Surface area of a rectangular prism:
[tex]\begin{gathered} SA=2(l\cdot h+w\cdot h+l\cdot w) \\ l=\text{lenght} \\ w=\text{width} \\ h=\text{height} \end{gathered}[/tex]For the given prims:
l=8cm
w=3cm
h=3cm
[tex]\begin{gathered} SA=2(8\operatorname{cm}\cdot3\operatorname{cm}+3\operatorname{cm}\cdot3\operatorname{cm}+8\operatorname{cm}\cdot3\operatorname{cm}) \\ SA=2(24cm^2+9cm^2+24cm^2) \\ SA=2(57cm^2) \\ SA=114cm^2 \end{gathered}[/tex]Then, the surface area is 114 square centimeters5) 40,20,10,5, _,_,_a) Explain and Complete the sequence.B) write an explicit and recursive formula for the sequence
We have the sequence: 40, 20, 10, 5,...
Each term is half the previous term, so it is a geometrical sequence with common ratio r = 0.5.
We can not complete the sequence, as it becomes infinitely smaller and does not have a last term.
But we can write the three next terms to complete the blank spaces: 2.5, 1.25, 0.625.
We can start by writing the recursive formula. We know that each term is half the value of the previous term, so we wil have:
[tex]a_n=0.5\cdot a_{n-1}[/tex]From this recursive formula, we can deduce the explicit formula (in terms of n) as:
[tex]\begin{gathered} a_1=40 \\ a_2=0.5\cdot40=20 \\ a_3=0.5\cdot20=0.5\cdot(0.5\cdot40)=0.5^2\cdot40=10 \\ a_4=0.5\cdot10=0.5\cdot(0.5^2\cdot40)=0.5^3\cdot40 \\ \Rightarrow a_n=40\cdot0.5^{n-1} \end{gathered}[/tex]Answer:
a) Geometric sequence with r = 0.5.
The sequence first terms are: 40, 20, 10, 5, 2.5, 1.25, 0.625.
b) The recursive formula is a(n) = 0.5*a(n-1).
The explicit formula is a(n) = 40*0.5^(n-1).
Valentina earned some money doing odd jobs last summer and put it in a savings account that earns 7% interest compounded quarterly after 5 years there is 500.00 in the account how much did valentina earn doing odd jobs
please help this is for my study guide thanks! (find volume) (don't round)
100,000π ft³
1) Let's find the volume of that Cylinder using this formula:
[tex]V=\pi r^2h[/tex]Note that the volume is the area of the base (a circle) times the height
2) Also, notice that in the picture we have the diameter, the radius is half the Diameter:
[tex]\begin{gathered} V=\pi\cdot(50)^2\cdot40 \\ V=100000\pi^{} \end{gathered}[/tex]3) So the volume is 100,000π ft³
help meeeee pleaseeeee!!!
thank you
The values of f(0), f(2) and f(-2) for the polynomial f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex] are 12, 28 and 52 respectively.
According to the question,
We have the following information:
f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex]
Now, to find the value of f(0), we will put 0 in place of x.
f(0) = [tex]-0^{3} +7(0)^{2} -2(0)+12[/tex]
f(0) = 0+7*0-0+12
(When a number has some power then it means that in order to solve this we have expand the expression and multiply the number as many times as the power is given. For example, in the case of 3 as power, we will multiply any number 3 times and in case of 2 as power, we will multiply the given number 2 times.)
f(0) = 0+0-0+12
f(0) = 12
Now, to find the value of f(2), we will put 1 in place of x:
f(2) = [tex]-2^{3} +7(2)^{2} -2(2)+12[/tex]
f(2) = -8+7*4-4+12
f(2) = -8+28-4+12
f(2) = 40 -12
f(2) = 28
Now, to find the value of f(2), we will put -2 in place of x:
f(-2) = [tex]-(-2)^{3} +7(-2)^{2} -2(-2)+12[/tex]
f(-2) = -(-8) + 7*4+4+12
f(-2) = 8+28+4+12
f(-2) = 52
Hence, the value of f(0) is 12, f(2) is 28 and f(-2) is 52.
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d1 = 16 m; d2 = 14 m what's the rhombus?
