Answer:
[tex]4x^{2} -8x+4[/tex]
Step-by-step explanation:
The average profit expression is for 1 piece of furniture
The amount of furniture is another expression
So we have to multiply both expressions to get the total profit.
(2x-2) (2x-2) = 4x^2 - 4x - 4x + 4
= 4x^2 - 8x + 4
Point O is the centroid of triangle ABC, BY = 3.3, CY= 3, Find BO.
Applying the centroid theorem, the length of BO is: A. 2.2.
What is the Centroid Theorem?Based on the centroid theorem, the length of BO equals two third of the length of BY.
That is:
BO = 2/3(BY)
Plug in the values
BO = 2/3(3.3)
BO = 2.2.
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Which is the graph of f(x) = √x?
The graph is shown in the attached image.
e.) Find the gradient of the line passes through the origin and point
[tex](2 \frac{1}{4} .4 \frac{1}{2} )[/tex]
What is the y coordinate of the line when x = 8? pls answer i will mark brainlest.
Answer:
y is x
Step-by-step explanation:
l don't know step by step explanation
solve:
7(2)^x=224
( help pls )
Answer:
5
Step-by-step explanation:
Original equation:
[tex]7(2)^x=224[/tex]
Divide both sides by 7
[tex]2^x=32[/tex]
Rewrite in log
[tex]log_232=x[/tex]
You can do mental math to realize this equals 5, or plug this into your calculate (if it allows you to set the base), but if you can't do either, you can use the change of base formula:
[tex]log_ba=\frac{log (a)}{log(b)}[/tex]
You get:
[tex]log_232=\frac{log(32)}{log(2)}[/tex]
When you calculate using a calculator you should get 5
Answer: x = 5
Step-by-step explanation:
[tex]7(2)^x=224[/tex]
start by dividing 7 from both sides
[tex]\frac{7(2)^x}{7} =\frac{224}{7}[/tex]
[tex]2^x=32[/tex]
take the log of both sides
[tex]log(2^x) = log(32)[/tex]
move the x to the left of the log
[tex]xlog(2) = log(32)[/tex]
divide both sides by log(2)
[tex]x=\frac{log(32)}{log(2)}[/tex]
use change-of-base formula
[tex]\frac{log(a)}{log(b)} =logx_{b} (a)[/tex]
[tex]x = log_{2} (32)[/tex]
since [tex]2^5 = 32[/tex], x = 5
Hope this helped :)Suppose that Aces can be either high or low; that is, that {A, 2, 3, 4, 5} is a straight, and so is {10, Jack, Queen, King, Ace}. Moreover, a hand that is an Ace-high beats a King-high, etc. The number of ways of getting a five card hand that is two pair from a standard deck of cards is (Q8) The probability of being dealt a five card hand that is two pair from a well shuffled standard deck of cards is
The probability of being dealt a five card hand that is two pair from a well shuffled standard deck of cards is 40.
According to the statement
I have 10 starting cards, from Ace to 10, and 4 suits,
and by this way we get the 40 subsets and because of these subsets there is a probability becomes 40.
So, The probability of being dealt a five card hand that is two pair from a well shuffled standard deck of cards is 40.
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Marjorie and Blaine make chairs together. Marjorie builds the seat and Blaine independently sews the cushions to rest on top of them. It takes Marjorie 1 1/2hours to build the seat and Blaine 40 minutes to sew the cushion. How long would it take for them to make 10 chairs?
Making 10 chairs would take Marjorie and Blaine 21 hours and 40 minutes.
How long does it take to make 10 chairs?The total time it takes Marjorie and Blaine to perform their respective tasks in building a chair is multiplied by 10 chairs, respectively. This time is known as their speed.
The resulting figures are summed to get the total time.
Data and Calculations:The total time it takes Marjorie to build a chair is 15 hours (1.5 hours x 10)
The total time it takes Baline to sew cushions per chair is 400 minutes (40 x 10) or 6 hours and 40 minutes.
Therefore, the total time to build 10 chairs is 21 hours, 40 minutes (15 hours + 6 hours and 40 minutes).
Thus, making 10 chairs would take Marjorie and Blaine 21 hours and 40 minutes.
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Which point corresponds to the real zero of the graph of y = log3 (x+2) - 1?
