Answer:
2800 cm^3, or 2.8 liters
Step-by-step explanation:
The base of the tank remains 14 cm × 25 cm. The remaining height is 15 -7 = 8 cm, so the remaining volume is ...
(14 cm)(25 cm)(8 cm) = 2800 cm^3 = 2.8 liters
_____
1 liter = 1000 cm^3
Expand the expression (5x + 3)2, and write the result in standard form.
Expand
2 × 5x + 2 × 3
Simplify 2 × 5x to 10x
10x + 2 × 3
Simplify 2 × 3 to 6
= 10x + 6
The expanded expression in standard form for the given equation is [tex]\(25x^2 + 30x + 9\).[/tex]
To expand the expression [tex]\((5x + 3)^2\)[/tex], we use the distributive property, which states that for any real numbers [tex]\(a\), \(b\), and \(c\):[/tex]
[tex]\((a + b)^2 = a^2 + 2ab + b^2\).[/tex]
In this case,[tex]\(a = 5x\)[/tex] and[tex]\(b = 3\)[/tex]. Substituting these values into the formula, we get:
[tex]\[(5x + 3)^2 = (5x)^2 + 2(5x)(3) + 3^2\][/tex]
Now, let's compute each term:
1.[tex]\( (5x)^2 = 25x^2 \) (since \((a)^2 = a \times a\)).[/tex]
2. [tex]\(2(5x)(3) = 30x\) (by multiplying \(2ab\) where \(a = 5x\) and \(b = 3\)).[/tex]
3. [tex]\(3^2 = 9\).[/tex]
Now, summing up all the terms, we get:
[tex]\[ (5x + 3)^2 = 25x^2 + 30x + 9 \][/tex]
So, the expanded expression in standard form is [tex]\(25x^2 + 30x + 9\).[/tex]
Complete question:
Expand the expression (5x + 3)2, and write the result in standard form.
Which of the following is a polynomial function in factored form with zeros at 0, -3, and 4
Answer:
Option A is correct.
Step-by-step explanation:
The polynomial with factors with zeros at 0,-3 and 4 means
x=0 and x =-3 and x=4
this can be written as:
x=0, x+3 =0 and x-4=0
or
x(x+3)(x-4) =0
or
f(x) = x(x+3)(x-4)
So, Option A is correct.
98% of the mules who were surveyed said that stubbornness was a good character trait. If 343 mules gave this response, how many were surveyed in total?
Do a part over whole fraction
98% is a part of 100%
343 is a part of the number of mules who were surveyed in an unknown quantity.
You can set what you know into two proportions equal to each other:
[tex]\frac{98}{100} =\frac{343}{x}[/tex]
***x is the unknown value
Now you can cross multiply/butterfly
98x = 34300
Isolate x by dividing 98 to both sides of the equation
98x/98 = 34300/98
x = 350
This means that a total of 350 mules were surveyed
Hope this helped!
~Just a girl in love with Shawn Mendes
Which is true about the line whose equation is y + 3 = 0?
The slope is zero.
The y-intercept is 3.
The slope is 3.
The value of x always equals the value of y.
the value of x always equals zero
Answer:
The slope is zero.
Step-by-step explanation:
The y-int is -3, the slope can't be 3, and the value of x isn't equal to y, if it was the lines would be intersecting
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = (x – 8). What is the slope-intercept form of the equation for this line?
y = x – 12
y = x – 4
y = x + 2
y = x + 6
Answer:
y = x - 4
Step-by-step explanation:
y - 4 = x - 8
y = x - 4
Answer:
slope-intercept form of the equation for this line is [tex]y=x -4[/tex]
Step-by-step explanation:
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = (x – 8).
To find slope intercept form of a equation of a line we solve for y
[tex]y - 4 = (x - 8)[/tex]
We remove the parenthesis
[tex]y -4 =x - 8[/tex]
To get y alone, we need to add 4 on both sides
[tex]y -4+4=x - 8+4[/tex]
[tex]y=x -4[/tex]
slope-intercept form of the equation for this line is [tex]y=x -4[/tex]
Solve the following system by any method
please and thanks!
Answer:
B infinitely many solutions
Step-by-step explanation:
8x+9y = -5
-8x-9y =5
Add the two equations together
8x+9y = -5
-8x-9y =5
-------------------
0 = 0
This is always true, so we have infinite solutions
Answer: B
Step-by-step explanation:
There are infinite ways to solve this solution. If you plug it in, you can get the answer of infinite.
