Let x be the number of books that need to be sold, then for the cost of the production and the profit to be the same we can set the following equation:
[tex]30456+10x=21.75x\text{.}[/tex]Subtracting 10x from both sides of the equation we get:
[tex]30456=21.75x-10x,[/tex]adding like terms we get:
[tex]30456=11.75x\text{.}[/tex]Dividing by 11.75 we get:
[tex]x=2592.[/tex]Then the producer must sell 2592 books.
Answer: 2592.
A line passes through the point (1, -6) and has a slope of 9.Write an equation in point-slope form for this line.
EXPLANATION
Given the point (1,-6) and the slope 9 the equation in point-slope form is given by the following form:
[tex]y-y_1=m(x-x_1)[/tex]Where m is the slope and (x_1,y_1)=(1,-6)
Replacing terms:
[tex]y-(-6)=9(x-1)[/tex]Applying the subtraction property:
[tex]y+6=9(x-1)\longrightarrow\text{ point-slope form}[/tex]
how fast is soil creep? group of answer choices 1 to 10 millimeters per year 1 to 10 meters per year 1 kilometer per hour over 10 kilometers per hour
The option-C is correct, that is 1 to 10 millimeter per year fast is soil creep.
Given that,
In the picture we can see the options.
We have to select the correct option for the given question.
What is the soil creep?The slow, downward movement of rock and soil down a low grade slope is known as downhill creep, sometimes referred to as soil creep or simply creep. Downhill creep can also refer to the slow deformation of such materials as a result of persistent strain and tension. While creep may appear continuous to the spectator, it actually represents the accumulation of multiple little, discontinuous movements of slope material produced by gravity.
Therefore, The option-C is correct, that is 1 to 10 millimeter per year fast is soil creep.
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2.) The information in the table below shows the
distance a car traveled during a number of hours.
Hours (h)
Miles (m)
1
45
2
90
3
135
4
180
Write an equation using the variables h and m that
represents the information in the table
Answer:
m = 45h
Step-by-step explanation:
Calculate the difference in y-values (miles):
[tex]45 \underset{+45}{\longrightarrow} 90\underset{+45}{\longrightarrow} 135\underset{+45}{\longrightarrow} 180[/tex]
As the number of miles increases by the same amount for every increase of an hour, the equation is linear.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given variables:
x = Hours (h)y = Miles (m)As the number of miles increases by 45 miles for each increase of an hour, the slope of the linear equation is 45:
[tex]\implies m=45h+b[/tex]
To find b, substitute one of the ordered pairs into the equation and solve for b:
[tex]\implies 45=45(1)+b[/tex]
[tex]\implies 45=45+b[/tex]
[tex]\implies b=45-45[/tex]
[tex]\implies b=0[/tex]
Therefore, the equation using the variables h and m that represents the information in the given table is:
[tex]\boxed{m=45h}[/tex]
The president of a bank projects that the earnings from one investment will be $47,000 this year. He also plans to buy some municipal bonds that yield 25% annual interest. How much money should he invest in the bonds so that the total earnings from the two investments will be at least $80,000?
The investment amount that the bank president should make in the bonds so that the total earnings from the two investments will be at least $80,000 is $132,000.
How is the amount determined?The earnings from the second investment are the difference between the total expected earnings and the first investment's earnings.
Using the above difference obtained by subtraction, the investment amount is computed by dividing the difference by the annual interest rate.
The total earnings from the two investments ≥ $80,000
The profits from one investment = $47,000
The earnings from the second investment should be ≥ $33,000 ($80,000 - $47,000)
The annual interest rate on municipal bonds = 25%
The investment amount = $132,000 ($33,000 ÷ 25%)
Thus, if $132,000 were invested in municipal bonds at 25% interest, its annual earnings would be $33,000.
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The cost of 8 meters of ribbon is $5.60.
A) What will be the cost of 5 meters of ribbon?
B) How many meters of ribbon can I buy with $16.80?
Answer:
Ok For A should be 3.50 For 5 Meters which in Centimeter is 500. For B you can get 24 meters of ribbon
Step-by-step explanation:
This is how you do it convert the meters to centimeter then see how much the ribbon cost per centimeter which is 0.007
8 meters to centimeters = 800
0.007 x 800 = 5.60
Then for B 24 Meters to Centimeters = 2,400
0.007 x 2,400 = 16.80
Noah manages trends orchard which produces many different types of fruit including pears there are more pastries that have been planted in the orchard the more barrels of pear the orchard will produce
From the information available, pear trees are planted and as more of them are planted then more barrels of pears will be produced.