O (-1,-1)
O (1,0)
O (-1,0)
O (0,-.369)
E
Answer:
(1, 0 )
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex] , then
y = [tex]log_{3}[/tex] (x + 2) - 1
to find the zero let y = 0 , that is
[tex]log_{3}[/tex] (x + 2) - 1 = 0 ( add 1 to both sides )
[tex]log_{3}[/tex] (x + 2) = 1 , then
x + 2 = [tex]3^{1}[/tex] = 3 ( subtract 2 from both sides )
x = 1
the zero is (1, 0 )
38 students are going on a field trip. parents will drive. each car can hold 4 students along with the driver. how many cars will be needed?
Answer:
8 cars :)
Step-by-step explanation:
1 car: 1 driver + 4 students = 5 people total
We must divide to solve :)
38/5 = 7 cars with 3 without a car.
Sine there is a remainder we will need 1 ore car so 8 cars altogether :)
Have an amazing day!!
Please rate and mark brainliest!!
dans dog walking job pays $15 per hour. his job as a car-wash attendant pays $400 each week. dan wants to know how many hours he needs to spend walking dogs to earn more than $520 in a week. which three inequalities can model this situation? select all the correct answers. x(15+400)>520 520<400+15x 15x>120 15x+520>400 520<15x+400x 15x+400>520
Answer: 400 520<15x+400x 15x+400>520
Step-by-step explanation:
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify. 6 more than the cube of a number.
Answer:
Step-by-step explanation:
Comment
Start with the algebraic expression. Always do that x cubed means x^3 power or x * x * x.
Answer x^3 + 6
Pls help solve part c
Answer:
See image below
Step-by-step explanation:
Every point starting at the y axis and extending left to ∞ represents the inequality x ≤ 0
Find the slope of the line containing the points (5, -1) and (-8, -4).
A.
B.
13
D.
5/3
OC. 13
PLEASE HELP!!! what function is graphed below?
The function in the given graph obtained from the y and x-intercept is the option;
[tex]y = cot \left( \frac{3}{4} \cdot \left(x - \frac{\pi}{6} \right)\right)[/tex]
Which method can be used to find the correct function?From the given graph, we have;
At x = 0, y < -2Similarly;
At x = (5/6)•π, y ≈ 0The above relationship corresponds with the following function;
[tex]y = cot \left( \frac{3}{4} \cdot \left(x - \frac{\pi}{6} \right)\right)[/tex]
The function graphed is therefore;
[tex]y = cot \left( \frac{3}{4} \cdot \left(x - \frac{\pi}{6} \right)\right)[/tex]
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He is offered a discount for the first five months. after this period, his rate increases by $8.50 per month. his total cost at the end of the year is $245.50. paul wrote the following equation represent his plan. 5x + 7(x + 8.50) = 245.50 part a: how much, in total, will paul pay during the five discounted months of his plan? (1 point
The first five months Paul paid and in the next seven months he paid 24.
What is a Discount ?Discounts are defined as lowered prices or the sale of an item for less than it would typically cost. The fundamental formula for calculating a discount is to multiply the original price by the given percentage rate in decimal form. We must deduct the discount from the original price to determine the item's sale price. A discount is an amount that is subtracted from the regular price of an item.
Paul represent his plan in the form of equation:
[tex]5 x+7(x+8.50)=245.50[/tex]
Where x is an amount for the first [tex]5[/tex] months that is paid by Paul after the discount and [tex](x+8.50)[/tex] is an amount for the next [tex]7[/tex] month after discount.
[tex]&\Rightarrow \quad 5 x+7 x+59.50=245.50 \\&\Rightarrow \quad 12 x=186 \\&\Rightarrow \quad x=\frac{186}{12} \\&\Rightarrow \quad x=15.50\end{aligned}[/tex]
For the next 7 month:
[tex](x+8.50)=(15.50+8.50)=\$ 24[/tex]
Therefore, The first [tex]5[/tex] months Paul paid $ 15.50, and in the next [tex]7[/tex] months he paid $ 24.
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1. There are two cyclists (Cyclist A: 225 lb. and Cyclist B: 145 lb.) riding the same course on the same style bike and
all other variables are the same. Using the four external forces of resistance, explain which cyclist will come to a
stop first if they stopped pedaling. Be sure to include each of the four factor's contribution and how each impacted
your answer. (5 points)
The cyclist that will come to stop first when the brake is applied, is the cyclist with lesser mass which is Cyclist B because of its lesser inertia.
