Answer:
47.2
Step-by-step explanation:
236/5
47.5
47.2
Step-by-step explanation:
Because,
= 236/5
= 47.2
Therefore, 47.2 tines 5 goes into 236.
Elena ate 2/8 of a pizza and Dylan ate 1/5. estimate how much of the pizza did they eat?
Pls Help need for tomorrow if u answer then i will give 10+ points and brainliest answer
Answer:
[tex]\frac{9}{20}[/tex]
Step-by-step explanation:
Given:
Elena ate 2/8 of a pizza.
Dylan ate 1/5 of a pizza.
Question asked:
How much of the pizza did they eat ?
Solution:
By simply adding.
Elena ate of a pizza. = [tex]\frac{2}{8}[/tex]
Dylan ate of a pizza = [tex]\frac{1}{5}[/tex]
Total of a pizza they ate = [tex]\frac{2}{8}[/tex] + [tex]\frac{1}{5}[/tex]
By taking LCM of 8 and 5 ; 40
[tex]\frac{10 + 8}{40} = \frac{18}{40} = \frac{9}{20}[/tex]
Thus, [tex]\frac{9}{20}[/tex] f the pizza they eat.
The sum of the square of a positive number and the square of 3 more than the number is 89. What is the number?
The number is 5 which sum of the square of a positive number and the square of 3 more than the number 89.
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
We have to determine the number which sum of the square of a positive number and the square of 3 more than the number 89.
Let the first number would be x
So second number = x + 3
According to the given condition,
⇒ x² + (x + 3)² = 89
⇒ x² + x² + 6x + 9 = 89
⇒ 2x² + 6x + 9 = 89
⇒ 2x² + 6x - 80 = 0
⇒ x² + 3x - 40 = 0
⇒ (x + 8)(x - 5) = 0
⇒ x + 8 = 0 or x - 5 = 0
⇒ x = -8 or x = 5
The answer is 5 because we are looking for a positive number.
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Final answer:
The positive number where the sum of its square and the square of 3 more than the number equals 89 is 5.
Explanation:
To determine the positive number where the sum of squares of the number and the square of 3 more than the number equals 89, we set up the following equation:
Let x be the positive number. Then:
x² + (x + 3)² = 89
Expanding the equation:
x² + x² + 6x + 9 = 89
Combining like terms, this becomes:
2x² + 6x + 9 = 89
Subtract 89 from both sides:
2x² + 6x - 80 = 0
We now have a quadratic equation. Dividing by 2 for simplicity:
x² + 3x - 40 = 0
Factor the quadratic equation:
(x + 8)(x - 5) = 0
Setting each factor equal to zero gives us two possible solutions for x:
x + 8 = 0, so x = -8 (which we can disregard as we are looking for a positive number)x - 5 = 0, so x = 5 (which is the positive number we're looking for)Therefore, the positive number is 5.
Find the 22nd term of the following sequence:
5, 8, 11, ...
63
71
14
68
68 is the 22nd term of the following sequence.
Step-by-step explanation:
The given sequence is with the same common difference between the two consecutive number in the series thus it is said to be the Arithmetic progression ( AP). For finding the nth term in the AP we have a formula tn = a + (n-1) × dHere a is the first term , n is the number of the term to be founded and d is the common difference between the two consecutive number in the series.Thus here tn = 5 + ( 22 - 1 ) × 3.On subtracting we get tn = 5 + (21 ) × 3 On multiplying we get tn = 5 + 63After adding we get tn = 68. It is the 22nd term in the given series.the twenty second (22) term of the sequence 5, 8, 11, ...... is: D. 68.
Given the following data:
First (1st) term = 5Second term = 8Third term = 11To find the twenty second (22) term of the sequence:
Mathematically, the [tex]n^{th}[/tex] term of a sequence is calculated by using the following formula;
[tex]a_n = a + (n - 1)d[/tex]
Where:
a is the first term.n is the term number.d is the common difference.First of all, we would determine the common difference.
[tex]d = 2^{nd} \; term - 1^{st}\;term\\\\d = 8 - 5 \\\\d = 3[/tex]
Substituting the given parameters into the formula, we have;
[tex]a_{22} = 5 + (22 - 1)3\\\\a_{22} = 5 + (21)3\\\\a_{22} = 5 + 63\\\\a_{22} = 68[/tex]
Therefore, the twenty second (22) term of the sequence is 68.