This means the number of barrels will DEPEND on the number of trees planted, whereas the number of trees planted can be any amount and does not depend on the number of barrels.
ANSWER:
P is independednt and B is dependent
Where
p = number of pear trees that have been planted in the orchard
b = the number of barrels of pears the orchad will produce
The Andrettis borrowed $25,000 to renovate their kitchen with a 4.5% annual simple interest rate. If they paid $11,250 in interest, how long did it take them to repay the loan?
They took 10 years to repay the loan.
Given, Andrettis borrowed $25,000 to renovate their kitchen with a 4.5% annual simple interest rate.
Interest he paid was, $11250
Now, we have to find the time period,
As, Simple Interest = (Principal×Rate×Time)/100
11250 = (25000×4.5×t)/100
11250 = 25×45×t
t = 10
Hence, they took 10 years to repay the loan.
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Convert 5 tons into kilograms (kg) using the measurement conversion: 1 kg= 2.2046 ibs. Round to two decimals.
Recall, 1 ton = 1000 kg
This means that
1 kg = 1/1000 = 0.001 tons
If
1 kg= 2.2046 lbs, it means that
0.001 tons = 2.2046 lbs
HELPPPP IM FAILING
In ^CDE, DE= CD and m/D = 29°. Find m/C.
Answer:
<C=75.5⁰
Step-by-step explanation:
<C=<E
<C+<E+<D= 180⁰
<C+<E= 180⁰-29⁰
<C+<C= 151⁰
2<C= 151⁰
<C= 151⁰/2
<C= 75.5⁰
Suppose line m is the line with the equation x = -5, line n is the line with the equation y = 1, line g is the line with the equation y = x, and line h is the line with the equation
y = -2. given a(9,-3), b(6,4), and c(-1,-5), what are the coordinates of the vertices of aa'b'c' for the reflection rg?
A' will be (-3,9) B' will be (4,6) and C' will be (-5,-1). t are the coordinates of the vertices of aa'b'c' for the reflection rg.
What is coordinates ?A pair of numbers that specify where a point is situated on a coordinate plane using the horizontal and vertical separations from the two reference axes. usually represented by a pair of x-values and y-values (x,y).
CalculationIn this problem, basically you have three points and 6 straight lines(4 described in the problem and x and y axis) in a 2-D plane. You have to find the reflection of these three points with respect to these 6 lines one by one.
Points are:
A(9,-3)
B(6,4)
C(-1,-5)
Case 1:
Line is X-axis i.e. y = 0.
If you take reflection about x-axis then you can observe that the x - co-ordinate will remain same while y-co-ordinate will change its sign.
So A' will be (9,3), B' will be (6,-4) and C' will be (-1,5)
Case 2:
Line is y-axis i.e. x = 0
Here the analogy will remain same except here the y - co-ordinate will remain same and x - co-ordinate will change ite sign.
So, A' will be (-9,-3) B' will be (-6,4) and C' will be (1,-5).
Case 3:
Reflection about line "m" i.e. x = -5
This is a vertical line. Suppose the point whose reflection is to be found about is line is at a perpendicular distance of "k" from the line on right side, then its reflection will be "k" distance on the left from this line on the same horizontal line. So y-co-ordinate will not change.
For A(9,-3), it is at a distance of 14 units from the line on the right side so its reflection will be 14 units on the left with same y - co-ordinate. So its x - co-ordinate will be -5-14 = -19
So A' will be (-19,-3)
Similarly for B, B' will be (-16,4) and C' will be (-9,-5).
This graph will help you understand better.
The red line is x = -5.
The case for line y = 1 and y = -2 will be similar.
Case 5:
Reflection about the line y = x
photos are attached .............
So, A' will be (-3,9) B' will be (4,6) and C' will be (-5,-1).
We can use these two observations to find the reflection of any point about any line:
(i) The midpoint of the given point and the reflection point will lie on the given line about which the reflection is to be found.
(ii) The product of slope of given line and the line joining the given point and the reflection point is -1.
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Which equation can be solved by using this system of equations? startlayout enlarged left-brace 1st row y = 3 x cubed minus 7 x squared 5 2nd row y = 7 x superscript 4 baseline 2 x endlayout
The equation 1st Row y = 3 x cubed minus 7 x squared 5 can be solved by using this system of equations,
What do you mean by system of equations?
