Find the length to the nearest whole number of the diagonal (hypotenuse) of a square with 30 cm on a side. Round answers to the nearest tenth if necessary. Your answer
Answers
Notice that we can draw a triangle in the square , and that the length of the square's diagonal is the same as the length of the triangle's hypotenuse. The triangle is a right triangle therefore it satisfies the Phytagorean Theorem. To calculate for it's hypotenuse , we will use:
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse, and a, b are the other legs of the triangle.
[tex]\begin{gathered} c^2=30^2+30^2 \\ c^2=1800 \\ c=\sqrt[]{1800} \\ c=42.43 \end{gathered}[/tex]Since the hypotenuse of the triangle is 42.43 cm. Therefore, the square's diagonal is also 42.43 cm
Answer:
The square's diagonal is 42.43 cm
Related Questions
The crew knows the amount of dirt the truck can hold each trip in cubic yards.
Answers
Given:
Measurements of hole are 48ft 39ft and and 9ft
Required:
Volume in cubic yd
total number of trip
total cost of trip
Explanation:
First we need to convert given measurements from ft to yd
[tex]\begin{gathered} 3ft=1yd \\ 48ft=16yd \\ 39ft=13yd \\ 9ft=3yd \end{gathered}[/tex]
A)
[tex]V=lhw=16*13*3=624yd^3[/tex]B)
11 cubic yd in 1 trip
then
624 cubic yd in x trip
[tex]x=\frac{624}{11}=56.7\approx57[/tex]C)
cost for 1 trip is $1175
then
cost for 57 trip is y
[tex]y=57*1175=66975[/tex]Final answer:
Volume in cubic yd is 624
total number of trips is 57
total cost of trip $66975
in slope intercept form what is the line perpendicular to y=2x -5 that passes through the (2, -5) point
Answers
The most appropriate choice for equation of line in slope intercept form will be given by-
[tex]y = -\frac{1}{2}x - 4[/tex] is the required equation of line
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
The given equation of line is y = 2x-5
Slope of this line = 2
Slope of the line perpendicular to this line = [tex]-\frac{1}{2}[/tex]
The line passes through (2 , -5)
Equation of the required line = [tex]y - (-5) = \frac{1}{2}(x - 2)[/tex]
[tex]y +5=-\frac{1}{2}x+1\\y = -\frac{1}{2}x +1 -5\\y = -\frac{1}{2}x -4[/tex]
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Lines AD and BC are parallel. What is the angle measurement of Angle DAE(Point A)?D150°45°BсFYour answer
Answers
Solution
For this case we can find the angle:
m < ECB = 30º
And we can find the angle CEB and we got:
m < CEB = 180 -30 - 45 = 105
And then the angle DAE would be:
m < DAE = 30º
Please help. I don't really understand monomials and negative exponets
Answers
The standard form of the monomial expression is -1x¹⁰
Monomial expression:
A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too.
Given,
Here we have the expression
(-2x³)².(-1/4 x⁴)
Now, we have to convert the expression into standard form.
To convert the expression into standard monomial form,
First we have to expand the terms, then we get,
=> (-2²x⁶).(-1/4x⁴)
Then we have to divide the variables and constants separately.
=> (4 x -1/4).(x⁶⁺⁴)
=> -1 . x¹⁰
=> -1x¹⁰
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54 is 120 percent of what number ?
Answers
Answer:
120% of 54 =
120% × 54 =
120/100 × 54 =
(120 ÷ 100) × 54 =
120 × 54 ÷ 100 =
6,480 ÷ 100 =
64.8
Percentage of 120% of 54
120% of 54 = 64.8
and to prove that we got the right answer do what we did above in reverse below
64.8 ÷ 54 =
1.2 =
1.2 × 100/100 =
(1.2 × 100)/100 =
120/100 =
120%
Step-by-step explanation:
Let v be the vector from initial point P1=(−4,−9) to terminal point P2=(6,2). Write v in terms of i and j.
