The explicit rule for the decreasing arithmetic sequence 13, 10.5, 8, 5.5, 3, 0.5, ... is 'aₙ = 15.5 - 2.5n'. This rule reflects the initial term and the common difference between terms.
The sequence provided is 13, 10.5, 8, 5.5, 3, 0.5, and we are finding the explicit rule for this sequence. To find the explicit rule, we will look at the differences between the terms. The differences are consistently -2.5, thus the sequence decreases by 2.5 each time. Assume the first term corresponds to n=1, the next step is to find the initial value at n=1.
Starting with the first term, when n=1, the value is 13. Keeping in mind the sequence decreases by 2.5 with each step, if we reverse one step back (which would be 0 steps), we would be at the initial value, which is 13 + 2.5 = 15.5. Therefore, the explicit rule can be written in the form aₙ = initial value - difference times (n-1), which simplifies to aₙ = 15.5 - 2.5n.
So, given the options provided, the explicit rule for the given sequence is aₙ = 15.5 - 2.5n.
When x = 12, y = 36. When x = 3, y = 9. What is the constant of proportionality? Enter your answer in the box.
Answer:
k = 3
Step-by-step explanation:
the equation relating x and y is
y = kx ← k is the constant of proportionality
to find use the given conditions
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{36}{12}[/tex] = [tex]\frac{9}{3}[/tex] = 3
can anybody help me fill in the blanks??
Answer:
1. 50%
2. 30.372
3. 569.99
5. 29.99
7. 479.99
8. 65%
9. 306.33
10. 20%
11. 31,491
A Web music store offers two versions of a popular song. The size of the standard version is 2.1 megabytes (MB). The size of the high-quality version is 4.3 MB. Yesterday, there were 1290 downloads of the song, for a total download size of 4403 MB. How many downloads of the high-quality version were there?
Answer:
770 high-quality songs were downloaded
Step-by-step explanation:
A web music store offerst two versions:
Standard Version = 2.1 MBHigh-Quality Version = 4.3MBThere were 1290 for a total download size of 4403MB.
According to the information above, we have the following system of equations:
A + B =1290
2.1A + 4.3B = 4403
Where 'A' referst to the number of Standard songs and 'B' refers to the number of High Quality songs.
Solving the sistem of equations we get that:
A + B =1290 ⇒ A = 1290 - B
2.1A + 4.3B = 4403 ⇒ 2.1(1290 - B) + 4.3B = 4403
⇒ 2709 - 2.1B + 4.3B = 4403 ⇒ 2.2B = 1694 ⇒ B=770
Now, let's find the value of 'A':
A + B =1290 ⇒ A = 1290 - 770 ⇒ A = 520.
Therefore, 770 high-quality songs were downloaded.
use the given to prove that m<cwe=m<fzh
Hello from MrBillDoesMath!
Answer:
See Discussion section below
Discussion:
We know that
m<1 = m<2 ("measure" of angle 1 = measure of angle 2)
and
m<3 = m< 4
Adding these two equations gives
m<1 + m<3 = m<2 + m<4
From the diagram, m<1 + m<3 = m<CWE and m<2+m<4= m<FZH. Substituting these in the above equation gives:
m<CWE = m<FZH
Regards,
MrB
Given equal angles in two figures, we prove that the angles formed by CWD and FZG, as well as DWE and GZH, are equal, thus showing m∠CWE = m∠FZH.
To prove that m∠CWE = m∠FZH, we can use the information given and apply the transitive property of equality. We have the following information:
Given:
1. m∠1 = m∠2 (angles 1 and 2 are congruent)
2. m∠3 = m∠4 (angles 3 and 4 are congruent)
We want to prove:
m∠CWE = m∠FZH
Now, let's construct a table to demonstrate the proof step by step:
| Statement | Reason | Lines Used |
|-------------------|--------------------------------------|------------------|
| 1. m∠1 = m∠2 | Given | Given |
| 2. m∠3 = m∠4 | Given | Given |
| 3. m∠CWD = m∠FZG | Corresponding angles are congruent | Definition of ∠ |
| 4. m∠DWE = m∠GZH | Corresponding angles are congruent | Definition of ∠ |
| 5. m∠CWD + m∠DWE = m∠FZG + m∠GZH | Adding equal quantities to equal quantities | Addition Property of Equality |
| 6. m∠CWE = m∠FZH | Angles CWD and DWE form ∠CWE, and angles FZG and GZH form ∠FZH | Definition of ∠ |
In lines 3 and 4, we use the definition of corresponding angles to show that angles CWD and FZG are congruent and angles DWE and GZH are congruent.