A group of equations comprising one or more variables is known as a system of equations.
The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
What three categories of equation systems are there?
There are three different sorts of solutions for two-variable linear equation systems.
There is only ever one solution pair for an autonomous system. The sole solution is the intersection of the two lines.A system that is inconsistent cannot be fixed.There are infinitely many solutions for a dependent system.To learn more about systems of equations, visit:
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Gary had a 40% discount for car speakers. The sale price of the speakers was $90.What was the original price of the speakers?
The original price of the speakers are found to be $150.
What is meant by the term discount?The discount is equal to the difference between both the purchase price and the par value. A discount is a reduction as well as deduction in a product's cost price. It is most commonly used in purchase and sale of products, where people are given discounts on a variety of products. The discount rate is expressed as a percentage.For the given question;
Gary had a 40% discount for car speakers.
The sales price of the speakers was $90.
Let the original price be 'x'.
Thus,
Sales price = original price - discount.
90 = x - 40% of x
90 = x - 40x/100
90 = 6x/10
x = 900/6
x = 150
Thus, the original price of the speakers are found to be $150.
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Nate placed $1800 in a one-year CD at the bank. The bank is paying simple interest of 5% for one year on the CD. How much interest will Nate earn in one year?
Answer: $360
Step-by-step explanation: $1800 divided by 5 equals $360 in one year. Hope it helps! :)
HELPPP PLEASEE!
Raul claims his graph shows a proportional relationship because the data forms a straight line. He also claims his graph shows he read 1.5 pages per minute. Are Raul’s claims correct? Justify your reasoning. Write an equation to represent the data in the graph.
the answer is below Learm!!!
Step-by-step explanation:
maybe if u learn in school u would get the answer bum
In the model, two of the flagpoles are 4 inches apart. How far apart will they be when they are installed?
ANSWER
36 feet
EXPLANATION
We are given that the scale of the model is 1 inch to 9 feet.
The two flagpoles are 4 inches apart in the model.
To find the distance between them when they are installed, we have to use ratio/proportion.
Let the distance between them be x.
We have that from the scale:
1 inch = 9 feet
=> 4 inches = x feet
Now, we can cross-multiply:
[tex]\begin{gathered} 1\cdot x=4\cdot9 \\ \Rightarrow x=36\text{ feet} \end{gathered}[/tex]Therefore, the distance between them when they are installed is 36 feet.
Javier has a balance of $216 on his game store gift card. He spends $59 on each game he buys from the store.
slope =
y-intercept =
PLEASE J NEED HELP NOWW
Hence, the slope is [tex]-59[/tex] and the y-intercept is [tex]216[/tex].
What is the slope?
The slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Here given that,
Javier has a balance of $[tex]216[/tex] on his game store gift card. He spends $[tex]59[/tex] on each game he buys from the store.
So, the equation is of the form
[tex]y=-59x+216[/tex]
But we know line of equation is
[tex]y=mx+c[/tex]
where [tex]m[/tex] is the slope and [tex]c[/tex] is the intercept.
i.e,
slope is [tex]-59[/tex]
[tex]y[/tex] int is [tex]216[/tex]
Hence, the slope is [tex]-59[/tex] and the y-intercept is [tex]216[/tex].
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What is the answer to this
Answer:
38.461538
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].
[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]
PLEASE NEED THIS NOW PLEASE!!
Write and simplify an expression to represent the perimeter of the triangle shown. What is the perimeter of the triangle if y equals 3 feet?
(please show work)
The perimeter of the triangle if the value of y is 3 feet is 31 feet
Perimeter of the triangle:
Perimeter of the triangle is calculated as the total distance around the edges of a triangle.
The formula for the perimeter of the triangle is
P = a + b + c.
where
a, b and c refers the sides of the triangle.
Given,
Here we have the triangle with the side values are (y + 5)ft, (3y + 5)ft, and (4y - 3)ft.
Now we have to find the perimeter of the triangle when the value of y is 3 feet.
As per the formula of the perimeter of triangle, first we have to calculate the side values of it, by apply the value of y as 3,
Then we get the sides are,
y + 5 => 3 + 5 = 8 ft
3y + 5 => 3(3) + 5 = 14ft
4y - 3 => 4(3) - 3 = 9ft.
Therefore, the sides of the given triangle are 9ft, 14 ft and 9 ft.
