Answers
Answer:
[tex]f(x)=(x-3)^{2}(x-2)(x-1)[/tex]
Step-by-step explanation:
we know that
The roots (or x-intercepts) of the equation are
x=1 -----> with multiplicity 1
x=2 -----> with multiplicity 1
x=3 -----> with multiplicity 2 (because is a turning point)
so
The factors are
[tex](x-1), (x-2), (x-3),(x-3)[/tex]
The equation is equal to
[tex]f(x)=(x-3)(x-3)(x-2)(x-1)\\ \\f(x)=(x-3)^{2}(x-2)(x-1)[/tex]
To write a quadratic equation in factored form, find two binomials that when multiplied together yield the original quadratic. Factoring is essential in understanding the roots and the shape of a parabolic graph. For more complex quadratics, techniques like completing the square might be required.
Explanation:When we are looking to write the equation of a graph in factored form, we are typically dealing with a polynomial function, and specifically when the graph is of a parabola, we are working with a quadratic equation. Factoring a quadratic equation involves finding two binomials that when multiplied together give us the original quadratic. For example, if we have a graph of a quadratic with its roots at x = p and x = q, the factored form would be y = a(x - p)(x - q), where a represents the leading coefficient.
If given an equation like 6x² + xy - y² - 17x - y + 12 = 0, it can be factored into two linear terms, which represents the intersection of two lines. In cases where completing the square is needed, such as x² - ( ) x = -() y, we add to each side (half the coefficient of x)² to form a perfect square on the left-hand side, leading us to an equation of the form (x − A)² = -4a(y − B).
Learning about graphing polynomials provides insights into how the constants in an equation affect the shape of the curve. By adjusting coefficients and analyzing the individual terms, we can understand how these terms combine to produce the overall graph of the polynomial.
Related Questions
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
4x - 3y + z = 22
4x + y + 5z = 30
3x-y-z = 4
Answers
The augmented matrix for this system is
[tex]\left[\begin{array}{ccc|c}4&-3&1&22\\4&1&5&30\\3&-1&-1&4\end{array}\right][/tex]
Subtract row 1 from row 2, and subtract 3(row 1) from 4(row 3):
[tex]\left[\begin{array}{ccc|c}4&-3&1&22\\0&4&4&8\\0&5&-7&-50\end{array}\right][/tex]
Multiply row 2 by 1/4:
[tex]\left[\begin{array}{ccc|c}4&-3&1&22\\0&1&1&2\\0&5&-7&-50\end{array}\right][/tex]
Subtract 5(row 2) from row 3:
[tex]\left[\begin{array}{ccc|c}4&-3&1&22\\0&1&1&2\\0&0&-12&-60\end{array}\right][/tex]
Multiply row 3 by -1/12:
[tex]\left[\begin{array}{ccc|c}4&-3&1&22\\0&1&1&2\\0&0&1&5\end{array}\right][/tex]
While this isn't exactly RREF, you can already solve the system quite easily:
[tex]\boxed{z=5}[/tex]
[tex]y+z=2\implies\boxed{y=-3}[/tex]
[tex]4x-3y+z=22\implies4x=8\implies\boxed{x=2}[/tex]
We can confirm this solution by continuing with the row reduction. Subtract row 3 from row 2:
[tex]\left[\begin{array}{ccc|c}4&-3&1&22\\0&1&0&-3\\0&0&1&5\end{array}\right][/tex]
Subtract -3(row 2) and row 3 from row 1:
[tex]\left[\begin{array}{ccc|c}4&0&0&8\\0&1&0&-3\\0&0&1&5\end{array}\right][/tex]
Finally, multiply row 1 by 1/4:
[tex]\left[\begin{array}{ccc|c}1&0&0&2\\0&1&0&-3\\0&0&1&5\end{array}\right][/tex]
and we end up with [tex]\boxed{(x,y,z)=(2,-3,5)}[/tex], as before.
Final answer:
To solve for x, y, and z, the given system of equations is represented as an augmented matrix, then reduced to its reduced row-echelon form through row operations, from which the solutions can be directly obtained.
