Grocery Store B ($1.33 per pound of bananas)
1) With these data we can write the following, and ,
Grocery Store A:
$ pounds
9.75 1/2
x--------------- 1
1/2x=9.75 x 2
x =19.5
Cross multiplying it:
Grocery Store B
$ pounds
5 3.75
y 1
3.75y=5
y=5/3.75
y=1.33
2) The best unit rate is at Grocery Store B ($1.33 per pound of bananas)
Can I just have a very quick simple answer to this question?
We have a feasibility region and we have to find at which point of the region the function P can be maximized:
[tex]P=3x+2y[/tex]As this is a linear function, the maximum value will be in one of the vertices of the region. We can identify the vertices as:
We can calculate the value of P for each of the vertices and see which one has a maximum value. We can already guess that P(8,0) will be greater than P(0,8) as the coefficient for x is greater than the coefficient for y.
We can calculate the three values as:
[tex]\begin{gathered} P(0,8)=3\cdot0+2\cdot8=0+16=16 \\ P(6,5)=3\cdot6+2\cdot5=18+10=28\longrightarrow\text{Maximum} \\ P(8,0)=3\cdot8+2\cdot0=24+0=24 \end{gathered}[/tex]Answer: the maximum value of P is 28.
A plastic candy container and its dimensions are shown in the figure.What is the closest to the value of the volume?
The volume of this composite figure is the sum of the volume of the cylinder and the cone.
Volume of Cylinder
The formula is
[tex]V=\pi r^2h[/tex]Where
V is the volume
r is the radius
h is the height
Given,
r = 5
h = 17.8
Substituting, we find the volume:
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi(5)^2(17.8) \\ V=1398.01 \end{gathered}[/tex]Volume of Cone
The formula is:
[tex]V=\frac{1}{3}\pi r^2h[/tex]Where
V is the volume
r is the radius
h is the height
Given,
r = 5
h = 6.2
Substituting, we find the volume:
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ V=\frac{1}{3}\pi(5)^2(6.2) \\ V=162.32 \end{gathered}[/tex]The total volume of the figure is:
1398.01 + 162.32 = 1560.33
finally surface area of the solid. use 3.14 for π. write your answer as a decimal.
To find the total surface area of this cone, we have that the total lateral area is given by the formula:
[tex]A_{\text{lateral}}=s\cdot\pi\cdot r[/tex]Where
s is the slant height of the cone, s = 12 inches.
r is the radius of the base of the cone, r = 7 inches.
To that area, we need to add the area of the base of the cone:
[tex]A_{\text{base}}=\pi\cdot r^2[/tex]That is, this is the area of a circle with this radius. Then, the total surface area is:
[tex]A_{\text{total}=}s\cdot\pi\cdot r+\pi\cdot r^2[/tex]Substituting the values in this formula, we have:
[tex]A_{\text{total}}=12in\cdot3.14\cdot7in+\pi\cdot(7in)^2=263.76in^2_{}+153.86in^2[/tex]Then
[tex]A_{\text{total}}=417.62in^2[/tex]Hence, the total area is equal to 417.62 square inches.
How should you solve the equation x + 10 = 80? What is the resulting equivalent equation?Choose the correct answer below.
Multiply each side by 10, then simplify
Here, we want to know how to proceed with solving the equation
As we can see, we have the division sign between the terms on the left hand side of the equation
To solve the equation, we have to find the value for x by isolating it
What this mean here is that we will have to multiply both sides by 10; so that we can isolate x
Thus, the correct answer here is to multiply each side by 10, then simplify
What is the volume of this cylinder in terms of Pi? radius=2height=5a.5πb.10πc.20πd.50πWhat is the volume of this cylinder? radius=7height=11a.77 cubic cmb.241.9 cubic cmc.539 cubic cmd.1,693.32 cubic cmWhat is the volume of this cylinder in terms of Pi? radius=10height=20a.2000πb.500πc.200πd.100πWhat is the volume of this cylinder? radius=34height=27a.98,055.39 cubic metersb.2,883.98 cubic metersc.24,513.85 cubic metersd.1,441.99 cubic meters
What is the volume of this cylinder in terms of Pi?
Volume
Wally's grandmother started a college savings account for him with $3,000. What is the total amount of money in the account after 5 years if the annual simple interest rate is 3%?
ANSWER
$3,450
EXPLANATION
She started the savings account with $3,000.