-7 2/3 + ( -5 1/2 ) + 8 3/4 = ?
A: -4 5/12
B: -21 11/12
C: -4 2/3
D: 6 7/12
Answer:
-4 5\12
Step-by-step explanation:
Identify the Least Common Denominator, 12, then just simply evaluate.
write 6.04 x 10 to the power of -3 as an ordinary number
Answer: 0.00604
Step-by-step explanation: 10^-3 would be 0.001. If you multiply that by 6.04, you will get 0.00604
I hope that helps! :D
Which equation can be used to solve forB?
Answer:tan 30 = 5/b
Step-by-step explanation:
From the diagram line BC is opposite to the angle 30 and line AC is adjacent to that same angle
From trigonometric ratios
Tan 30 = opposite /adjacent
Answer:
The correct answer is first option
Step-by-step explanation:
Points to remember
Trigonometric ratio
Tan θ = Opposite side/Adjacent side
From the figure we can see that a right angled triangle ABC
BC = 5 cm, <A = 30° and <C = 90°
To find the correct equation
We have,
Tan θ = Opposite side/Adjacent side
Tan 30 =BC/AC
Tan 30 = 5/b
The correct answer is first option.
how do i become smarter
Answer:
You become smarter by working hard in school to get good grades and to get good grades you have to put in work and study to get the grades you want and probably deserve.
Step-by-step explanation:
Identify the function in which y varies directly with x
Answer:
y = kx
Step-by-step explanation:
You'll need to share the possible answer choices in all future posts.
A function in which y varies directly with x has the form
y = kx, where k is the constant of proportionality.
With more data, it'd be possible for you and me both to identify this constant.
To identify if a function represents a direct variation relationship between \( y \) and \( x \), we need to determine if the function can be written in the form \( y = kx \), where \( k \) is a non-zero constant known as the constant of variation.
Here are the steps to determine if a function shows that \( y \) varies directly with \( x \):
1. Have a function \( f(x) \) to test. The function should be expressed in terms of \( x \).
2. Attempt to write the function in the form \( y = kx \).
3. Analyze the function:
- If there are no constant terms (that is, no term without \( x \)) and the only term is a multiple of \( x \), then the function shows direct variation. The coefficient of \( x \) is the constant \( k \).
- If there is a constant term not involving \( x \) (other than when \( x = 0 \)), or if \( x \) is raised to a power other than 1, then \( y \) does not vary directly with \( x \).
Let's look at a few examples:
**Example 1**: \( f(x) = 3x \)
This function is in the form \( y = 3x \), which matches the direct variation form \( y = kx \). Here \( k = 3 \). Therefore, \( y \) varies directly with \( x \).
**Example 2**: \( g(x) = 5x^2 \)
\( g(x) \) does not show direct variation because it does not have the form \( y = kx \); instead, \( x \) is raised to the second power, so it cannot represent a direct variation.
**Example 3**: \( h(x) = -2x + 1 \)
\( h(x) \) has a constant term, \( +1 \), which means it does not match the form \( y = kx \) for direct variation since \( y \) should have no constant term other than the coefficient of \( x \). Thus \( y \) does not vary directly with \( x \).
**Example 4**: \( j(x) = \frac{1}{4}x \)
\( j(x) \) reflects a direct variation. The function can be written as \( y = \frac{1}{4}x \), so \( y \) varies directly with \( x \) with a constant of variation \( k = \frac{1}{4} \).
In conclusion, to determine if \( y \) varies directly with \( x \) within a given function, you only need to inspect the function's form to ensure it is a linear equation with a slope \( k \) and no constant term (other than 0 when \( x = 0 \)).
how do you plot f(x)= (x + 4) ^2
I hope this helps please tell me if it doesn’t
The length of your classroom is about 3.5 x 10^2 inches. If the hallway is ten times as long as the classroom, what is the length of the hallway, expressed in scientific notation?
Answer:
3.5x10^3
Step-by-step explanation:
3.5x10^2 = 350
350x10 = 3500
3500 = 3.5x10^3
A coin is tossed twice. Let H represents heads, T represents tails, and the combination of the two letters represent the outcome of both tosses (e.g., if the coin landed heads on the first toss and tails on the second, we'd represent that with HT). Which of the following sets includes all possible outcomes of both tosses?