Explanation:
To solve the system of equations by finding the reduced row-echelon form of the augmented matrix, we first write the system as an augmented matrix:
[ 4 -3 1 | 22 ]
[ 4 1 5 | 30 ]
[ 3 -1 -1 | 4 ]
Next, we perform row operations to convert the matrix to its reduced row-echelon form. Once we have the reduced form, we can directly read off the solutions for the variables x, y, and z.
These row operations usually involve scaling rows, adding and subtracting rows, and swapping rows to systematically bring the matrix into the desired form. The final reduced row-echelon form should look like:
[ 1 0 0 | x ]
[ 0 1 0 | y ]
[ 0 0 1 | z ]
Where x, y, and z are the solutions to the original equations. At this stage, each row corresponds to an equation of the form x=..., y=..., z=..., making it straightforward to determine the values of the variables.
Two friends shared 3/4 gallon of ice cream equally. What fraction of a gallon did each friend get ?
Answers
Answer:
I've done this question before and the answer is really weird. its 3/8
The triangles below are similar.
Which similarity statements describe the relationship between the two triangles? Check all that apply.
Answers
Answer:
B,C,D,E
Step-by-step explanation:
The similarity statement that describe the relationship is similarities by (AAA)
What are similar triangles?Similar triangles have corresponding angles equal and proportional sides. Their shapes are identical, but sizes may differ.
For two triangles to be similar, the corresponding angles must be equal, and the ratio of the corresponding sides must be equal.
From the diagram, The similarity statement that describe the relationship is similarities by (AAA)
angle R =angle Z
angle S = angle X
angle P = angle Y.
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Find the area of the kite
Answers
Step-by-step answer:
Area of a kite is half of the product of the diagonals.
The length of diagonal in the x-direction is 4+5 = 9
The length of diagonal in the y-direction is 4+4 = 8
Therefore
Area of kite = 8*9/2 = 36 units.
ANSWER
The correct answer is A.
EXPLANATION
If you know the diagonals of a kite you can easily find the area.
The area of a kite is half the product of the diagonals.
From the graph, the from -5 to 4.
Using the number line approach. The longer diagonal is
[tex] |4 - - 5| = |4 + 5| = |9| = 9 \: \: units[/tex]
Similarly the shorter diagonal is from -4 to 4
[tex] |4 - - 4| = |4 + 4| = |8| = 8 \: \: units[/tex]
The area of the kite is:
[tex]Area= \frac{1}{2} \times 8 \times 9[/tex]
[tex]Area=4 \times 9[/tex]
This implies that
[tex]Area=36 \: square \: \: units[/tex]
The first choice is correct.
Find the greatest common factor of the
following monomials:
2n 36n
Answers
Answer:
2n
Step-by-step explanation:
2n = 2*n
36n = 2*3*2*3 n
They both have 2*n in common, so the greatest common factor is 2n
15p!!!!What is the percent of change from 85 to 64? round to the nearest percent
Answers
Subtract the new amount from the original amount:
64 - 85 = -21
Now divide that by the original amount:
-21 / 85 = -0.247
Multiply that by 100 for the percentage:
-0.247 x 100 = -24.7%
Rounded to the nearest percent is -25%
Calculate each probability, given that P(A) = 0.3, P(B) = 0.7, and A and B are independent.
P(A and B)
Answers
Answer:
0.21
Step-by-step explanation:
If A and B are independent, then:
P(A and B) = P(A) × P(B)
Given P(A) = 0.3 and P(B) = 0.7:
P(A and B) = 0.3 × 0.7
P(A and B) = 0.21
Answer:
P(A and B) = 0.21
Step-by-step explanation:
Two events are said to be independent when the occurrence of event 1 does not affect the occurrence of event 2
Given two probabilities A and B whose probabilities are given as follows
P(A) = 0.3, P(B) = 0.7
P(A and B) is calculated as follows;
P(A and B) is calculated by multiplying both probabilities together
P(A and B) = P(A) * P(B)
P(A and B) = 0.3 * 0.7
P(A and B) = 0.21
Hence, P(A and B) = 0.21
6. Ashlee has already taken 1 page of notes on ber own, and she will take 3 pages during each hour of
class. After attending 2 hours of clans, how many total pages of notes will Ashlee have in her
notebook? Write and solve an equation to find the answer.
