y=250\\y=50[/tex]
And x is:
x = 105 - y
x = 105 - 50
x = 55
1st mechanic charges $55 per hour
2nd mechanic charges $50 per hour
How many 4 sided figures are in this diagram?
Answer:
?
Step-by-step explanation:
theres nothing there
Leona purchased a $1,000 bond having a quoted price of 99.875. She had to pay a 5.5% brokerage fee (of the selling price). What was the total cost of the bond (to the nearest whole cent)?
$943.82
$1,064.44
$534.77
$2,054.22
None of these choices are correct.
Answer:
The total cost of the bond is none of the given choices.
Step-by-step explanation:
The selling price of a $1000 bond = $99.875
The brokerage fee = 5.5 %
Now, 5.5% of $99.875 = [tex]\frac{5.5}{100} \times 99.875 = 5.493[/tex]
So, the brokerage fee = $5.493
Now, to find out the total cost of the bond:
Total Cost = The selling Price + Brokerage Price
= $99.875 + $5.493
= $105.368
or, the total price of the $1000 bond is $ 105.368.
Hence, the total cost of the bond is none of the given choices.
There are 5 boys in a class of 14 students (a)what is the ratio of girls to boys (b)what is the ratio of all students in the class to girls
Answer: a. 9:5
b: 14:9
Step-by-step explanation:
if there are 14 people in a class given 5 boys, then there are 9 girls. The values needed are boys (5), girls (9), and total students (14). Ratio Girls : Boys is 9 : 5 and Ratio All Students : Girls is 14 : 9
Answer:
9:5
Step-by-step explanation:
if there are 14 people in a class given 5 boys, then there are 9 girls.
What is the slope and y intercept of y-4x=-2
Answer:
Step-by-step explanation:
y=4x-2
Solve the right triangle ABC, with Cequals90degrees. Aequals58.3degrees, cequals24.8 ft
m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft
Step-by-step explanation:
If ABC is a right triangle, where the right angle is B, then
The hypotenuse of the triangle is b and a , c are its legssin(A) = [tex]\frac{a}{b}[/tex]sin(C) = [tex]\frac{c}{b}[/tex][tex]b=\sqrt{a^{2}+c^{2}}[/tex]The sum of the measures of the two acute angles A and C is 90°∵ ABC is a right triangle
∵ m∠C = 90°
∴ c is the hypotenuse and a , b are its legs
∵ m∠A = 58.3°
- The sum of the two acute angles in the right triangle = 90°
∴ m∠A + m∠B = 90°
- Substitute the measure of angle A
∴ 58.3 + m∠B = 90
- Subtract 58.3 from both sides
∴ m∠B = 31.7°
∵ sin(A) = [tex]\frac{a}{c}[/tex]
∵ c = 24.8 feet
∴ sin(58.3) = [tex]\frac{a}{24.8}[/tex]
- By using cross multiplication
∴ a = (24.8) × sin(58.3)
∴ a = 21.1 ft
∵ sin(B) = [tex]\frac{b}{c}[/tex]
∵ c = 24.8 feet
∴ sin(31.7) = [tex]\frac{b}{24.8}[/tex]
- By using cross multiplication
∴ b = (24.8) × sin(31.7)
∴ b = 13.0 ft
m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft
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Period:
1. Your cell phone plan costs 15 dollars a month, plus 10 cents per minute. Fill out a table, create a graph,
and write an equation to model the money you will spend each month on your cell phone.
Graph
Equation
Table
minutes cost
To model the money spent on a cell phone plan each month, the equation Cost = $15 + $0.10 × minutes can be used. A table and graph can be created by choosing different values for minutes and calculating the corresponding cost. The slope of the line represents the rate of change and the y-intercept represents the fixed cost.
To model the money you will spend each month on your cell phone, you can use the equation:Cost = $15 + $0.10 imes minutes
This equation represents a linear relationship where the fixed cost is $15 and the variable cost is $0.10 per minute. To create a table and graph, you can choose different values for minutes and calculate the corresponding cost. For example:Minutes Cost
0 $15
10 $16
20 $17
Using this data, you can plot the points on a Cartesian coordinate plane and draw a straight line through them. The slope of the line represents the rate of change (0.10 in this case) and the y-intercept represents the fixed cost ($15).how many square feet of outdoor carpet will we need for this hole?
please need help asap
disclaimer: if u do not know the answer please do not guess.please and thankyou
Answer:
36 sqaured feet
Step-by-step explanation:
24 plus 12 i believe?