The simple interest rate is 3% and the number of years is 5 years.
To find the amount of money in the account after 5 years, we have to first find the interest and then add it to the initial amount saved.
Simple Interest on an amount of money (Principal) at a rate R for a number of years T is given as:
[tex]I\text{ = }\frac{\text{P }\cdot\text{ R }\cdot\text{ T}}{100}[/tex]Therefore, the interest is:
[tex]\begin{gathered} I\text{ = }\frac{3000\cdot\text{ 5 }\cdot\text{ 3}}{100} \\ I\text{ = \$450} \end{gathered}[/tex]Therefore, the amount in the account after 5 years is:
Amount = Principal + Interest
Amount = 3000 + 450
Amoun = $3,450
That is the amount in the account.
4. Which is the best first step to write 2(x-4)^2-3=8 in standard form?A. Factor.B. Clear the parentheses.C. Set the function equal to 0.D. Combine like terms.
We will have that the best way to write it in standard form is B, we clear the parentheses and solve for x.
*That is because the function is already factored, and we will combine like terms and equal to 0 in the remaining steps.
what is the whole number equal to 1000 / 4
In this case, the answer is very simple.
We must perform the division and verify that the result is a whole number.
1000 / 4 = 250 ===> 250 is a whole number
The answer is:
The number is 250 .
Answer:
250, hope this helped my love have a good rest of your day ^^
Step-by-step explanation:
if you simply devide 1000 by 4 then you get 250 wich yes , is indeed a whole number ^^
What is the equation of this line? Responses y=−2x y equals negative 2 x y = 2x y, = 2, x y=−1/2x y equals fraction negative 1 half end fraction x y=1/2x y equals 1 half x
The equation of line which shown in graph will be;
⇒ y = 2x
Option 3 is true.
What is Equation of line?The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope 'm' is defined as;
y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The graph for the equation of line is shown in figure.
Now,
Take two points on the line of the graph.
Two points are ( 1, 2) and (2, 4)
Find the slope of the line with two points (1, 2) and (2, 4) as;
⇒ m = (4 - 2) / (2 - 1)
⇒ m = 2 / 1
⇒ m = 2
Thus, The equation of line passing through the points (1, 2) and (2, 4) with slope 2 is;
⇒ y - 2 = 2 ( x - 1 )
⇒ y - 2 = 2x - 2
⇒ y = 2x - 2 + 2
⇒ y = 2x
Therefore,
The equation of line will be;
⇒ y = 2x
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At a parking garage in a large city, the charge for parking consists of a flat fee of $1.00 plus 1.60 /hr.(a) Write a linear function to model the cost for parking for hours.(Pt)(b) Evaluate P(1.4 )and interpret the meaning in the context of this problem.please make this right I keep making it wrong
Given:
The charge for parking consists of a flat fee of $1.00 and $1.60 per hour.
To find:
a) Write a linear function P(t).
b) Evaluate P(1.4)
Explanation:
a)
Since the flat fee is $1.00 and the varying fee is $1.60 per hour.
So, the linear function of the total cost for parking is,
[tex]P(t)=1.00+1.60t[/tex]Where t be the number of hours.
b)
Substituting t = 1.4 in the above function we get,
[tex]\begin{gathered} P(1.4)=1.00+1.60(1.4) \\ =1+2.24 \\ P(1.4)=\text{ \$}3.24 \end{gathered}[/tex]That means,
The total cost for parking for 1.4 hours is $3.24.
Final answer:
a) The linear function is,
[tex]P(t)=1.00+1.60t[/tex]b) The value is,
[tex]P(1.4)=3.24[/tex]10 Which number line represents the solution to the inequality -7x - 13 2 8?A-10-5НЕН1005B-10-50510с-10-50510D-10-50510оооо
The correct option is option A
Explanation:
First we solve the inequality:
-7x -13 ≥ 8
collect like terms:
-7x ≥ 8 + 13
-7x ≥ 21
Divide through by -7:
x ≤ 21/-7
Note: when you divde an inequality by negative number, the iequality sign changes.
x ≤ -3
Since x is less than or equal to -3, the number line starts at -3 and moves towards the left of the number line.
