Answer:
50
Step-by-step explanation:
20 / (2/5)
To divide by a fraction, multiply by the reciprocal.
20 × (5/2)
50
He can feed 50 cats.
50 cats
20 pounds is 100/5 pounds when written with a denominator of 5. Then you divide 100 by 2 and get 50.
14. A cleaning company charges by the square
foot. The company charged $600 to clean
4,800 square feet of space. How much
would the company charge to clean
12,000 square feet of space?
(A) $950
(B) $1,200
(C) $1,400
(D) $1,500
What is the domain of f(x) = 3*?
A. All nonnegative real numbers
B. All real numbers
C. All real numbers greater than or equal to 3
D. All real numbers greater than 3
Answer:
B. All real numbers
Step-by-step explanation:
I assume the function is f(x) = 3^x, where x is an exponent.
Since an exponent can be a positive number, a negative number, and zero, x can be any real number. The domain of a function is the set of values that can be used for x.
Answer: B. All real numbers
For f(x) = 3*x
Domain of given function is B. All real numbers
What is domain?It is a set of all values that gives a valid value if we put it in a function.
Any value which can be substituted in function and doesn't return infinity or complex form is part of domain.
How to solve?Check for which value f(x) can return infinite?
Answer is none.
for which value f(x) can give complex number?
Answer is none.
since there exists no such value for which f(x) return infinity or complex number, Domain of f(x) is all real numbers.
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0.45x - 0.2(x - 5) = 0.25
Answer:
[tex]\boxed{\bold{x=-3}}[/tex]
Explanation:
Multiply Both Sides By 100
[tex]\bold{0.45x\cdot \:100-0.2\left(x-5\right)\cdot \:100=0.25\cdot \:100}[/tex]
Refine
[tex]\bold{45x-20\left(x-5\right)=25}[/tex]
Expand [tex]\bold{-20\left(x-5\right): \ -20x+100}[/tex]
= [tex]\bold{45x-20x+100=25}[/tex]
Add Similar Elements: [tex]\bold{\:45x-20x=25x}[/tex]
= [tex]\bold{25x+100=25}[/tex]
Subtract 100 From Both Sides
[tex]\bold{25x+100-100=25-100}[/tex]
Simplify
[tex]\bold{25x=-75}[/tex]
Divide Both Sides By 25
[tex]\bold{\frac{25x}{25}=\frac{-75}{25}}[/tex]
Simplify
[tex]\bold{x=-3}[/tex]
Mordancy.
What is true concerning the lines graphed by the system of equations shown below?
Answer:
H
Step-by-step explanation:
Solve each equation for y.
First equation:
8x + 6 = 2y
2y = 8x + 6
y = 4x + 3
This line has y-intercept 3, and slope 4.
Second equation:
12x - 3 = 3y
3y = 12x - 3
y = 4x - 1
This line has y-intercept -1 and slope 4.
Since the two lines have the same slope and different y-intercepts, they are parallel lines.
Answer: H
Answer:
The correct answer is H.
Step-by-step explanation:
In order to solve this exercise we have two paths. The first one uses less calculation than the second.
First way of solution: Isolate the variable [tex]y[/tex] in the right hand side of each equation. To do this you only need to divide the first equation by 2, and then divide the second equation by 3. Thus, you will obtain [tex]4x+3=y[/tex] and [tex]4x-1=y[/tex].
Now, notice that both lines have the same slope, so they are parallel. But before to give a definite answer we need to check if both lines are the same or not. Evaluate at [tex]x=0[/tex], in the first equation you have [tex]y=3[/tex] and in the second one [tex]y=-1[/tex]. As they have different intercepts with the X-axis, they parallel.
Second way of solution: Solve the system of equations. Isolate [tex]y[/tex] in the first equation:
[tex]4x+3=y[/tex].
Then, substitute this expression in the second equation:
[tex]12x-3=3(4x+3)[/tex]
[tex]12x-3=12x +9[/tex].
Which is equivalent to [tex]0=9+3[/tex] and this is impossible. Hence, the system of equations has no solution and the lines are parallel.
1
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the expressions with their simplified versions.
