3.
Similar triangles: the sides are proportional
Length /width
8/2 =20 /x
Solve for x
4 =20/x
x=20/4
x= 5 ft
The width of the second triangle is 5 ft.
Using the net below, find the surface area of the pyramid. Blin 2 in Surface Area . - [?] in.2 Enter
The Solution:
The correct answer is 16 square in.
Given the net in the picture on the Question section, we are asked to find the surface area of the pyramid that can form using the given net.
The pyramid (or the net) has a total of 5 surfaces, these are:
4 similar triangles, each with a base of 2 inches and a height of 3 inches; and a square of side 2 inches.
So,
The required surface area is the total area of all 5 surfaces.
By formula, the area of a triangle is
[tex]A=\frac{1}{2}bh[/tex]While the area of a square is
[tex]A=l\times l[/tex]So, the required area of the pyramid is
[tex]\text{Area}=4(\frac{1}{2}bh)+(l\times l)[/tex]In this case,
[tex]\begin{gathered} =\text{base}=2\text{ in.} \\ h=\text{height}=3\text{ in.} \\ l=\text{side}=2\text{ in.} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]\text{Area}=4(\frac{1}{2}\times2\times3)+(2\times2)=(4\times3)+4=12+4=16in.^2[/tex]Therefore, the correct answer is 16 square in.
)) How many terms are in this expression? 7c+ 3d Submit
The number of terms is the expression is equal to 2.
7c
3d
In algebra, terms are the values on which the mathematical operations take place in an expression.
A term can be a constant or a variable or both in an expression.
In the expression, 7ca + 3d, 7c and 3d are terms.
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Hey there! I know this is prob really simple and I am beginning to understand it, but my problem isSec 60°Now I know all the SOH CAO TOH stuff, and things like that, I just don't understand how to find the value because it changes all the time with the right triangle and the number of their sides. Really just need the formula on how to solve stuff.
Formula to solve a triangle
Lets begin with
Tan 45
is a right traingle, with angles 45,45 and 90°
Then, to find Tan 45
Tan 45= [√(1^2) + (1^2) ]/2 = √2/2
Tan 45= √2/2
NOW find Sec 60°
Sec 60° = 1/Sin 60°
Sin 60°is found by a triangle, with angles 30,60,90
Sin 60°= √3/2 , thats because
A suit was marked with a 10% discount.
If the discount is $10.00, what was the original price of the suit?
Answer:
The suit originally cost $100.
Step-by-step explanation:
To find the original price of the suit, you can set up a ratio and solve for the missing variable. In this case, we can set up a ratio as such:
10%/100% = $10.00/x, where x is the original price, and $10.00 is 10% of the original. In fraction form, this looks like [tex]\frac{10}{100} =\frac{10}{x}[/tex]. Here, it is clear that for these two to be equal, x must be equal to 100.
Need to know the answers or how to do them.#1 please
Looking at angle G, it inscribes the arc FH, which is a diameter of the circle.
Since an inscribed angle measures half the inscribed arc (and arc FH measures 180°), angle G measures 90°.
Now, let's calculate angle F:
[tex]\begin{gathered} F+G+H=180\\ \\ F+90+48=180\\ \\ F+138=180\\ \\ F=180-138\\ \\ F=42° \end{gathered}[/tex]Arc GH is inscribed by the angle F, so we have:
[tex]\begin{gathered} F=\frac{1}{2}GH\\ \\ 42=\frac{1}{2}GH\\ \\ GH=2\cdot42\\ \\ GH=84° \end{gathered}[/tex]So the indicated arc measures 84°.
I have to solve to p but I need help with this I don't understandkn + mp = q
kn + mp = q
Solve for p
Subtract kn from both sides of the equation:
kn-kn+mp = q - kn
mp= q-kn
Divide both sides by m
mp/m = (q-kn)/m
p= (q-kn)/m
In the diagram below, AD bisects ZC AB, mZADB = 95º and mZCAD = 34°. Find mZB.