In line 5, we use the addition property of equality to add the two equal quantities, m∠CWD and m∠DWE on the left side, and m∠FZG and m∠GZH on the right side.
In line 6, we use the definition of angles to establish that m∠CWE is equal to m∠FZH.
In conclusion, we have successfully proven that m∠CWE = m∠FZH using the given information and the properties of angles.
For more such information on: angles
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You and your friend are both saving your allowance for your summer vacation you have $48.50 in the bank
Answer:
B
Step-by-step explanation:
Which set of lengths could NOT be the sides of a triangle?A) 9 inches, 12 inches, 21 inches) 9 inches, 11 inches, 12 inches) 12 inches, 14 inches, 16 inches) 16 inches, 18 inches, 25 inches. HURRY help for brainiest
If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
A) 9, 12, 21
9 + 12 = 21 YES :)
B) 9, 11, 12
9 + 11 = 20 > 12 NOT :(
C) 12, 14, 16
12 + 14 = 26 > 16 NOT :(
D) 16, 18, 25
16 + 18 = 34 > 25 NOT :(
Answer: A) 9 in, 12 in, 21 in.You can buy 20 ounces of cereal for 4.40$ or 16 ounces of the same brand for 3.68$ which is the better buy?
To find the better buy, we can find how much they cost for an ounce and find it by comparison.
First option:
20/4.4
=$4.545454...
Second option:
16/3.68
=$4.3478...
As $4.3478..< $4.5454.., the second option is cheaper and therefore is the better buy.
Hope it helps!
The 20 ounces for $4.40 is the better deal at $0.22 per ounce, compared to the 16 ounces for $3.68 at $0.23 per ounce.
To determine which cereal is the better buy, we need to calculate the cost per ounce for each option. For the first option of 20 ounces at $4.40, the cost per ounce is:
[tex]\frac{0.44}{20} = 0.22 ~per ounce[/tex]
For the second option of 16 ounces at $3.68, the cost per ounce is:
[tex]\frac{3.68}{16} = 0.23[/tex]
Comparing these two costs per ounce, the 20 ounces for $4.40 is the better buy because it has a lower cost per ounce.
800,000,000,000 + 20,000,000,000 + 3,000,000,000 + 50,000,000 + 4,000,000 + 600,000 + 50,000 + 8,000 + 700 + 80 + 6
) The function g(x) = x^3 + (x + 1)^2
is used to create this table. Find the missing values. Must show work
for full credit.
Answer:
g(-1) = -1
g(1) =5
Step-by-step explanation:
g(x) = x^3 + (x + 1)^2
If x=-1 substitute this into the equation
g(-1) = (-1) ^3 + (-1+1)^2
g(-1) = 1+0 =-1
If x=1 substitute this into the equation
g(1) = (1)^3 + (1+1)^2 = 1+2^2 = 1+4 =5
Hi There!
--------------------------------------
Function: g(x) = x³ + (x + 1)²
Substitute: -1
Substitute: g(-1) = -1³ + (-1 + 1)²
Remember to follow PEMDAS.
Parenthese's: g(-1) = -1³ + (0)²
Exponents: g(-1) = -1 + 0
Simplify: g(-1) = -1
--------------------------------------
Function: g(x) = x³ + (x + 1)²
Substitute: 1
Substitute: g(1) = 1³ + (1 + 1)²
Remember to follow PEMDAS.
Parenthese's: g(1) = 1³ + (2)²
Exponents: g(1) = 1 + 4
Simplify: g(1) = 5
--------------------------------------
Hope This Helps :)
A baker pays $0.90 per pound for sugar and $2.75 per pound butter. How much will the baher spend if he puts 8 pounds of butter and 10 pounds of sugar?
This year the paradas had 127 floats . That was 34 fewer floats than last year how many floats were in the parade last year
Answer:
161
Step-by-step explanation:
We will use the math operation addition to find last year's number of floats. We know this year was 127 and was fewer than 34. So 127+34=last year's floats.
127+34=161
Describe the possible lengths of the third side of a triangle given that the lengths of the other two sides are 5 and 12 units long. Please express your response as a compound inequality.