The correct option is option A
Brian glues together 4 wooden cubes as shown. Each cube has an edge of 5 centimeters. He covers the surface area of this new figure with metallic paper that is cut to size for each face.A. 125 square cm B. 150 square cm C. 450 square cm D. 600 square cm
Explanation:
The new figure is a square prism, with the sides that measure 4x5 = 20 cm.
We have to find the surface area of this prism. To do this we have to find the area of the rectangular faces and the area of the base, which is the same as the area of the top. The total surface area is 4 times the area of the rectangular face plus 2 times the area of the base/top.
[tex]A_{\text{rectangular face}}=20\operatorname{cm}\times5\operatorname{cm}=100\operatorname{cm}^2[/tex][tex]A_{\text{base}}=5\operatorname{cm}\times5\operatorname{cm}=25\operatorname{cm}^2[/tex][tex]\begin{gathered} S=4\cdot A_{\text{rectangular face}}+2\cdot A_{base} \\ S=4\cdot100\operatorname{cm}+2\cdot25\operatorname{cm}^2 \\ S=400\operatorname{cm}+50\operatorname{cm}^2 \\ S=450\operatorname{cm}^2 \end{gathered}[/tex]Answer:
C. 450 cm²
NO LINKS!! Show that the triangle with vertices A, B, and C is a right triangle.
Answer:
[tex][d(A, B)]^2=\boxed{85}[/tex]
[tex][d(A,C)]^2+[d(B,C)]^2=\boxed{85}[/tex]
[tex]\sf Area=\boxed{17}\; units^2[/tex]
Step-by-step explanation:
From inspection of the given diagram, the vertices of the triangle are:
A = (-5, 5)B = (1, -2)C = (-1, 6)If ΔABC is a right triangle, the sum of the squares of the two shorter sides will equal the square of the longest side. This is the definition of Pythagoras Theorem.
Use the distance formula to find the side lengths of the triangle.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
[tex]\begin{aligned}d[(A,B)]&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(1-(-5))^2+(-2-5)^2}\\&=\sqrt{(6)^2+(-7)^2}\\&=\sqrt{36+49}\\&=\sqrt{85}\end{aligned}[/tex]
[tex]\begin{aligned}d[(A, C)]&=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\&=\sqrt{(-1-(-5))^2+(6-5)^2}\\&=\sqrt{(-4)^2+(1)^2}\\&=\sqrt{16+1}\\&=\sqrt{17}\end{aligned}[/tex]
[tex]\begin{aligned}d[(B, C)]&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-1-1)^2+(6-(-2))^2}\\&=\sqrt{(-2)^2+(8)^2}\\&=\sqrt{4+64}\\&=\sqrt{68}\end{aligned}[/tex]
Therefore:
The longest side of the triangle is line segment AB.The two shorter sides of the triangle are line segments AC and BC.[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
The triangle is a right triangle if:
[tex][d(A,C)]^2+[d(B,C)]^2=[d(A,B)]^2[/tex]
Substitute the found side lengths into the formula:
[tex]\implies [\sqrt{17}]^2+[\sqrt{68}]^2=[\sqrt{85}]^2[/tex]
[tex]\implies 17+68=85[/tex]
[tex]\implies 85=85[/tex]
Therefore, this proves that ΔABC is a right triangle.
To find the area of a right triangle, half the product of the two shorter sides:
[tex]\begin{aligned}\implies \sf Area &= \dfrac{1}{2}bh\\&=\dfrac{1}{2} \cdot [d(A,C)] \cdot [d(B,C)]\\&=\dfrac{1}{2} \cdot \sqrt{17} \cdot \sqrt{68}\\&=\dfrac{1}{2} \cdot \sqrt{17 \cdot 68}\\&=\dfrac{1}{2} \cdot \sqrt{1156}\\&=\dfrac{1}{2} \cdot \sqrt{34^2}\\&=\dfrac{1}{2} \cdot 34\\&=17 \sf \; units^2\end{aligned}[/tex]
Therefore, the area of the given triangle is 17 units².