Answer:
its so easy : 36 square feet
Step-by-step explanation:
add 24+12=36
What is the 7th term in the geometric sequence described by this explicit formula? An=7•3(n-1)
A.15,309
B.823,543
C.729
D.5103
The 7th term of the geometric sequence described by this explicit formula [tex]a_{n}=7*3^{(n-1)}[/tex] is 5103 ⇒ answer D
Step-by-step explanation:
The explicit formula of nth term in the geometric sequence is
[tex]a_{n}=a(r)^{n-1}[/tex] , where
a is the first termr is the common ratio between each two consecutive terms∵ The explicit formula of a geometric sequence is [tex]a_{n}=7*3^{(n-1)}[/tex]
∵ The explicit formula of nth term in the geometric sequence
is [tex]a_{n}=a(r)^{n-1}[/tex]
∴ a = 7 and r = 3
∵ We need to find the 7th term
∴ n = 7
- Substitute n by 7 in the formula
∴ [tex]a_{7}=7*3^{(7-1)}[/tex]
∴ [tex]a_{7}=7*3^{(6)}[/tex]
∵ [tex]3^{(6)}=729[/tex]
∴ [tex]a_{7}=7(729)[/tex]
∴ [tex]a_{7}=5103[/tex]
The 7th term of the geometric sequence described by this explicit formula [tex]a_{n}=7*3^{(n-1)}[/tex] is 5103
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How does this get solved? I am a bit confused on what to do next. Help is very appreciated.
Answer:
The Proof is given below.
Step-by-step explanation:
Given:
AD ≅ BD ≅ FD ≅ GD
To Prove:
AC ≅ GE
Proof:
In Δ ADF and Δ GDB
AD ≅ DG ……….{Given}
∠ ADF ≅ ∠ BDG …………..{Vertically Opposite angles are equal}
FD ≅ BD ……….{Given}
Δ ADF ≅ Δ GDB ….{Side-Angle-Side test}
∴∠ FAD ≅ ∠ BGD .....{corresponding angles of Congruent Triangle ( c.p.c.t}
i.e ∠ CAD ≅ ∠ EGD.....{ F-C-A and B-E-G straight line}.......( 1 )
Now ,
In Δ CAD and Δ E GD
∠ CAD ≅ ∠ EGD ……….{From ( 1 ) above}
AD ≅ GD ……….{Given}
∠ ADC ≅ ∠ EDG …………..{Vertically Opposite angles are equal}
Δ ADF ≅ Δ GDB ….{Angle-Side-Angle test}
∴ AC ≅ GE .....{corresponding sides of Congruent Triangle ( c.p.c.t}
[tex]\overline {AC} \cong \overline{GE}\ \textrm{......Proved}[/tex]
Write -0.048 as a fraction In simplest form
Answer:
-6/125
Step-by-step explanation:
well first, the decimal is negative so automatically whatever fraction you write is going to be negative
the you look at the decimal:
-0.048
there is a 0 in the tenths place, a 4 in the hundredths place, and an 8 in the thousandths place
so that means, the fraction would be -48/1000
but since it isnt simplified, that what you have to do
both can be divided by 2
which will give you:
-24/500
but those can be divided by 2 again:
-12/250
these can also be divided by 2 again:
-6/125
since the 125 cannot be divided into 2 evenly again, this is the fraction in simplest form
The simplest form of -0.048 is -6/125.
Use the concept of fraction defined as:
A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.
The given decimal number is -0.048
Since there are 3 numbers after decimal,
Therefore,
In fractional the the number can be written as,
-0.048 = -48/1000
Divide both numerator and denominator by 8,
-0.048 = -6/125
Hence,
The simplest form of -0.048 is -6/125.
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A rectangular piece of land has an area of 3/4 square mile. The land is 21/2 mile. What is its width
Answer:
The width of the rectangle is [tex]\frac{1}{14}[/tex] miles
Step-by-step explanation:
Given as for rectangle
The area of rectangle = A = [tex]\frac{3}{4}[/tex] mile²
The Length of rectangle = L = [tex]\frac{21}{2}[/tex] mile
Let The width of rectangle = W miles
Now, From area of rectangle
I.e Area of Rectangle = Length × Width
Or , A = [tex]\frac{21}{2}[/tex] mile × W mile
Or, [tex]\frac{3}{4}[/tex] mile² = [tex]\frac{21}{2}[/tex] mile × W mile
or, W = [tex]\frac{\frac{3}{4}}{\frac{21}{2}}[/tex] mile
or, W = [tex]\frac{3\times 2}{4\times 21}[/tex]
∴ W = [tex]\frac{1}{14}[/tex] miles
Hence The width of the rectangle is [tex]\frac{1}{14}[/tex] miles Answer
Final answer:
The width of the rectangular piece of land is 0.3 miles.