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we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
In the triangle ADB we have that
mwe have that
m because AD bisects angle CAB
so
msubstitute
34+95+m
mmPlease, Do you understand all the steps so far?Does the explanation satisfy your question and do you understand the answer?
If you don’t need further explanation on this question, we can end the session. A pleasure to attend you, Remember that after our session, the answer is saved in your profile. Thanks and have a great day! Good Bye.
Gave a nuclear physicist needs 50 liters of a 60 percent acid solution. He currently has a 20% solution and a 70% solution. How many liters of each does he need to make the needed 50 liters of 60% acid solution?
Let the number of liters of 20% solution be "x"
Let the number of liters of 70% solution be "y"
According to the problem, we need 50 liters of the solution. Thus, we can write >>>>
[tex]x+y=50[/tex]Also, given, we need 50 L of 60% solution. Thus, we can write >>>>>
[tex]0.2x+0.7y=0.6\times50[/tex]Let's substitute first equation into the second and solve for "x" >>>>>
[tex]\begin{gathered} x+y=50 \\ 0.2x+0.7y=0.6\times50 \\ --------------- \\ y=50-x \\ \text{Substituting,} \\ 0.2x+0.7(50-x)=30 \\ 0.2x+35-0.7x=30 \\ 0.5x=5 \\ x=\frac{5}{0.5} \\ x=10 \end{gathered}[/tex]So, the "y" value is >>>
[tex]\begin{gathered} x+y=50 \\ 10+y=50 \\ y=50-10 \\ y=40 \end{gathered}[/tex]So, he needs,
Answer10 liters of 20% solution
40 liters of 70% solution
Joe has brownies the length of each brownies is 7 cm and the width is 5 cm is its total area of the pan is 560 cm how many brownies did Joe have
Start by calculating the area of a single brownie using
[tex]A=L\cdot W[/tex][tex]\begin{gathered} A=7\operatorname{cm}\cdot5\operatorname{cm} \\ A=35\operatorname{cm} \end{gathered}[/tex]To find the amount of brownies Joe can make in his pan, divide the area of the pan into the single brownie area
[tex]\frac{560}{35}=16[/tex]Joe had 16 brownies.
Exercise 3. A farmer raises chickens and pigs. His animals together have a total of 95 heads and 310 legs,How many chickens and how many pigs does the farmer have?
How Much Paint Would Cover This Pyramid Without The Square Base ?
To answer this question, we will assume that the pyramid's slant height is 10ft.
We have a square pyramid in which we have:
• The pyramid's base is a square with a side that measures 6ft.
,• The height of the pyramid is equal to 8ft.
,• The slant height is 10ft
Then we need to find the surface area of the pyramid without the square base, and we can see that:
1. We can see that the surface area of the pyramid without the square base is represented by four (4) triangles with equal base (6ft) and equal height (10ft). Then since the area of a triangle is given by:
[tex]A___{triangle}=\frac{bh}{2}[/tex]2. Therefore, we need to find the area of one of the triangles, and then multiply this result by 4 to find the asked area as follows:
[tex]A_{triangle}=\frac{6ft*10ft}{2}=\frac{60ft^2}{2}=30ft^2[/tex]3. Then the total area of the pyramid without the square base is:
[tex]\begin{gathered} A_{4triangles}=4(30ft^2)=120ft^2 \\ \\ A_{4triangles}=120ft^2 \end{gathered}[/tex]Therefore, in summary, the paint would cover 120ft² (square feet) without the square base.
Solve the system. 2x + y + 3z = 20 x + 2y - z = -11 3x 2z = -3 Enter your answer as an ordered triple
The procedure 20 x + 2y - z = -11 3x 2z = -3 denotes an ordered triple with x = 1, z = 3, and y = 2.