Solve 8sin(pi/6 x) = 4 for the four smallest positive solutions
Simplify the given expression as shown below
[tex]\begin{gathered} 8sin(\frac{\pi}{6}x)=4 \\ \Rightarrow sin(\frac{\pi}{6}x)=\frac{4}{8}=\frac{1}{2} \\ \Rightarrow sin(\frac{\pi}{6}x)=\frac{1}{2} \end{gathered}[/tex]On the other hand,
[tex]\begin{gathered} sin(y)=\frac{1}{2} \\ \end{gathered}[/tex]Solving for y using the special triangle shown below
Thus,
[tex]\begin{gathered} \Rightarrow y=30\degree\pm360\degree n=\frac{\pi}{6}\pm2\pi n \\ and \\ y=150\degree+360\degree n=\frac{5\pi}{6}+2\pi n \end{gathered}[/tex]Then,
[tex]\begin{gathered} \Rightarrow\frac{\pi}{6}x=y \\ \Rightarrow\frac{\pi}{6}x=\frac{\pi}{6}+2\pi n \\ \Rightarrow x=1+12n \\ and \\ \frac{\pi}{6}x=\frac{5\pi}{6}+2\pi n \\ \Rightarrow x=5+12n \end{gathered}[/tex]The two sets of solutions are
[tex]x=1+12n,5+12n[/tex]Then, the four smallest positive solutions are[tex]\Rightarrow x=1,5,13,17[/tex]The answers are 1,5,13,17How do you solve 3/4x-9=27
Solve;
[tex]\begin{gathered} \frac{3}{4}x-9=27 \\ \text{Add 9 to both sides and you now have;} \\ \frac{3}{4}x-9+9=27+9 \\ \frac{3}{4}x=36 \\ Cross\text{ multiply and you now have;} \\ x=\frac{36\times4}{3} \\ x=48 \end{gathered}[/tex]The solution is x = 48
Graph the line that passes through the points (-2,-7) and (5,0) anddetermine the equation of the lineKuationSubmit Answer
Given points:
(-2,-7) and (5,0)
To get the equation of the line, we will use the formula below:
[tex]y_{}-y_1=m(x_{}-x_1)[/tex]From the points given
[tex]\begin{gathered} x_1=-2,y_1=-7 \\ x_2=5,y_2=0 \end{gathered}[/tex]Where
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-7)}{5-(-2)}=\frac{7}{7}=1 \\ m=1 \end{gathered}[/tex]Substituting the values into the equation
[tex]\begin{gathered} y-(-7)=1(x-(-2)) \\ y+7=1(x+2) \\ y+7=x+2_{} \\ \end{gathered}[/tex]simplifying further
The equation of the line is:
[tex]y=x-5[/tex]The graph of the points (-2,-7) and (5,0) is given below:
The options are A,B,C,D can we make this quick please I am in a rush to turn this in!! thank you so much.
The function we have is:
[tex]y=-x+4[/tex]First, we need to find the rate of change of this function and then we can compare it with the rate of change of each option.
To find the rate of change, we compare the given equation with the general slope-intercept equation:
[tex]y=mx+b[/tex]Where m is the slope, also called the rate of change and b is the y-intercept.
By comparing the two equations, we find that the rate of change is:
[tex]m=-1[/tex]So now we will analyze the given options to see in which of them we find a rate of change of -1.
Option A:
In this option (and in option B) we have a table of values for x and y.
We calculate the rate of change by taking two (x,y) points from the table,
Here, we will take the first two (x,y) values and label them as follows:
[tex]\begin{gathered} x_1=-4 \\ y_1=1 \\ x_2=-2 \\ y_2=2 \end{gathered}[/tex]And we calculate the rate of change "m" using the slope formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]Substituting the values we get:
[tex]m=\frac{2-1}{-2-(-4)}[/tex]Solving the operations:
[tex]\begin{gathered} m=\frac{1}{-2+4} \\ m=-\frac{1}{2} \end{gathered}[/tex]The rate of change if NOT -1, this option is not correct.
Option B. We do the same as in the first option.
Label the first two (x,y) values as follows:
[tex]\begin{gathered} x_1=4 \\ y_1=5 \\ x_2=8 \\ y_2=8 \end{gathered}[/tex]And use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the values:
[tex]\begin{gathered} m=\frac{8-5}{8-4} \\ m=\frac{3}{4} \end{gathered}[/tex]Again, the slope or rate of change is NOT -1, this is also not the option we are looking for,
Option C. In options, C and D we have a graph. To find the rate of change from the graph of a line, we take two points where the line passes, and find the rate of change as follows:
[tex]m=\frac{\text{change in y}}{change\text{ in x}}[/tex]For the graph in C, we will take the following red points
Drawing a triangle between the points we can find the change in y and the change in x:
[tex]\begin{gathered} \text{change in y=-1} \\ \text{change in x=1} \end{gathered}[/tex]Thus, the rate of change is:
[tex]\begin{gathered} m=-\frac{1}{1} \\ m=-1 \end{gathered}[/tex]C is the correct option.
