7x - 18
Explanations:The given expression is:
3 (x - 6) + 4x
Open the brackets by expanding the expression
3x - 18 + 4x
Combine like terms
3x + 4x - 18
7x - 18
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 $360 in one year. Hope it helps! :)
Given H = f(t) where H is the height in meters of an object and t is the time in
seconds since it was launched, which of the following is the best interpretation of f(2) =18?
A. The object travels 2 meters for every 18 seconds.
B. 18 seconds after the object is launched it is traveling 2 meters per second.
C. The object is 36 meters in the air.
D. 2 seconds after the object is launched it is 18 meters in the air.
E. The object travels 18 meters for every 2 seconds.
F. 2 seconds after the object is launched it is traveling 18 meters per second.
G. 18 seconds after the object is launch it is 2 meters in the air.
Answer:
D
Step-by-step explanation:
Well, since t = time in air, we already know that it traveled 2 seconds.
H = height in meters, and H = 18
So, after 2 seconds the object is 18m in the air
So, option D
2.) The information in the table below shows the
distance a car traveled during a number of hours.
Hours (h)
Miles (m)
1
45
2
90
3
135
4
180
Write an equation using the variables h and m that
represents the information in the table
Answer:
m = 45h
Step-by-step explanation:
Calculate the difference in y-values (miles):
[tex]45 \underset{+45}{\longrightarrow} 90\underset{+45}{\longrightarrow} 135\underset{+45}{\longrightarrow} 180[/tex]
As the number of miles increases by the same amount for every increase of an hour, the equation is linear.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$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]
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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5multipled 10the power 5 multipiled 4 multipled 10 to the power 3 divided by 2 multipled by 10 to the power minus 3
Step-by-step explanation:
answer
Are you clear your doubt with my answer?
Solve the compound inequality.2x-5 33 and 3x-12-19Graph the solution on the number line:
Consider the system of inequalities,
[tex]\begin{gathered} 2x-5\leq3 \\ 3x-1\ge-19 \end{gathered}[/tex]Simplify the first inequality as follows,
[tex]\begin{gathered} 2x-5+5\leq3+5 \\ 2x\cdot\frac{1}{2}\leq8\cdot\frac{1}{2} \\ x\leq4 \end{gathered}[/tex]So, the solution to this inequality will be the set of points including and lying on the left of point 4 on the number line.
Simplify the second inequality as follows,
[tex]\begin{gathered} 3x-1+1\ge-19+1 \\ 3x\cdot\frac{1}{3}\ge-18\cdot\frac{1}{3} \\ x\ge-6 \end{gathered}[/tex]So, the solution to this inequality will be the set of points including and lying on the right of point -6 on the number line.
The solution to the compound inequality will be the common solution of both the inequalities, that is, the set of real numbers ranging from -6 to 4.
The solution can be seen on the number line as follows,
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 $2500The 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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How can I draw a vertical bar chart to represent the recorded data shown above using the approximate heights in metres where necessary?
Hello!
As this exercise informs the approximate heights, you can consider just this value (don't need to write two heights in this case).
To make this chart, I used the heigths:
• Mercedario: 6770m
,• Misti, Volcán: 5820m
,• Pular: 6230m
,• Sajama: 6520m
,• Talima: 5220m
Look at the chart below:
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
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]
Two points determine a line. Find an equation of the line passing through the points.
(2,−7) and (5,−19)
An equation of the line is y=
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-19}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-19}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{2}}} \implies \cfrac{-19 +7}{3} \implies \cfrac{ -12 }{ 3 } \implies - 4[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- 4}(x-\stackrel{x_1}{2}) \implies y +7 = - 4 ( x -2) \\\\\\ y+7=-4x+8\implies {\Large \begin{array}{llll} y=-4x+1 \end{array}}[/tex]
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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a) what are the coordinates of points P and Q?b)Evaluate f(b)c) solve f(x)=e for xd)suppose c=f(z) and z=f(x).what is x?e) suppose f(b)=-f(d).what additional information does this give you?
a) Remember that the coordinates for any given point in the cartesian system have two components, one in the X axis and the secon one in the Y axis. (X,Y)
The coordinates for P and Q are:
P (b,a)
Q(d,e)
b) If you have the formula for the function, you'll se that to determine the value on the Y axis for a given value of X you have to replace that value in the formula. This means that Y= f(x).