Then the perimeter of the triangle is,
P = 8 + 14 + 9
P = 31
Therefore, the perimeter of the triangle is 31 feet.
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identify the area od the rhombus.
Calculate the height of the upper triangle, using the Pythagoras theorem
[tex]\begin{gathered} 25^2=7^2+h^2 \\ h^2\text{ = }625\text{ - 49} \\ h^2\text{ = }576 \\ h\text{ = }\sqrt[]{576} \\ h\text{ = }24 \end{gathered}[/tex]The length of the vertical diagonal = 2 x 24
The length of the vertical diagonal = 48m
[tex]\begin{gathered} \text{Area = }\frac{48\times14}{2} \\ \text{Area = }48\times7 \\ \text{Area = 336 m}^2 \end{gathered}[/tex]Can someone please help me
Answer:
m∠B < m∠C < m∠A
Step-by-step explanation:
We know that the opposite angle of the smallest arm is the smallest angle
For a certain company , the cost for producing items is 45x + 300 and the revenue for selling items is 85x - 0.5x ^ 2. Part a: set up an expression for the profit from producing and selling x items and solve. we assume the company sells all of the items it produces. Part B: find two values of x thatvwill create a profit of $50. Part C: is it possible for the company to make a profit if $2500?
Producing cost:
[tex]45x+300[/tex]Revenue:
[tex]85x-0.5x^2[/tex]The profit (P) is equal to substract the producing cost for the revenue:
[tex]\begin{gathered} P=(85x-0.5x^2)-(45x+300) \\ P=85x-0.5x^2-45x-300 \\ P=40x-0.5x^2-300 \end{gathered}[/tex]
You can write also as:
[tex]P=-0.5x^2+40x-300[/tex]----------------------------------
P=50:
[tex]50=-0.5x^2+40x-300[/tex]To solve for x:
Substract 50 in both sides of the equation:
[tex]\begin{gathered} 50-50=-0.5x^2+40x-300-50 \\ 0=-0.5x^2+40x-350 \end{gathered}[/tex]Use the quadratic formula:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-40\pm\sqrt[]{40^2-4(-0.5)(-350)}}{2(-0.5)} \\ \\ x=\frac{-40\pm\sqrt[]{1600-700}}{-1} \\ \\ x=\frac{-40\pm\sqrt[]{900}}{-1} \\ \\ x=\frac{-40\pm30}{-1} \\ \\ x_1=\frac{-40+30}{-1}=\frac{-10}{-1}=10 \\ \\ x_2=\frac{-40-30}{-1}=\frac{-70}{-1}=70 \end{gathered}[/tex]Then, the two values of x that make a profit of $50 are: 10 and 70------------------ ----------------------
P=2500
[tex]2500=-0.5x^2+40x-300[/tex]Solve for x:
[tex]\begin{gathered} 0=-0.5x^2+40x-300-2500 \\ 0=-0.5x^2+40x-2800 \\ \\ x=\frac{-40\pm\sqrt[]{40^2-4(-0.5)(-2500)}}{2(-0.5)} \\ \\ x=\frac{-40\pm\sqrt[]{1600-5000}}{-1} \\ \\ x=\frac{-40\pm\sqrt[]{-34000}}{-1} \end{gathered}[/tex]As the number under the square root is a negative number the equation has no solution (value of x) in the real numbers.
No, is not possible for the company to make a profit of $2500Given H = f(t) where H is the height in meters of an object and t is the time in
seconds since it was launched, which of the following is the best interpretation of f(2) =18?
A. The object travels 2 meters for every 18 seconds.
B. 18 seconds after the object is launched it is traveling 2 meters per second.
C. The object is 36 meters in the air.
D. 2 seconds after the object is launched it is 18 meters in the air.
E. The object travels 18 meters for every 2 seconds.
F. 2 seconds after the object is launched it is traveling 18 meters per second.
G. 18 seconds after the object is launch it is 2 meters in the air.
Answer:
D
Step-by-step explanation:
Well, since t = time in air, we already know that it traveled 2 seconds.
H = height in meters, and H = 18
So, after 2 seconds the object is 18m in the air
So, option D
In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC 1 BD, then find
The measure of the angle ∠BEC is 60°.
We are given two parallelograms: ABCD and BDCE. They have a common base CD. It is given that BC is perpendicular to BD. We need to find the measure of the angle ∠BEC.