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The focus of a parabola is (0, - 2) The directrix of the parabola is the line y = - 3 What is the equation of the parabola
Answer:
Option B: [tex]$ \textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}} $[/tex]
Step-by-step explanation:
When the focus (h, k) of a parabola and the equation of the directrix y = c are given, the equation of the parabola is given by:
[tex]$ \textbf{(x - h)}^{\textbf{2}} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{k}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{c}^{\textbf{2}} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{2(k - c)y}} $[/tex]
Here, we are given the focus: (h, k) = (0, -2)
Directrix: y = c = -3.
We substitute in the formula to get the equation of the parabola.
[tex]$ (x - 0)^2 + (-2)^2 - (-3)^2 = 2(-2 - (-3))y $[/tex]
[tex]$ \implies x^2 + 4 - 9 = 2(- 2 + 3)y $[/tex]
[tex]$ \implies x^2 - 5 = 2(1) y$[/tex]
[tex]$ \implies 2y = x^2 - 5 $[/tex]
Dividing by 2, throughout we get:
[tex]$ \textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}} $[/tex] which is the required answer.
Simplify:
2(d + 3) + 3(d – 3)
A. –5d – 1
B. 5d – 3
C. 5d + 15
D. 6d – 3
Answer:
I would say it is c but im not sure.
Step-by-step explanation:
Well you use distributive property to solve this to get a simplified answer.
[tex]b. \: 5d - 3 \\ \\ 1. \: 2d + 6 + 3(d - 3) \\ 2. \: 2d + 6 + 3d - 9 \\ 3. \: (2d + 3d) + (6 - 9) \\ 4. \: 5d - 3[/tex]
Which number is irrational?
A. 3/17
B. Square root of 25
C. 0.666
D. Square root of 33
Answer:
B. Square root of 25
Step-by-step explanation:
It is a whole number.
Thus, it is not an irrational number.
The square root of 25 is equal to 5
Therefore
An irrational number is a number that cannot be written as a ratio of two integers. It is a non-terminating and non-repeating decimal.
3. The product of 7/10 and another factor
is greater than 7/10. Which could be
the other factor?
A. 4/3
B. 5/9
C. 10/12
D. 7/7
Answer:
C
Step-by-step explanation:
product of 7 and 10 is 70
product of 10 and 12 is 120
a = 12
b =45
c =120
d =49
round the fraction 3^3/2 to the nearest whole number
Evaluating 3^3/2 gives us 5.196152423, so we can round this to 5.
Describe the error made in subtracting the two
rational expressions shown
1 1
x-
2x+1
x + 1
x-2
(x-2)(x+1) (x - 2)(x +1)
(x-2)(x+1)
Answer:
(This is in my own words)
ALL terms of the numerator must be subtracted out, not just the first term. -2 should be subtracted out to get a numerator of x+1-x+2. Thus, the difference of the numerator should be 3, and not –1. This is when simplified correctly.
On solving the expression correctly, we get -
3/(x - 2)(x + 1)
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is the following equation -
1/(x - 2) - 1/(x + 1)
We have -
1/(x - 2) - 1/(x + 1)
[(x + 1) - (x - 2)]/(x - 2)(x + 1)
3/(x - 2)(x + 1)
Therefore, on solving the expression correctly, we get -
3/(x - 2)(x + 1)
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Every jump a game piece makes measures 8 9 . The piece starts at point A = 7 and jumps to the right. As soon as the piece jumps over B = 24, it switches direction and jumps to the left. The piece then stops at point A. How many jumps did the game piece take?
Answer:
The number of jumps that the game piece took, was 40.
Step-by-step explanation:
Every jump a game piece makes measures [tex]\frac{8}{9} = 0.889[/tex].
Now, the piece starts at point A = 7 and jumps to the right.
So, the number of jumps required by the piece to jump over B = 24 will be
[tex]\frac{24 - 7}{0.889} = 19.122[/tex] jumps ≈ 20 jumps {As the piece crosses the point B}
Now, as soon as the piece jumps over B = 24, it switches direction and jumps to the left. And the piece then stops at point A.