Valeria is ordering medals for her school's track meet. Company A charges $4.50 for each medal and a one-time engraving fee of$40. Company B charges $6.50 for each medal and a one-time engraving fee of $20. Which inequality can be used to find x, theleast number of medals that can be ordered so that the total charge for Company A is less than the total charge for Company B?esA)4.5+ 40x<6.5 + 20xB)4.5+ 40x > 6.5 + 20xo4.5x + 40 < 6.5x + 20D)4.5x + 40 > 6.5x + 20
We will determine the inequality as follows:
*First: We will determine the interception point of the two equations, that is:
[tex]y=4.50x+40[/tex][tex]y=6.50x+20[/tex]So:
[tex]4.50x+40=6.50x+20\Rightarrow4.50x-6.50x=20-40[/tex][tex]\Rightarrow-2x=-20\Rightarrow x=10[/tex]Now, we replace x = 10 on any of the two equations:
[tex]y=4.50x+40\Rightarrow y=4.50(10)+40[/tex][tex]\Rightarrow y=45+40\Rightarrow y=85[/tex]So, the interception point is located at (10, 85).
*Second: We determine the inequality that represents the problem, that is:
[tex]6.50x+20>4.50x+40[/tex][This is overall, the second equation represents greater cost].
*Third: The least number of medals that cab ve ordered so company's A cost is less than company's B cost is 10 medals.
6Question(15 Points)6. The volume of the cylinder below is 150 cubic centimeters. What is the area of its base?a. 20 cmb. 20 cmc. 10 cmd. 10 cm7.5 cm
The given cylinder has a height of 7.5 cm and volume of 150 cubic centimeters,
[tex]\begin{gathered} h=7.5\text{ cm} \\ V=150\text{ cm}^3 \end{gathered}[/tex]Consider that the volume and base area of a right circular cylinder are related as,
[tex]V=A\times h[/tex]Substitute the values and solve for A,
[tex]\begin{gathered} 150=A\times7.5 \\ A=\frac{150}{7.5} \\ A=20 \end{gathered}[/tex]Thus, the base area of the given cylinder is 20 sq. cm.
Therefore, option b is the correct choice.
Jacob is taking part in a month long Reading challenge at his school. He can earn point for each book he reads, up to two dozen books. As shown in the graph P (b) gives the number of points Jacob earns as a function of the number of books he reads.
Observe the given graph carefully.
It is evident that 'b' is the independent variable (representing the number of books read) for the function f(b) (representing the number of points earned).
The domain of a function is the set of all values of the independent variable that lie within the function.
The graph is plotted from x=0 to x=24.
And the number of books cannot be fractional.
So it can be concluded that the domain of the function is the set of whole numbers from 0 to 24. Also, the function is also defined at the end-points. So the set will be inclusive of the end-points 0 and 24.
Therefore, the 2nd option is correct for the first blank.
The domain is a subset of all possible values of variable 'b'. So it will represent the number of books that Jacob reads.
Thus, the 1st option is the correct choice for the second blank.
Factorise 3x^2 + 5x + 2
After factorizing the expression we get the result as -1 and -2/3.
Given,
the expression is:
3x²+5x+2
Multiply the terms and get the factors.
6x²
Now split the numbers according to the term
3x² + 3x + 2x + 2
collect the like terms.
Arrange the like terms.
3x(x+1) + 2(x+1)
re arrange the terms.
(x+1)(3x+2)
now get the value of x:
x+1 = 0
x = -1
or
3x+2 = 0
3x=-2
x=-2/3
Hence the factors of x are -1 and -2/3
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Based on the graph, find the range of y = f(x).[0,^3sqrt13 ][0, 8][0, ∞)[0, 8)
Given the function:
[tex]f(x)=\begin{cases}4;-5\le x<-2 \\ |x|;-2\le x<8 \\ ^3\sqrt[]{x};8\le x<13\end{cases}[/tex]The graph of the function is as shown in the figure:
The range of the function will be as follows:
The minimum value of y = 0
And the maximum value of y = 8 (open circle)
So, the range of the function = [0, 8)
Explain why the two right triangles are not the same.