What is meant by mathematical equations?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. The true power of equations lies in their ability to precisely describe various aspects of the world. (This is why, when one can be found, a solution to an equation can be useful.)Therefore,
let x + 2y + 3z = 14...…(1)
3x + y + 2z = 11.....(2)
2x + 3y + z = 11.....(3)
multiplying (2) by 2 and subtracting (1) from it we get,
=5x + z = 8...…..(4)
again multiplying (2) by 3 and subtracting (3) from it we get,
= 7x + 5z = 22.....(5)
Now multiply (4) by 5 and subtract (5) from it we get 18x = 18
therefore x = 1
substituting the x in (4) we get the value of z as
= 5(1) + z = 8
∴ z = 8 - 5 = 3
and substitute x and z in (1) we get
1 + 2y + 3(3) = 14
2y = 14 - 1 - 9 = 4
∴ y=2
The complete question is:
The solutions of the equations x+2y+3z=14, 3x+y+2z = 11, 2x + 3y + z = 11
A [tex]$\quad \mathrm{x}=\mathrm{O}, \mathrm{y}=2, \mathrm{z}=4$[/tex]
B [tex]$\quad \mathrm{x}=1, \mathrm{y}=\mathrm{O}, \mathrm{z}=4$[/tex]
C [tex]$\mathrm{x}=\mathrm{O}, \mathrm{y}=1, \mathrm{z}=8$[/tex]
D [tex]$x=1, y=2, z=3$[/tex]
To learn more about mathematical equations, refer to:
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-10 -8 -6 -4 -2 0 2 4 6 8 10 Use the number line to help you answer the question. 8 10 Which statements are true? Check all that apply. -4<-8|-4|<|-8||-5|>1-5>1|-2|=|2|
a) |-4| < |-8| This is true
b) |-5| > 1 This is true
c) -5 > 1 This is false
d) |-2| = |2| This is true
Determine the domain and range of the quadratic function. (Enter your answer using interval notation.)f(x) = 2x2 − 4x + 2domain range
we have the equation
[tex]f\mleft(x\mright)=2x^2−4x+2[/tex]The domain of any quadratic equation is all real numbers
so
The domain is the interval (-infinite, infinite)To find out the range, we need the vertex
Convert the given equation into vertex form
[tex]\begin{gathered} f\mleft(x\mright)=2x^2−4x+2 \\ f(x)=2(x^2-2x)+2 \end{gathered}[/tex]Complete the square
[tex]\begin{gathered} f(x)=2(x^2-2x+1-1)+2 \\ f(x)=2(x^2-2x+1)+2-2 \\ f(x)=2(x^2-2x+1) \\ f(x)=2(x-1)^2 \end{gathered}[/tex]The vertex is the point (1,0)
The vertical parabola opens upward (the leading coefficient is positive)
The vertex is a minimum
therefore
The range is the interval [0, infinite)All real numbers greater than or equal to zero
Parallel lines never meet and will never cross each other.
True
Parallel lens are never meet and cross each other
8. Pentagon MNOPQ with M(-4,1),N(-2,3). O(0, 3), P(4, 3), and Q(2,-7): rotate 90° counterclockwise, then dilate by a factor of 2/3 120 What are the two arrow rules to show this composition? 12 b. Is the dilation an enlargement or reduction? How do you know? 710 с. What are the vertices of the image after the transformation?
Given data:
The given coordinates of the pentagon are M(-4,1),N(-2,3). O(0, 3), P(4, 3), and Q(2,-7).
The coordinatte after 90 degrees counterclockwise rotation is,
[tex]\begin{gathered} M(-4,1)\rightarrow M^{\prime}(-1,\text{ -4)} \\ N(-2,\text{ 3)}\rightarrow N^{\prime}(-3,\text{ -2)} \\ O(0,\text{ 3)}\rightarrow O^{\prime}(-3,\text{ 0)} \\ P(4,\text{ 3)}\rightarrow P^{\prime}(-3,\text{ 4)} \\ Q(2,\text{ -7)}\rightarrow Q^{\prime}(7,\text{ 2)} \end{gathered}[/tex]The final coordinates after 2/3 dilation factor is,
[tex]\begin{gathered} M^{\doubleprime}\rightarrow\frac{2}{3}(-1,\text{ -4)} \\ \rightarrow(-\frac{2}{3},\text{ - }\frac{8}{3}) \\ N^{\prime\prime}\rightarrow\frac{2}{3}(-3,\text{ -2)} \\ \rightarrow(-2,\text{ -}\frac{4}{3}) \\ O^{\doubleprime}\rightarrow\frac{2}{3}(-3,\text{ 0)} \\ \rightarrow(-2,\text{ 0)} \\ P^{\doubleprime}\rightarrow\frac{2}{3}(-3,\text{ 4)} \\ \rightarrow(-2,\frac{8}{3})^{} \\ Q^{\doubleprime}\rightarrow\frac{2}{3}(7,\text{ 2)} \\ \rightarrow(\frac{14}{3},\text{ }\frac{4}{3}) \end{gathered}[/tex]Thus, the final coordinates after transformation are M''(-2/3, -8/3), N''(-2, -4/3). O''(-2, 0), P''(-2, 8/3), and Q''(14/3, 4/3).