Therefore, the number of jumps that the game piece took, was (20 × 2) = 40. (Answer)
Final answer:
Calculating the jumps based on the jump size of 8 / 9 units, the piece makes 20 jumps to go from point A past point B, and then 23 jumps to return to point A, for a total of 43 jumps.
Explanation:
To solve the question, we must calculate the total number of jumps the game piece takes from the starting point A at 7, over point B at 24, and back to A. Each jump measures 8 / 9 units. To calculate the number of jumps to reach just past point B (24 units), we can set up a division problem to find the number of jumps it would take to first reach or pass 24 starting from 7. The formula for this is (B - A) / jump size.
So, the calculation for jumps to point B is: (24 - 7) / 8 / 9 = 17 × 9 / 8 = 153 / 8 = 19.125. Since the game piece cannot make a partial jump, we must round up to 20 jumps to reach beyond 24 units.
After the piece switches direction, we perform a similar calculation to find how many jumps it takes to go back to point A (7 units).
Here, since the piece is already beyond 24, it only needs to jump back to the next integer value before 7 which is 6.
Now, the game piece is at (20 × 8 / 9) + 7 = approximately 24.222 + 7 = approximately 31.222 units along the path.
To calculate the jumps back to 6, we have (31.222 - 6) / 8 / 9 which is approximately 22.556 jumps, and rounding up gives us 23.
Therefore, the total number of jumps made is the sum of the jumps to point B and back to point A,
which is 20 + 23 = 43 jumps.
kristy earns money based on the number of hours worked, with the same amount paid for each hour. she earned $110.50 after working 13 hours
Answer:
She earned $8.5 per hour.
Step-by-step explanation:
110.5/13=8.5
Calculate the surface area of the following triangular prism:
A. 156 cm^2
B. 240 cm^2
C. 336 cm^2
D. 288 cm^2
Answer:
B- 240 cm²
Step-by-step explanation:
Hope it can help you lovelots
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((7,-1) and (21,-5) what is the equation in slope intercept form?
Answer:
y=-2/7x+1
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-5-(-1))/(21-7)
m=(-5+1)/14
m=-4/14
simplify
m=-2/7
y-y1=m(x-x1)
y-(-1)=-2/7(x-7)
y+1=-2/7(x-7)
y=-2/7x+2-1
y=-2/7x+1
The equation of the line in slope-intercept form is: [tex]\[ \boxed{y = -\frac{2}{7}x + 1} \][/tex]
To find the equation of the line in slope-intercept form y = mx + b that passes through the points 7, -1 and 21, -5 we need to follow these steps:
1. Find the slope m of the line.
2. Use the slope and one of the points to find the y-intercept b
3. Write the equation in the form y = mx + b
Step 1: Find the slope m
The formula for the slope between two points [tex]\((x_1, y_1)\) and \((x_2, y_2)\) is:[/tex]
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
For the points 7, -1 and 21, -5
[tex]\[ x_1 = 7, y_1 = -1 \][/tex]
[tex]\[ x_2 = 21, y_2 = -5 \][/tex]
Substitute these values into the slope formula:
[tex]\[ m = \frac{-5 - (-1)}{21 - 7} = \frac{-5 + 1}{21 - 7} = \frac{-4}{14} = -\frac{2}{7} \][/tex]
Step 2: Find the y-intercept b
Use the slope[tex]\( m = -\frac{2}{7} \)[/tex] and one of the points
[tex]\[ -1 = -\frac{2}{7}(7) + b \][/tex]
b = 1
Step 3: Write the equation
Now that we have the slope [tex]\( m = -\frac{2}{7} \)[/tex] and the y-intercept b = 1 we can write the equation in slope-intercept form:
[tex]\[ y = -\frac{2}{7}x + 1 \][/tex]
Thus, the equation of the line in slope-intercept form is:
[tex]\[ \boxed{y = -\frac{2}{7}x + 1} \][/tex]
Nicole has five times as many stickers in her sticker collection as her sister her sister has 32 stickers how do you stickers does Nicole have
Answer:
160 stickers
Step-by-step explanation:
32 x 5=160
Answer:
160
Step-by-step explanation:
Let x = sister's number of stickers
Then 5x = Nicole's number of stickers
x = 32
5x = 5 × 32 =160
Nicole has 160 stickers.
