SOLUTION
The given polynomail is
[tex]3x^3-4x^2-14x+3[/tex]To be divided by
[tex]3x+5[/tex]Since the question requires to find the remainder
Then following remainder theorem
Set 3x+5 to zero and solve for x
[tex]\begin{gathered} 3x+5=0 \\ x=-\frac{5}{3} \end{gathered}[/tex]Substitute x=-5/3 into the given polynomial to get the remainder
[tex]\begin{gathered} 3(-\frac{5}{3})^3-4(-\frac{5}{3})^2-14(-\frac{5}{3})+3 \\ =3(-\frac{125}{27})-4(\frac{25}{9})+14(\frac{5}{3})+3 \\ =-\frac{125}{9}-\frac{100}{9}+\frac{70}{3}+3 \\ =\frac{-125-100+210+27}{9} \\ =\frac{12}{9} \\ =\frac{4}{3} \end{gathered}[/tex]Therefore, the remainder is
[tex]\frac{4}{3}[/tex]The regular price of an item is $350. The store is having a 25% off sale,plus an additional 20% off discount. What is the price, before tax, you would pay for this item?
the price before taxes is:
[tex]350\cdot0.75\cdot0.8=210[/tex]$210 is the price before taxes
finding slop on the line
As per given diagram:
Take two points on the line (1,1) and (0,4)
For the slope of the line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Now put the values in the formula:
[tex]\begin{gathered} m=\frac{4-1}{0-1} \\ m=\frac{3}{-1} \\ m=-3 \end{gathered}[/tex]So the slopw of the given line is -3.
Where C(x) is in hundreds Of dollars. How many bicycles should the shop build to minimize the average cost per bicycle
The average cost is given by the next equation:
[tex]C(x)=0.1x^2-0.5x+5.582[/tex]The graph of the function is
As we can see the parabola opens upwards therefore the minim will be located in the vertex
[tex]x=\frac{-b}{2a}[/tex]in our case
b=-0.5
a=0.1
[tex]x=\frac{0.5}{2(0.1)}=2.5[/tex]2.5 hundred
Then
[tex]2.5\times100=250[/tex]Therefore, the shop should build 250 bicycles
angie drew a rectangle. the length of a rectangles she drew is 2 less than three times the width. find the dimensions of the rectangle if the rectangle if the area is 65 square meters
Answer:
The width of the rectangle is 5
The length of the rectangle is 13
Explanation:
Let's call x the length of the rectangle and y the width of the rectangle.
The length is 2 less than 3 times the width, so
x = 3y - 2
And the area is 65 square meters. Since the area is length times width, we get:
xy = 65
Now, we can replace the first equation x = 3y - 2 on the second one to get
(3y - 2)y = 65
3y(y) - 2y = 65
3y² - 2y = 65
3y² - 2y - 65 = 0
So, using the quadratic equation, we get that the solutions to 3y² - 2y - 65 = 0 are
[tex]\begin{gathered} y=\frac{-(-2)\pm\sqrt[]{(-2)^2-4(3)(-65)}_{}}{2(3)} \\ y=\frac{2\pm\sqrt[]{784}}{6} \\ y=\frac{2\pm28}{6} \\ \text{Then} \\ y=\frac{2+28}{6}=\frac{30}{6}=5 \\ or \\ y=\frac{2-28}{6}=\frac{-26}{6}=-\frac{13}{3} \end{gathered}[/tex]The solution is y = 5 because the width can't have a negative length.
Then, replacing y = 5 on the first equation, we get:
x = 3y - 2
x = 3(5) - 2
x = 15 - 2
x = 13
Therefore, the length of the rectangle is 13 meters and the width of the rectangle is 5 meters
Find the equation for a polynomial f(x) that satisfies the following:Degree 5- Root of multiplicity 1 at 2 = 1- Root of multiplicity 2 at x = 2- Root of multiplicity 2 at x = -2y-intercept of (0,–32)
The equation for this polynomial is:
[tex]\begin{gathered} 2(x-1)(x-2)^2(x+2)^2 \\ 2x^5-2x^4-16x^3+16x^2+32x-32 \end{gathered}[/tex]So that's the equation we're asking for.