Which point is located at (0, -7)? O 4 8
The point with the coordinates x=0 and y=-7 is point E
A roast beef sandwich costs $6.75. A customer buys multiple roast beef sandwiches. write an equation that represents the situation. Use x to represent the number of roast beef sandwiches. then determine how many sandwiches tje customer buys. Amount Used for payment =$50Change Received = $16.25The Customer buys. sandwiches ?
Let x be the number of sandwiches.
Since each sandwich has a cost of $6.75, then for x sandwiches the cost would be:
[tex]\text{6}.75x[/tex]The change received is the difference between the amount used for payment and the cost of the sandwiches.
The difference between the amount used for payment and the cost of the sandwiches can be represented algebraically as:
[tex]50-6.75x[/tex]This number must be equal to the change received. Then:
[tex]50-6.75x=16.25[/tex]Solve for x. To do so, substract 50 from both sides:
[tex]\begin{gathered} \Rightarrow-6.75x=16.25-50 \\ \Rightarrow-6.75x=-33.75 \end{gathered}[/tex]Next, divide both sides by -6.75:
[tex]\begin{gathered} x=\frac{-33.75}{-6.75} \\ \Rightarrow x=5 \end{gathered}[/tex]Therefore, the customer buys 5 sandwiches.
Which equation describes a line of symmetry for square ABCD? x = 0 y = x x = -2 y = -2
The equation of the line is DB from y = mx + b
From the graph y = 0 when x =0
this means y = x
The graph cuts through the origin, Meaning the y -intercept = 0
answer is: y = x
Write the nth rule for each geometric sequence.4) -3, 1, -1/3, 1/9...
In a geometric sequence each term is found by multiplying the previous term by a constant.
To find the nth term in a geometric sequence we use:
[tex]a_n=ar^{n-1}[/tex]where a is the first term and r is the common ratio.
To find the common ratio we can divide the second term by the first:
[tex]\frac{1}{-3}=-\frac{1}{3}[/tex]and the third one by the second:
[tex]\frac{-\frac{1}{3}}{1}=-\frac{1}{3}[/tex]we notice that this in fact is the common ratio. Now we plug it in the formula above, therefore the geometric sequence is:
[tex]a_n=-3(-\frac{1}{3})^{n-1}[/tex]Find θ for 0 < θ< 2 pisin θ =0.3148
The given trigonometric expression is:
sin θ =0.3148
To find the value of θ, we need to find the arc sin of 0.3148
[tex]\begin{gathered} θ=\sin^{-1}0.3148 \\ θ=18.35^0,161.65^0\text{ } \end{gathered}[/tex]A car manufacturer collects data on the number of gallons of gasoline left in the gas tank after driving for different numbers of miles. The manufacturer creates a scatter plot of the data and determines that the correlation coefficient is −0.92.Select each true statement based on this correlation coefficient.g
Solution
- A correlation coefficient of -0.92 implies that:
1. As one variable is increasing, the other variable is decreasing.
2. Since the correlation is close to -1, there is a strong correlation between the variables.
3. Since the correlation is -0.92, there is a negative correlation between the variables.
4. Since correlation coefficient measures the linear relationship between variables, a correlation of -0.92 implies that there is very good reason to believe that a linear correlation/relationship exists between both variables.