Answer:
[tex]4\sqrt{2}.\sqrt{2} = 8\\3\sqrt{7}-2\sqrt{7} =\sqrt{7}\\\frac{\sqrt{7}}{2\sqrt{7}} = \frac{1}{2}\\2\sqrt{5}.2\sqrt{5} = 20[/tex]
Step-by-step explanation:
[tex]4\sqrt{2}.\sqrt{2}\\=4 . (\sqrt{2})^2\\=4*2\\=8\\\\3\sqrt{7}-2\sqrt{7}\\As\ the\ square\ root\ is\ same\ in\ both\ terms\\= (3-2)\sqrt{7}\\=\sqrt{7}\\\\\frac{\sqrt{7}}{2\sqrt{7}} \\The\ square\ roots\ will\ be\ cancelled\\= \frac{1}{2}\\ \\2\sqrt{5}.2\sqrt{5}\\=(2*2)(\sqrt{5})^2\\=4*5\\=20[/tex]
Answer:
Below we present each expression with its simplest form.
[tex]4\sqrt{2} \sqrt{2}=4(2)=8[/tex]
[tex]3\sqrt{7} -2\sqrt{7}=(3-2)\sqrt{7} = \sqrt{7}[/tex]
[tex]\frac{\sqrt{7} }{2\sqrt{7} } =\frac{1}{2}[/tex]
[tex]2\sqrt{5} 2\sqrt{5}=4(5)=20[/tex]
So, the first expression matches with 8.
The second expression matches with the square root of seven.
The third expression matches with one-half.
The fourth expression matches with 20.
What is angle DFE? 119 42 19 78
Answer:
∠DFE=119°
Step-by-step explanation:
step 1
Find the measure of angle BFD
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
so
∠BFD=(1/2)[arc BD+arc CE]
substitute the given values
∠BFD=(1/2)[38°+84°]
∠BFD=61°
step 2
Find the measure of angle DFE
we know that
∠BFD+∠DFE=180° -----> linear pair (supplementary angles)
substitute
61°+∠DFE=180°
∠DFE=180°-61°=119°
Which coordinates will best represent point A'?
A. (-2, 5)
B. (4, -3)
C. (-2, -3)
D. (4, 5)
Answer: OPTION A.
Step-by-step explanation:
You know that the rule that will be used for the translation of the figure ABC is:
[tex](x,y)[/tex]→[tex](x-3,\ y+4)[/tex]
You can observe in the figure that the coordinates of the point A is this:
[tex]A(1,1)[/tex]
Then, in order to find the coordinates that will best represent point A', you need to subtract 3 from the x-coordinate of the point A and add 4 to the y-coordinate of the point A:
[tex]A'(1-3,\ 1+4)\\\\A'(-2,5)[/tex]
Answer:
A. (-2,5)
Step-by-step explanation:
The figure ABC is translated to A'B'C' by the rule (x-3, y+4)
The Image of the triangle will therefore be as follows:
A' (1-3,1+4)
B'(2-3,5+5)
C'(3-3,2+5)
The vertices will thus be A'(-2,5), B'(-1,10) and C'(0,7)
Thus the correct answer will be A. (-2,5)
a child lies on the ground and looks up at the top of a 14-ft tree nearby. the child is 7 ft away from the tree. what is the angle if elevation from the child to the top of th tree? round to the nearest whole degree.
Answer:
63°
Step-by-step explanation:
From the diagram, the angle of elevation from the child to the top of the tree can be calculated using the tangent ratio.
Recall SOH-CAH-TOA from your Trigonometry class.
The tangent is opposite over adjacent.
[tex] \tan(A) = \frac{14}{7} [/tex]
[tex]A = \tan^{ - 1} ( 2)[/tex]
[tex]A = 63.43 \degree[/tex]
The angle of elevation is 63° to the nearest degree.
Triangle ABC has coordinates A(-2, -3), B(1, 1), and C(2, -1). If the triangle is translated 1 unit right and 3 units up, what are the coordinates of A'?
Answer: [tex]A'(-1, 0)[/tex]
Step-by-step explanation:
By definition, a Translation is a transformation that moves an object a fixed distance. In Transalation the size, shape and orientation of the object don't change.