Both could be the answers. However, this is the final one:
[tex]2x^5-2x^4-16x^3+16x^2+32x-32[/tex]6) 3x2 + 10X - 8We have to find the vertex
Given:
[tex]3x^2+10x-8[/tex]To find the vertex, use the vertex formula below:
[tex]y\text{ = }a(x-h)^2+k[/tex]Where the vertex is: (h, k)
Thus, we have:
[tex]y=3x^2+10x-8[/tex][tex]\begin{gathered} y+8=3x^2+10-8+8 \\ \\ y+8=3x^2+10 \end{gathered}[/tex]Factorize:
[tex]undefined[/tex]Stephen began a baseball card collection by purchasing some cards. He increase the number of cards in the collection by a constant amount each week after that. The table below shows the total number of cards in the collection at the end of several weeks. Weeks completed since initial purchase :• 3• 6• 11Number of cards in the collection: •285•420•645How many cards did Steve initially purchase to the beginning of his collection?
The situation can be represented by a linear function, which is represented by the following expression:
[tex]\begin{gathered} y=mx+b \\ \text{Where, } \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Since he increased the number of cards by a constant amount each week, that means we have proportionality:
[tex]\begin{gathered} ^{}m=\frac{\Delta y}{\Delta x} \\ m=\frac{420-285}{6-3} \\ m=\frac{135}{3}=45 \end{gathered}[/tex]Then, by the slope-point form of the line, we can find the equation and then substitute x=0.
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-285=45(x-3) \\ y=45x-135+285 \\ y=45x+150 \end{gathered}[/tex]Substituting, x=0.
[tex]\begin{gathered} y=45(0)+150 \\ y=150 \end{gathered}[/tex]At the beginning of the collection, he has 150 cards.
Evaluate the expression for the given variable values. (p+g) P-29 if p = 4 and q = 8-13-122024
We have the expression:
[tex]\frac{(p+q)^2}{p-2q}[/tex]We have to evaluate it for p = 4 and q = 8.
To do that, we replace the variables p and q with the given values and calculate:
[tex]\begin{gathered} f(p,q)=_{}\frac{(p+q)^2}{p-2q} \\ f(4,8)=\frac{(4+8)^2}{4-2\cdot8} \\ f(4,8)=\frac{12^2}{4-16} \\ f(4,8)=\frac{144}{-12} \\ f(4,8)=-12 \end{gathered}[/tex]Answer: The value of the expression when p = 4 and q = 8 is -12 [Second option]
Can someone please help me with this ? I just need the answer
SOLUTION:
The graph of g(x) is the graph of f(x) translated 5 units to the left.
Thus, the equation is;
[tex]g(x)=(x+5)^2[/tex]1/8, 2/7, 1/2, 4/5 what are the next two numbers?
ANSWER:
5/4 and 2
STEP-BY-STEP EXPLANATION:
If we look closely, we notice that the pattern is that 1 is added to the numerator and one is subtracted from the denominator, as follows:
[tex]\begin{gathered} \frac{1}{8} \\ \frac{1+1}{8-1}=\frac{2}{7} \\ \frac{2+1}{7-1}=\frac{3}{6}=\frac{1}{2} \\ \frac{3+1}{6-1}=\frac{4}{5} \\ \text{therefore, the next two numbers are:} \\ \frac{4+1}{5-1}=\frac{5}{4} \\ \frac{5+1}{4-1}=\frac{6}{3}=2 \end{gathered}[/tex]Yasmine makes doll clothes for sewing project she used the pattern below to make the front of a skirt for her sister's doll how many square inches of fabric will Yasmine use the skirt pattern
The area of the fabric can be determined as,
[tex]\begin{gathered} A=\frac{1}{2}\times(3.5\text{ in+6 in)}\times4\text{ in} \\ =19in^2 \end{gathered}[/tex]Thus, the required area of the fabric is 19 square inch.