Final Answer
The answers are:
1, 2, and 4
Find the mean for the scores: 3,860; 5,300; 8,560; 4,400, 5,360..The mean for the scores is
We have to find the mean of this list of scores.
We can calculate the mean as:
[tex]\begin{gathered} M=\dfrac{1}{n}\sum ^n_{i=1}\, x_i \\ M=\dfrac{1}{5}(3860+5300+8560+4400+5360) \\ M=\dfrac{27480}{5} \\ M=5496 \end{gathered}[/tex]Answer: The mean of this set of values is 5,496.
what's 3/4 put of 12?
Maria had 12 pieces of fruit. Three-fourths were apples.
We want to find how many fruits were apples,
That would be;
[tex]\begin{gathered} \frac{3}{4}\times12=\frac{36}{4} \\ =9 \end{gathered}[/tex]Therefore, 9 of the fruits were apples.
Consider the following function.f(x) = 6x^2 − 4xFind the limit.
Given:-
[tex]f(x)=6x^2-4x[/tex]To find:-
[tex]\lim _{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}_{}[/tex]So now we substitute the known values we get,
[tex]\frac{f(x+\Delta x)-f(x)}{\Delta x}_{}=\frac{6(x+\Delta x)^2-6x^2+4x}{\Delta x}[/tex]So by furthur simplification. we get,
[tex]\frac{6(x+\Delta x)^2-6x^2+4x}{\Delta x}=\frac{6x^2+12x\Delta x+(\Delta x)^2-6x^2+4x}{\Delta x}[/tex]So we get is,
[tex]\frac{6x^2+12x\Delta x+(\Delta x)^2-6x^2+4x}{\Delta x}=\frac{12x\Delta x+(\Delta x)^2^{}+4x}{\Delta x}[/tex]So by furthur simplification we get,
[tex]undefined[/tex]3(x-y) when x=4 and y=1
write an equation for the line that has a slope of 1/2 and passes through the point (2,4)!!
Answer:
x-2y=-6.
Explanation:
Given a line with a slope of 1/2 that passes through the point (2,4):
[tex]\begin{gathered} m=\frac{1}{2} \\ (x_1,y_1)=(2,4) \end{gathered}[/tex]Substitute these into the point-slope form of the equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]This gives:
[tex]\begin{gathered} y-4=\frac{1}{2}(x-2) \\ y-4=\frac{1}{2}x-\frac{1}{2}(2) \\ y-4=\frac{1}{2}x-1 \end{gathered}[/tex]We can simplify further:
[tex]\begin{gathered} y=\frac{1}{2}x-1+4 \\ y=\frac{1}{2}x+3 \\ \implies y=\frac{x+6}{2} \\ 2y=x+6 \\ x-2y=-6 \end{gathered}[/tex]The equation of the line is x-2y=-6.
What percent of 33 is 21?
33 represents 100%. To find what percent represents 21, we can use the next proportion:
[tex]\frac{33}{21}=\frac{100\text{ \%}}{x\text{ \%}}[/tex]Solving for x:
[tex]\begin{gathered} 33\cdot x=21\cdot100 \\ x=\frac{2100}{33} \\ x=63.6\text{ \%} \end{gathered}[/tex]write the equation of the slope intercept form with the given point and slope or two points. (-7,13) slope = -2
Slope-intercept form of a line:
y = mx+ b
where m is the slope and b is the y-intercept.
Replacing into the equation with m = -2 and point (-7, 13) we get:
13 = -2(-7)+ b
13 = 14+ b
13 - 14 = b
-1 = b
Then, the equation is:
y = -2x - 1
two angles in a triangle measure (2.3×+25)° and (5.8×+11)°. what is the value of x if the angles are congruent to one another?
If the angles are congruent to one another, we can conclude:
[tex]\begin{gathered} (2.3x+25)=(5.8x+11) \\ \end{gathered}[/tex]solving for x:
[tex]\begin{gathered} 25-11=5.8x-2.3x \\ 14=3.5x \\ x=\frac{14}{3.5} \\ x=4 \end{gathered}[/tex]