Answers
Step 1;
P1 = ( - 4 , -9 )
P2 = ( 6 , 2 )
Step 2:
[tex]\begin{gathered} \text{Let P}_1=(x_1,y_1)_{} \\ P_2=(x_2,y_2\text{ ) } \end{gathered}[/tex]Step 3:
[tex]\text{v = (x}_2-x_1)i+_{}(y_2-y_1\text{ ) j}[/tex]Step 4:
[tex]\begin{gathered} \text{v = (x}_2-x_1)i+_{}(y_2-y_1\text{ ) j} \\ \text{v = (6}-(-4))i+_{}(2-(-9)\text{) j} \\ v\text{ = (6+4)i + (2 + 9)j} \\ v\text{ = 10i + 11 j} \end{gathered}[/tex]Solve for x in the parallelogram below.
Answers
Answer:
3
Step-by-step explanation:
In parallelogram, opposite sides are equal.
Here,
5x + 2 and 17 are opposite sides.
5x + 2 = 17
5x = 17 - 2
5x = 15
x = 15 / 5
x = 3
The equation should look like this:
5x + 2 = 17
Why 17? Because if you look at the opposite side of the parallelogram, you can see a parallel line that is the exact same length. Since it also isn’t an equation, we can tell this would be the true length of it.
Okay, to solve it, first subtract 2 on both sides of the equation. Why? Because on the left side of the equation (the numbers before the equal sign) we can see that there is one coefficient (number with a variable) and one constant (just a plain number). In equations like this, you want only coefficients or constants per side. To remove the constant from the left side, do the inverse of the number. Always remember that whatever you do on one side, has to be done to the other.
5x + 2 - 2 = 17 - 12
This equals:
5x = 15
Now, just divide by the coefficient, in this case 5, on both sides. This removes the 5.
5x/5 = 15/5
This leaves:
x = 3
A triangle has squares on its three sides as shown below. What is the value of x? 4 centimeters 7 centimeters 5 centimeters 3 centimeters
Answers
Find the area of a circle with a Diameter = 12 ft. Use 3.14 for π and round to 2 decimal places.
Answers
Given:
Diameter of circle = 12ft
pi = 3.14
Solution
The area (A) of a circle can be calculated using the formula:
[tex]\begin{gathered} A\text{ = }\pi r^2 \\ \text{where r is the radius of the circle} \end{gathered}[/tex]Recall that the diamter (d) and radius (r) are related by the formula:
[tex]\begin{gathered} \text{radius = }\frac{diameter}{2} \\ r\text{ = }\frac{d}{2} \end{gathered}[/tex]We can now find the radius (r) of the circle to be:
[tex]\begin{gathered} r\text{ = }\frac{12}{2} \\ r\text{ = 6 ft} \end{gathered}[/tex]We can now find the area by the applying the formula given above:
[tex]\begin{gathered} A\text{ = }\pi\times r^2 \\ A\text{ = 3.14 }\times6^2 \\ =113.04ft^2\text{ (2.dp)} \end{gathered}[/tex]Answer: 113.04 square feet
The volume of the rectangular prism is 105 cubic yards. What is the surface area of the prism in square feet?
Answers
Answer:
198.18 is the answer
Step-by-step explanation:
the answer is 198.18
hope it helps
a point is chosen at random in the large square. find the probability that the point is in the smaller shaded square. each side of the large square: 16 cmeach side of the shaded square: 6 cm*round to the nearest hundredth
Answers
The Probability of the point being in the smaller shaded square is 0.79.
What is meant by probability?Probability equals possibility. It is a branch of mathematics concerned with the occurrence of a random event. The value ranges from 0 to 1. Probability has been introduced in mathematics to predict how likely events are to occur.Probability = the number of possible outcomes. the total number of possible outcomes For example, the probability of flipping a coin and getting heads is 12, because there is only one way to get a head and the total number of possible outcomes is two (a head or tail).The probability is a measure of the likelihood of an event occurring. It assesses the event's likelihood. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the probability formula.Therefore,
|Ω| = 6² = 36
< br / > |A| = 3.14.3² = 278.26
Then we get,
< br / > P |A| = 28.26/36 ≈ 0.79
∴ the probability that the point is in the smaller shaded square is 0.79
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The function table below is intended to represent the relationship y=-5x+1. However, one of the entries for y does not correctly fit the relationship with x.
Answers
Answer:
Step-by-step explanation:
none of the answers are correct
graph the function y=sqrt(x+6)+2. which point lies on the graph
Answers
Explanation
We are given the following function:
[tex]y=\sqrt{x+6}+2[/tex]We are required to graph the function.
Using a graphing calculator, we have:
Hence, the answer is (-2, 4).