Answers
Answer:
7 pages
Step-by-step explanation:
this is because 2 times 3 equals 6 and plus one equals 7
Final answer:
Ashlee starts with 1 page of notes and will take 3 pages of notes for each hour of class she attends. After attending 2 hours of class, she will have a total of 7 pages of notes in her notebook.
Explanation:
The question involves solving a simple algebraic equation to find the total number of pages of notes Ashlee will have after attending 2 hours of class. Ashlee starts with 1 page of notes and takes 3 pages of notes for each hour of class. To find the total number of pages of notes, we can use the equation:
Total pages = Initial pages + (Pages per hour × Number of hours)
Substituting the given values into the equation:
Total pages = 1 + (3 × 2) = 1 + 6 = 7 pages
Therefore, Ashlee will have 7 pages of notes in her notebook after attending 2 hours of class.
Find xif f(x) = 2x + 7 and f(x) = -1.
Answers
Answer: -4
Step-by-step explanation:
Solve 2x+7=-1
2x. =-8
x. =-4
Answer:
-4
Step-by-step explanation:
To find the value you have to substitute x for -1. because f(x) = -1.
-2x + 7 = -1
-7= -7
-2x =-8
÷-2
x=-4
Hope it helps!
24. Mr. Tucker earns $250 per week working in an appliance store. In add
of his sales. Last week he sold $2,800 worth of app
in an appliance store. In addition, he earns 2% commission on all
le sold $2,800 worth of appliances. What was Mr. Tucker's total income for the week
Answers
Answer:$306
Step-by-step explanation:
firstly Mr. Tucker 250 weekly
sold 2800 appliances and earn 2%, so find the 2% of 2800 which is
x/2800 X 2/100 = 56
this mean he earn $56 dollars on the sales . add his weekly earn which is $250 to the $56 which will be $250 + 56 = $306 for the week
Answer:
306$
Step-by-step explanation:
2,800*0.02=56
250+56=306
The graph of g(x) = (x + 1) is a transformation of the graph of f(x) = x. Which of the following describes the transformation?
Question 2 options:
a)
translation 1 unit up
b)
translation 1 unit left
c)
translation 1 unit right
d)
translation 1 unit down
Answers
Answer:
a) translation of 1 unit up
Step-by-step explanation:
85/18 divided by 17/18
Answers
Answer:
5
Step-by-step explanation:
85 * 18 / 18 * 17
18 cancels out.
85/17
= 5
Your answer for this question is 5
1.) When you divide 85/18 by 17/18, the first step you want to take is switch the reciprocal.
[tex]\frac{85}{18}[/tex]÷[tex]\frac{17}{18}[/tex]=
[tex]\frac{85}{18}[/tex]×[tex]\frac{18}{17}[/tex]
2.) When you switch the reciprocal, you then division sign is changed to times.
[tex]\frac{85}{18}[/tex]×[tex]\frac{18}{17}[/tex]
3.) Now you simply multiply
[tex]\frac{85}{18}[/tex]×[tex]\frac{18}{17}[/tex]=[tex]\frac{1530}{306}[/tex]
4.) Last step, you divide
[tex]\frac{1530}{306}[/tex] = 5
Hope This Helps.
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Use the elimination method to solve the system of equations. Choose the
correct ordered pair.
5x+3y = 13
-5x-12y = 23
Answers
Answer:
x = 5, y = -4 → (5, -4)Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}5x+3y=13\\-5x-12y=23\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-9y=36\qquad\text{divide both sides by (-9)}\\.\qquad y=-4\\\\\text{put the value of y to the first equation:}\\\\5x+3(-4)=13\\5x-12=13\qquad\text{add 12 to both sides}\\5x=25\qquad\text{divide both sides by 5}\\x=5[/tex]
Factor out the greatest common factor from this expression using the distributive property.