Answer:
7<x<17
Step-by-step explanation:
a+b>x
5+12>x
17>x
5+x>12
x>7
12+x>5
x>-7 (ignore then since it is negative and you would use the one that makes the range smaller which is the one above)
5a + 5b + 5c + 5d
Which expression is another way to write the expression shown here?
A) 5abcd
B) 5a + bcd
C) 5(a + b + c + d)
D) (5a)(5b)(5c)(5d) what the answer
Answer:
c
Step-by-step explanation:
A motorist traveled 250 miles on 11 gallons of gas. With the same vehicle, about how far could he go on 16 gallons of gas? Round to the nearest tenth.
Given:
A motorist traveled 250 miles on 11 gallons of gas.
To Find:
In the same vehicle, the distance that can be traveled in 16 gallons.
Answer:
Rounding to the nearest tenth, the distance traveled on 16 gallons of gas is 363.5 miles.
Step-by-step explanation:
We first find the number of miles that can be traveled on 1 mile of gas.
We do this by using the unitary method.
Given that in 11 gallons, 250 miles can be traveled in a certain vehicle.
So in 1 gallon, 250 ÷ 11 miles can be traveled. This is roughly equal to 22.72.
Next we will calculate how much distance he can go in 16 gallons. We multiply the distance traveled in 1 gallon by 16.
That is, in 16 gallons, the number of miles that can be traveled is 22.72 x 16 = 363.52.
Rounding to the nearest tenth, the distance traveled on 16 gallons of gas is 363.5 miles.
Answer:363.6miles
Step-by-step explanation:
∆ABC is transformed with the center of dilation at the origin.
Pre-image: ∆ABC with vertices A(−5, −4), B(−7, 3), C(3, −2)
Image: ∆A'B'C' with vertices A' (−3.75, −3), B' (−5.25, 2.25), C' (2.25, −1.5)
What is the scale factor of the dilation that maps the pre-image to the image?
Answer:
3/4
Step-by-step explanation:
We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−5, −4), B(−7, 3) and C(3, −2) to the image triangle A'B'C' with vertices A' (−3.75, −3), B' (−5.25, 2.25) and C' (2.25, −1.5).
Center of dilation is at the origin.
To find the scale factor, we will divide the corresponding vertices of the image and pre-image.
A(−5, −4) ---> A' (−3.75, −3) = [tex]\frac{-3.75}{-5} , \frac{-3}{-4}=(\frac{3}{4} , \frac{3}{4})[/tex]
B(−7, 3) ---> B' (−5.25, 2.25) = [tex]\frac{-5.25}{-7} , \frac{2.25}{3}=(\frac{3}{4} , \frac{3}{4})[/tex]
C(3, −2) ---> C' (2.25, −1.5) = [tex]\frac{2.25}{3} , \frac{-1.5}{-2}=(\frac{3}{4} , \frac{3}{4})[/tex]
Therefore, the scale factor of the dilation is 3/4.
50 points.
Right triangle ABC has its right angle at C.
AC=3 and BC=4.
Which trigonometric ratios are correct?
Select each correct answer.
1.) sinB= 3/5
2.) tanB= 4/3
3.) cosA= 4/5
4.) sinA= 4/5
5.) tanA= 4/3
sinB= 3/5 is correct
tanA= 4/3 is correct
and sinA= 4/5 is correct
hope this helps ^
What is the probability that she would get heads two of the times?
There are 8 possibilities: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. Of these 4 have at least two heads. Assuming a fair coin, the probability of tossing at least two heads is 4/8 or 1/2. The Answer would probably be 3/8 though.
C) 3/8
Step-by-step explanation:The probability of heads is 1/2, so the probability of not-heads is 1/2.
Then the probability of 2 heads and a tails is (1/2)²·(1/2) = 1/8.
There are 3 choose 2 = (3·2)/(2·1) = 3 ways that the pair of heads may appear among the three tosses. Thus the probability of 2 heads in 3 tosses is ...
... 3·(1/8) = 3/8
_____
Or you can simply count the favorable outcomes among the possible outcomes:
TTT TTH THT THH HTT HTH HHT HHH . . . . 3 of 8 are favorable.
What is the approximate solution to the equation 2t=38 ? 0.1906 3.6380 5.2479 19.0000
Answer:
The answer is 19.0000. 38 divided by two = t. (19)
Step-by-step explanation:
The approximate solution of an equation is simply an estimate of the solution.