Answer:
{HH, HT, TH, TT}
Step-by-step explanation:
The set of all possible outcomes in tossing a coin twice is;
{HH, HT, TH, TT}
In the first toss the coin may land Heads. In the second toss the coin may land Heads or Tails. This can be represented as;
HH, HT
Heads in the first and second tosses. Heads in the first toss followed by a Tail in the second toss.
In the first toss the coin is also likely to land Tails. In the second toss the coin may land Heads or Tails. This can be represented as;
TH, TT
Tails in the first toss followed by a Head in the second toss. Tails in the first and second tosses.
Combining these two possibilities will give us the set of all possible outcomes in tossing a coin twice is;
{HH, HT, TH, TT}
1/5 can paint covers 1 wall how many with walls with 2 cans
Answer:
10
Step-by-step explanation:
1/5*10=2 cans so 1*10 is 10 walls
One cell phone plan charges $20 per month plus $0.15 per minute used. A second cell phone plan charges $35 per month plus $0.10 per minute used. Write and slice an equation to find the number of minutes you must talk to have the same cost for both calling plans.
Answer:
300 minutes
Step-by-step explanation:
Let
x----> the numbers of minutes used
y ---> the cost per month
we know that
First cell phone plan
y=0.15x+20 ---> equation A
Second cell phone plan
y=0.10x+35 ---> equation B
equate the equation A and equation B
0.15x+20=0.10x+35
Solve for x
0.15x-0.10x=35-20
0.05x=15
x=15/0.05
x= 300 minutes
Find the cost y
y=0.15(300)+20 =$65
That means
For x=300 minutes
The cost for both calling plans is y=$65
Kyle needed about 1 liter of water to fill a container. Did Kyle most likely fill a small glass, a spoon, or a vase?
The answer is vase.
A spoon is less than 3 ounces for sure.
A small glass is 8 ounces or less.
A vase is probably a liter of more.
Good luck!
Find the slop of the line shown.
Answer:
1/3
Step-by-step explanation:
Look up on google "how to find slope" and your answer will be right at the top
The answer is x=3 since its a vertical line. hope this helps.please add brainliest
if 2x- 3 + 3x = 28 what is the value of x
Answer:
x= 31/5 (Exact form)
x= 6.2 (Decimal Form)
x= 6 1/5 (Mixed number form)
Step-by-step explanation:
What is the system of equations by graphing
Answer:
(x, y) = (0, 4)
Step-by-step explanation:
The two lines intersect at their y-intercept: (x, y) = (0, 4).
a water sprinkler sprays water outward in a cirular pattern what area will be watered if the the radius of the spray from the sprinkler is 18ft write an exact answerin terms of pie/3.14
Answer:
circle area = PI * radius^2
circle area = 3.14 * 18^2
circle area = 1,017.36 square feet
Step-by-step explanation:
water sprinkler sprays water outward in a cirular pattern what area will be watered if the the radius of the spray from the sprinkler is 18ft write an exact answerin terms of pie/3.14 answer equal 324ñ²ft
Which basic calculation or process in mathematics relates to factors?
Final answer:
Dimensional analysis, also known as the factor-label method, is a mathematical process related to factors, specifically used for unit conversions and complex computations to ensure correct units are obtained in the results.
Explanation:
The basic calculation or process in mathematics that relates to factors is known as dimensional analysis or the factor-label method. This method is integral in solving problems involving unit conversions and more complex computations, where the orientation of factors according to their units is essential to ensure that quantities cancel out or combine correctly to give a result with the desired units.
Through the factor-label method, we can transform quantities into different units by multiplying by conversion factors, which are ratios that equal one, to achieve the intended units for the result. This approach ensures that we conduct operations on the units of the quantities in the same way we do on the numbers.
For example, if we want to convert meters into inches, we multiply the quantity in meters by a conversion factor that expresses the number of inches in a meter. This factor, being a ratio of inches to meters, aligns the units so that 'meters' cancel out, leaving only 'inches' in the result.
Maria wrote the equation log(x/2)+log(20/x2) What is the solution to Maria’s equation?