90 + 60
A) 30(3+2)
B) 10(9+6)
C) 15(6+4)
D) 6(15+10)
Answers
Answer:
30(3+2)
Step-by-step explanation:
90=3(30)=3(3)(10)=3(3)(2)(5)
60=3(20)=3(5)(4)=3(2)(2)(5)
The factors that 90 and 60 have in common are a pair of 3,2, and 5's.
So the biggest factor we can factor out is 3*2*5 which is 30
So 30(3+2)
Leftovers from the prime factorizations above stayed in the ( )
Find the discriminant if 3x^2-10x=-2
Answers
[tex]3x^2-10x=-2\\3x^2-10x+2=0\\\\\Delta=(-10)^2-4\cdot3\cdot2=100-24=76[/tex]
Answer:
The discriminate is 76
Step-by-step explanation:
* Lets explain what is the discriminant
- In the quadratic equation ax² + bx + c = 0, the roots of the
equation has three cases:
1- Two different real roots
2- One real root or two equal real roots
3- No real roots means imaginary roots
- All of these cases depend on the discriminate value (D)
- The discriminate D = b² – 4ac determined from the coefficients of
the equation ax² + bx + c = 0.
# If the value of D positive means greater than 0
∴ There are two different real roots
# If the value of D = 0
∴ There are two equal real roots means one real root
# If the value of D is negative means smaller than 0
∴ There is real roots but the roots will be imaginary roots
∴ We use the discriminant to describe the roots
* Lets solve the problem
∵ 3x² - 10x = -2
- Put it in the form of ax² + bx + c = 0
- Add 2 for both sides
∴ 3x² - 10x + 2 = 0
- Compare between this equation and the form up to find a , b , c
∵ 3x² - 10x + 2 = 0 and ax² + bx + c = 0
∴ a = 3 , b = -10 , c = 2
- Lets find the discriminate D
∵ D = b² - 4ac
∵ a = 3 , b = -10 , c = 2
∴ D = (-10)² - 4(3)(2)
∴ D = 100 - 24 = 76
* The discriminate is 76
What is the product in simplest form? 3/5 x 2/3 = ?
1) 6/15
2) 9/10
3)5/8
4)2/5
Answers
Answer:
option 4
Step-by-step explanation:
Given
[tex]\frac{3}{5}[/tex] × [tex]\frac{2}{3}[/tex]
Cancel the 3's on the numerator/denominator of the fractions, leaving
= [tex]\frac{1}{5}[/tex] × [tex]\frac{2}{1}[/tex] = [tex]\frac{2}{5}[/tex] ← in simplest form
The product of 3/5 x 2/3, in simplest form, is 2/5 after multiplication and reduction.
Explanation:In order to answer your question about the product of 3/5 x 2/3, you need to multiply the two fractions. To do this, you multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. So, for this problem, you would multiply 3 by 2 to get 6, and 5 by 3 to get 15. Therefore, 3/5 x 2/3 = 6/15. However, to put it in simplest form, you should always reduce the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common factor, which in this case is 3. Therefore, 6/15 reduces to 2/5.
Learn more about Fraction Multiplicationhttps://brainly.com/question/34807229#SPJ3the length of a rectangle is 9 cm more than the width the perimeter is 270 cm find the length and the width
Answers
Answer:
length=72
width=63
Step-by-step explanation:
Let us start by supposing the following:
w=w
l=9+w
2l+2w=p(perimeter)
2(9+w)+2*w=270
2w+2w+18=270
4w+18=270
4w=252
w=63
l=72
We used the perimeter formula, 2l+2w=P(perimeter)
Final answer:
To calculate the dimensions of the rectangle, we use the perimeter formula P=2l+2w. After setting up an equation with the given perimeter and relationship between length and width, we find the width to be 63 cm and the length to be 72 cm.
Explanation:
The problem states that the length of a rectangle is 9 cm more than its width and that the perimeter is 270 cm. To find the dimensions of the rectangle, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Let's denote the width of the rectangle as w cm. Then the length would be w + 9 cm. We can substitute these expressions into the perimeter formula to obtain:
270 = 2(w + 9) + 2w
Simplify and solve for w:
270 = 2w + 18 + 2w
270 = 4w + 18
252 = 4w
w = 63 cm
Now that we have the width, we can find the length:
l = w + 9 = 63 + 9 = 72 cm
Therefore, the width is 63 cm, and the length is 72 cm.