The approximate solution of 2t = 38 is (d) 19.0000
The equation is given as:
[tex]\mathbf{2t =38}[/tex]
Start by dividing both sides of the equations by 2
[tex]\mathbf{\frac{2t}{2} =\frac{38}2}[/tex]
Divide 2t by 2, to give 2
So, we have
[tex]\mathbf{t =\frac{38}2}[/tex]
Divide 38 by 2 to give 19
[tex]\mathbf{t =19}[/tex]
From the list of given options, 19.0000 approximates to 19.
So, the solution of the equation can be rewritten as:
[tex]\mathbf{t =19.0000}[/tex]
Hence, the approximate solution is (d) 19.0000
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Please help!!!
Which best explains the relationship between the two triangles below?
Answer:
1. [tex]\Delta ADC\sim \Delta RTS[/tex] because [tex]\angle A\cong \angle R[/tex], [tex]\angle C\cong \angle S[/tex] and [tex]\angle D\cong \angle T[/tex]
Step-by-step explanation:
We have been given two triangles [tex]\Delta ADC[/tex] and [tex]\Delta RTS[/tex]. We are asked to find the relationship between these triangles.
By angle sum property let us find measure of angle C of triangle ADC.
[tex]m\angle C+m\angle D+m\angle A=180^{o}[/tex]
[tex]m\angle C+51.2^{o}+96.5^{o}=180^{o}[/tex]
[tex]m\angle C+147.7^{o}=180^{o}[/tex]
[tex]m\angle C=180^{o}-147.7^{o}[/tex]
[tex]m\angle C=32.3^{o}[/tex]
Let us find measure of angle T of triangle RTS.
[tex]m\angle T+m\angle R+m\angle S=180^{o}[/tex]
[tex]m\angle T+96.5^{o}+32.3^{o}=180^{o}[/tex]
[tex]m\angle T+128.8^{o}=180^{o}[/tex]
[tex]m\angle T=180^{o}-128.8^{o}[/tex]
[tex]m\angle T=51.2^{o}[/tex]
We can see that [tex]m\angle C=m\angle S[/tex], [tex]m\angle A=m\angle R[/tex] and [tex]m\angle D=m\angle T[/tex]. Therefore, [tex]\Delta ADC\sim \Delta RTS[/tex] and 1st option is the correct choice.
Which of the following statements best describes an angle that is in standard position? A. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the negative ​ x-axis. B. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive​ y-axis. C. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the negative​ y-axis. D. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive​ x-axis.
Answer: D. an angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive x-axis.
D. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive [tex]x-[/tex]axis.
A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis.
An angle can be defined as the figure formed by two rays meeting at a common end point.
D. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive [tex]x-[/tex]axis.
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Caitlin went to the store to buy school clothes .She had a store credit from from a previous return in the amount of $39.58 if she bought 4 of the same style shirt in different colors and spent atotal of $52.22 after the store credit was taken off her total, what was the price of each shirt she bought?
Answer: The price of each shirt she bought was $22.95.
Step-by-step explanation:
Hi, to answer this, first, we have to add to the discounted price (52.22) the amount of the credit (39.58), to obtain the original total cost (without discount).
So:
52.22+39.58 = $91.8
Since she bought 4 shirts, we have to divide the total cost by 4:
91.8 /4 = $22.95
The price of each shirt she bought was $22.95.
How do you solve this problem?
What is the length of a radius of the circle represented by the equation x^2+y^2-4x+4y=0 ?
Will award brainliest for best explanation.
so, if you checked the link above, you know what we'll be doing, lemme run through it without much fuss.
[tex]\bf \stackrel{\textit{firstly some grouping}}{(x^2-4x)+(y^2+4y)=0}\implies (x^2-4x+\boxed{a}^2)+(y^2+4y+\boxed{b}^2)=0 \\\\[-0.35em] ~\dotfill\\\\ 2\cdot x\cdot \boxed{a}=4x\implies \boxed{a}=\cfrac{4x}{2x}\implies \boxed{a}=2 \\\\\\ 2\cdot y\cdot \boxed{b}=4y\implies \boxed{b}=\cfrac{4y}{2y}\implies \boxed{b}=2[/tex]
now, let's recall, we're simply borrowing from our very good friend Mr Zero, 0, so if we add whatever, we also have to subtract whatever.