Answer:
log x - log 2 + log 20 - 2 log x
Step-by-step explanation:
We need to solve the equation:
[tex]log(\frac{x}{2}) + log(\frac{20}{x^2})[/tex]
We know that log(x/y) = log x - log y and
log(x^2) = 2logx
Solving we get:
[tex](log x - log 2) + (log20 - log x^2)\\(log x - log 2) + (log20 - 2 log x)[/tex]
The solution is:
log x - log 2 + log 20 - 2 log x
Answer:
The solution to Maria's equation is x=5/4
solve for x: 6(4x+5)=3(x+8)+3
Answer:
x=-1/7
Step-by-step explanation:
6(4x+5)=3(x+8)+3
Distribute
24x +30 = 3x+24 +3
Combine like terms
24x+30 = 3x +27
Subtract 3x from each side
24x-3x+30 = 3x-3x+27
21x +30 = 27
Subtract 30 from each side
21x +30-30 = 27-30
21x = -3
Divide each side by 21
21x/21 = -3/21
x = -1/7
Answer:
-1/7
-0.14
Step-by-step explanation:
Which value is an output of the function?
Answer: An output is the function
Step-by-step explanation:
marcia makes a cut through a block of frozen spinach, as shown. what are the dimensions of the exposed cross section?
The answer is D. 6cm*8cm because the cross section is exactly parallel to the side with those exact dimensions.
Hope this helps!
6cm*8cm because the cross section is exactly parallel to the side with those exact dimensions.
What is cross-section?A cross section is the non-empty intersection of a solid body in three dimensions with a plane in geometry and science, or its equivalent in higher dimensions. Multiple parallel cross-sections are produced when an item is cut into slices.
Given,
6cm*8cm because the cross section is exactly parallel to the side with those exact dimensions.
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Double the quotient of q and r
Answer:
(q/r)*2
Step-by-step explanation:
divide q and r, then multiply the result
The result of doubling the quotient of q and r is equal to 2 times the value obtained by dividing q by r.
To double the quotient of q and r, you would perform the following mathematical operation:
Double the quotient of q and r = 2 * (q / r)
In this expression, "q" and "r" are variables representing two numerical values. To get the result, you would divide "q" by "r" and then multiply the quotient by 2.
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Complete Question:
Write the expression for the below statement:
Double the quotient of q and r.
Kristen has $16.26 for a buffet. There is an entrance fee of $5.31 with a $2.96 charge for every pound of crab legs ordered. This situation is modeled by the equation 2.96p + 5.31 = 16.26, where p represents the number of pounds of crab legs ordered. How many pounds of crab legs can Kristen eat at the buffet? (round to the nearest tenth of a pounds of crab legs ordered)
Answer:
Step-by-step explanation:
8 pounds
Answer:
8 pounds
Step-by-step explanation:
A display of gift boxes has 1 box in the top row, 3 boxes in the next row, 5 boxes in the next row, and so on. There are 7 rows in all. How many gift boxes are in the display? Question 19 options: 64 boxes 47 boxes 36 boxes 49 boxes
Answer:
36 boxes
Step-by-step explanation:
For this case we have to increase two boxes each time we go to the next row. So:
1 row: 1
2 row: 3
3 row: 5
4 row: 7
5 row: 9
6 row: 11
7 row: 13
Adding the number of boxes we have:
[tex]1 + 3 + 5 + 7 + 9 + 11 + 13 = 49[/tex]
There are 49 boxes!
Answer:
Option D
What is the least common multiple of the two denominators 6/8 and 4/32
The least common multiple (LCM) of the denominators 6/8 and 4/32 is 12.
Explanation:The least common multiple (LCM) of two numbers is the smallest number that is divisible by both numbers.
To find the LCM of the denominators 6/8 and 4/32, we need to find the LCM of 6 and 4.
The LCM of 6 and 4 is 12.
Therefore, the LCM of 6/8 and 4/32 is 12.
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To find the LCM of the denominators 8 and 32, we prime factorize them, identify the highest power of each prime number, and multiply these together. The LCM of 8 and 32 is 32.
To find the Least Common Multiple (LCM) of the denominators from the fractions 6/8 and 4/32, follow these steps:
Identify the denominators: 8 and 32.
Prime factorize each denominator:
8 = 2 × 2 × 2 (2³)32 = 2 × 2 × 2 × 2 × 2 (2⁵)Identify the highest power of each prime number that appears in the factorizations. Here, the highest power of 2 is 2⁵.
Multiply the highest powers of all the primes together to find the LCM: LCM = 2⁵ = 32.
So, the LCM of the denominators 8 and 32 is 32.