The translation of a point [tex]P(x,y)[/tex] "a" units right and "b" units up is:
[tex]P'(x+a,y+b)[/tex]
In this case we know that the coordinates of A of the Triangle ABC is A(-2, -3) and the Triangle ABC is translated 1 unit right and 3 units up. Therefore, the the coordinates of A' are:
[tex]A'(-2+1, -3+3)[/tex]
[tex]A'(-1, 0)[/tex]
Can someone please explain why the answers for question 1 and 2 are different than the answers for 3 and 4
Answer:
1) Parabola is opened up with no x-intercepts so the graph is fully above the x-axis which means all the y-coordinates in our points are positive so that is why the solution is all real numbers because it asked you to solve y>0 for x.
2) Parabola is opened up with no x-intercepts so the graph is fully above the x-axis which means all the y-coordinates in our points are positive so that is why the solution is all real numbers because it asked you to solve y>=0 for x.
3) Parabola is opened up with no x-intercepts so the graph is fully above the x-axis which means all the y-coordinates in our points are positive so that is why the solution is none because we are looking for when y<0 for x. (y<0 means y is negative)
4) Parabola is opened up with no x-intercepts so the graph is fully above the x-axis which means all the y-coordinates in our points are positive so that is why the solution is none because we are looking for when y<=0 for x. (y<=0 means negative or 0)
Step-by-step explanation:
[tex]y=ax^2+bx+c[/tex forms a parabola when graph assuming [tex]a \neq[/tex].
If [tex]a=0[/tex], we would have a parabola.
Anyways here are few things that might help when solving these:
1) Write ax^2+bx+c in factored form; it can lead to the x-intercepts quickly once you have it
2) The discriminant b^2-4ac:
A) It tells you if you have two x-intercepts if b^2-4ac is positive
B) It tells you if you have one x-intercept if b^2-4ac is zero
C) It tells you if you have zero x-intercepts if b^2-4ac negative
3) If a>0, then the parabola opens up.
If a<0, then the parabola opens down.
4) You might choose to test before and after the x-intercepts too, using numbers between or before and after.
Let's look at questions labeled (1)-(4).
(1) x^2-x+2>0
a=1
b=-1
c=2
I'm going to use the discriminant to see how many x-intercepts I have:
b^2-4ac
(-1)^2-4(1)(2)
1-8
-7
Since -7 is negative, then we have no x-intercepts.
The parabola is also opened up.
So if we have no-x-intercepts and the parabola is opened up (a is positive), then the parabola is above the x-axis.
So the y values for x^2-x+2 where y=x^2-x+2 is positive for all real numbers.
The solution to x^2-x+2>0 is therefore all real numbers.
(2) x^2+5x+7>=0
a=1
b=5
c=7
b^2-4ac
(5)^2-4(1)(7)
25-28
-3
Since -3 is negative, we have no x-intercepts.
The parabola is also opened up because a=1 is positive.
So again x^2+5x+7>=0 has solutions all real numbers.
(3) x^2-4x+5<0
a=1
b=-4
c=5
b^2-4ac
(-4)^2-4(1)(5)
16-20
-4
Since -4 is negative, we have no x-intercepts.
The parabola is opened up because a=1 is positive.
All the y-coordinates for our points are positive.
So y=x^2-4x+5<0 has no solutions because there are no y's less than 0.
(4) x^2+6x+10<=0
a=1
b=6
c=10
b^2-4ac
6^2-4(1)(10)
36-40
-4
Since -4 is negative, the parabola has no x-intercepts.
The parabola is opened up because a=1 is positive.
All the y-coordinates on our parabola are positive.
So y=x^2+6x+10<=0 has no solutions because there are no y's less than 0 or equal to 0.
The value of a collector’s item is expected to increase exponentially each year. The item is purchased for $500 and its value increases at a rate of 5% per year. Find the value of the item after 4 years
Answer:607.81
Step-by-step explanation:that’s what I got believe me on this one guys
The value of the collector's item after 4 years is $607.75.
Given :
Item is purchased for $500.
Value increases at a rate of 5% per year.
Solution :
We know that the exponential growth function is
[tex]y = a(1+r)^x[/tex]
where,
a = $500
r = 0.05
x = 4
The value of the item after 4 years is,
[tex]= 500(1+0.05)^4[/tex]
[tex]= 500\times(1.05)^4[/tex]
[tex]= 607.75[/tex]
The value of the item after 4 years is $607.75.
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There are 30 contestants playing a game. Off the 30, 16 are men and 20 are wearing glasses. If all of the women are wearing glasses, what is the probability that when a contestant's name is randomly pulled from the hopper, it is a man wearing glasses?