The perimeter of triangle XYZ is 24 units.
What is the area of triangle XYZ? Round to the nearest
tenth of a square unit.
Trigonometric area formula: Area=1/2absin(C)
o 14.7
square units
14.9 square units
15.0 square units
15.3 square units
To the nearest tenth, the area of triangle XYZ is approximately 14.7 units².
What is a triangle?A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon.
There are three sides and three angles in every triangle, some of which may be the same.
Triangles can be divided into three groups based on the lengths of their sides, and these groups are as follows: Scalene, Isosceles, and Equilateral.
So, the area of the triangle is:
We know that:
<YXZ = 102°
Length of XY = z = 3
Length of YZ = x = 11
Length of XZ = y = ?
The perimeter of the triangle:
x+y+z = 24 units
Length XZ = y:
11+y+3 = 24
14+y = 24
y = 24 - 14
Therefore, y = 0.
Area of triangle XYZ:
The formula for trigonometric area is area of XYZ = 12(yz)sin X.
Putting values of x, y, and z as follows:
Area of ∆ XYZ = ½×10×3×sin 102
= ½×30×0.9782
= 15 × 0.9782
= 14.673
Therefore, to the nearest tenth, the area of triangle XYZ is approximately 14.7 units².
Know more about triangles here:
https://brainly.com/question/28889256
#SPJ1
Correct question:
What is the area of triangle XYZ? Round to the nearest tenth of a square unit. Trigonometric area formula: Area 14.7 square units 14.9 square units 15.0 square units 15.3 square units
What is the vertex of the absolute value function below?
Step-by-step explanation:
come on !
the vertex is typically a corner or a (general or local) extreme value or turning point of the curve.
so, what can that point be ?
there is only one candidate : (4, 1).
that means x = 4, y = 1.
that is the 4th answer option.
how to you write out and solve this math problem 1.79.1619.90
EXPLANATION
Considering the addition
Write the numbers one under the other, line up the decimal points.
Add trailing zeroes so the numbers have the same length.
1. 7 9
+ 0. 1 6
+ 1 9. 9 0
----------------
Add each columns of digits, starting on the right and working left.
If the sum of a column is more than ten, 'carry' digits to the net column on the left.
Add the digits of the bolded column: 9 + 6 + 0 = 15
0 1. 7 9
+ 0 0. 1 6
+ 1 9. 9 0
----------------
Carry 1 to the column on the left and write 5 in the bolded column:
1
0 1. 7 9
+ 0 0. 1 6
+ 1 9. 9 0
----------------
5
Add the digits of the bolded column: 1 + 7 + 1 + 9 = 18
1
0 1. 7 9
+ 0 0. 1 6
+ 1 9. 9 0
----------------
8 5
Carry 1 on the colum to the left and write 8 in the bolded column:
1 1
0 1. 7 9
+ 0 0. 1 6
+ 1 9. 9 0
----------------
8 5
Place the decimal point in the answer directly below the decimal points in the term:
1 1
0 1. 7 9
+ 0 0. 1 6
+ 1 9. 9 0
----------------
.8 5
Add the digits of the bolded column : 1 + 1 + 0 + 9 = 11
1 1
0 1. 7 9
+ 0 0. 1 6
+ 1 9. 9 0
----------------
.8 5
Carry 1 to the column on the left and write 1 in the bolded column:
1 1 1
0 1. 7 9
+ 0 0. 1 6
+ 1 9. 9 0
----------------
1 .8 5
Add the digits of the bolded column: 1 + 0 + 0 + 1 = 2
1 1 1
0 1. 7 9
+ 0 0. 1 6
+ 1 9. 9 0
----------------
2 1 .8 5
The answer is 21.85
This is my math homework, I don’t understand how to find the seconds of the ball hit the ground
When the ball hits the ground, the height of the ball to the ground is h(t) = 0.
Therefore, we can now substitute h(t), and solve the function using quadratic formula.
