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
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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
Related Questions
Find the volume of a rectangular prism with the following dimensions.length: 4.2 cmwidth: 7 cmheight: 15 cmvolume = ____ cm3
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Given:
length: 4.2 cm
width: 7 cm
height: 15 cm
Required:
volume = ____ cm3
Explanation:
volume of prism=
[tex]\begin{gathered} l\times w\times h \\ 4.2\times7\times15 \\ =441cm^3 \end{gathered}[/tex]Required answer:
[tex]441cm^3[/tex]
O GEOMETRY Perimeter involving rectangles and circles A rectangular paperboard measuring 20 in long and 13 in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.) Explanation +0 13 in 20 in Check 0 in X in² 5 in³ 3/5 ? Nikida E: 6 C E E 121
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The perimeter of the paperboard that remains after the semicircle is removed is 185.66in.
It is given to us that the measurement of rectangular paperboard are -
Length = 20in
Width = 13in
A semicircle is cut out of it.
We have to find out the perimeter of the paperboard that remains after the semicircle is removed.
Now, according to the given figure,
Radius of the semi circle = 1/2 (Width of the paperboard) ---- (1)
Let us say the radius of the semi circle is "[tex]r[/tex]".
So, from equation (1),
[tex]r = \frac{13}{2}\\ = > r = 6.5[/tex] in ---- (2)
Now, Perimeter of the paperboard that remains after the semicircle is removed =
Bottom length + Left width + Top length + Right circumference of the semicircle
= 20 + 13 + 20 + ([tex]\pi r^{2}[/tex]) [Circumference of semicircle = [tex]\pi r^{2}[/tex]]
= 53 + [[tex]\pi (6.5)^{2}[/tex]] [From equation (2), we have [tex]r = 6.5[/tex] in]
= 53 + 132.66
= 185.66 in
Thus, the perimeter of the paperboard that remains after the semicircle is removed is 185.66in.
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Find the X-intercept and Y-Intercept of the line. Write your answer as exact values. do not write your answer as order pairs
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The equation of the line is given as,
[tex]8x-5y=14[/tex]The intercepts are the points at which the curve intersects the coordinate axes.
The x-intercept of the line will be the value of 'y' at which the x-coordinate becomes zero. This can be calculated as follows,
[tex]\begin{gathered} 8x-5(0)=14 \\ 8x=14 \\ x=\frac{7}{4} \\ x=1.75 \end{gathered}[/tex]Similarly, the y-intercept is the point at which the line intersects the y-axis. This can be calculated as,
[tex]\begin{gathered} 8(0)-5y=14 \\ -5y=14 \\ y=\frac{-14}{5} \\ y=-2.8 \end{gathered}[/tex]Thus, the x-intercept and y-intercept are obtained as,
[tex]\begin{gathered} \text{ x-intercept}=1.75 \\ \text{ y-intercept}=-2.8 \end{gathered}[/tex]The Dover Symphony categorizes its donors as gold, silver, or bronze depending on the amount donated.
Answers
Explanation
Given the donors as
[tex]\begin{gathered} Gold=4 \\ silver=7 \\ Bronze=9 \end{gathered}[/tex]The total number of donors are
[tex]9+7+4=20[/tex]Therefore, the percent of donors at the bronze or silver level is
[tex]\frac{sum\text{ }of\text{ }bronze\text{ }and\text{ }silver\text{ donors}}{number\text{ of donors}}=\frac{9+7}{20}\times100=16\times5=80\text{\%}[/tex]Answer:
can you help me solve this
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If y varies directly with x, and y = 12 when x = 8, write the direct linear variationequation.O y=8xO y = 12xO y=2/3xO y= 3/2 x
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A direct linear variation of y with x has the general form:
[tex]y=mx[/tex]Where m is the ratio of y to x, which is a y divided by x.
Since we know that when x equals 8, y equals 12, we can calculate m, like this:
[tex]m=\frac{y}{x}=\frac{12}{8}=\frac{6}{4}=\frac{3}{2}[/tex]Now that we know that m=3/2, the linear variation equation would be:
[tex]y=\frac{3}{2}x[/tex]
Question 41: Find the product and express it in rectangular form.
