Answer:
you can get 11 DVDs if they cost 18 dollars
Answer:
Step-by-step explanation:
198/18=11. You can buy 11 packs
0=(1x+1)(1x-3) if m(x) =10, find the value of x
Answer:
x=1+sqrt(14) & 1-sqrt(14).
Step-by-step explanation:
(1x+1)(1x-3)=0
(x+1)(x-3)=0
m(x)=(x+1)(x-3)=10
(x+1)(x-3)=10
x^2+x-3x-3=10
x^2-2x-3=10
x^2-2x-3-10=0
x^2-2x-13=0
Apply the quadratic formula with a=1, b=-2 and c=-13.
The answer is x=1+sqrt(14) & 1-sqrt(14).
What is Half of 7 minutes 24 seconds
Answer:
3 min 42 seconds
Step-by-step explanation:
1 minute=60 seconds so 7 minutes = 420 seconds. Plus the other 24 is 444 seconds. 444/2=222 so its 222 seconds or 3 minutes and 42 seconds
7 min = 7 x 60 sec = 420 sec
420 sec + 24 sec = 444 sec
444sec : 2 = 222 sec
222 sec = 3x60sec + 42sec = 3 min 42 sec
The population of Australia is more than 20,000,000 people. You can write 20,000,000 as 2 × 10,000,000. Write 10,000,000 using exponents.
Answer:
10^7
Step-by-step explanation:
So we would start with 10 and a trick to help you is when your turning a number with 10 at the start with each number you raise it by is how many 0 it will have behind it for example 10,000,000 would be 10^7 cause you have 0 zeros in it.
10,000,000 in exponent form is 10⁷. Therefore, 20,000,000 can be written as 2 × 10⁷. This provides a concise mathematical way of expressing large numbers.
To write 10,000,000 using exponents, we recognize that this number is a power of 10. Specifically, 10,000,000 can be written as 10 to the power of 7. This is because:
10,000,000 = 10⁷
When you multiply 10 by itself 7 times (10 × 10 × 10 × 10 × 10 × 10 × 10), you get 10 million. Therefore, the population of Australia, which is more than 20,000,000 people, can be written as:
20,000,000 = 2 × 10,000,000 = 2 × 10⁷
When you isolate the variable, the goal is to get the variable
A
to equal 1.
B
on both sides of the equal sign to show they are equal.
C
by itself on one side of the equal sign and a value on the other.
D
by itself on one side of the equal sign and zero on the other side.
Answer:
C
Step-by-step explanation:
For example
[tex]y = 77 \\[/tex]
The answer is C: by itself on one side of the equal sign and a value on the other.
Let's go through the detailed steps of isolating the variable with each option in mind.
Option: C - by itself on one side of the equal sign and a value on the other.
Given equation:[tex]\(3x + 7 = 16\)[/tex]
Step 1: Identify the Variable
The variable in the equation is [tex]\(x\).[/tex] We want to isolate [tex]\(x\)[/tex] to find its value.
Step 2: Isolate Terms with the Variable
Move terms containing the variable to one side of the equation. Here, we'll move [tex]\(3x\)[/tex] to the left side by subtracting [tex]\(7\)[/tex] from both sides:
[tex]\[3x + 7 - 7 = 16 - 7\][/tex]
This simplifies to:
[tex]\[3x = 9\][/tex]
Now, the term [tex]\(3x\)[/tex] is isolated on the left side of the equation.
Step 3: Perform Inverse Operations to Isolate the Variable
Since [tex]\(x\)[/tex] is being multiplied by [tex]\(3\),[/tex] to isolate [tex]\(x\),[/tex] we divide both sides by [tex]\(3\):[/tex]
[tex]\[\frac{3x}{3} = \frac{9}{3}\][/tex]
This simplifies to:
[tex]\[x = 3\][/tex]
Now, the variable [tex]\(x\)[/tex] is isolated on the left side of the equation, and its value is [tex]\(3\).[/tex]
By following these detailed steps, we have successfully isolated the variable [tex]\(x\)[/tex] on one side of the equal sign and a specific value (option C) on the other side, demonstrating equality between the two sides of the equation.