Solve the compound inequality 6b < 42 or 4b + 12 > 8.
Answers
Step-by-step explanation:
6b < 42 or 4b + 12 > 8
6b < 42
= 6b/6 < 42/6
= b < 7
4b + 12 > 8
=4b - 12 + 12 < -12+8
= 4b > - 12 + 8
= 4b > -4
= 4b/4 = -4/4
b > -1
so
7 > b > -1
The solution of the compound inequality 6b < 42 or 4b + 12 > 8 is -1 < b < 42.
What is the inequality?The inequality represent the relationship between two expression, it can represent by < is less than > is greater than.
The inequality is;
[tex]\rm 6b < 42\\\\\dfrac{6b}{6} < \dfrac{42}{6}\\\\b < 7[/tex]
The solution of the inequality 6b < 42 is b < 7.
The inequality is;
[tex]\rm 4b + 12 > 8\\\\4b+12-12 > 8-12\\\\4b > -4\\\\\dfrac{4b}{b} > \dfrac{-4}{4}\\\\b > -1[/tex]
The solution of the inequality 4b + 12 > 8 is b > -1.
So combining both conditions, the compound equality will be:
-1 < b < 42
It depicts b is greater than -1 and smaller than 42.
Hence, the solution of the compound inequality 6b < 42 or 4b + 12 > 8 is -1 < b < 42.
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Leticia spends $18.45 on a shirt. She spends a maximum of $3.00 more than Humberto spends. If h represents the amount
Humberto spends, which symbol can be used to complete the inequality below to represent this situation?
18.45_3+h
Answers
Answer: C
Step-by-step explanation:
Final answer:
The correct symbol to complete the inequality 18.45_3+h is ≤, representing that Leticia spends at most $3 more than Humberto, so her spending of $18.45 is less than or equal to Humberto's spending plus $3.
Explanation:
Leticia spends a certain amount on a shirt, and we have an inequality to show that she spends at most $3 more than Humberto. The inequality to represent this situation, where h represents the amount Humberto spends, is 18.45 ≤ 3 + h. This means that Leticia's spending of $18.45 is less than or equal to Humberto's spending plus an additional $3. The symbol ≤ (less than or equal to) completes the inequality because it indicates that the amount Leticia spends is not greater than the cost of the shirt plus an extra $3. In other words, Humberto's spending could be exactly $3 less than Leticia's, or even less, but not more.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Polygon ABCD, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image A′B′C′D′.
The slope of is
.
Answers
Answer:
The answer is 2
Step-by-step explanation:
Answer: The slope of C'D' = 2
Step-by-step explanation:
From the given picture, we can that the coordinates of point C and D are (5,4) and (4,2).
After dilation with scale factor of 8 with the origin as the center of dilation , the coordinates of C' and D' will be :-
[tex]C'=(8\times5,8\times4)=(40,32)[/tex]
[tex]D'=(8\times4,8\times2)=(32,16)[/tex]
Now, the slope of line segment C'D' will be
[tex]\text{Slope}=\dfrac{\text{Change in y-coordinate}}{\text{Changein x-coordinate}}\\\\\Rightarrow\text{Slope}=\dfrac{16-32}{32-40}\\\\\Rightarrow\text{Slope}=\dfrac{-16}{-8}\\\\\Rightarrow\text{Slope}=2[/tex]
The solutions to the inequality y<2x - 4 are shaded on the
graph. Which point is a solution?
(-1,1)
(1,-1)
(3,2)
(2,3)
Answers
Answer:
None
Step-by-step explanation:
y<2x - 4
Substitute points to determine if they are a solution
(-1,1)
1<2(-1) - 4
1 < -2-4
1 < -6 False not a solution
(1,-1)
-1<2(1) - 4
-1 < 2-4
-1 < -2 False not a solution
(3,2)
2<2(3) - 4
2 < 6-4
2 < 2 False not a solution
(2,3)
3<2(2) - 4
3 < 4-4
3 < 0 False not a solution
Which statement accurately describes how to perform a 90° clockwise rotation of point A (1,4) around the origin?