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ANSWER:
[tex]-18-18\sqrt[]{3}i[/tex]SOLUTION:
what is the simplified form of the expression x^2+4x-21 over 4(x+7)
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Answer:
x-3 over 4
Let me know if you need elaboration
In the relationship shown by the data linear ? If so , model the data with an equation A. The relationship is not linear B. The relationship is linear; y+2=4/5 (x+9) C . The relationship is linear; y + 9 = - 4/5 (x+2) D. The relationship is linear; y+ 2 = -5/4 (x+9)
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Let's take two points so that we can get the equation of the line which goes through those points. P1 (-9, -2), P2 (3, -17):
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-17-(-2)}{3-(-9)}=\frac{-17+2}{3+9}=-\frac{15}{12}=-\frac{5}{4}[/tex][tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=-\frac{5}{4}\cdot(x-(-9)) \\ y+2=-\frac{5}{4}\cdot(x+9)_{} \\ y=-\frac{5}{4}x-\frac{45}{9}-2 \\ y=-\frac{5}{4}x-7 \\ f(x)=-\frac{5}{4}x-7 \end{gathered}[/tex]So, y is the line which goes through the first and last points of the chart.
To proof that the rest of points go through the line as well, we will evalute each point
[tex]\begin{gathered} f(-5)=-\frac{5}{4}\cdot(-5)-7=\frac{25}{4}-7=-\frac{3}{4}\ne-7 \\ f(-1)=-\frac{5}{4}(-1)-7=\frac{5}{4}-7=-\frac{23}{4}\ne-12 \end{gathered}[/tex]Since the evaluation of these points don't correspond to the values of the chart we can assure that the relationship is not linear
What is the smallest figure in geometry?
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By definition, a point is the smallest figure in geometry.
just need help with this one real quick. What do I put for B.I know the maximum value is (3,24)
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We were given:
[tex]\begin{gathered} f(x)=-3x^2+18x-3 \\ f(x)=y \\ \Rightarrow y=-3x^2+18x-3 \\ y=-3x^2+18x-3 \\ a=-3,b=18,c=-3 \end{gathered}[/tex]We will calculate the minimum point as shown below:
[tex]\begin{gathered} min=c-\frac{b^2}{4a} \\ min=-3-\frac{18^2}{4(-3)} \\ min=-3-\frac{324}{-12} \\ min=-3-(-27) \\ min=-3+27 \\ min=24 \\ \text{This is the maximum value (not minimum)} \\ x=-\frac{b}{2a} \\ x=-\frac{18}{2(-3)} \\ x=\frac{-18}{-6} \\ x=3 \\ \\ \therefore Maximum\text{ point is (3, 24)} \end{gathered}[/tex]This quadratic equation opens downward because the value of ''a'' is negative. Hence, the function only has a maximum point, it does not have a minimum point
The maximum value of the function is 24 and it occurs at x equals 3
Graph g(x)= 2|x-2|-3 and the parent function f(x)=|x|. Describe the transformations that occurred from f(x) to g(x). Then, describe the domain and range.
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The first thing to do is to graph both equations, as follows:
It is possible to check from the equations that there is no restriction for the value of x in both equations, and from the graph, we see that for each value of x, there is always a value of Y well defined. For this reason, we are able to conclude that the domain of both equations is all the real numbers.
Now, for the range of each, we can see that the values of Y for both are restricted to real numbers higher than the minimum value. For equation g(x), the range is the real numbers higher or equal to -3, while for f(x) the range is the real numbers higher or equal to 0.
15 Points and branliest for all three!
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According to SAS Congruence Theorem and the reflexive property of congruence, it can be proved that ΔSPQ ≅ ΔTPQ.
It is given to us that -
PQ bisects ∠SPT
SP ≅ TP
We have to prove that ΔSPQ ≅ ΔTPQ
Now, as PQ bisects ∠SPT,
∠SPQ = ∠TPQ
Also, according to the Reflexive Property of Congruence, PQ is a common side of both triangles - ΔSPQ and ΔTPQ.
Thus, according to SAS Congruence Theorem,
"If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent."
Therefore, according to SAS Congruence Theorem, we have proved that ΔSPQ ≅ ΔTPQ.