[tex]\begin{gathered} h(t)=-16t^2+16t+400 \\ 0=-16t^2+16t+400 \\ \\ \text{The function is now in standard form where} \\ a=-16,b=16,c=400 \end{gathered}[/tex]Using the quadratic formula, substitute the following values a,b, and c.
[tex]\begin{gathered} t=\frac{ -b \pm\sqrt{b^2 - 4ac}}{ 2a } \\ t=\frac{ -16 \pm\sqrt{16^2 - 4(-16)(400)}}{ 2(-16) } \\ t=\frac{-16\pm\sqrt[]{256-(-25600)}}{-32} \\ t=\frac{ -16 \pm\sqrt{25856}}{ -32 } \\ t=\frac{ -16 \pm16\sqrt{101}\, }{ -32 } \\ \\ t=\frac{-16+16\sqrt{101}}{-32} \\ t=-4.52494 \\ \\ t=\frac{-16-16\sqrt[]{101}\, }{-32} \\ t=5.52494 \end{gathered}[/tex]We have two solutions, t = -4.52494, and t = 5.52494. However, we will disregard the negative time value.
Therefore, the ball will hit the ground after 5.52494 seconds.
question will be in picture
Given that the total money Elise had, was $30.
Since she spent $18 on gifts and the rest on 3 corn dogs.
Let the cost of a corn god be 'x' dollars. Then the cost of 3 corn dogs will be,
[tex]\begin{gathered} \text{Expense on corn dogs}=\text{ No. of corn dogs}\times\text{ Cost of 1 corn dog} \\ \text{Expense on corn dogs}=3\times x \\ \text{Expense on corn dogs}=3x \end{gathered}[/tex]So it is found that Elise spent $(3x) on corn dogs.
Since she had spent all the money in buying these two things, the total exprense must be equal to the total money Elise had in the beginning,
[tex]\begin{gathered} \text{Expense on corn dogs}+\text{ Expense on gifts}=30 \\ 3x+18=30 \end{gathered}[/tex]Thus, the required equation is obtained.
Therefore, option (a) is the correct choice.
During a 60 minute boxing class Abby burns 480 calories, on a 40 minute run, Abby burns 440 calories, while cycling for 30 minutes which exercise is the most efficient at burning calories?
Explanation:
Given that;
In a 60 minute boxing class Abby burns 480 calories.
The rate at which calories are burn during boxing is;
[tex]\begin{gathered} r_1=\frac{480}{60} \\ r_1=8\text{ calories/minute} \end{gathered}[/tex]Also;
on a 40 minute run,Abby burns 440 calories,
The rate at which calories are burn during cycling is;
[tex]\begin{gathered} r_2=\frac{440}{40} \\ r_2=11\text{calories/minute} \end{gathered}[/tex]while cycling for 30 minutes,
From the above rate the most efficient exercise at burning calories is the exercise with the highest rate of burning calories.
given a function's domain values: -9, -6, -3, 0, 1.5, and 3, what is the range of the function's inverse?
Answer:
[tex]-9,-6,-3,0,1.5,3[/tex]Explanation:
Given the domain of the function as;
[tex]-9,-6,-3,0,1.5,3[/tex]Note that the range of the inverse of a function is the same as the domain of a function is the original function.
So the range of the inverse of the function will be;
[tex]-9,-6,-3,0,1.5,3[/tex]What is the equation of the line perpendicular to the function f(x)=x^2+2x-2 at the point (1,1)?
Equation of a Line
The equation of a line that passes through the point (h, k) and has a slope m, is given by:
[tex]y-k=m(x-h)[/tex]This is known as the point-slope form of the line.
We already know the coordinates of the point (1, 1) but we don't know the value of the slope m. We will find it out by using the rest of the data.