Factor the expression.
6y^2 + 13y + 5
Answer:
Step-by-step explanation:
Answer:
If you factorise it you should get (3y+5)(2y+1)
the size of the largest angle in a triangle is 3 times the size of the smallest angle.
the third angle is 10° more than the smallest angle
work out the size, in degrees, of each angle in the triangle.
You must show your working (let X be the smallest angle).
The sizes of the angles are 34° , 44° , 102°
Step-by-step explanation:
The given is:
The size of the largest angle in a triangle is 3 times the size of the smallest angleThe third angle is 10° more than the smallest angleThe size of the third angle is xWe need to find the size of each angle in the triangle
∵ The size of the smallest angle = x°
∵ The size of the largest angle is 3 times the size of the smallest angle
∴ The size of the largest angle = x × 3 = (3x)°
∵ The third angle is 10° more than the smallest angle
∴ The size of the third angle = (x + 10)°
Add the size of the three angles and equate the sum by 180°
∵ The sum of the sizes of the interior angles of a Δ is 180°
∴ x + (3x) + (x + 10) = 180
∴ x + 3x + x + 10 = 180
- Add like terms
∴ 5x + 10 = 180
- Subtract 10 from both sides
∴ 5x = 170
- Divide both sides by 5
∴ x = 34
∵ x is the size of the smallest angle
∴ The size of the smallest angle is 34°
∵ 3x is the size of the largest angle
∴ The size of the largest angle = 3(34) = 102°
∵ x + 10 is the size of the third angle
∴ The size of the third angle = 34 + 10 = 44°
The sizes of the angles are 34° , 44° , 102°
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find the solution in slope-intercept form y+7=-3(x-1) and 3x+y=-4
Answer:
The slope intercept form of both given equations is : y = - 3 x - 4.
Step-by-step explanation:
Here, the given equations are:
y +7 = -3 ( x - 1 )
and 3 x + y = - 4
Now,the SLOPE INTERCEPT FORM of any given equation is given as:
y = m x + C : here, C = Y - intercept, m = Slope
Consider equation (1):
y +7 = -3 ( x - 1 ) ⇒ y + 8 = - 3 x + 3
or, y = -3x + 3 - 7 = -3x - 4
⇒ y = -3x -4
Hence, the slope-intercept form of the given equation is y = -3x -4.
Consider equation (2):
3 x + y = - 4 ⇒ y = -4 - 3 x
⇒ y = -3 x - 4
Hence, the slope-intercept form of the given equation is y = -3x -4.
Final answer:
The solution in slope-intercept form for both given equations is y = -3x - 4, showing that they represent the same line.
Explanation:
To find the solution in slope-intercept form for the given equations y+7=-3(x-1) and 3x+y=-4, we need to solve for y in terms of x for each equation.
For the first equation, solve for y:
y + 7 = -3(x - 1)
y = -3x + 3 - 7
y = -3x - 4 (Slope-intercept form of the first equation)
For the second equation, solve for y:
3x + y = -4
y = -3x - 4 (Slope-intercept form of the second equation)
After solving, we observe that both equations have the same slope-intercept form, which indicates that these are actually the equations of the same line.
Write the factored form of the equation of a polynomial that has a root of x=3, a zero of x=-2, and an x-intercept of x=-1. Then write that equation in standard form
Answer:
[tex]f(x)=x^3-7x-6[/tex]
Step-by-step explanation:
If x = 3 is a root of a polynomial f(x), then x - 3 is a factor of this polynomial.
If x = -2 is a zero of a polynomial function f(x), then f(-2) = 0 and x - (-2) = x + 2 is a factor of f(x).