Explanation:
To find the width of the rectangular piece of land, we need to divide the area of the land by its length.
Area = 3/4 square mile
Length = 2 1/2 miles = 5/2 miles
Width = Area / Length
Width = (3/4) / (5/2) = (3/4) * (2/5) = 6/20 = 0.3 miles
So, the width of the land is 0.3 miles.
what is the slope of y= -4
Answer:
the slope is 0
Step-by-step explanation:
If 7 = -4, then the line will be horizontal on (-4) going on forever, never moving up or down. Therefore, there will be no slope.
DOES ANYBODY KNOW THIS??
h = 3a + 28.6
A pediatrician uses the model above to estimate the
height h of a boy, in inches, in terms of the boy's
age a, in years, between the ages of 2 and 5. Based
on the model, what is the estimated increase, in
inches, of a boy's height each year?
A) 3
B) 5.7
C) 9.5
D) 14.3
The estimated increase in height each year for a boy, according to the model h = 3a + 28.6, is 3 inches.
The equation h = 3a + 28.6 is used to estimate the height h of a boy, in inches, in terms of the boy's age a, in years. The coefficient of a in this linear equation represents the rate of change of height with respect to age. Given that the coefficient is 3, this indicates that the estimated increase in height each year is 3 inches. Therefore, the answer to the question is A) 3.
Someone please help!
Answer:
1. 35, 32, 29, 26 are in Arithmetic Sequence having common difference - 3.
5. -7, -9, -11, -13 are in Arithmetic Sequence having common difference - 2.
Step-by-step explanation:
1. 35, 32, 29, 26 are in Arithmetic Sequence having common difference - 3.
2. -1. 6, -36, 216 are not in Arithmetic Sequence.
3. -2, -4, -8, -16 are not in Arithmetic Sequence.
4. -1, 1, 4, 8 are not in Arithmetic Sequence.
5. -7, -9, -11, -13 are in Arithmetic Sequence having common difference - 2.
6. 1, -5, 25, -125 are not in Arithmetic Sequence. (Answer)
vincent’s copier can print in 7 hours. chris’s printer can do the same in 13 hours. how long would it take to do the job using both copiers
Answer:
Step-by-step explanation:
1/7+1/13=1/t
multiply both sides by 7*13*t
13t+7t=7*13
21t=91
t=91/19
it will take 4 hours and 8 minutes
7. A vending machine only accepts dimes and quarters. There are 85 coins
in the machine with a total value of $16.75. How many of each coin are in
the machine?
There are 55 quarters and 30 dimes in the machine.
Step-by-step explanation:
Total coins = 85
Total amount = $16.75 = 16.75*100 = 1675 cents
1 quarter = 25 cents
1 dime = 10 cents
According to given statement;
x+y=85 Eqn 1
25x+10y=1675 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=85)\\10x+10y=850\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](25x+10y)-(10x+10y)=1675-850\\25x+10y-10x-10y=825\\15x=825[/tex]
Dividing both sides by 15
[tex]\frac{15x}{15}=\frac{825}{15}\\x=55[/tex]
Putting in Eqn 1;
[tex]55+y=85\\y=85-55\\y=30[/tex]
There are 55 quarters and 30 dimes in the machine.
Keywords: linear equation, subtraction
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What are the terms in the expression 2x−4y+8 ?
2x and 4y
8
2, 4, and 8
2x, −4y , and 8 i looked at the other answers of others but i only need one answer so please help
Answer:
The correct answer is D. 2x, -4y, and 8.
Step-by-step explanation:
The concept of the terms of an equation is used for the monomials of each member participating in the equation. In Mathematics we distinguish between two types of terms:
1. The terms in x: when the terms are accompanied by a literal.
2. The independent terms: when the terms are constituted by numerical elements.
Help me solve this intermediate algebra problem
Answer:
x + 1 + 4√(x-3)
Step-by-step explanation:
Given: [tex]$ (\sqrt{x - 3} + 2)^2 $[/tex]
We know that: (a + b)² = a² + b² + 2ab
Using this formula, we expand the given expression:
⇒ [tex]$ (\sqrt{x - 3} + 2)^2 = (\sqrt{x - 3})^2 + 2.\sqrt{x - 3}. 2 + 2^2 $[/tex]
⇒ [tex]$ x - 3 +4\sqrt{x - 3} + 4 $[/tex]
⇒ [tex]$ (\sqrt{x - 3} + 2)^2 $[/tex] = x + 1 +4√(x - 3).