Our line is perpendicular to the function:
[tex]f(x)=x^2+2x-2[/tex]At the given point. To find the slope of the tangent line, we use derivatives:
[tex]f^{\prime}(x)=2x+2[/tex]Substitute x = 1:
[tex]\begin{gathered} f^{\prime}(1)=2\cdot1+2 \\ f^{\prime}(1)=4 \end{gathered}[/tex]Now we know the slope of the tangent line, but our line is perpendicular to that line, so we find the perpendicular slope with the formula:
[tex]\begin{gathered} m_2=-\frac{1}{m} \\ m_2=-\frac{1}{4} \end{gathered}[/tex]We're ready to find the required equation. Substituting the coordinates of the point and the just-found slope:
[tex]y-1=-\frac{1}{4}(x-1)[/tex]This is the point-slope form, but maybe it's required to find the slope-intercept form. Multiply by 4:
[tex]\begin{gathered} 4y-4=-x+1 \\ \text{Add 4:} \\ 4y=-x+5 \\ \text{Divide by 4:} \\ y=-\frac{1}{4}x+\frac{5}{4} \end{gathered}[/tex]This is the answer is slope-intercept form
two cyclists, 112 miles apart riding toward each other at the same time. One cycles 3 times as fast as the other. if they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?
distance= 112 miles apart
time = 4 hours
Speed of a = 3 *speed of b
Distance covered by a = 3 * distance covered by b
Speed = distance / time
3b+b = 112
4b = 112
b= 112/4
b= 28 miles
a = 3b
a = 3 *28
a= 84 miles
Since both travelled for 4 hours:
Speed of A = 84 /4 = 21 mph
Speed of b= 28 /4 = 7 mph
Speed of the faster cyclist : 21 mph
Need to find equation f(x) = a(b)^xfor these 2 sets of points.(0, -3) (1, -³/2)
y = a b^x
Substitute the first set of points into the equation
-3 = a * b^0
-3 = a * (1)
-3 = a
y = (-3)* b^ x
Now using the second point
-3/2 = -3 * ( b)^1
-3/2 = -3 *b
Divide each side by -3
1/2 = b
y = -3 ( 1/2) ^x
When information is presented in the form of a bar graph or time- series graph, you could get more exact values if all the data were just listed out in table form. Then why not always do that. Why bother with graphs?
Step 1:
Graphs are essentially a visual display of quantitative information along two axes. Visuals are used as a way for our brains to quickly understand information, which is a powerful tool if used correctly. Graphs can show a large amount of data quickly in a way that is easy to process, without distracting people with a bunch of numbers.
Question Sally, an investor, purchases 3,000 shares in company X at $1.75 per share. After purchasing the shares the share price increases to $2.25 per share, after which Sally decides to sell her shares. Sally is required to pay 25% tax on all profits that she makes from the sale of the shares (called Capital Gains tax). Calculate the amount of tax that Sally must pay. Give your answer to the nearest dollar. Give your answer in dollars without the dollar sign or commas.
We are given the following information
Number of shares = 3,000
Buying price of a share = $1.75
Selling price of a share = $2.25
Capital Gains tax = 25% = 0.25
We are asked to calculate the amount of tax that Sally must pay.
Let us first calculate the profit.
Profit is given by
Profit = Selling price - Buying price
The buying price is given by
Buying price = (Number of shares)×(Buying price of a share)
Buying price = 3,000×1.75
Buying price = $5,250
The selling price is given by
Selling price = (Number of shares)×(Selling price of a share)
Selling price = 3,000×2.25
Selling price = $6,750
Profit = Selling price - Buying price
Profit = $6,750 - $5,250
Profit = $1,500
Finally, the amount of tax is given by
Amount of tax = profit × Capital Gains tax
Amount of tax = 1500 × 0.25
Amount of tax = $375
Therefore, Sally is required to pay a tax of $375
May I please get help with this I need help with finding the original Final point. I also need help with the graphing part, I am confused as to how I should do it after many tries Or where I should reflect it
We need to reflect the given figure across the y-axis. Then, we need to write the coordinates of the original and the reflected large dot.