If x = -1 is an x-intercept of the function, then y = 0 and x - (-1) = x + 1 is also a factor of the function f(x).
Therefore, the polynomial expression is
[tex]f(x)=(x-3)(x+2)(x+1)[/tex]
In standard form:
[tex]f(x)=(x-3)(x^2+2x+x+2)=(x-3)(x^2+3x+2)=x^3+3x^2+2x-3x^2-9x-6=x^3-7x-6[/tex]
2.
Rock can read 10 books in 30 minutes. How long does it take
Rock to read 15 books, if the speed is consistent?
Answer:
The answer is 45 minutes.
Step-by-step explanation:
30 divided by 10 is 3. So it's 3 minutes per book. 3 multiplied by 15 is 45.
In an ordered pair, what axis represents the input
In an ordered pair for a Cartesian coordinate system, the input is represented by the x-axis. It is denoted as the first value in an (x, y) pair and represents the horizontal direction in a two-dimensional space.
Explanation:In an ordered pair, the input is typically represented by the x-axis in a Cartesian coordinate system. An ordered pair is denoted as (x, y), where 'x' represents the input or independent variable, and 'y' represents the output or dependent variable. For instance, in a function such as y = mx + b, 'x' would be the input and 'y' would be the output. This input value corresponds to the position along the horizontal x-axis.
While the y-axis represents the vertical direction or output value, the x-component of a vector is a dot product with the unit vector in the x-direction. For two-dimensional vector problems, it's also easier to pick a coordinate system that has one horizontal axis (x) and one vertical axis (y), projecting the vectors onto these axes.
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Final answer:
In an ordered pair (x, y), the x-axis represents the input which is the horizontal direction on the Cartesian coordinate system.
Explanation:
In an ordered pair, such as (x, y), the x-axis represents the input, which is the horizontal direction, and the y-axis represents the output, which is the vertical direction. In the Cartesian coordinate system, the origin, where the x and y axes intersect, is the point of projection.
By convention, the positive x-axis generally extends to the right, and the positive y-axis extends upwards. The x-coordinate corresponds to the position along the x-axis while the y-coordinate corresponds to the position along the y-axis.
One side of a triangle is 2 times the second side. The third side is 5 ft longer than the second side. The perimeter of a triangle is 81 ft. Find the length of each side.
Answer:
The length of each side of triangle are 19 ft, 24 ft and 38 ft.
Step-by-step explanation:
Let the length of second side be x.
Now given:
Length of first side is 2 times length of second side.
Length of first side = 2x
Also, Length of third side is 5 ft longer than the second side.
Length of third side = 5+x
Perimeter of triangle = 81 ft.
We need to find the length of each side.
Now perimeter of triangle is sum of all three sides of triangle.
Therefore;
Perimeter of triangle = Length of first side + length of second side + Length of third side.
[tex]2x+x+5+x=81 ft\\4x+5=81ft\\4x= 81 -5 ft\\4x = 76ft\\x= \frac{76}{4} = 19 ft[/tex]
Length of Second Side = 19 ft.
Length of First side = [tex]2x= 2\times19 = 38 ft[/tex]
Length of Third side = [tex]5+x= 5+19=24ft[/tex]
Hence the Length of triangles are 19 ft,38 ft,24 ft.
Select all the expressions that are equivalent to (–60) ÷ 5.
A(60)÷(−5)
B(−60)÷(−5)
C(−60)×15
D(60)×(−15)
E(−60)÷(−15)
Answer:
I think the only one is A
$4,000 invested in Fund A returned 5% profit. Amount invested in Fund B returned a 2% profit. How much was invested in Fund B if both funds returned 4%?
as I read it, what I get is that
x = returned profits or yielded interest from investment in A
y = returned profits or yielded interest from investment in B
T = total amount invested or namely A + B.