Step 1:
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.
Step 2:
Write the corresponding sides and angles
The angles are not corresponding to the sides
Step 3
[tex]\begin{gathered} \angle T\text{ }\ne\text{ }\angle E \\ \angle S\text{ }\ne\text{ }\angle D \\ \angle R\text{ }\ne\angle F \end{gathered}[/tex]Final answer
The two right angles are not the same because the sides and the angles are not corresponding.
George was painting a picture frame. The frame was 5inches wide & 3inches tall. What is the perimeter of the picture frame?
The perimeter can be calculated by adding the legnths off all 4 sides.
Since it is 5 inches wide and 3 inches tall, it has 2 sides of 5 inches and 2 sides of 3 inches. So, the perimeter is:
[tex]P=5+5+3+3=16[/tex]16 inches.
Which expression is equivalent to 64 -1/2
A. 8
B. 8^2
C. 1/4
D. 1/8
The expression is 64 - 1/2 is equivalent to 127/2.
Given,
In the question:
Which expression is equivalent to 64 -1/2
Now, According to the question:
The ex[pression is given as:
64 - 1/2
Find common denominator and write the numerator above common denominator
[tex]= \frac{64 . 2}{2} - \frac{1}{2}[/tex]
Calculate the product or quotient:
128/2 - 1/2
Write the numerator over common denominator:
(128 - 1)/2
= 127/2
Hence, The expression is 64 - 1/2 is equivalent to 127/2.
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I need help to determine weather the slope on this graph is A. ZeroB. Negative C. Positive
The slope usually indicates the behavior of a line:
In the above picture there are 3 different lines with different slopes, let's describe them:
-L1. This red line has a positive slope, it means that as "x" increases, then "y" increases as well.
-L2. This blue line has a negative slope, which means that as "x" increases, then the value of "y" decreases.
-L3. This green line is horizontal and has zero slope . This means that it doesn't matter the value of "x", "y" always has the same value.
Using this description, we can now assure that the slope in your graph is NEGATIVE
State the rule of the perfect squares given the sequence shown below that starts with n = 1 1, 4, 9, 16, 26...
Given:
the sequence shown below that starts with n = 1
[tex]1,4,9,16,25,\ldots[/tex]The rule of the sequence will be as follows"
The first term = 1, when n = 1
The second term = 4 = 2², when n = 2
The third term = 9 = 3², when n = 3
..
..
So, the rule will be:
[tex]a_n=n^2[/tex]HELP graph the solution of system of linear inequality's
y< - 5x - 3
y>x+5
The graph of solution of system of linear inequality can be obtained by plotting the given equations and and then shading the region according to the inequality sign.
How to graph two linear inequality?
To graph Linear equations with inequality consider the equations as linear equation in two variable.Obtain two points for each line which satisfies the equations and plot them on graph. For example (1,6) and (-1,4) satisfies the equation y=x+5.Now shade the region according to the inequality: < : below the line> : above the lineHence you obtain the graph for the solution of system of the given linear equation with inequality.Any point in this region will satisfy both the linear inequalities (check the graph attached below).To know more about linear inequality visit
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Point M is the midpoint of segment QR. If QM = 2x + 5 and MR = 5x – 1, find the length of QR. QR = 18 QR = 9 QR = -9QR = 8
Asnwer:
QR = 18
Explanation:
If Point M is the midpoint of segment QR, then the following expressions are true
QM = MR and;
QM + MR = QR
Given
QM = 2x + 5 and MR = 5x – 1,
Recall that QM = MR
2x + 5 = 5x - 1
2x - 5x = -1-5
-3x = -6
x = -6/-3
x = 2
Get the length of QR
QR = QM + MR
QR = 2x+5 + 5x -1
QR = 7x +4
QR = 7(2) + 4
QR = 14+4
QR = 18
Hence the length of QR is 18
can you help me with my work
Conn Math increase by 3 , each week
Conn Sci increase doubling number, every week
Then now fill table
. Week. 1. Conn Math. Conn Sci
. Week 1. 25. 25
. Week 2. 28. 50
. Week 3. 31. 75
. Week 4. 34. 100
Now part. B
A linear model is when data fits in a straight line
hence Then
Then
First model of Conn Math is
Visitors. = 25 + 3 W
Second model for Conn Sci
Visitors = 25 x