When we reflect a point across the y-axis, its y-coordinate remains the same, and its x-coordinate changes the sign:
[tex](x,y)\rightarrow(-x,y)[/tex]The original coordinates of the large dot is: (5,3).
Thus, the coordinates after the reflection will be: (-5,3).
Doing the same with the coordinates of the other vertices and joining them, we obtain the reflected figure, as shown below:
Over the past 6 seasons, one baseball player's batting averages were 0.248, 0.302, 0.248, 0.307, 0.295, and 0.369. A second player's batting averages were 0.349, 0.231, 0.272,0.263, 0.275, and 0.384. What are the range and mean of each player's batting averages? Use your results to compare the players' batting skills.Find the range and mean of the first player's batting averages.The range is (Type an integer or a decimal.)(Round to the nearest thousandth as needed.)The mean is
First let's write down the batting averages of the first player in ascending order:-
0.248, 0.248, 0.295, 0.302, 0,307, 0,369
The difference between the largest value and the minimum value will give us the range:-
So range for the first player will be = 0.369 - 0.248 = 0.121
Now let;s calculate the mean of the first palyer's batting averages
[tex]\begin{gathered} \text{Mean}_1=\frac{0.248+0.248+0.295+0.302+0.307+0.369}{6} \\ =\frac{1.769}{6} \\ =0.295\text{ (approx)} \end{gathered}[/tex]Now let's write down the batting averages of the second player in ascending order
0.231, 0.263, 0.272, 0.275, 0.349, 0.384
So the range for second player will be:-
0.384-0.231= 0.153
Now let;s calculate the mean of the second palyer's batting averages
[tex]\begin{gathered} \operatorname{mean}=\frac{0.231+0.263+0.272+0.275+0.349+0.384}{6} \\ =\frac{1.774}{6} \\ =0.296(approx) \end{gathered}[/tex]The mean for second player is 0.296 (approx)
And the mean for the first player is 0.295 (approx)
Since the mean avarage of both the players is almost same but the range of second player is more than that of first player, so the second player has good batting skills as compared to the first player.
rewrite using a single positive exponent (7^8)/(7^5)
Given
[tex]\frac{7^8}{7^5}[/tex]When you divide two exponents with the same base number, to simplify the expression you have to calculate the difference between the index from the numberator and the index from the denominator.
In this case the base number is "7"
The index of the numerator is "8"
The index of the denominator is "5"
You can simplify the expression as follows
[tex]\frac{7^8}{7^5}=7^{8-5}=7^3[/tex]The solution is
[tex]7^3[/tex]y = 43 - 9Complete the missing value in the solution to theequation.(3,
We have the following:
[tex]y=4x-9[/tex]We have a solution pair is (x, y), in this case then x = 3, replacing we have
[tex]\begin{gathered} y=4\cdot3-9 \\ y=12-9 \\ y=3 \end{gathered}[/tex]The answer is: (3, 3)
An escalator at a shopping center is 200 ft long and has a vertical rise of 52 feet.What is the measure of the angle formed by the escalator and the ground? Round to the nearest degree
A right triangle is made, with measure:
From definition:
sin(α) = opposite/hypotenuse
From the picture: opposite to α is side of 52 long and the hypotenuse is 200 ft long. Then:
sin(α) = 52/200
sin(α) = 0.26
α = arcsin(0.26)
α = 15°
What is an equation of the line that passes through the points (4,7) and (2,-1)? Answer in fully reduced form.
The eqaution of a line between two points is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Plugging our points we have:
[tex]\begin{gathered} y-(-7)=\frac{-1-(-7)}{2-4}(x-4) \\ y+7=\frac{6}{-2}(x-4) \\ y+7=-3(x-4) \\ y+7=-3x+12 \\ y=-3x+12-7 \\ y=-3x+5 \end{gathered}[/tex]Therefore the equation is:
[tex]y=-3x+5[/tex]A What is the length of side BC of the triangle? 2x+7 4x7 В Enter your answer in the box. 4x units
Solution
For this case we can see from the image given that the value for BC is:
4x units
since that represent the lenght of the side