Naomi solves a system of equations using substitution. The system has infinitely many solutions. Which of the following could be the last step in Naomi's solution? A. x = 0 B. 3 = –3 C. 2 = 2 D. 5 = y
Answer:
Option C) 2=2 is the last step of Naomi and it is the correct answer
Step-by-step explanation:
Given that Naomi solves a system of equation by Substitution method :
The given system has infinite many solutions
Naomi's last step is 2=2
For : A system of equations after solved then its constant value must be same in both the sidesThen the system of equations has infinite many solutions
Therefore it must be 2=2
Hence option C) 2=2 is the last step and it is the correct answer
The correct last step in a solution with infinitely many solutions is option C, '2 = 2,' which shows that the system of equations is dependent and represents an identity.
Explanation:When Naomi solves a system of equations using substitution and finds that the system has infinitely many solutions, this means that the two equations are essentially the same line. Therefore, the last step in her solution would demonstrate that the two expressions are identical. Option C, which states 2 = 2, would be the correct answer because it represents an identity, showing that the two sides of the equation are the same no matter what value is chosen for the variables. This is consistent with a situation where the system of equations is dependent, having an infinite number of solutions.
Write down two rational numbers between 4/5 & 5/6
⁶⁾4/5 = ¹⁰⁾24/30 = 240/300
⁵⁾5/6 = ¹⁰⁾25/30 = 250/300
Rational numbers between 4/5 & 5/6 :
241/300
242/300
243/300
.................
248/300
249/300
Yo sup??
There are infinite numbers possible but since we are asked to find only 2 we can say
4/5=0.8000
5/6=0.8334
Therefore the possible numbers are:
0.81=81/100
0.82=82/100=41/50
0.83=83/100
and so on
Hope this helps.
1/3x+1/2y=10
1/5x-3y=-3/5
Step-by-step explanation:
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What is the equation of the line that is parallel to the given
line and passes through the point (-2, 2)?
y=1/5x+4
y =1/5x+12/5
y=-5+4
y=-5x12/5
Answer:
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
Step-by-step explanation:
Complete Question: What is the equation of line that is parallel to the line [tex]y=\frac{1}{5}+4[/tex] and passes through [tex](-2,2).[/tex]
[tex]Let\ the\ equation\ of\ line\ is\ y=mx+c\\\\Since\ it\ is\ parallel\ to\ the\ line\ y=\frac{1}{5}x+4,\ the\ slope\ of\ both\ the\ lines\ will\ be\ same.\\\\Slope\ of\ y=\frac{1}{5}x+4\ is=\frac{1}{5}\\\\m=\frac{1}{5}\\\\Equation: y=\frac{1}{5}x+c\\\\It\ passes\ through\ (-2,2),\ This\ point\ will\ satisfy\ the\ equation.\\\\2=\frac{1}{5}\times (-2)+c\\\\c=2+\frac{2}{5}\\\\c=\frac{12}{5}\\\\The\ Equation\ is: y=\frac{1}{5}x+\frac{12}{5}[/tex]
To find the equation of a line parallel to a given line and passing through a given point, use the point-slope form of a line.
Explanation:To find the equation of a line parallel to the given line, we need to remember that parallel lines have the same slope. The given line has a slope of 1/5. So, the parallel line will also have a slope of 1/5. We can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values, we get:
y - 2 = 1/5(x + 2)
To simplify the equation, we can multiply through by 5 to get rid of the fraction:
5y - 10 = x + 2
Finally, we can rearrange the equation to the standard form:
x - 5y = -12
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You can access your funds easier if your account has_
liquidity.
A. more
B. less
Answer:
if it as more
Step-by-step explanation:
no need to thank me just add me on snap wgilpenn
What is the equation of the line that passes through the points (-4, 0.5) and (4, -0.5?
Answer:
y=-1/8x
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-0.5-0.5)/(4-(-4))
m=(-1)/(4+4)
m=-1/8
y-y1=m(x-x1)
y-0.5=-1/8(x-(-4))
y-0.5=-1/8(x+4)
y=-1/8x-4/8+0.5
y=-1/8x-1/2+1/2
y=-1/8x
HELP
A gardener is planting two types of trees:
Type A is 2 feet tall and grows at a rate of 25 inches per year.