What is law of inertia?
The law of inertia states that an object at rest or uniform motion in a straight line will continue in that path unless acted upon by an external force.
Inertia depends on mass of the object, the more massive an object is, the more reluctant it will be to stop and vice versa.
Thus, the cyclist that will come to stop first when the brake is applied, is the cyclist with lesser mass which is Cyclist B because of its lesser inertia.
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Consider the relation given by the graph shown below.
a) Is the relation a function? Why or why not?
b) Determine the domain and range of this graph.
admission to a carnival is $4 for children and $6 for adults. what is the ratio of the number of children to the number of adults in this group
The ratio of the number of children to the number of adults in this group is 2 : 3
How to determine the ratio?The admission is given as:
Children=4
Adult = 6
Express as ratio
Ratio = Children : Adult
This gives
Children : Adult = 4 : 6
Simplify
Children : Adult = 2 : 3
Hence, the ratio of the number of children to the number of adults in this group is 2 : 3
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Each treasure hunt team will have 5 people. So far 42 people have signed up. How many more people are needed to make every team equal? How many teams will there be?
Answer:
1) 3 more people
2) 9 teams
Step-by-step explanation:
The divisibility rule for 5 is that it must end in 5 and 0
so the next one is 45, so 3 more people
----------------------- ----------------------- ----------------------- -----------------------
45/5=9 teams
math!! please please helppp!!!
What is the slope of the line below?
(i attached an image)
a) (0,4)
b) -1/3
c) (-1.5,0)
d) 3
e) 4
f) (0,4)
g) -3
h) 1/3
Answer:
D
Step-by-step explanation:
you can use the slope intercept form: y = mx + b.
y = y cooordinate
m = slope
x = x coordinate
b = y intercept
the y intercept is 4.
the point (1, 7) is what we're going to use.
so the new equation is
7 = m + 4 (it would be 1m, but i rewrote it to be mathmatically correct)
subtract 4 from both sides, you should have 3 = m.
the slope is 3
Translate the triangle.
Then enter the new coordinates.
(3,4) A
C
(1,2)
B
(4,2)
<-2,4>
A' (1.8)
B'([?], [])
C'([] [])
The coordinates of the vertices of the translated triangle are A'(x, y) = (1, 8), B'(x, y) = (2, 6) and C'(x, y) = (- 1, 6).
How to translate a triangle by transformation rules
Graphically speaking, triangles can be generated by knowing its three vertices. In this question we must apply a kind of rigid transformation known as translation, whose formula is:
P'(x, y) = P(x, y) + T(x, y) (1)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vectorIf we know that A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (1, 2) and T(x, y) = (-2, 4), then the new coordinates are:
A'(x, y) = (3, 4) + (- 2, 4)
A'(x, y) = (1, 8)
B'(x, y) = (4, 2) + (- 2, 4)
B'(x, y) = (2, 6)
C'(x, y) = (1, 2) + (- 2, 4)
C'(x, y) = (- 1, 6)
Remark
The statement presents typing mistakes, correct form is:
Translate the triangle with the vector <- 2, 4>, then enter the new coordinates:
Original coordinates - A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (1, 2).
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1/2 of the women in the Spring Garden Club are over 60 years old. 1/4 of the remainder are under 40. What part of the membership is between 40 and 60 years old?
(Please explain with steps!! thank you)
A) 1/4
B) 3/8
C) 3/4
D) 5/8
A)1/4
Step-by-step explanation:
1/2=2/4
2/4+1/4=3/4
4/4-3/4=1/4
If EF = 2x – 12, FG = 3x – 15, and EG = 23, find the values of x, EF, and FG.
The values of x, EF, and FG from the line segment are 10, 8 and 15 respectively.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
EG = EF + FG (segment addition postulate)
Hence:
23 = (2x - 12) + (3x - 15)
x = 10
EF = 2(10) - 12 = 8
FG = 3(10) - 15 = 15
The values of x, EF, and FG from the line segment are 10, 8 and 15 respectively.