4000 were invested in A, and it yielded 5%, what's 5% of 4000? (5/100)(4000) = 200 = x.
we know the total amount is T, since A get 4000, B must have gotten T - 4000, or the slack. We also know that B yielded a 2% profit, well, what's 2% of T - 4000? (2/100)(T-4000) = y.
we also know that, whatever "x" and "y" are, their sum total yielded a 4% returns from T, or the total principal, what's 4% of T? (4/100)T = 0.04T.
[tex]\bf \begin{cases} T=\textit{total principal}\\[-0.5em] \hrulefill\\ A=4000\\ x = \stackrel{\textit{5\% of A}}{200}\\[-0.5em] \hrulefill\\ B=T-4000\\ y=\stackrel{\textit{2\% of B}}{0.02(T-4000)} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{5\% of A}}{200}+\stackrel{\textit{2\% of B}}{0.02(T-4000)}~~=~~\stackrel{\textit{4\% of T}}{0.04T} \\\\\\ 200+0.02T-80=0.04T\implies 120+0.02T=0.04T\implies 120=0.02T \\\\\\ \cfrac{120}{0.02}=T\implies 6000=T~\hfill \stackrel{~\hfill \textit{invested in B}}{6000-4000\implies 2000}[/tex]
9 lb 4 oz − 2 lb 12 oz
Answer: 6 LB 12 OZ
16 OZ in a LB
9 LB - 2 LB = 7 LB
4 OZ - 12 OZ difference of 8 OZ
4 - 4 = 0 then 16 OZ in a LB
4 remaining - 16 = 12 dropping the 7 LB to 6 LB
Step-by-step explanation:
First, turn into just ounces (1lb. = 16oz.)
9 lb 4 oz = 148 oz
2 lb 12 oz = 44 oz
Second, subtract.
148 - 44 = 104 oz
Third, turn into pounds and ounces.
104 oz = 6 lb 8 oz
______
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What are the factor paira of 48
Answer:
1 x 48 = 48
2 x 24 = 48
3 x 16 = 48
4 x 12 = 48
6 x 8 = 48
8 x 6 = 48
12 x 4 = 48
16 x 3 = 48
24 x 2 = 48
48 x 1 = 48
Step-by-step explanation:
Answer:
The factor pair for 48 is 1,2,3,4,6,8,12,16,24 and 48
Your welcome!
The probability that a family visits City Museum is 0.46, and the probability that a family rides on the Three Rivers Ferry is 0.47. The probability that a family does both is 0.12. Find the probability that the family visits the museum or rides the ferry.
Considering the definition of probability, the probability that the family visits the museum or rides the ferry is 81%.
Definition of Probabitity
Probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
Union of events
The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.
Events and probability in this case
Let A be the event that a family visits the City Museum, and B be the event that a family rides the Three Rivers Ferry. The given probabilities are:
P(A)= 0.46
P(B)= 0.47
P(A and B)= P(A∩B)= 0.12
In this case, considering the definition of union of eventes, the probability that a course has a final exam or a research project is calculated as:
P(A∪B)= P(A) + P(B) -P(A∩B)
P(A∪B)= 0.46 + 0.47 -0.32
P(F∪R)= 0.81= 81%
Finally, the probability that the family visits the museum or rides the ferry is 81%.