[tex]\bf (x^2-4x+2^2-2^2)+(y^2+4y+2^2-2^2)=0 \\\\\\ (x^2-4x+2^2)+(y^2+4y+2^2)-4-4=0 \\\\\\ (x-2)^2+(y+2)^2-8=0\implies (x-2)^2+(y+2)^2=8 \\\\[-0.35em] ~\dotfill\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] ~\dotfill\\\\ (x-2)^2+(y+2)^2=(\sqrt{8})^2\qquad \impliedby radius=\sqrt{8}[/tex]
Solve by multiplication and addition. Show each step of your work. 2x – 3y = 18 4x + y = 8 Please help me!!!! I am giving 50 points!
Answer:
(x, y ) = (3 , - 4 )
Step-by-step explanation:
given the 2 equations
2x - 3y = 18 → (1)
4x + y = 8 → (2)
multiply (2) by 3
12x + 3y = 24 → (3)
add (1) and (3) term by term to eliminate the term in y
(2x + 12x) + (- 3y + 3y) = (18 + 24)
14x = 42 ( divide both sides by 14 )
x = 3
substitute x = 3 in (1) or (2) to evaluate for y-coordinate
(2) → 12 + y = 8 ⇒ y = 8 - 12 = - 4
solution is (3, - 4 )
Determine which of the following exponential formula(s) represents II and IV in the graph above.
Answer:
A [tex]\alpha ,\beta[/tex]
Step-by-step explanation:
Step 1
The first step is to notice that the graphs of II and iv have the same y intercept. This means that we are looking for functions that match the condition that when t=0, the two functions have the same value. The functions [tex]10(1.02)^t,10(1.05)^t[/tex] meet that condition. Additionally the functions [tex]30(0.95)^t,30(1.05)^t[/tex] meet this condition.
Step 2
The other condition that must be met by the 2 functions is that they should both increase with the increase in increasing values of t. the function [tex]30(0.95)^t[/tex] does not meet this condition. This means that only the functions [tex]\alpha ,\beta[/tex] are the only functions that meet this condition.
Answer:
a. α and β
Step-by-step explanation:
One way to solve this exercise is by analyzing the y - intercept of the functions.
By looking at the graph, we can see that II and IV have the same y - intercept.
All the formulas below depend of the variable ''[tex]t[/tex]'' so if we want to find the y - intercept we only need to replace by ''[tex]t=0[/tex]'' in the formulas.
We can also see that the y - intercept of II and IV will be the lower that the another y - intercept of the functions.
If we replace by [tex]t=0[/tex] :
(α)(t) = [tex]10.(1.02)^{t}[/tex] ⇒ [tex]10.(1.02)^{0}=10[/tex]
(β)(t) = [tex]10.(1.05)^{t}[/tex] ⇒ [tex]10.(1.05)^{0}=10[/tex]
(χ)(t) = [tex]20.(1.02)^{t}[/tex] ⇒ [tex]20.(1.02)^{0}=20[/tex]
(δ)(t) = [tex]30.(0.85)^{t}[/tex] ⇒ [tex]30.(0.85)^{0}=30[/tex]
(ε)(t) = [tex]30.(0.95)^{t}[/tex] ⇒ [tex]30.(0.95)^{0}=30[/tex]
(Φ)(t) = [tex]30.(1.05)^{t}[/tex] ⇒ [tex]30.(1.05)^{0}=30[/tex]
We find that the lowest y - intercept (also equal) are the y - intercept of α and β. Therefore, the correct option is a. α and β
There are 3 girls and 4 boys in the Reese's family. Mr Reese's booth 6 1/2 pounds of candy. How much will each kid get
Answer:
Each Child get = 0.928 pounds of candy
Step-by-step explanation:
Total no of girls are 3
total no of boys are 4
Total no boys and girls are = 3 + 4
= 7
Now it is given that Mr Reese booth have some pound of candies and he wants to distribute it equally among each children
total candy Mr Reese have is [tex]6\frac{1}{2}[/tex]
Now converting it to proper fraction
[tex]6\frac{1}{2}[/tex] =[tex]\frac{6*2+1}{2}[/tex]
= [tex]\frac{13}{2}[/tex]
Now the amount of candy have =[tex]\frac{13}{2}[/tex]
Now we have to divide it into 7 kids
so
each kid get = total candy / total children
=[tex]\frac{13}{2}[/tex]÷7
Changing the divide sign to multiplication
[tex]=\frac{13}{2}*\frac{1}{7}[/tex]
Which becomes
[tex]=\frac{13}{14}[/tex]
solving it gives
Each Child get = 0.928 pounds of candy
Please help! I only have 4 questions left!!!