Please help!!!!!!!
Answer:
1/5
Step-by-step explanation:
There are 30 contestants. 16 are men, which means 14 are women.
All 14 women wear glasses. Since 20 of the contestants wear glasses, that means there are 6 men who wear glasses.
So the probability that a randomly selected contestant will be a male with glasses is 6/30 or 1/5.
If EFGH is a parallelogram, then ________
Answer:
A parallelogram is a quadrilateral whose opposite sides are parallel and equal, opposite angles are equal, the sum of the interior angles is 360 degrees. Therefore, the parallelogram EFGH might be a rhombus.
Step-by-step explanation:
Answer:
then it might be a rhombus
Step-by-step explanation:
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities. The student body of 165 students wants to elect 3 representatives
Answer:
735,130.
Step-by-step explanation:
The order of election of the 3 representatives does not matter so it is a combination.
The number of possible combinations
= 165! / 162! 3!
= (165 * 164 * 163) / (3*2*1)
= 735,130.
Final answer:
The scenario of electing 3 representatives from a student body of 165 students involves combinations since the order of selection does not matter. Using the combination formula, there are 4,598,340 possible ways to choose the representatives.
Explanation:
The scenario described involves electing 3 representatives from a student body of 165 students. In this context, we are dealing with combinations, not permutations, because the order of selection does not matter; it only matters who is chosen, not in which order they are elected.
To calculate the number of possible combinations of 165 students taken 3 at a time, we can use the combination formula:
C(n, k) = n! / [k!(n - k)!]
where:
n = total number of items,k = number of items to choose,! indicates a factorial, which is the product of all positive integers up to that number.Therefore, the number of possibilities is:
C(165, 3) = 165! / [3!(165 - 3)!]
Calculating this gives us:
165! / (3! * 162!) = (165 * 164 * 163) / (3 * 2 * 1) = 4,598,340 combinations.
What is the product of the binomials below?
(2x +5)(4x +4)
A. 9x2 +28x + 20
B. 8x2 +28x+9
C. 8x1 +28x+20
D. 9x2 +28x+9
Answer:
The correct answer is 8x^2+28x+20.
Step-by-step explanation:
(2x+5)(4x+4)
Multiply the first bracket with each element of second bracket:
=4x(2x+5)+4(2x+5)
=8x^2+20x+8x+20
Now solve the like terms:
=8x^2+28x+20
Thus the correct answer is 8x^2+28x+20....
What is the standard form of the line parallel to the given line y=3x ? Please show steps!
Answer:
3x - y = -b (b ∈ R ∧ b ≠ 0)Step-by-step explanation:
Parallel lines have the ame slope.
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
We have the line y = 3x → m = 3.
Therefore:
y = 3x + b convert it to the standard form Ax + By = C
y = 3x + b subtract 3x from both sides
-3x + y = b change the signs
3x - y = -b where b is any real number except 0.
The required standard of the parallel line to the line y = 3x is y = 3x + c.
Given that,
What is the standard form of the line parallel to the given line y=3x is to be determined.
What is a Line?A line can be defined by the shortest distance between two points is called a line.
What is the slope of the line?
The slope of the line is the tangent angle made by the line with horizontal. i.e. m =tanx where x in degrees.
Here, there is a property of the parallel lines that the slope of the equation is always the same. Thus
The equation of the line,
y = 3x
the slope of the above line is m = 3
A standard form of parallel line
y = mx +c
put the value of m in above equation,
Now the equation of the parallel lines can be given as y =3x + c
Thus, the required standard of the parallel line to the line y = 3x is y = 3x + c.
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If Lee Trucks buys at cost a truck for $10,000 and plans
to sell it for $12,000, the percent markup on cost is:
O
16.5%
o 25%
20%
o none of the above
Answer:
20% markup
Step-by-step explanation:
10,000 x 1.20 = 12,000
Answer:
20%
Step-by-step explanation:
10,000×120%=12,000
Graph of f(x) = 2(3)^x?
Please and Thank You
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]f(x)=2(3)^{x}[/tex]
This is a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
a is the initial value (y-intercept)
b is the base
r is the rate of change
b=(1+r)
In this problem
a=2
b=3
1+r=3
r=3-1=2
r=200%
using a graphing tool
The graph in the attached figure
Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds that he is off course and 160 miles from island B. What bearing should he turn to, so he is heading straight towards island B?