In this example the value of Y for X=b is equal to a, so f(b)= a
c) For f(x)=e, you have to identify the value of x that croses to Y=e, in this grapfic that value is d
d) f(z)=c and f(x)=z
If you watch the graphic, c is in the y-axis, this means that the x value of its coordinate is zero. So z=0
Now for f(x)=z, this means that you have to find the value of x when the value of Y is zero. To determine this value you have to see where the function crosses the X-axis.
The function crosses the X-axis in point h, so when f(x)= z, x=h
e) If f(b)=-f(d) this means that both |b| and |d| are equal, you can express it as:
b=-d
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
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]Mario received $0.40 in change from
$20.00 when he bought trail mix. How
many pounds of trail mix did Mario buy?
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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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 this
Answer:
38.461538
Step-by-step explanation:
The volume of a cube is 2744m^3. What is the length of an edge of the cube?
Answer:14
Step-by-step explanation
The answer is PROBABLY a whole number.
(2) 10^3 = 1000; 20^3 = 8000. So the number is between 10 and 20; and closer to 10.
(3) Of the possible answers 11, 12, 13, and 14, only one of them has units digit 4 when raised to the 3rd power.
Answer:
L=14m
Step-by-step explanation:
volume of a cube =L×L×L
V=L³
2744=L³
L=³√2744
L=14m
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
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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What equation below has a linear graph that is parallel to the graph of y 2 on the Cartesian coordinate system
x=2
y=7
y=-2r
y=2r
Answer:
x=2
Step-by-step explanation:
The required equation x = 2 has a linear graph that is parallel to the graph of the y-axis on the Cartesian coordinate system. which is the correct answer would be option (A).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
A vertical line is a line on the coordinate plane with all of its points having the same x-coordinate. When we plot the points for a function x = an on a coordinate plane, we discover that connecting the coordinates results in a vertical line.
As per the given question, we have
The required equation x = 2 is the required vertical line.
Thus, the required equation x = 2 has a linear graph that is parallel to the graph of the y-axis on the Cartesian coordinate system.
Hence, the correct answer would be an option (A).
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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
The width of a rectangle measures (7r - 2s) centimeters, and its length measures
(r-5s) centimeters. Which expression represents the perimeter, in centimeters, of
the rectangle?
The perimeter of the given rectangle is 16r-14s centimeters.
Let width be represented by=w
Let length be represented by=l
Let perimeter be represented by=p
Then,
l=(r-5s)centimeters (Given in the question)
while w=(7r-2s)centimeters (Given in the question)
The formula for the perimeter of a rectangle= 2(l+b)
where l is the length while b is the breadth of the rectangle.
On putting values in the equation:
p=2(l+b)
p=2(l+w)
p=2[(7r-2s)+(r-5s)]
on opening the bracket 2 is multiplied by both terms.
p=2(7r-2s)+2(r-5s)
p=(2x7r-2x2s)+(2xr-2x5s)
p=(14r-4s)+(2r-10s)
p=14r-4s+2r-10s
p=14r+2r-4s-10s
p=14r+2r-(4s+10s)
p=14r+2r-(14s)
p=16r-(14s)
Thus,
p=16r-14s centimeters
The perimeter of the given rectangle is 16r-14s centimeters.
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Find the real zeros of f (x) =45x -5x^3
We will have the following:
[tex]f(x)=45x-5x^3\Rightarrow f(x)=-5x(x^2-9)[/tex][tex]\Rightarrow f(x)=-5x(x-3)(x+3)[/tex]So, its zeros are x = -3, x = 0 & x = 3.
what is this???????????????????????/
Answer:
5rs^3t^2 cubed root rt
Step-by-step explanation:
so 5rs-cubed t-squared and inside the cube root is rt
PLEASE HELP, Simplify: 4/9+3/7
Answer:
7/16
Step-by-step explanation:
To find the answer, simply just add the numbers together:
For the numerators:
4 + 3 = 7
For the denominators:
9 + 7 = 16
So, we have 7/16 because this cannot be simplified down anymore.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
Exact Form:
55/63
Decimal Form:
¯¯¯¯¯¯¯¯¯¯¯¯
0.873015
Step-by-step explanation:
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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