Answers
(1,4) -> (4,-1)
Hope this helps!
I was expecting a choice that said A(1,4) is in the first quadrant so 90 degrees clockwise is fourth quadrant. For perpendicularity we reverse the coordinates, negating one of them. For the fourth quadrant, it must be the y coordinate that's negative. We end up at A'(4,-1).
The answer is the second choice: create a circle with the center at the origin. The image of A' will be on the circle, 90 degrees clockwise from A.
It took Amir 2 hours to hike 5 miles. On the first part of the hike, Amir averaged 3 miles per hour. For the second part of the hike, the terrain was more difficult so his average speed decreased to 1.5 mile per hour. Which equation can be used to find t, the amount of time Amir spent hiking during the second, more difficult part of the hike? 3(2 – t) = 1.5t 3t = 1.5(2 – t) 3t + 1.5(2 – t) = 5 3(2 – t) + 1.5t = 5
Answers
The equation that will be used to find t is:
[tex]3(2-t)+1.5t=5[/tex]
Step-by-step explanation:Total distance that is traveled by Amir is: 5 miles.
and the total time taken by him is: 2 hours.
On the first part of the hike, Amir averaged 3 miles per hour.
Let t denote the time he spent hiking during the second i.e. difficult part of the hike.
Hence, the time he spent in first part of hike is: 2-t( Since, the total time was 2 hours)
Also, we know that:
[tex]Distance=Speed\times Time[/tex]
Hence, distance traveled in first part of hike is:
[tex]Distance=3\times (2-t)[/tex]
Now, the distance he will travel in second part of hike will be: 5-3(2-t)Since the total distance traveled by him is 5 miles.
It is given that his speed decreased to 1.5 miles per hour.
Now, we know that:
[tex]Time=\dfrac{Distance}{Speed}[/tex]
Hence, time spent by him in second part of hike is:
[tex]t=\dfrac{5-3(2-t)}{1.5}\\\\i.e.\\\\1.5t=5-3(2-t)\\\\i.e.\\\\3(2-t)+1.5t=5[/tex]
Which is a graph of a proportional relationship?
Answers
Answer:
bottom left graph
Step-by-step explanation:
A proportional relationship is linear, represented by a straight line graph passing through the origin.
The graph on the bottom left is straight line passing through the origin.
Which graph corresponds to the function f(x) = x2 + 4x – 1?
Answers
Answer:
See below
Step-by-step explanation:
I don't know if this helps you, but I wanted to get you an answer as quickly as I could in case you needed it really soon. This is what a graph of this function would look like. Choose the answer that looks like this one.
I really hope this helps!
The graph for the given function is plotted. The graph of a function is represented by y = f(x).
How to graph a function?Consider the given function as y = f(x)Consider some values for x and find y-valuesPair these x and y values as coordinates and plot them in the graphConnect all the points forming a curve (since it is a quadratic function)Graphing the given function:The given function is f(x) = x² + 4x - 1
Consider x values as {-5, -4, -3, -2, -1, 0, 1, 2}
Substituting these values in the function for finding y-values
When x = -5
y = f(-5) = (-5)² + 4(-5) -1 = 4
∴ (-5, 4)
When x = -4
y = f(-4) = (-4)² + 4(-4) -1 = -1
∴ (-4, -1)
When x = -3
y = f(-3) = (-3)² + 4(-3) -1 = -4
∴ (-3, -4)
When x = -2
y = f(-2) = (-2)² + 4(-2) -1 = -5
∴ (-2, -5)
When x = -1
y = f(-1) = (-1)² + 4(-1) -1 = -4
∴ (-1, -4)
When x = 0
y = f(0) = 0 + 4(0) -1 = -1
∴ (0, -1)
When x = 1
y = f(1) = 1² + 4(1) -1 = 4
∴ (1, 4)
When x = 2
y = f(2) = 2² +4(2) -1 = 11
∴ (2, 11)
Plotting these points in the graph and connecting them gives a curve (parabola).
Checking for the vertex:
f(x) = a(x - h)² + k
⇒ x² + 4x - 1
⇒ (x - (-2))² -5
So, the vertex is (h, k) = (-2, -5).