In the parallelogram ABCD, ∠BCD is equal to ∠DAB because opposite angles in a parallelogram are equal to each other.
∠BCD = 30°
In the triangle BCD, we will use the angle sum property. The sum of all the angles in a triangle is 180°.
∠DBC + ∠BCD + ∠CDB = 180°
90° + 30° + ∠CDB = 180°
∠CDB = 180° - 120°
∠CDB = 60°
Now, in the parallelogram BDCE, ∠BEC is equal to ∠CDB because opposite angles in a parallelogram are equal to each other.
∠BEC = 60°
Hence, the measure of the angle ∠BEC is 60°.
The complete question is given below.
In the figure given below, ABCD and BDCE are parallelograms with common base DC . If BC ⊥ BD , then find ∠BEC.
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Which equation in standard form has a
graph that passes through the point
(-3, 4) and has a slope of 3/2?
A.
B.
C.
D.
3x - 2y = -17
3x - 2y = 18
2x - 3y = -18
2x-3y = 17
3x-2y=-17
12
+2y=
72
33/22
-3x-17
2
The standard form of a graph that passes (-3,4) and has a slope of [tex]\frac{3}{2}[/tex] is
The standard form of the graph can be found as follows:
The point-slope form of a graph is
[tex](y-y_{1})=m(x-x_{1})[/tex]
where [tex](x_{1}, y_{1})[/tex] is the point that passes the graph and m is the slope.
Substitute [tex]x_{1}=-3[/tex], [tex]y_{1}=4[/tex], and m=[tex]m=\frac{3}{2}[/tex] into point slope form.
[tex](y-4)=\frac{3}{2} (x-(-3))[/tex]
Simplify the equation.
[tex]y-4=\frac{3}{2} (x+3)[/tex]
Multiply both sides by 2
[tex]2(y-4)=3(x+3)[/tex]
Simplify.
[tex]2y-8=3x+9[/tex]
Add both sides by 8.
[tex]2y=3x+17[/tex]
Subtract both sides by 3x
[tex]2y-3x=17[/tex]
Multiply by -1.
[tex]3x+2y=-17[/tex]
Remember the standard form of the graph is:
Ax+By=C
Then, the standard form of the linear equation is A. [tex]3x-2y=-17[/tex].
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what is the answer to - 4a - 5b + 7a - 3b
The perimeter of a square is 44 centimeters. What is its area in square centimeters?
Answer:
121cm^2
Step-by-step explanation:
44/4=11 so each side equals 11cm
to find the area multiply height by width
11*11=121
121cm^2
Find the coordinate of the given point.
The point Y between X(1,-2) and Z(11, 3) such that the ratio of XY to YZ is 3:2
[tex]\textit{internal division of a line segment using ratios} \\\\\\ X(1,-2)\qquad Z(11,3)\qquad \qquad \stackrel{\textit{ratio from X to Z}}{3:2} \\\\\\ \cfrac{X\underline{Y}}{\underline{Y} Z} = \cfrac{3}{2}\implies \cfrac{X}{Z} = \cfrac{3}{2}\implies 2X=3Z\implies 2(1,-2)=3(11,3)[/tex]
[tex](\stackrel{x}{2}~~,~~ \stackrel{y}{-4})=(\stackrel{x}{33}~~,~~ \stackrel{y}{9}) \implies Y=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{2 +33}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-4 +9}}{3+2} \right)} \\\\\\ Y=\left( \cfrac{ 35 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies {\Large \begin{array}{llll} Y=(7~~,~~1) \end{array}}[/tex]
How many 1/5s are in 9?
Answer:
About 90 1/5's are in 9.
Question
A line goes through the point (–4, –2) and (–1, y) and has a negative slope. Select all of the values below that could represent y.
A.-5
B.-4
C.-3
D.-2
E.-1
F.0
The values that can represent 'y' when the slope is negative are:
A) -5(B) -4(C) -3What is a slope?A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x). Slope usually referred to as rise over run, is the "steepness" of the line. By dividing the difference in y values between two points by the difference in x values, we may determine the slope.So, values that can represent y are:
Slope formula: m = y2-y1/x2-x1Substitute values as follows:
m = y2-y1/x2-x1m = y+2/-1+4m = y+2/3We know that the slope is negative.
So, the value of y needs to be greater than 2 and negative. Then,
(A) -5(B) -4(C) -3Therefore, values that can represent 'y' when the slope is negative are:
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