Type B is 10 feet tall and grows at a rate of 9 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:
It will take 1/2 of a year or 6 months for these trees to be the same height.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Type A is 2 feet tall and grows at a rate of 25 inches per year.
Type B is 10 feet tall and grows at a rate of 9 inches per year.
2. Algebraically determine exactly how many years it will take for these trees to be the same height.
x = Number of years
Type A = 2 + 25x
Type B = 10 + 9x
Let's solve for x, using the following equation:
Type A = Type B
2 + 25x = 10 + 9x
25x - 9x = 10 - 2
16x = 8
x = 8/16 = 1/2
It will take 1/2 of a year or 6 months for these trees to be the same height.
Let's prove it, this way:
2 + 25x = 10 + 9x
2 + 25 (1/2) = 10 + 9 (1/2)
2 + 25/2 = 10 + 9/2
29/2 = 29/2
14.5 = 14.5
if 1/5 of the remaining blueberries is used to make muffins, how many pounds of blueberries are left in the container
To determine how many pounds of blueberries are left in the container after using 1/5 for muffins, calculate 4/5 of the initial amount, as this represents the remaining 80%. The ability to work with fractions and percentages is crucial here.
Explanation:The question involves understanding percentages and unit conversion. If 1/5 of the remaining blueberries is used to make muffins, that means 80% (or 4/5) of the blueberries are left in the container. To find out how many pounds of blueberries are left, we first need to know the total quantity before using any for muffins. Assuming we had a specific weight to begin with, we would calculate 4/5 of that weight to determine what remains.
For example, if there were 10 pounds of blueberries initially, 2 pounds (1/5) would be used for muffins, leaving 8 pounds (4/5) of blueberries in the container. It's essential to be comfortable with fractions and percentage calculations when dealing with such problems in mathematics.
a. Each bowl contains 1/12 of the total blueberries.
b. There were 72 ounces of blueberries in the full container.
c. There are 3 pounds of blueberries left in the container.
a. What fraction of the blueberries is in each bowl?
Initially, 1/6 of the blueberries are poured equally into two bowls. Therefore, each bowl receives 1/6 * 1/2 = 1/12 of the total blueberries.
b. If each bowl has 6 ounces of blueberries in it, how many ounces of blueberries were in the full container?
Since each bowl has 6 ounces of blueberries, and there are two bowls, the total amount of blueberries poured into the bowls is 6 * 2 = 12 ounces. Since this represents 1/6 of the total blueberries, we can set up the equation:
Total blueberries = 12 * 6 = 72 ounces
c. If 1/5 of the remaining blueberries are used to make muffins, how many pounds of blueberries are left in the container?
After pouring 1/6 of the blueberries into the bowls, 5/6 of the blueberries remain. Then, 1/5 of these remaining blueberries are used to make muffins. So, the fraction of blueberries remaining after making muffins is 5/6 * 4/5 = 20/30 = 2/3.
To convert the remaining blueberries to pounds, since 1 pound equals 16 ounces, we divide the total remaining ounces by 16:
Remaining blueberries in pounds = (72 ounces * 2/3) / 16 ounces/pound = (72 * 2) / (3 * 16) = 144 / 48 = 3 pounds
So, there are 3 pounds of blueberries left in the container.
The probable question maybe:
A container is filled with blueberries. 1/6 of the blueberries are poured equally into two bowls.
a. What fraction of the blueberries is in each bowl?
b. If each bowl has 6 ounces of blueberries in it, how many ounces of blueberries were in the full container?
c. If 1/5 of the remaining blueberries are used to make muffins, how many pounds of blueberries are left in the container?
Find the missing value so that the two points have a
slope of -
(-2,y) and (0, -4)
Answer:
y = -2
Step-by-step explanation:
Use the formula for slope: [tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
"m" means slope, and we know it is -1.