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Julie is buying chocolate chip and oatmeal cookies from the bakery. Chocolate chip cookies cost 25¢ each and oatmeal cookies cost 20c each. She wants to buy a mixture of at least 50 cookies. Julie is planning to spend less than $10. Let: C = number of chocolate chip cookies she can buy. M = number of oatmeal cookies she can buy. Select the system of inequalities that represents this situation.
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Kristy is paid semimonthly. The net amount of each paycheck is$750.50. What is her net annual income?a. $18,012b. $4,503c. $19,513d. $9,006
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SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Define semimonthly
A semimonthly payroll is paid twice in a month.
STEP 2: Calculate the net annual income
[tex]\begin{gathered} Net\text{ annual income means the total money received in a year.} \\ \text{If net amount of each paycheck is \$750.50 and it is a semimonthly payment, then;} \\ \text{monthly payment=\$750.50}\times2=\text{\$}1501 \\ \\ There\text{ are 12 months in a year,} \\ \text{If Kristy earns in month, then the amount earned in a year is:} \\ 12\times\text{\$1501=\$18,012} \end{gathered}[/tex]Hence, her net annual income will be $18,012
OPTION a
The graph of y= 2x^2 - kx + 6 touches the x-axis. What are the possible value(s) of k?
Answers
Given:
The graph of
[tex]y=2x^2-kx+6[/tex]Required:
What are the possible value(s) of k?
Explanation:
[tex]Set\text{ y = 0, evaluate the quadratic at }h=-\frac{b}{2a}and\text{ solve for k}[/tex]You want to find the value the value of k such that the y coordinate of the vertex is 0.
[tex]\begin{gathered} y=2x^2-kx+6 \\ 0=2x^2-kx+6 \end{gathered}[/tex]The x coordinate, h , of the vertex is found, using the following equation:
[tex]\begin{gathered} D=b^2-4ac \\ b^2-4ac=0 \\ k^2-4\times2\times6=0 \\ k^2-48=0 \\ k^2=48 \\ k=\pm4\sqrt{3} \end{gathered}[/tex]Answer:
So, values of k are above.
In a dog race of 9 equally talented runners, what is the probability that Dasher, Dancer, and Prancer will finish first,second, and third, respectively?21/907201/3628801/5041/3
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Combinations and Variations of Elements
Let's suppose we have two dogs only, A and B. They can only finish in two possible orders: AB or BA.
If we add a third dog, let's say C, the combinations (better-called variations here) are now ABC, ACB, BAC, BCA, CAB, and CBA, a total of 6 variations.
Note that we added a 3rd element and the variations changed from 2 to 6, that is, the number was multiplied by 3.
If we add a fourth dog, the total number of possible variations is 6*4 = 24
Following this very same pattern, for 9 dogs, there will be a total of
9*8*7*6*5*4*3*2 = 362880 variations.
Out of these possibilities, we are trying to find the probability that the first three places are occupied by three specific dogs, and the other 6 positions can be filled up with a random variation that will give us
6*5*4*3*2 = 720 variations.