Step 1 : To determine the area of the rhombus
[tex]\begin{gathered} d_1=16m,d_2\text{ = 14m } \\ Area\text{ = }\frac{1}{2}\text{ }\times d_1\text{ }\times d_2 \\ Area\text{ = }\frac{1}{2}\text{ }\times\text{ 16 }\times\text{ 14} \\ Area\text{ = }\frac{224}{2} \\ Area=112m^2 \end{gathered}[/tex]Therefore the area of the rhombus = 112m²
Find the slope of the line defined by each pair of points.:( points :(-1,4). Points. (-1,-5)
Notice that the x coordinate of both points is the same, therefore the line is a vertical line.
Answer: The slope is undefined.
help in this question
A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.
A vertex example is what?f(x)=3(x−1)2
Find the given parabola's characteristics.
Lessen the steps you tap...
Vertex form is to be used, y=a(x−h)2+k,
to calculate the values of a, h, and k.
a=3
h=1
k=0
The parabola widens because the value of an is positive.
opens up
Find the (h,k) vertex. ( 1 , 0 )
Calculate p, the distance between the focus and the vertex.
To continue, tap...
1/ 12
Locate your focus.
To continue, tap... ( 1 , 1/ 12 )
By identifying the line that connects the vertex with the focus, you may determine the axis of symmetry.
x = 1
The horizontal line that results from deducting p from the vertex's y-coordinate k depends on whether the parabola opens up or down. This line is known as the directrix.
y = k − p
Simplify the formula after substituting the known p and k values.
y = − 1 /12
Analyze and graph the parabola using its characteristics.
Direction: opens up
vertices: ( 1, 0 )
Focus: ( 1 , 1 /12 )
x = 1 is the symmetry axis.
Direction: y = /1 12.
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If 12 gallons of gas cost $26.68, howmuch will 15 gallons cost? (proportion)
It is expected that the cost of gas will increase as the number of gallons increases and decrease as the number of gallons decrease. This is a direct proportion
As such, if
12 gallons of gas cost $26.68
15 gallons will cost 15/12 * $26.68
= $33.35
15 gallons of gas will cost $33.35
Please help me with this sample question.Find f(0)Find f(1)Find f(2)
In order to find the values of f(0), f(1) and f(2), we just need to find in the graph for the value of the function (that is, the value of y) for the values of x equal to 0, 1 and 2 respectively.
Looking at the graph, for x = 0 we have y = -7, therefore f(0) = -7
For x = 1 we have y = -2, therefore f(1) = -2
For x = 2 we have y = -5, therefore f(2) = -5
parallelogram pqrs has diagonals PR in SQ that intersect at T given s p equals 2 a + 5 + r q equals 5 a - 1 St equals 3 b - 3 + SQ equals 7 b - 9 what are the values of RQ and TQ
SP = 2a+5
RQ= 5a-1
ST = 3b-3
SQ = 7b-9
RQ=?
TQ=?
SP = RQ
2a+5 = 5a-1
Solve for a
5+1 = 5a-2a
6 = 3a
6/3 = a
2=a
RQ= 5a-1 = 5(2)-1 = 10-1 = 9
RQ= 9
ST + TQ = SQ
ST= TQ
TQ= 3b-3
3b-3+3b-3= 7b-9
Solve for b
6b-6 = 7b-9
-6+9 = 7b-6b
3=b
TQ = 3b-3= 3(3)-3= 9-3 =6
TQ= 6
Multiply.4y=2y3v2.4v7
Let's recall one of the properties of exponents:
[tex]x^4\ast x^5=x^{4\text{ + 5}}=x^9[/tex]Therefore, in our exercise we have:
[tex]4y\text{ }\ast2y^3=8y^{4\text{ }}andv^2\ast4v^7=4v^9[/tex][tex]8y^4\ast4v^9=32y^4v^9[/tex]Solve for x.2x + 3 ≤ x + 5
Answer:
x ≤ 2
Explanation:
Given the inequality:
[tex]2x+3\le x+5[/tex]First, we subtract x from both sides.
[tex]\begin{gathered} 2x-x+3\le x-x+5 \\ x+3\le5 \end{gathered}[/tex]Next, we subtract 3 from both sides.
[tex]\begin{gathered} x+3-3\leqslant5-3 \\ x\leqslant2 \end{gathered}[/tex]Mr.Gonzalez spent $50 more than Mr.Silva on school supplies. together, they spent $174. How much money did each of them spent?