Decide which points will be point 1 and point 2
Point 1 (-2, y) x₁ = -2 y₁ = y
Point 2 (0, -4) x₂ = 0 y₂ - -4
Substitute the "x" and "y" values into the formula
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \frac{-4-y}{0-(-2)}[/tex] Simplify
[tex]-1 = \frac{-4-y}{2}[/tex] Remember m = -1. Get rid of the fraction
[tex]2*-1 = 2*\frac{-4-y}{2}[/tex] Multiply both sides by 2
[tex]-2 = \frac{2(-4-y)}{2}[/tex] The "2"s cancel out on the right
[tex]-2 = -4-y[/tex] Start isolating "y"
[tex]-2 +4= -4-y + 4[/tex] Add 4 to both sides
[tex]2= -y[/tex]
[tex]2/-1= -y/-1[/tex] Divide both sides by -1 to isolate "y"
-2 = y Answer
y = -2 Variable on left side
if theres 56 docks and 20 of them join and then 5 of them leave how many ducks are left
Answer:
Step-by-step explanation:
Answer:
71 ducks
Step-by-step explanation:
1. 56 + 20 = 76
2. 76 - 5 = 71
How do you write 10+3x and 4x on a graph?
See the graph below
Explanation:First of all, let's rename those expressions as follows:
[tex]\left\{ \begin{array}{c}y=10+3x\\y=4x\end{array}\right[/tex]
So we we have two lines written in slope-intercept form. In order to graph those lines, let's find two points for each:
First line:
[tex]For \ x=0: \\ \\ y=10+3(0) \\ \\ y=10 \\ \\ \\ For \ x=-10/3: \\ \\ y=10+3(-10/3) \\ \\ y=10-10 \\ \\ y=0 \\ \\ \\ So \ the \ line \ passes \ through \ (0,10) \ and \ (-10/3,0)[/tex]
This line is the green one shown below.
Second line:
[tex]For \ x=0: \\ \\ y=4(0) \\ \\ y=0 \\ \\ \\ For \ x=1: \\ \\ y=4(1) \\ \\ y=4 \\ \\ \\ So \ the \ line \ passes \ through \ (0,0) \ and \ (1,4)[/tex]
This line is the red one shown below.
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A girl 160 cm tall stands 360 cm from a lamp post at night. Her shadow from the light is 90 cm long. How high is the lamp post?
The answer is.
The Lamp post is 800cm
x = height of lamp post
160/90 = x/450
450 is the length from the base of the lamp post to the end of the shadow (360+90)
cross multiple
90x = 72000
x =800cm
Have a great day!
The lamp post is 800 cm high
From the diagram in the attachment below,
The height of the girl is /AG/ = 160cm
The length of her shadow is /SG/ = 90cm
The height of the lamp post is /LP/ = /LM/ + /MP/ = x + 160cm
To determine the height of the lamp post, we will calculate the value of x
Consider ΔASG
Determine <ASG = θ
From
[tex]tan\theta = \frac{opposite}{adjacent}[/tex]
Opposite = /AG/ = 160 cm
Adjacent = /SG/ = 90 cm
∴ [tex]tan\theta = \frac{160}{90}[/tex]
Also, Consider ΔLAM
[tex]tan\theta = \frac{/LM/}{/AM/}[/tex]
NOTE: <LAM = θ (Corresponding angles) since line AM is parallel to line SP
∴[tex]\frac{160}{90} = \frac{/LM/}{/AM/}[/tex]
But, /LM/ = x and /AM/ = 360 cm
∴[tex]\frac{160}{90} = \frac{x}{360}[/tex]
[tex]90x = 360 \times 160[/tex]
[tex]x = \frac{360 \times 160}{90}[/tex]
[tex]x = 4 \times 160 \\[/tex]
[tex]x = 640 cm[/tex]
x = 640 cm
Recall that, the height of the lamp post is /LP/ = /LM/ + /MP/ = x + 160cm
∴ The height of the lamp post is 640 cm + 160cm
The height of the lamp post is 800 cm
Hence, the lamp post is 800 cm high
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A bag contains 6 white marbles and 4 black marbles. A marble is drawn from the bag and then a second marble is drawn without replacing the first one.
What is the probability of drawing a white marble on the first draw, followed by a black marble on the second?
[tex]\frac{?}{?}[/tex]
Answer:
4/15
Step-by-step explanation:
P(drawing white marble and black marble)
= 6/10 × 4/9 [9 as there is no replacement]
= 4/15
Final answer:
The probability of drawing a white marble first and a black marble second without replacing the first one from a bag of 6 white and 4 black marbles is 12/45, which simplifies to 4/15.
Explanation:
The question is asking to find the probability of drawing a white marble first and then a black marble second from a bag of 6 white marbles and 4 black marbles, without replacing the first marble. To solve this, we calculate the probability of each event separately and then multiply them because the events are independent.