A. 111.65
B. 119.84
C. 21.65
D. 135.53
Answer:
A. 111.65
Step-by-step explanation:
This scenario can be interpreted like a triangle ABC where A and B are islands and C is the point from where the captain is 160 miles from island B.
a = 160
b = 260
c = 250
Law of cosines
[tex]c^2 = a^2 + b^2 - 2(ab)Cos(C)\\Arranging\ as\\2ab \ cos\ C = a^2+b^2-c^2\\2(160)(260)\ cos\ C = (160)^2+(260)^2- (250)^2\\83200\ cos\ C=25600+67600-62500\\83200\ cos\ C=30700\\cos\ C= \frac{30700}{83200}\\cos\ C=0.36899\\C = arccos\ (0.36899)\\C = 68.35[/tex]
The internal angle is 68.35°
We have to find the external angle to find the bearing the captain should turn
Using the rule of supplimentary angles:
The external angle = 180 - 68.35 = 111.65°
Therefore, the captain should turn 111.65° so that he would be heading straight towards island B.
Hence, option 1 is correct ..
Answer: Option 'a' is correct.
Step-by-step explanation:
Since we have given that
AB = 250 feet
AC = 260 feet
BC = 160 feet
We need to find the angle C that is heading straight towards island B.
We will apply "Law of cosine":
[tex]\cos C=\dfrac{a^2+b^2-c^2}{2ab}\\\\\cos C=\dfrac{160^2+260^2-250^2}{2\times 160\times 260}\\\\\cos C=0.368\\\\C=\cos^{-1}(0.368)\\\\C=68.40^\circ[/tex]
Exterior angle would be
[tex]180-68.40=111.65^\circ[/tex]
Hence, Option 'a' is correct.
What is the following product? 3sqrt4 * sqrt3
Answer:
[tex]6\sqrt{3}[/tex]
Step-by-step explanation:
We need to find the product of [tex]3\sqrt{4} \sqrt{3}[/tex]
We know that:
[tex]3\sqrt{4} \sqrt{3}[/tex] ⇒ [tex]3\sqrt{12}[/tex] ⇒[tex]6\sqrt{3}[/tex]
Therefore, the product is [tex]6\sqrt{3}[/tex]
The product of 3sqrt4 and sqrt3 can be calculated as 6sqrt3. This result is obtained by multiplying 3 by the square root of 4, which is 2, giving you 6, and then multiplying that by the square root of 3.
Explanation:The product of 3sqrt4 and sqrt3 can be calculated following the rules of multiplication for square roots. Firstly, sqrt4 is 2. Therefore, 3sqrt4 is 3*2, which equals 6. Secondly, you multiply this result by sqrt3 to get the final product:
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Which of the following is equivalent to the radical expression below?
For this case we must indicate an expression equivalent to:
[tex]\sqrt {10x ^ 7}[/tex]
By definition of properties of powers and roots we have that:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
Then, we can rewrite the expression as:
[tex]10 ^ {\frac {1} {2}} * x ^ {\frac {7} {2}}[/tex]
Answer:
OPTION A
I’ve been stuck on this and I tried but I can’t get it can someone please help me please
The last cut off answer is 19 over 40
Answer:
-19/40
Step-by-step explanation:
-3/8-1/10
Convert -3/8 to -15/40
Convert 1/10 to 4/40
-15/40-4/40=-19/40
Answer:
-19/40
Step-by-step explanation:
First thing to notice is they don't have a common denominator.
It is easy to see that 8 and 10 both go into 80 because 8(10)=80.
Let's see if we can think of smaller number 8 and 10 both go into.
8=2(2)(2)
10=2(5)
The greatest common factor of 8 and 10 is 2.
The least common multiple of 8 and 10 is 2(2)(2)(5)=40.
That first 2 was what they had in common and then I wrote down all the left over numbers from when we did the greatest common factor.
So 8 and 10 both go into 40.
8(5)=40 and 10(4)=40.