Answer: You need to spend more than $5.00
Step-by-step explanation:
Jane needs $20 to buy her radio.She has saved $15.What precent of the cost of the radio has she saved?
Let's begin by listing out the information given to us:
Cost of Radio (c) = $20
Jane's saving (s) = $15
% of radio cost saved = (Jane's saving / Cost of Radio) * 100%
[tex]\begin{gathered} x=\frac{s}{c}\cdot100 \\ x=\frac{15}{20}\cdot100=75 \\ x=75 \end{gathered}[/tex]Jane has saved 75% of the radio cost
Endpoint 19,-10) Midpoint (4,8).What is the other endpoint
Let the first end point be x1 y1 and the second x2 y2 the midpoint would be
x1 + x2 / 2 y1 + y2 / 2
Hence
(19 + x2)/2 = 4
19 + x2 = 8
x2 = 8 -19
x2 = -11
(-10 + y2)/2 =8
- 10 + y2 = 8
y2 = 8 + 10
= 18
The other end point is (-11, 18)
Evaluate g(-3)Determine the coordinates of the point given by the answer aboveEvaluate g(2a)Step By Step Explanation Please
Given the quadratic equation:
[tex]g(x)=3x^2-5x+4[/tex]Let's solve for the following:
• (a) g(-3)
To solve for g(-3), substitute -3 for x and evaluate.
Thus, we have:
[tex]\begin{gathered} g(x)=3x^2-5x+4 \\ \\ g(-3)=3(-3)^2-5(-3)+4 \\ \\ g(-3)=3(9)+15+4 \\ \\ g(-3)=27+15+4 \\ \\ g(-3)=46 \end{gathered}[/tex]Hence, we have:
g(-3) = 46
• (b) To determine the coordinates of the point given in question (a).
In the function, g(x) can also be written as y.
Thus, from g(-3), we have the following:
x = -3
y = 46
When x = -3, the value of y = 46
In point form, we have the coordinates:
(x, y) ==> (-3, 46)
Therefore, the coordinates of the given point by the answer in (a) is:
(-3, 46)
• (c) Evaluate g(2a).
To evaluate g(2a), substitute 2a for x in the equation and evaluate.
Thus, we have:
[tex]\begin{gathered} g(x)=3x^2-5x+4 \\ \\ g(2a)=3(2a)^2-5(2a)+4 \\ \\ g(2a)=3(4a^2)-5(2a)+4 \\ \\ g(2a)=12a^2-10a+4 \end{gathered}[/tex]ANSWERS:
• (a) g(-3) = 46
• (b) (-3, 46)
• (c) g(2a) = 12a² - 10a + 4
Choose the equation below that represents the line passing through the point (2, -4) with a slope of(1 point)Oy=kx-3Oy -x+5Oy-1x+3Oy=1x-5
The equation of a line in slope-intercept form can be written like this:
y = mx + b
Where m is the slope and b is the y-intercept of the line.
In this case, the slope of the line is 1/2, then we can rewrite the above equation like this:
y = (1/2)x + b
We are also told that this line passes through (2, -4), by replacing 2 for x and -4 for y into the above equation, we can solve for the value of b, like this:
-4 = 2(1/2) + b
-4 = 1 + b
-4 - 1 = 1 - 1 + b
-5 = b
b = -5
Then, we can rewrite the equation of the line, like this:
y = (1/2)x - 5
Then, the last option is the correct answer
Cai says you can divide both quantities in a ratio by the same non-zero number to find an equivalent ratio. Explain why cai is correct.
In this case, Cai is right.
Basically, Cai is right because a ratio is a fraction. So, if you divide the numerator and denomirator by the same number, the fraction won't be changed, in that case you would get an equivalent fraction.
For example, if we have 4/6, and we divide both numbers by 2, we get 2/3, these operations are valid because you are dividing both numbers by the same (2).
the number of regular telephones in use is how many times the number of cellular phones? 45% regular phones15% cellular phones6% others34% Cordless phones
Solution
For this case we have the following info:
45% regular phones
15% cellular phones
6% others
34% Cordless phones
We know that the total regular of phones is 45% and the total of cellular phones are 15% then we can find the ratio like this:
45/15 = 3
May I please get help with this math problem it’s so confusing
We have to find the value of z and x.