The last option is correct.
The area of a semicircle is 0.5652 square inches. What is the semicircle's diameter? Use 3.14 for a inches Submit can you explain
Answers
Given :
The area of semicircle is given as 0.5652 sq.inches.
To find:
The diameter of semicircle which is denoted as d.
Explanation:
The area of semicircle is given as
[tex]A=\frac{\pi r^2}{2}[/tex]The relation between radius and diameter is
[tex]d=2r[/tex]Now substitute the given area in the area of semicircle formula.
[tex]0.5652=\frac{3.14\times r^2}{2}[/tex][tex]r=\sqrt[]{\frac{2\times0.5652}{3.14}}=\sqrt[]{0.36}[/tex][tex]r=0.6in[/tex]The semicircle diameter is determined as
[tex]d=2r\Rightarrow2\times0.6=1.2in[/tex]Answer:
Hence the diameter of semicircle is determined as 1.2 in.
what is 9.77 with 8% tax
Answers
it will be 9.77+0.08(9.77)=10.5516
IN Date OUT IN OUT Employee Time Card: 7:30 10/1 11:30 4:15 12:00 John Apple 10/2 8:15 11:00 5:15 11:45 10/3 11:15 3:55 7:00 12:10 Dept: Cust. Serv. 4:30 10:55 12:00 6:25 10/4 NOTE: NO OVERTIME 1:30 5:00 12:45 10/5 6:00 TOTAL HOURS RATE per hour: $13.75 What is John's total pay for the week? deneaker notes
Answers
I can see it now
thank you
11:30-7:30= 4h
11:00-8.15=2:45h
11:15-7:00=4:15h
10:55-6:25=4:30h
10:45-6:00=4:45h
Total = 4+2.75+4.25+4.5+4.75=20.25
4:15-12:00=4:15h
5:15-11:45=5:30h
3:55-12:10=3:45h
4:30-12:00=4:30h
5:00-1:30=3:30h
Total = 4.25+5.5+3.75+4.5+3.5=21.5
Total hours = 21.5+20.25=41.75
ok, the total pay would be:
Rate per hour * total hours:
[tex]13.75\times41.75=574.0625[/tex]Did you get the same value? hello? are you still with me? ok
do you have any question? oh, remember: After our session, the answer is saved in your profile . My pleasure
Find the missing number so that the equation has infinitely many solutions.
Answers
we have the equation
-2x-9=-2x-?
Remember that
If in a system of two linear equations, we have two identical lines
then
The system has infinite solutions
therefore
the missing number is 9
-2x-9=-2x-9Which parabola corresponds to the quadratic function y = 2x2 + 4x - 16? D. A. B. C. 10:13 1618 10- 12 =10 10 28 -20
Answers
We can see that the y-intercept would be (0,-16) since this is the result of replacing x=0 in the function.
We can also find the x-intercepts solving the equation 0=2x^2+4x-16. Doing so, we have:
[tex]\begin{gathered} 0=2x^2+4x-16 \\ 0=x^2+2x-8\text{ (Dividing by 2 on both sides of the equation)} \\ 0=(x+4)(x-2)\text{ (Factoring)} \\ \text{ We can see that the solutions of the equation are x=-4 and x=2} \\ \text{Therefore the x-intercepts are (-4,0) and (2,0)} \end{gathered}[/tex]The graph that satisfies the conditions we have found previously is the option A.
A homeowner estimates that it will take 9 days to roof his house. A professional roofer estimates that he could roof the house in 5 days. How long ( in days ) will it take if the homeowner helps the roofer?
Answers
Solution:
If x denote the days, the rate unit being Jobs per day is:
[tex]\frac{1}{x}=\frac{1}{9}+\frac{1}{5}[/tex]this is equivalent to
[tex]\frac{1}{x}=\frac{5+9}{45}=\frac{14}{45}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{45}{14}=3.2\text{ days}[/tex]that is just a little more than 3 days.
Parallel and Perpendicular LinesDetermine whether the following lines are parallel, perpendicular, orneither. Write the corresponding letter on the line next to the question.A = parallel, B = perpendicular, or C = neither1. y = }x+6 and y =- *x + 4
Answers
One of the criteria for lines being perpendicular is the fact that the slope of the function in a perpendicular line is the inverse of the slope of the first times -1.