Through (-1,4) and a perpendicular to 4y-2x=12
Answer:
y = -2x + 2 → 2x + y = 2Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-\text{slope}\\b-\text{y-intercept}\\\\\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\\text{then}\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\k\ ||\ l\iff m_1=m_2[/tex]
[tex]\text{We have the equation of a line in the standard form:}\ Ax+By=C.\\\\\text{Convert to the slope-intercept form:}\\\\4y-2x=12\qquad\text{add}\ 2x\ \text{to the both sides}\\\\4y-2x+2x=2x+12\\\\4y=2x+12\qquad\text{divide both sides by 4}\\\\\dfrac{4y}{4}=\dfrac{2x}{4}+\dfrac{12}{4}\\\\y=\dfrac{1}{2}x+3\to\boxed{m_1=\dfrac{1}{2}}[/tex]
[tex]\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{Put the value of the slope and the coordinates of the given point (-1, 4)}\\\text{to the equation of a line:}\\\\4=-2(-1)+b\\\\4=2+b\qquad\text{subtract 2 from the both sides}\\\\4-2=2-2+b\\\\2=b\to b=2\\\\\bold{FINALLY:}\ y=-2x+2[/tex]
[tex]\text{Convert to the standard form:}\\\\y=-2x+2\qquad\text{add}\ 2x\ \text{to the both sides}\\\\y+2x=-2x+2x+2\\\\2x+y=2[/tex]
Researchers wanted to learn more about people who rent apartments and who have pets. They
began a study of 971 renters. The researchers found that 216 of the renters in their study
reported that they owned pets. Of the renters who owned pets, 2/3 of the renters owned a dog.
What percentage of all renters in the study owned a dog?
HELP ME PLEASE!!!!!!!!!!!! Correct answer only, just don't write or guess or you will get reported!
A plumber charges a flat fee of $45 to answer a service call in addition to an hourly rate of $30.50. The plumber has estimated he will earn at least $197.50 from his next repair job. Which inequality can be used to determine the number of hours, h, that the plumber will work on his next job?
Group of answer choices
$30.50h + 45 > $197.50, with a solution of h>6
$30.50h + 45 < $197.50, with a solution of h<6
$30.50h + 45 ≤ $197.50, with a solution of h≤6
$30.50h + 45 > $197.50, with a solution of h>6
Answer: The second one is correct I believe
Step-by-step explanation:
Which triangles are congruent in the diagram?
Sarah is sellng bracelets for $5 and necklaces for $10. If the equation below represents her total revenue (R), what is the meaning of '10y'?
R = 5x + 10y
Question 10 options:
Number of bracelets sold
Money earned from bracelets
Number of necklaces sold
Answer:
Number of necklaces sold
Step-by-step explanation:
Every necklace sold becomes added up to make up y, and then you multiply that by $10(the money for necklaces).
what expression shows a way to find 20% of 950?
The expression that can be used to find 20% of 950 is 20/100 × 950
How to write percentage expressions?20% of 950
= 20/100 × 950
= 0.2 × 950
= 190
Therefore, the 20% of 950 is given by 190
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To find 20% of 950, you use the formula (Percentage / 100) × Whole. By applying the formula, 20% of 950 is calculated to be 190.
To find 20% of 950, you can use the formula for finding a percentage of a number:
Part = (Percentage / 100) × Whole
In this case, the percentage is 20 and the whole is 950. Now apply the formula:
Part = (20 / 100) × 950
Part = 0.2 × 950
Part = 190
Therefore, 20% of 950 is 190.
To find the value of the following expression, what operation should you do first? 20-(7+4) x5
Answer:
Distributive Property.
Answer:
-35
Step-by-step explanation:
20-(7+4)*5
20-(11)(5)
20-55
-35
David did not have time to wait for the elevator on the first floor of the building so he decided to go up the stairs. If it took him 2 minutes to get to the third floor, how long will it take him to get to the ninth floor?
Answer:
8 minutes
Step-by-step explanation:
It takes 2 minutes every 2 floors, and Floor 9 is 8 floors away from Floor 1, so 2x4=8.
Write the polynomial 4x2 - 6x6 + 2x3 + 12 - 5x3 + 4x4 in standard form.
Answer:
[tex]\large\boxed{-6x^6+4x^4-3x^3+4x^2+12}[/tex]
Step-by-step explanation:
[tex]4x^2-6x^6+2x^3+12-5x^3+4x^4\\\\=-6x^6+4x^4+2x^3-5x^3+4x^2+12\qquad\text{combine like terms}\\\\=-6x^6+4x^4+(2x^3-5x^3)+4x^2+12\\\\=-6x^6+4x^4-3x^3+4x^2+12[/tex]
HELP ASAP! A store clerk is unpacking a box of cameras. The line plot displays the weight of each camera. How much do all the cameras in the box weigh?