We assume that lines g and h are parallel.
Then, z and the angle with measure 85° are consecutive interior angles.
As they are conscutive interior angles, their measures add 180°.
Then, we can write:
[tex]\begin{gathered} z+85\degree=180\degree \\ z=180-85 \\ z=95\degree \end{gathered}[/tex]Then, we can relate the angle with measure z with the angle with measure (6x-109). They are vertical angles and, therefore, they have the same measure.
Then, we can write:
[tex]\begin{gathered} z=6x-109 \\ 95=6x-109 \\ 95+109=6x \\ 204=6x \\ x=\frac{204}{6} \\ x=34 \end{gathered}[/tex]Answer: z = 95 and x = 34.
A landscape supply business charges $35 to deliver mulch. The cost of the mulch is
$29 per cubic yard. Write a linear equation to find the cost of having x cubic yards of
mulch delivered to a site.
The linear function to represent the number of mulch delivered to a site is y = 29x + 35
What is a linear function?In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
For this question, we can represent the cost of having x cubic yards of mulch delivered to a site. For a standard linear function, it can be represented as y = mx + c
m = slope
c = intercept
We can use this concept to write a linear function to represent this problem:
y = mx + c
y = 29x + 35
In this case, the slope is 29 and the intercept is 35. The slope in this situation is the cost of the mulch and the amount charged by the business is the intercept.
The equation representing this problem is y = 29x + 35
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Question Evaluate. 7⋅5+42−23÷4 Responses 49 49 41 41 34 34 9 9
Answer: 71.25
This is not of of the options, but is the right answer.
Step-by-step explanation:
7 x 5 + 42 - 23 / 4 =
Step 1: Make parentheses
(( 7 x 5 ) + 42) - ( 23 / 4) =
Step 2: Solve parentheses ( Multiplication and division first )
(35 + 42) - 5.75 =
Step 3: Solve parentheses ( Addition )
77 - 5.75 =
Step 4: Subtract
= 71.25
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2. Factor completely
2x^2 + 8x + 6
The factors are -3 and -1
What is a Quadratic equation ?
A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.
The given expression is,
2x² + 8x + 6
Put it equal to 0 so that we can solve for 'x'
2x² + 8x + 6 = 0
Now, its factors are 6x and 2x
2x² + 6x + 2x + 6 = 0
2x(x + 3) + 2(x + 3) = 0
To cross check your solution is correct or not. You've to just see the the brackets value should be same after taking common. Here the bracket value is (x+3) which is same.
(2x + 2) (x+3) = 0
split the values to solve further,
2x + 2 = 0 | x + 3 = 0
2x = -2 | x = -3
x = -2/2
x = -1
Hence, the factors are -3 and -1
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Sales tax in South Carolina is 5%. Mr. Smith bought a new car there for $18,700. What did he pay in sales tax?
Answer: $935
Step-by-step explanation:
Mr. Smith paid $935 in sales tax
I need help on thisChange the equation into a equivalent equation written in the Slope-intercept form. x -7y + 5 =0
The slope-intercept form is an equation as follows:
[tex]y=mx+b[/tex]Then, we need to change the original equation in this equivalent:
[tex]-7y=-5-x\Rightarrow-7y=-x-5\Rightarrow7y=x+5[/tex]Dividing the total equation by 7, we have:
[tex]\frac{7}{7}y=\frac{x}{7}+\frac{5}{7}\Rightarrow y=\frac{1}{7}x+\frac{5}{7}[/tex]Therefore, the slope-intercept form is:
[tex]y=\frac{1}{7}x+\frac{5}{7}[/tex]An electronics store makes a profit of $59 for everystandard DVD player sold and $69 for every portableDVD player sold. The manager's target is to make atleast $345 a day on sales from standard and portableDVD players. Write an inequality that represents thenumbers of both kinds of DVD players that can besold to reach or beat the sales target. Let s representthe number of standard DVD players sold and prepresent the number of portable DVD players sold.Then graph the inequality.
The profit on one standard DVD player is $59 and on one portable DVD player is $69.
If there are s number of standard DVD player then total profit on standard DVD players is $59s. Simillarly total profit on portable DVD players is $69p.
The total profit on DVD player shoul be at least $345, which means total profit on DVD players is $345 or more than $345.