[tex]\frac{-3}{8}-\frac{1}{10}[/tex]
Multiply first fraction by 5/5 and second fraction by 4/4:
[tex]\frac{-3(5)}{8(5)}-\frac{1(4)}{10(4)}[/tex]
Simplify/Multiplied a little:
[tex]\frac{-15}{40}-\frac{4}{40}[/tex]
Wrote as one fraction since they had the same denominator:
[tex]\frac{-15-4}{40}[/tex]
Time to add 15 and 4 since they are both negative and their result also be negative:
[tex]\frac{-19}{40}[/tex]
Which statement is true about the product (9x2 – 4y2)(3x – 2y)?
If it is multiplied by (3x – 2y), the product of all of the terms will be a difference of squares.
If it is multiplied by (3x – 2y), the product of all of the terms will be a perfect square trinomial.
If it is multiplied by (3x + 2y), the product of all of the terms will be a difference of squares.
If it is multiplied by (3x + 2y), the product of all of the terms will be a perfect square trinomial
Answer:
It's the last choice.
Step-by-step explanation:
1. (3x - 2y)(3x -2y)
= 9x^2 - 12xy + 4y^2
The product is (9x^2 - 4y^2) (9x^2 - 12xy + 4y^2)
which is neither a difference of 2 squares or perfect square trinomial.
2. (3x - 2y)(3x + 2y)
= 9x^2 - 6xy + 6xy - 4y^2
= 9x^2 - 4y^2
and (9x^2 - 4y^2(9x^2 - 4y^2) is a perfect square.
Statement 4 is true about the product (9x² – 4y²)(3x – 2y) that if it is multiplied by (3x + 2y), the product of all of the terms will be a perfect square trinomial. This can be obtained by multiplying the product in the question with each term in the question and check whether the it is a difference of squares or a perfect square trinomial.
What is difference of square formula?
Difference of squares can be factored using the identity
a²-b²=(a+b)(a-b)
What is perfect square trinomial ?Algebraic expressions in which there are three terms that can be obtained by multiplying a binomial with itself.
Formulas required,
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
Which statement is true?Given product is, (9x² – 4y²)(3x – 2y)
Using difference of squares it can be written as, ((3x)² – (2y)²)(3x – 2y)
=(3x + 2y)(3x – 2y)(3x – 2y)
=(3x + 2y)(3x – 2y)²
Statement 1: multiplied by (3x – 2y)(3x + 2y)(3x – 2y)²× (3x – 2y)
=(3x + 2y)(3x – 2y)³
This is not in the form of difference of squares.
Statement 2: multiplied by (3x – 2y)(3x + 2y)(3x – 2y)²× (3x – 2y)
=(3x + 2y)(3x – 2y)³
This is not in the form of a perfect square trinomial.
Statement 3: multiplied by (3x + 2y)(3x + 2y)(3x – 2y)²× (3x + 2y)
=(3x + 2y)(3x – 2y)³
This is not in the form of difference of squares.
Statement 4: multiplied by (3x + 2y)(3x + 2y)(3x – 2y)²× (3x + 2y)
=(3x + 2y)²(3x – 2y)²
=[(3x + 2y)(3x – 2y)][(3x + 2y)(3x – 2y)]
=(9x² – 4y²)(9x² – 4y²)
=(9x² – 4y²)² = (a - b)², where a = 9x² and b = 4y²
This is in the form of a perfect square trinomial.
Hence statement 4 is true about the product (9x² – 4y²)(3x – 2y) that if it is multiplied by (3x + 2y), the product of all of the terms will be a perfect square trinomial.
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3. A catering service paid $520 for 10 center pieces and 60 glasses. The guest list grew, requiring an
additional 2 centerpieces and 36 glasses at a cost of $152. Follow the steps outlined below in order
to use a system of equations to find the cost of each centerpiece and each glass.
a. Name your variables.
Let x = the cost of a single centerpiece.
Let y = the cost of a single glass
b. Fill in the table.
First Bill- cost of centerpieces-cost of glasses-total cost
Second Bill-cost of centerpieces-cost of glasses-total cost
c. Write a system of equations to represent both orders.
10x+60y=520.
2x+30y=152
d. Solve the system using any preferred method.
e. Interpret your answer to part d using a complete sentence.
How could 1.75 metres be written as a fraction?
Answer:
1 3/4 meters
Step-by-step explanation:
1.75 = 1 3/4 [think of it as since 3 quarters equals 75 cents, and 4 quarters equals 100 cents or a dollar.]