Factor the expression completely.
25x2-65x - 30
Answer:
[tex]\large\boxed{25x^2-65x-30=5(x+3)(5x-2)}[/tex]
Step-by-step explanation:
[tex]25x^2-65x-30=5(5x^2-13x-6)\\\\=5(5x^2-15x+2x-6)=5\bigg(5x(x-3)+2(x-3)\bigg)\\\\=5(x-3)(5x+2)[/tex]
Solve.
−1.5x−3.1<5.5
Drag and drop a number or symbol into each box to show the solution.
Answer:
[tex]x>-5.733[/tex]
Step-by-step explanation:
Given : Expression [tex]-1.5x-3.1<5.5[/tex]
To find : Solve the expression ?
Solution :
Step 1 - Write in inequality,
[tex]-1.5x-3.1<5.5[/tex]
Step 2 - Add 3.1 both side,
[tex]-1.5x-3.1+3.1<5.5+3.1[/tex]
[tex]-1.5x<8.6[/tex]
Step 3 - Divide by 1.5 both side,
[tex]-\frac{1.5x}{1.5}<\frac{8.6}{1.5}[/tex]
[tex]-x<5.733[/tex]
Step 4 - Multiply by -1 both side,
[tex]x>-5.733[/tex]
The number is -5.733 and symbol is greater (>).
Colin and Brian were playing darts. Colin scored 62. Brian scored 59 more than Colin. What was their combined score?
Answer:
183
Step-by-step explanation:
Add 62 and 59 to get Brians score and then add another 62 to find the combined score.
Their combined score is 183.
To find the combined score of Colin and Brian, we need to add their individual scores.
Given:
- Colin's score: 62
- Brian's score: 59 more than Colin's score
We'll find Brian's score first, then add it to Colin's score to get the combined score.
Brian's score = Colin's score + 59
[tex]\[ \text{Brian's score} = 62 + 59 \][/tex]
[tex]\[ \text{Brian's score} = 121 \][/tex]
Now, to find the combined score:
[tex]\[ \text{Combined score} = \text{Colin's score} + \text{Brian's score} \][/tex]
[tex]\[ \text{Combined score} = 62 + 121 \][/tex]
[tex]\[ \text{Combined score} = 183 \][/tex]
So, their combined score is 183.
carol is excited to get a new kitten from the animal shelter. the kitten had an $299 adoption fee. carol had $50 off coupon for the adoption and will also have to pay $20 per month for food and supplies. how longg will it take for carol to spend $250
Answer:
1 month
Step-by-step explanation:
249 is the amount she spends for buying the kitten, (299-50=249) which she only has to pay once.
20 is the amount she has to spend every month, the rate of change.
The problem can be modeled with the general equation:
y = 20x + 249
In this equation, x the the time in months and y is the amount of money spent.
Substitute 250 for y.
y = 20x + 249
250 = 20x + 249 <= isolate x to get the number of months
1 = 20x
x = 1/20
Carol will only spent money every month, not for 1/20 of a month.
It will only take Carol 1 month to spent $250.
Check answer:
Substitute x for 1
y = 20x + 249
y = 20(1) + 249
y = 269
269 is more than 250 already.
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My nickname - Lovely
Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form. (1.4), m=3
The slope is already given in the question, so we only ned to solve for the y-intercept using y = mx + b.
4 = 3(1) + b
4 = 3 + b
4 - 3 = 3 + b - 3
1 = b
Now, write the equation in slope-intercept form.
y = 3x + 1
_____
Best of Luck,
Wolfyy :)
You have 7 books,but only 3 will fit on the shelf.how many different arrangements of 3 books out of 7 could you make
To find the number of different arrangements of 3 books from 7, we use permutations, specifically P(7, 3) = 7! / (7-3)! = 210. Thus, there are 210 different arrangements possible.
Explanation:The student's question involves determining the number of different arrangements of 3 books that can be made from a set of 7 books. In mathematics, this is known as a permutation problem, since the order in which the books are placed matters.
To calculate permutations, we use the formula P(n, k) = n! / (n-k)!, where n is the total number of items to choose from, in this case, 7 books, and k is the number of items to arrange, in this case, 3. Using the formula:
P(7, 3) = 7! / (7-3)! = 7! / 4! = (7 × 6 × 5 × 4!) / 4! = 210.
Therefore, there are 210 different arrangements possible when selecting and arranging 3 books out of 7.