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A circular sheet of paper of radius 6 inches is cut into 3 equal sectors, and each sector is formed into a cone with no overlap. What is the height in inches of the cone
The height of the cone is 4√2 inches.
The circumference of the base of each cone will be the arc length of one of the sectors
= 2 [tex]\pi[/tex] (6) / 3
= 4 [tex]\pi[/tex] inches
So, the radius, r, of each cone (in inches) is given by :
4pi = 2 [tex]\pi[/tex] * r
4 = 2r
2 = r
Using the Pythagorean Theorem, the cone height, h, is given by :
h = √[ slant height^2 - radius^2 ]
= √ [ 6^2 - 2^2 ]
= √32
= 4√2 inches
In arithmetic, the Pythagorean theorem, or Pythagoras' theorem, is a essential relation in Euclidean geometry a few of the three facets of a right triangle. It states that the vicinity of the square whose facet is the hypotenuse is identical to the sum of the regions of the squares on the other two facets.
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Find the best fit line for the scatter plot.
I find this question kinda hard
Answer:
Step-by-step explanation:
Which expression is equivalent to (tangent (startfraction theta over 2 endfraction) ) (negative sine theta)?
The given expression is equivalent to -1 + cos θ. Option B
What is trigonometry?
Trigonometry can be seen as the branch of mathematics that deals with the relations of the sides and angles of triangles and with the functions of any angles.
The problem deduced from the information is;
[tex]-tan\frac{\alpha }{2} ( -5 sin\alpha)[/tex]
It is simplified thus
[tex]\frac{\frac{sin\alpha }{2} }{\frac{cos \alpha }{2} }[/tex] × [tex](- 2 sin\frac{\alpha }{2} * cos \frac{\alpha }{2} )[/tex]
We then have
[tex]-1 + cos \alpha[/tex]
Therefore, the given expression is equivalent to -1 + cos θ. Option B
The complete question is;
Which expression is equivalent to (tangent (StartFraction theta Over 2 EndFraction) ) (negative sine theta)?
– 1 – cos(ϴ)
– 1 + cos(ϴ)
1 + cos(ϴ)
1 – cos(ϴ)
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i don't know this problem someone help please
Answer:
Points shouldn't be connected by straight lines but rather a curve
Step-by-step explanation:
None of the points seem to be incorrect, and the x and y-axis are labeled correctly as well as the points, the only issue I would say there is, is that this is a quadratic equation, so Brogan shouldn't be drawing straight lines between points, but rather a curve.
simplify:
5 whole, 3 out of 10 + 2 whole, 1 out of 5.
Fractions are written as the ratio of two integers. The sum of 5 3/10 and 2 1/5 is 7 1/2
Sum of fractionsFractions are written as the ratio of two integers. Given the following expression
5 3/10 + 2 1/5
convert the mixed into improper fraction
53/10 + 11/5
Find the LCM
53+22/10
75/10
7.5
Hence the sum of 5 3/10 and 2 1/5 is 7 1/2
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For parallelogram RYFU, let N be the intersection point of the diagonals. Let RF = 7x-11 and NF = 2x+2. Find the measurement of EVERYTHING that you know, if possible.
The diagonals of parallelogram RYUF each measure 24 units.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Diagonals of parallelogram are congruent and bisect each other.
Point N is the intersection point of the diagonals of parallelogram RYFU. Hence, RF is the diagonal and N is the midpoint:
2 * NF = RF
2(2x + 2) = 7x - 11
x = 5
RF = 7(5) - 11 = 24
The diagonals of parallelogram RYUF each measure 24 units.
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What is the ratio of the two values and what new value do they produce?
$280 in 7m
(Write Explaination)
The required ratio is give by $40/m, 4 miles/min, 30 mile/liter. .
Let, just assume a vehicle is given an economy of $280 of 7m.
The ratio can be defined as the comparison of the fraction of one quantity towards others. E.g.- water in milk.
Now,
The ratio can be given as for economy = 280/7
= $40/m
here for new values,
suppose the vehicle travel for 40miles in 10 mins
ratio = 40/10= 4 miles/min
and vehicle consumes 2 liter fuel on 60 miles of distance ratio can be given as
ratio = 60/2 = 30 mile/liter.
Thus the required ratios can be given as $40/m, 4 miles/min, 30 mile/liter.
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