Thus the required probability is:
[tex]\begin{gathered} p=\frac{720}{362880} \\ \text{Simplifying the result, we get:} \\ p=\frac{1}{504} \end{gathered}[/tex]Can you help me find the discriminant of this quadratic question aswell as the number and type of solutions?Problem: 2x^2+2=-5x
Answers
Given the quadratic equation:
[tex]2x²+2=-5x[/tex]we can write it like this:
[tex]2x²+5x+2=0[/tex]the discriminant is the expression b²-4ac. In this case, a = 2, b = 5 and c = 2, then, the discriminant is:
[tex]b²-4ac=(5)²-4(2)(2)=25-16=9[/tex]notice that the discriminant is 9 > 0, therefore, the quadratic function has two real solutions
complete the table using y=5x+9 (x)-1,0,1,2,3(y)
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To complete the table, plug each given x value into the equation. Then,
[tex]\begin{gathered} \text{ If x = -1} \\ y=5x+9 \\ y=5(-1)+9 \\ y=-5+9 \\ y=4 \\ \text{ So, you have the point} \\ (-1,4) \end{gathered}[/tex][tex]\begin{gathered} \text{ If x = 0} \\ y=5x+9 \\ y=5(0)+9 \\ y=0+9 \\ y=9 \\ \text{ So, you have the point} \\ (0,9) \end{gathered}[/tex][tex]\begin{gathered} \text{ If x = 1} \\ y=5x+9 \\ y=5(1)+9 \\ y=5+9 \\ y=14 \\ \text{ So, you have the point} \\ (1,14) \end{gathered}[/tex][tex]\begin{gathered} \text{ If x = 2} \\ y=5x+9 \\ y=5(2)+9 \\ y=10+9 \\ y=19 \\ \text{ So, you have the point} \\ (2,19) \end{gathered}[/tex][tex]\begin{gathered} \text{ If x = 3} \\ y=5x+9 \\ y=5(3)+9 \\ y=15+9 \\ y=24 \\ \text{ So, you have the point} \\ (3,24) \end{gathered}[/tex]Therefore, you would get the table
Enter the equation of the circle with the given center and radius. Center: (7,0); radius: 3 The equation is
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Given data:
The given coordinate of centre of the circle is (7,0).
The given radius of the circle is r=(3)^(1/2).
The equation of the circle is,
[tex]\begin{gathered} (x-7)^2+(y-0)^2=(\sqrt[]{3})^2 \\ (x-7)^2+y^2=3 \end{gathered}[/tex]Thus, the equation of the circle is (x-7)^2 +y^2 =3.
Instructions: For the following real-world problem, solve using any method. Use what you've learned to determine which method would be best. Put your answer in the context of the problem and determine the appropriate final answer. A sprinkler is set to water the backyard flower bed. The stream of water and where it hits the ground at the end of the stream can be modeled by the quadratic equation -22 + 14x + 61 = 0 where x is the distance in feet from the sprinkler. What are the two solutions in exact form? 2 x V X or What are the rounded values (to two decimal places)? Which of these answers makes sense in context to be the value of the number of products? x =
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Given the next quadratic equation:
[tex]-x^2+14x+61=0[/tex]we can use the quadratic formula to solve it, as follows:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{-14\pm\sqrt[]{14^2-4\cdot(-1)\cdot61}}{2\cdot(-1)} \\ x_{1,2}=\frac{-14\pm\sqrt[]{196+244}}{-2} \\ x_{1,2}=\frac{-14\pm\sqrt[]{440}}{-2} \\ x_1=\frac{-14+\sqrt[]{440}}{-2}=\frac{-14}{-2}-\frac{\sqrt[]{440}}{2}=7-\sqrt[]{110} \\ x_2=\frac{-14-\sqrt[]{440}}{-2}=\frac{-14}{-2}+\frac{\sqrt[]{440}}{2}=7+\sqrt[]{110} \end{gathered}[/tex]The rounded values (two decimal places) are:
[tex]\begin{gathered} x_1=7-10.49=-3.49 \\ x_2=7+10.49=17.49 \end{gathered}[/tex]Since x is the distance, in ft, from the sprinkler, it cannot be negative, then the answer which makes sense in the context of this problem is 17.49 ft
of the 800 participants in a marathon, 120 are running to raise money for a cause. How many participants out of 100 are running for a cause?a.8 b. 20c. 15d. 12OMG i hate iready please heeeelp
Answers
To find how many participants out of 100 are running for a cause we can use the next proportion:
[tex]\frac{800\text{ total participants}}{100\text{ total participants}}=\frac{120\text{ running for a cause}}{x\text{ running for a cause}}[/tex]Solving for x:
[tex]undefined[/tex]What is the reason these triangles are congruent? M N Р o Not Congruent
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Since the line in red is common to both triangles and segments PM and ON are parallel, then the angles in purple are congruent and so are the angles in green. So they are congruent by ASA
You are to show how to correctly graph y = -x - 5
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Answer and Explanation:
The slope-intercept form of the equation of a line is generally given as;
[tex]y=mx+b[/tex]where m = the slope of the line
b = the y-intercept of the line
So given the equation;
[tex]y=-x-5[/tex]Comparing the two equations, we can deduce the following;
* m = -1
This means that the line will have a negative slope
* b = -5
This means that the line will cut the y-axis at -5.