The linear inequalty for total profit is,
[tex]59s+69p\ge345[/tex]The graph of the linear inequality is,
In graph, lines pointing away the origin represent the region for the equation.
See the attached for the math problem
1. If the cake rises by ¹/₃ as it bakes, the number of cups of cake batter needed for the four cakes is 140.
2. If ¹/₄ in. is used between layers and ¹/₂ in. is used on the top and sides, the number of cups of icing needed for the four cakes is 47.
How are the numbers determined?The number of cups of cake batter and icing can be determined using the mathematical operations of multiplication, addition, division, and subtraction.
First, the volumes of each cake and its batter are calculated using the given dimensions and the rise.
Using the division operation, the number of cups of cake batter for each cake is determined and multiplied by four.
We understand that the normal volume of the cake will increase with the icing, helping us to calculate the increased volume after the icing.
The difference between the two volumes becomes the volume of the icing required, which is divided by 14.4 in³ to get the number of cups of icing required.
a) Cups of Cake Butter:The volume of each cake = Length x Width x Height
Length = 14 inches
Width = 12 inches
Height = 4 inches (2 x 2)
= 12 x 14 x 4
= 672 in³.
Rise of the cake as it bakes = ¹/₃
The normal volume before rising = 1
Risen volume = 1¹/₃
1¹/₃ = 672 in³
The normal volume of cake batter before the ¹/₃ rise = 504 in³ (672/1¹/₃).
1 cup = 14.4 in³, the total cups for each cake = 35 cups (504 in³/14.4 in³).
The total cups of cake batter for the 4 cakes = 140 cups (35 x 4).
b) Cups of Icing:The total quantity of icing = 1¹/₄ (¹/₄ + ¹/₂ + ¹/₂).
The new volume after the icing = 840 in³ (672 x 1¹/₄)
The difference in volume after the icing = 168 in³ in (840 in³ - 672 in³)
If 1 cup = 14.4 in³, the cups of icing for each cake = 11.67 cups (168 in³/14.4 in³).
The total cups of icing for the 4 cakes = 47 cups (11.67 x 4).
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Question Completion:Four double-layered cakes, each 12.0 in. x 14.0 in., have been ordered for a special event. Each layer is 2.0 in. high.
a) If the cake rises by ¹/₃ as it bakes, how many cups of cake batter are needed? (1 cup = 14.4 in³. Hint: The ¹/₃ rise should be treated as a constant.)
b) How many cups of icing are needed if ¹/₄ in. is used between layers and ¹/₂ in. is used on the top and sides? (Assume icing is not layered on top of the icing. 1 cup = 14.4 in³.)
The illustration below shows the graph of y as a function of x.complete the following sentences based on the graph of the function.* initially, as x increases, y (increases, decreases or stays constant).* the slope of the graph is equal to ___ for all x between x = 0 and x = 3.* starting at x = 3, the function value y (increases, decreases, or stays constant) as x increases.* the slope of the graph is equal to ___ for x between x = 3 and x = 5.* for x between x = 0 and x = 4, the function value y (≤, ≥, or =) 0.* for x between x = 4 and x = 8, the function value y (≤, ≥, or =) 0.
We will have the following:
*Initially, as x increases, y decreases.
*The slope of the graph is equal to -1 for all x between x = 0 & x = 3.
*Starting at x = 3, the function value y increases as x increases.
*The slope of the graph is equal to 3 for x between x = 3 & x = 5.
*For x between x = 0 & x = 4, the function value y ≤ 0.
*For x between x = 4 & x = 8, the function value y ≥ 0.
Which pair of numbers are not opposites?
47 and- 47
74 and -74
|4| and -4
47 and |-47|
FOR THE PAIRS TO BE OPPOSITE IT MEANS THE NUMBERS SHOULD ALSO CONTRAST IN SIGNS.
47 AND -47 ARE OPPOSITE
74 AND - 74 ARE OPPOSITE
|4|=4 AND -4 ARR OPPOSITE
47 AND |-47|=47 ARE NOT OPPOSITE BECAUSE THEY BOTH HAVE THE SAME SIGNS.
THE LAST OPTION IS THE ANSWER.
Can you please help me out with a question
S = 2(a*b + a*c + b*c)
= 2 (12*15 + 12*6 + 15*6)
= 2 (342)
= 684 ft^2