And as you can see m (being the slope of the first equation) is the inverse of the second equiation:
[tex]m=\frac{7}{3},m_1=-\frac{1}{m}[/tex][tex]-\frac{1}{m}=-\frac{1}{\frac{7}{3}}=-\frac{3}{7}[/tex]Therefore line 1 is perpendicular to line 2.
How do I do this, I’m unsure how to go about it
Answers
Given:
[tex]\sqrt{\frac{6}{x}}\cdot\sqrt{\frac{x^2}{24}}[/tex]Simplify:
[tex]=\sqrt{\frac{6}{x}}\cdot\frac{\sqrt{x^2}}{\sqrt{24}}=\sqrt{\frac{6}{x}}\cdot\frac{x}{2\sqrt{6}}[/tex]Apply the properties of fractions:
[tex]=\frac{\sqrt{\frac{6}{x}}x}{2\sqrt{6}}[/tex]Simplify:
[tex]=\frac{\frac{\sqrt{6}}{\sqrt{x}}x}{2\sqrt{6}}=\frac{\sqrt{6}\sqrt{x}}{2\sqrt{6}}[/tex]Eliminate common terms:
[tex]=\frac{\sqrt{x}}{2}[/tex]Answer:
[tex]\frac{\sqrt{x}}{2}[/tex]a triangular pyramid has four faces h = b = 1. What is the pryimands surface area?(There's no image)(
Answers
Let's find the area of one face
[tex]A=\frac{bh}{2}[/tex]Where h = b = 1.
[tex]A=\frac{1\cdot1}{2}=\frac{1}{2}[/tex]Given that there are four faces, we have to multiply the area above by 4
[tex]S=4\cdot\frac{1}{2}=2[/tex]Hence, the answer is 2 square units.What is an equation of the line that passes through the points (-3,-5) and (-5, -3)? Put your answer in fully reduced form.
Answers
Express the general equation of a line passing through two points (x1,y1) and (x2,y2).
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Put (-3,-5) for (x1,y1) and (-5,-3) for (x2,y2) implies,
[tex]\begin{gathered} y+5=\frac{-3+5}{-5+3}(x+3) \\ y+5=\frac{2}{-2}(x+3) \\ y+5=-x-3 \end{gathered}[/tex]Further simplifying gives,
[tex]y=-x-8[/tex]Therefore, the equation of the line is y=-x-8.
A tank in the shape of a hemisphere has a diameter of 10 feet. If the liquid that fills the tank has a density of 74.4 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
Step 1
State the volume of a hemisphere.
[tex]v=\frac{2}{3}\pi r^3[/tex]Where;
[tex]\begin{gathered} r=\frac{diameter}{2}=\frac{10}{2}=5ft \\ \end{gathered}[/tex]Step 2
Find the volume of the hemisphere
[tex]v=\frac{2}{3}\times\pi\times5^3=\frac{250\pi}{3}ft^3[/tex]Step 3
Find the total weight of the liquid in the tank
[tex]\begin{gathered} \text{Density}=\frac{mass}{\text{volume}} \\ 74.4=\frac{mass}{\frac{250\pi}{3}} \\ \text{mass}=19477.87445lb \\ \text{mass}\approx19478lb \end{gathered}[/tex]Hence the total weight of the liquid in the tank to the nearest full pound = 19478lb
If a,b ,and c represent the set of all values of x that satisly the equation below, what is the value(A+ b+ c) + (abc)?X^3-20x = x^2(A) -1(B) 0(C) 1(D) 9
Answers
First, we need to find the solutions a, b, and c of the equation:
[tex]x^3-20x=x^2[/tex]We can rewrite it as:
[tex]\begin{gathered} x^3-x^{2}-20x=0 \\ \\ x(x^{2}-x-20)=0 \\ \\ x=0\text{ or }x^{2}-x-20=0 \end{gathered}[/tex]Thus, one of the solutions is a = 0.