First, the probability of drawing a white marble is calculated by dividing the number of white marbles by the total number of marbles:
P(White first) = 6/10 or 3/5.
Since the first marble is not replaced, there are now only 9 marbles left in the bag, with 5 white and 4 black marbles. Next, the probability of drawing a black marble after drawing a white marble is the number of black marbles over the remaining total number of marbles:
P(Black second | White first) = 4/9.
To find the combined probability of both events happening in sequence, multiply the probabilities:
P(White first and Black second) = P(White first) × P(Black second | White first) = (3/5) × (4/9) = 12/45.
Therefore, the probability of drawing a white marble first followed by a black marble is 12/45, which simplifies to 4/15.
Cube Root Function Question! 15 points!
The graph of h(x) is a translation of f (x) = Root Index 3
Which equation represents h(x)?
Answer: Second option.
Step-by-step explanation:
Below are some transformations for a function f(x) :
1. If [tex]f(x)+k[/tex], the function is shifted "k" units up.
2. If [tex]f(x)-k[/tex], the function is shifted "k" units down.
3. If [tex]f(x-k)[/tex], the function is shifted "k" units right.
4. If [tex]f(x+k)[/tex], the function is shifted "k" units left.
The Cube root parent function is:
[tex]f(x)=\sqrt[3]{x}[/tex]
By definition, the graph of this function passes through the origin, as you can observe in the picture attached.
In this case, you need to analize the graph given in the exercise. You can see that the the graph of the function h(x) is like the parent function f(x), but shifted 2 units left.
Therefore, based on the transformations explained above, you can determine that the equation of the function h(x) is the following:
[tex]h(x)=f(x+2)\\\\h(x)=\sqrt[3]{x+2}[/tex]
9(x + 8) +63
what is the answer?
Answer:
9x +135
Step-by-step explanation:
9(x + 8) +63 (by PEDMAS distribute 9 into parentheses first)
= x(9) + 8(9) +63
= 9x + 72 + 63
= 9x +135 [ =9(x+15) ]
Answer: 9x+135
Step-by-step explanation:
9(x + 8) +63
9x+72+63
9x+(72+63)
9x+135
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)
- Cutiepatutie ☺❀❤
Mr Patel is planning to drive 325 miles. He will stop one hour for lunch and take a 15 min rest break.
How many hours will the trip if he averages 65 mph?
A) 3 3/4
B)5
C)6
D)6 1/4
E)6.5
Option D
The trip lasts for [tex]6\frac{1}{4}\ hours[/tex]
Solution:
Mr Patel is planning to drive 325 miles
Average speed is 65 mph
He will stop one hour for lunch and take a 15 min rest break
Let us first find the time taken
[tex]Time = \frac{distance}{speed}[/tex]
[tex]Time = \frac{325}{65}\\\\Time = 5[/tex]
Thus he covers 325 miles in 5 hours
Also, given that, he will stop one hour for lunch and take a 15 min rest break
Therefore, total time taken for trip is:
Total time = 5 hours + 1 hour + 15 minutes
Total time = 6 hours 15 minutes
We know that,
1 hour = 60 minutes
Therefore,
[tex]6\ hours\ 15\ minutes\ = 6 + \frac{15}{60}\ hours = 6 + \frac{1}{4} = 6\frac{1}{4}\ hours[/tex]
Thus the trip lasts for [tex]6\frac{1}{4}\ hours[/tex]
Mr. Patel's trip will last a total of 6.25 hours, including his driving time, lunch break, and rest break. The calculation was done using the formula Time = Distance / Speed, and factoring in the break times.
Explanation:First, we need to calculate how many hours Mr. Patel will spend driving. To do this, we use the formula Distance = Speed * Time. We rework this formula to find time, giving us Time = Distance / Speed. So, Mr. Patel’s total driving time is 325 miles divided by 65 mph (miles per hour), which equals 5 hours.
The next task is to factor in Mr. Patel’s lunch and rest breaks. He takes one hour for lunch and 15 minutes for a rest break. Note that 15 minutes is 0.25 of an hour. Add these two periods to our initial 5 hours of driving time, and we get a total of 6.25 hours. So, Mr. Patel's trip will last 6.25 hours, which corresponds to answer choice D).
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