So, 1 3/4 meters
Need help asap!! Whats the answer
Answer:
The correct answer is option B. 11√2
Step-by-step explanation:
From the figure we can see two isosceles right angled triangle.
Therefore the sides are in the ratio 1 : 1 : √2
It is given that equal sides of the triangle is 11 units
So we can write, 11 : 11 : x = 1 : 1 : √2
x = 11√2
Therefore the value of x = 11√2
The correct answer is option B. 11√2
2. Let f(x) = -2x - 7 and g(x) = -4x + 6. Find(gof)(-5).
[tex](g\circ f)(x)=-4(-2x-7)+6=8x+28+6=8x+34\\\\(g\circ f)(-5)=8\cdot(-5)+34=-6[/tex]
According to the fundamental theorem of algebra, which polynomial function has exactly 11 roots
Answer:
f(x) = (x+2)³(x²−7x+3)⁴
Step-by-step explanation:
The fundamental theorem of algebra (in its simplest definition), tells us that a polynomial with a degree of n will have n number of roots.
recall that the degree of a polynomial is the highest power that exists in any variable.
i.e.
polynomial, p(x) = axⁿ + bxⁿ⁻¹ + cxⁿ⁻² + .........+ k
has the degree (i.e highest power on a variable x) of n and hence has n-roots
In our case, if we expand all the polynomial choices presented, if we consider the 2nd choice:
f(x) = (x+2)³(x²−7x+3)⁴ (if we expand and simplify this, we end up with)
f(x) = x¹¹−22x¹⁰+150x⁹−116x⁸−2077x⁷+3402x⁶+11158x⁵−8944x⁴−10383x³+13446x²−5076x+648
we notice that the term with the highest power is x¹¹
hence the polynomial has a degree of 11 and hence we expect it to have exactly 11 roots
Answer:
B
Step-by-step explanation:
Just did it on edge2020
Need Help Answer Plz!
Answer:
The third choice.
The third choice doesn't contain corresponding parts because L is 3rd and Q is 2nd.
Step-by-step explanation:
Triangle JKL is congruent to Triangle PQR tells us what parts are corresponding. The answer is in the order that things occur.
This means that the following angles are congruent:
Angles J and P are corresponding (congruent in this case) because J and P share the same position in the order, 1st.
Angles K and Q are corresponding (congruent in this case) because K and Q share the same position in the order, 2nd.
Angles L and R are corresponding (congruent in this case) because L and R share the same position in the order, 3rd.
You still look for the same thing when dealing with segments:
JK is congruent or corresponding to PQ (1st to 2nd in both)
KL is congruent or corresponding to QR (2nd to 3rd in both)
LJ is congruent or corresponding to RP (3rd to 1st in both)
So I have named all the pairs of corresponding sides and angles.
The only one that I didn't list in your choices is:
The third choice.
The third choice doesn't contain corresponding parts because L is 3rd and Q is 2nd.
ALGEBRA 2 QUESTION URGENT HELP PLEASE!!
Simplify the expression the root of negative sixteen all over the quantity of three minus three i plus the quantity of one minus two i.
ANSWER CHOICES
a. the quantity of negative twenty minus sixteen i all over nine.
b. the quantity of eight plus four i all over fifteen.
c. the quantity of eight minus four i all over fifteen.
d. the quantity of negative twenty plus sixteen i all over forty one.
Answer:
d. the quantity of negative twenty plus sixteen i all over forty one.
Step-by-step explanation:
We want to simplify the complex number:
[tex]\frac{\sqrt{-16} }{(3-3i)+(1-2i)}[/tex]
We rewrite to obtain:
[tex]\frac{\sqrt{16}\times \sqrt{-1} }{(3+1)+(-3i-2i)}[/tex]
Recall that: [tex]\sqrt{-1}=i[/tex] and [tex]-1=i^2[/tex]
We simplify to get:
[tex]\frac{4i}{4-5i}[/tex]
We rationalize to get:
[tex]\frac{4i}{4-5i}\times\frac{4+5i}{4+5i} [/tex]
[tex]\frac{4i(4+5i)}{(4-5i)(4+5i)}[/tex]
[tex]\frac{16i+20i^2}{4^2+5^2}[/tex]
[tex]\frac{16i-20}{16+25}[/tex]
[tex]\frac{-20+16i}{41}[/tex]
The correct answer is D