Answer:
3\8 I think is the answer
Step-by-step explanation:
I know because I know!
Answer:
8 3/8
Step-by-step explanation:
I have study island too
Which expressions are equivalent to the one below? Check all that apply.
log 2 - log 6
A. log(2) + log(1/6)
B. log 2
C. log(1/3)
D. log 3
Answer:
C. log(1/3)
Step-by-step explanation:
Remember the quotient/subtraction rule for logs:
log2 - log6 can be written as log(2/6)
Hence, it's equal to C. log(1/3)
Hope this helps!
Mark brainliest if you think I helped! Would really appreciate!
The expressions that are equivalent to [tex]\( \log 2 - \log 6 \)[/tex] are options A and C.
The correct option is (A&C).
To solve [tex]\( \log 2 - \log 6 \)[/tex], we can use the property of logarithms that states:
[tex]\[ \log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right) \][/tex]
Given [tex]\( \log 2 - \log 6 \)[/tex], applying the above property:
[tex]\[ \log 2 - \log 6 = \log\left(\frac{2}{6}\right) = \log\left(\frac{1}{3}\right) \][/tex]
So, the expression \[tex]( \log 2 - \log 6 \)[/tex] is equivalent to [tex]\( \log\left(\frac{1}{3}\right) \)[/tex], which matches option C.
Now, let's check the other options:
A. [tex]\( \log(2) + \log\left(\frac{1}{6}\right) \)[/tex]
This expression can be simplified using the properties of logarithms to [tex]\( \log\left(2 \times \frac{1}{6}\right) = \log(1/3) \),[/tex] which is equivalent to the original expression. So, option A is also correct.
B. [tex]\( \log 2 \)[/tex]
This option is not equivalent to the original expression. It only represents [tex]\( \log 2 \),[/tex] not the difference of [tex]\( \log 2 \) and \( \log 6 \).[/tex]
D. [tex]\( \log 3 \)[/tex]
This option is not equivalent to the original expression. It only represents [tex]\( \log 3 \)[/tex], which is unrelated to the expression [tex]\( \log 2 - \log 6 \).[/tex]
So, the expressions that are equivalent to [tex]\( \log 2 - \log 6 \)[/tex] are options A and C.
The perimeter of a semicircle is 35.98 meters. What is the semicircle's diameter?
To find the diameter of the semicircle, divide the circumference of the whole circle by 2. Given that the perimeter of the semicircle is 35.98 meters, the diameter would be approximately 22.87 meters.
Explanation:To find the diameter of the semicircle, we first need to find the circumference of the entire circle and then divide it by 2. The formula for the circumference of a circle is C = π * d, where C is the circumference and d is the diameter.
Given that the perimeter of the semicircle is 35.98 meters, the circumference of the whole circle will be twice that value. So, 2 * 35.98 = 71.96 meters.
Now we can use the formula C = π * d to solve for the diameter: 71.96 = π * d. Dividing both sides of the equation by π gives us d = 71.96 / π.
Using a calculator, we can approximate π to 3.14. So, d = 71.96 / 3.14 = 22.87 meters.
How did the gulf of Tonkin resolutions affect US involvement in the Vietnam war?
Answer:
I don't know how this is math but...
The Gulf of Tonkin Resolution authorized President Lyndon Johnson to “take all necessary measures to repel any armed attack against the forces of the United States and to prevent further aggression” by the communist government of North Vietnam. Hope I helped! ☺
Answer:
It gave the president the ability to send troops without congressional approval.
Step-by-step explanation:
there are 50 jelly beans in a jar. 32 percent are black, 52 percent are green, and 16 percent are purple. how many green jelly beans are in the jar?