We can now choose values for x and determine the corresponding values of y and then proceed to plot the graph.
When x = 1;
[tex]\begin{gathered} y=-1-5 \\ y=-6 \end{gathered}[/tex]When x = 0,
[tex]\begin{gathered} y=-0-5 \\ y=-5 \end{gathered}[/tex]When x = -2,
[tex]\begin{gathered} y=-(-2)-5 \\ y=2-5 \\ y=-3 \end{gathered}[/tex]When x = -4,
[tex]\begin{gathered} y=-(-4)-5 \\ y=4-5 \\ y=-1 \end{gathered}[/tex]When x = -6;
[tex]\begin{gathered} y=-(-6)-5 \\ y=6-5 \\ y=1 \end{gathered}[/tex]With the above values and information, we can then go ahead and plot our graph as shown below;
How do I find the area of different shapes? Is it the same exact as finding the area of a square?Please help! e.g. Trapezoid, Triangle, Octagon
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Then area of each shape can be find ina different form. Each figure have a formula to find the area.
For example
Trapezoid:
[tex]A=\frac{1}{2}(B_1+B_2)\cdot h[/tex]Where B1 is one of the bases and B2 the other base. h is the vertical height.
Triangle:
[tex]A=\frac{1}{2}(b\cdot h)[/tex]b is the base and h is the vertical height.
Regular polygon:
[tex]A=\frac{P\cdot a}{2}[/tex]P is the perimeter of the regular polygon and a is the apothem (the distance for the center of the polygon to the mind-point of a side.
The salesperson earned a commission of $1110.20 for selling $7930 worth of paper products. Find the commission rate
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Commision = $1110.20
Selling= $7930
x is the commission rate
[tex]7930\cdot\frac{x}{100}=1110.20[/tex]Then we isolate the x
[tex]x=\frac{1110.20\cdot100}{7930}=14\text{ \%}[/tex]ANSWER
The commission rate is 14%
Question 6 of 21Which of the following best describes the graph of the polynomial functiibelow?5Х-55-5-
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Solution:
The zeros of a polynomial function are the points at which the graph of the function cuts the x-axis.
Given the graph of the polynomial function as shown below:
[tex]\begin{gathered} When\text{ the curve cuts the x-axis twice, this implies that the graph has 2 zeros.} \\ When\text{ the curve cuts the x-axis once, this implies that the graph has only 1 zero.} \\ \end{gathered}[/tex]Since the curve on the graph cuts the x-axis once, it implies that the graph has one zero.
The correct option is D.
Diego is trying to write the expression 2 + 1 - in a way that makes it easier tocalculate. He says, “I can switch the order of 1 and and write 2+- 1 then I canget an equivalent expression that's easier to compute.Do you agree with Diego's reasoning? Why or why not?
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While switching the order during adding or substraction,
1.) Your 3 year investment of $20,000 received 5.2% interested compounded semi annually. What is your total return? ASW
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Let's begin by listing out the information given to us:
Principal (p) = $20,000
Interest rate (r) = 5.2% = 0.052
Number of compounding (n) = 2 (semi annually)
Time (t) = 3 years
The total return is calculated as shown below:
A = p(1 + r/n)^nt
A = 20000(1 + 0.052/2)^2*3 = 20000(1 + 0.026)^6
A = 20000(1.1665) = 23,330
A = $23,330
Jessica and her father are comparing their ages. At the current time, Jessica's father is 24 years older than her l. Three years from now, Jessica father will be five times her age at the pointQUICK PLEASE
Answers
Current ages
Jessica's age = x
Jessica's father = x + 24
In 3 years time, there ages will be:
Jessica's age = x+ 3
Jessica's father = x + 24 + 3 = x + 27
But Jessica's father will be 5 times her age
Hence;
x + 27 = 5(x+3)
Open the parenthesis
x + 27 = 5x + 15
collect like term
5x - x = 27 - 15
4x = 12
Divide both-side of the equation by 4
x = 3
In the current time;
Jessica is 3 years old
Jessica's father is x + 24 = 3 + 24 = 27 years old