To find the other solutions, we can use the quadratic formula. We obtain:
[tex]\begin{gathered} x=\frac{-(-1)\pm\sqrt[]{(-1)^{2}-4(1)(-20)}}{2(1)} \\ \\ x=\frac{1\pm\sqrt[]{1+80}}{2} \\ \\ x=\frac{1\pm\sqrt[]{81}}{2} \\ \\ x=\frac{1\pm9}{2} \\ \\ b=\frac{1-9}{2}=-4 \\ \\ c=\frac{1+9}{2}=5 \end{gathered}[/tex]Now, we need to find the value of the expression:
[tex]\mleft(a+b+c\mright)+abc[/tex]Using the previous solutions, we obtain:
[tex]\mleft(0-4+5\mright)+0(-4)(5)=1+0=1[/tex]Therefore, the answer is 1.
Which of the following is the horizontal asymptote for the graph below?10A x=-7B. X=0ООC. y - 0C D. y = -7
Answers
A horizontal like y = k, where k is not part of the graph, but guides the function for x-values “far” to the right and/or “far” to the left.
The horizontal asymptote can be observed in the figure below:
Answer: y = 0.
The quadratic equation y= -16t^2 +4t+2 represents a moving objects trajectory where y is the objects height in feet above the ground after t seconds . At what time will the objects hit the ground ?
Answers
Since y is the object's height, it will be on the ground when y = 0. So let's do that:
[tex]0=-16t^2+4t+2[/tex]Here, we can use Bhaskara's Formula to find the roots of the equation:
[tex]\begin{gathered} t=\frac{-4\pm\sqrt[]{4^2-4\cdot(-16)\cdot2}}{2\cdot(-16)} \\ t=\frac{-4\pm\sqrt[]{16+128}}{-32}=\frac{-4\pm\sqrt[]{144}}{-32}=\frac{-4\pm12}{-32} \\ t_1=\frac{-4+12}{-32}=\frac{8}{-32}=-0.25 \\ t_2=\frac{-4-12}{-32}=\frac{-16}{-32}=0.5 \end{gathered}[/tex]Since the time at start is 0, we can't have a negative sign, it would be like saying what happened before the object was in the air. The it will hit the ground at t = 0.5 s.
Simplify 2(2x-7) show work
Answers
Given:
[tex]2(2x-7)[/tex]Aim:
We need to simplify the given expression.
Explanation:
Use the distributive property.
[tex]a(b+c)=ab+ac.\text{ Here a =2, b=2x and c=-7.}[/tex][tex]2(2x-7)=(2\times2x)+(2\times(-7))[/tex]Multiply 2 and 2x, we get 4x and multiply 2 and (-7), we get (-15).
[tex]=4x+(-14)[/tex][tex]Use\text{ \lparen +\rparen\lparen-\rparen=\lparen-\rparen.}[/tex][tex]=4x-14[/tex]Final answer:
[tex]2(2x-7)=4x-14[/tex]Kristy downloads two songs to her MP3 player. The songs are 3 1/10 minutes and 4 2/3 minutes long. About how many minutes of memory will these two songs use altogether?
Answers
We have:
Song 1 = 3 1/10 minutes
Song 2 = 4 2/3 minutes
Minutes of memory of two songs:
[tex]3\frac{1}{10}+4\frac{2}{3}=\frac{31}{10}+\frac{14}{3}=\frac{3\times31+10\times14}{30}=\frac{93+140}{30}=\frac{233}{30}=7\frac{23}{30}[/tex]Answer:
[tex]7\frac{23}{30}\text{ minutes}[/tex]what is the answer to a negative 4 divided by a positive 6?
Answers
The expression given as negative 4 divided by a positive 6 has a value of -2/3
How to evaluate the expression?From the question, the expression is given as
negative 4 divided by a positive 6
Rewrite the expression properly
This is rewritten as follows
-4 divided by +6
This can be represented as
-4/6
There are no like terms in the above expression
So, we have the following equation
-4/6 = -4/6
Divide 4 and 6 by a common factor
The common factor is 2
So, we have
-4/6 = -2/3
The expression cannot be further simplified
So, we have the following equation
-4/6 = -2/3
Hence, the value of the expression is -2/3
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The expression given as "negative 4 divided by a positive 6" has a value of that is -2/3
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
From the problem, the expression is given as;
"negative 4 divided by a positive 6"
Rewrite the expression properly then;
-4 divided by +6
This can be express as;
-4/6
There are no like terms in the expression
So, we have the equation;
-4/6 = -4/6
Divide 4 and 6 by a common factor;
The common factor is 2
-4/6 = -2/3
So, we have the equation;
-4/6 = -2/3
Hence, the value of the expression will be; -2/3
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