Which set of angle measures could be the measures of the interior angles of a triangle?
A) 60°, 45°, and 70°
B) 30°, 85°, and 25°
C) 55°, 90°, and 35°
D) 110°, 15°, and 45°
The set of angle measures could be the measures of the interior angles of a triangle are,
⇒ 55°, 90°, and 35°
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
To find the set of angle measures could be the measures of the interior angles of a triangle.
Now, We know that;
Sum of all interior angles of a triangle is 180 degree.
A) 60°, 45°, and 70°
⇒ 60 + 45 + 70
⇒ 175 ≠ 180
Hence, It is not possible.
B) 30°, 85°, and 25°
⇒ 30 + 85 + 25
⇒ 140 ≠ 180
Hence, It is not possible.
C) 55°, 90°, and 35°
⇒ 55 + 90 + 35
⇒ 180
Hence, It is possible.
Thus, The set of angle measures could be the measures of the interior angles of a triangle are,
⇒ 55°, 90°, and 35°
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Why are units of area inappropriate to measure volume? A) Units of area are too small to measure volumes. B) Units of area are too large to measure volumes. C) Area is a two-dimensional attribute and volume is a three-dimensional attribute. D) Area is a three-dimensional attribute and volume is a two-dimensional attribute.
Answer:
The correct answer is option C
Step-by-step explanation:
Area is usually the planar lamina of a two dimensional figure and usually expressed in units square meter, square feet, square inches etc.
While Volume is the total space occupied by an object in a 3-D setting and is usually expressed in cubic meter, cubic feet, cubic inches etc.
A 2-D dimension can not represent a 3-D structure and thus units of area inappropriate to measure volume
The perimeter of the base of a pentagonal prism is 45 cm. what is the width of the rectangular side of that prism?
Answer:
Width of the rectangular side of that prism is, 9cm
Step-by-step explanation:
The formula for Perimeter of pentagonal prism is given by:
[tex]P = 5b[/tex]
where
P represents the perimeter of the pentagonal prism and
b is the base length of the pentagonal prism.
Given: Perimeter of pentagonal prism(P) is 45 cm.
Then;
45 = 5b
Divide both sides by 5 we get;
[tex]b = \frac{45}{5} = 9 cm[/tex]
Therefore, the width of the rectangular side of that prism is, 9cm
Answer:
Width of the rectangular side of that prism is, 9cm
Step-by-step explanation:
which of the following is the coefficient in the algebraic expression x2 +16y ?
A.2
B. Y
C. X
D.16
Answer:
16
D is correct.
Step-by-step explanation:
Coefficient: The coefficient is a number front of variable.
[tex]Expression: x^2+16y[/tex]
In the given expression there are two terms
x² and 16y
First term: x²
The coefficient of x² is 1
Second term: 16y
The coefficient of 16y is 16
Hence, The coefficient of 16 of the given expression.
PLEASE HELP ME!!! and if you could give me an explanation that would be good but if you can’t at least give me the answer please :(
Answer: g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96 which is choice C
=============================
Explanation:
Given roots: -2, 4, 4, 3
Based on that, we know that x = -2, x = 4, x = 4, and x = 3. The repeat x value of 4 is needed to help deal with a double root (multiplicity 2)
x = -2 leads to x+2 = 0, so (x+2) is one factor
x = 4 leads to x-4 = 0, making (x-4) another factor. We have two copies of (x-4) as a factor
x = 3 leads to x-3 = 0 so (x-3) is the last factor
Overall, the four factors are: (x+2) and (x-4) and (x-4) and (x-3)
Use the distributive property to expand everything out
g(x) = (x+2)(x-4)(x-4)(x-3)
g(x) = ( (x+2)(x-4) ) * ( (x-4)(x-3) )
g(x) = ( x^2 - 2x - 8 ) * ( x^2 - 7x + 12 )
g(x) = x^2( x^2 - 7x + 12 ) - 2x( x^2 - 7x + 12 ) - 8( x^2 - 7x + 12 )
g(x) = x^4 - 7x^3 + 12x^2 -2x^3 + 14x^2 - 24x - 8x^2 + 56x - 96
g(x) = x^4 - 9x^3 + 18x^2 + 32x - 96
which shows how I got choice C as the answer