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Calvin is 150 cm tall, which is 75% of Darryl's height. How many centimeters tall is Darryl?
Answers
Answer:
200
Step-by-step explanation:
150=75% * X
X= 150/0.75
X-200
Darry is 200 centimeters tall
What are examples of things you can measure in centimeters?the meter has 100 centimeters.10 millimeters make 1 centimeter.The centimeter could be written as cm.While calculating the surface area of the object, the unit of measurement becomes cm 2.What are examples of objects we can measure in centimeters?These are the common measurements:
MillimetersCentimetersMetersKilometersGiven,
Calvin = 150 centimeters and 75% of Darryl's height.
we have to find x
150=75% * X
X= 150/0.75
X-200
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Rachel works as a tutor for $15 an hour and as a waitress for $8 an hour. This month, she worked a combined total of 109 hours at her two jobs. Let t be the number of hours Rachel worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.
Answers
Answer:
$ (7t+872)
Step-by-step explanation:
Earning for 1 hour as a tutor= $15
Earnings for 1 hour as a waitress= $8
Total hours worked in the month combined jobs= 109 hrs
Number of hours worked as tutor for the month= t
Find the number of hours worked as waitress for the month= 109-t hours
Total amount earned that month = amount earned as a tutor+ amount earned as a waitress
Amount earned as a tutor= $15 × t = $15t
Amount earned as a waitress= $8× (109-t)= $ (872-8t)
Total amount earned combined= $ 15t + $ (872-8t)
=$ ( 15t-8t +872)
= $ (7t+872)
Final answer:
Rachel's total earnings from both jobs can be expressed as the sum of her hourly rates multiplied by the hours worked in each job, which gives the equation: Total Earnings = 15t + 8(109 - t), where t is the number of hours she worked as a tutor.
Explanation:
To write an expression for the combined total dollar amount Rachel earned this month through her two jobs, we can start by indicating that she earns $15 an hour for tutoring and $8 an hour as a waitress. Given that t represents the number of hours she worked as a tutor, we can calculate her earnings from tutoring as 15t. If the total number of hours worked is 109, then the remaining number of hours worked as a waitress would be 109 - t. Her earnings from working as a waitress would thus be 8(109 - t).
Adding these two amounts together gives us the expression for Rachel's total earnings:
Total Earnings = 15t + 8(109 - t)
Alana has 12.5 cups of flour with which she is baking four loaves of raisin bread and one large pretzel. The pretzel requires 2.5 cups of flour to make. How much flour is in each loaf of raisin bread? Explain the steps to follow to get the answer.
Answers
Answer:2.5 cups of flour in each loaf of raisin bread
Step-by-step explanation:
The pretzel uses 2.5 cups of flour so the remaining flour is 10(12.5-2.5)
Since there are four loaves and 10 cups of flour left
Therefore one loaf has 10/4 or 2.5 cups of flour
Answer:
Four times the amount of flour for the raisin bread plus 2.5 cups equals 12.5 cups total. The equation is 4x + 2.5 = 12.5. First, I subtract 2.5 from both sides, and then I divide both sides by 4. Each loaf contains 2.5 cups of flour.
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If 3x +b = c, what is the value of x in terms of c and b?
Answers
Answer:
x=(c-b)/3
Step-by-step explanation:
we have
3x+b=c
Solve for x
That means -----> Clear variable x
Subtract b both sides
3x+b-b=c-b
3x=c-b
Divide by 3 both sides
x=(c-b)/3
Which phrase best describes the translation from the graph y = 2(x – 15)2 + 3 to the graph of y = 2(x – 11)2 + 3?
Answers
Answer:
The translation is left 4 units
Step-by-step explanation:
we know that
[tex]y=2(x-15)^{2}+3[/tex]
Is a vertical parabola open upward with vertex at (15,3)
[tex]y=2(x-11)^{2}+3[/tex]
Is a vertical parabola open upward with vertex at (11,3)
so
The rule of the translation of (15,3) ----> (11,3) is equal to
(x,y) ----> (x-4,y)
That means ----> The translation is left 4 units