Answer:
Let a = side length of a cube
Let S = surface area of a cube
Area of a square = a²
Since a cube has 6 square sides: S = 6a²
To make a the subject:
S = 6a²
Divide both sides by 6:
[tex]\sf \implies \dfrac{S}{6}=a^2[/tex]
Square root both sides:
[tex]\sf \implies a=\sqrt{\dfrac{S}{6}}[/tex]
(positive square root only as distance is positive)
-----------------------------------------------------------------------------------------------
[tex]\sf x=-3-\sqrt{2} \implies (x+[3+\sqrt{2}])=0[/tex]
[tex]\sf x=-3+\sqrt{2} \implies (x+[3-\sqrt{2}])=0[/tex]
Therefore,
[tex]\sf y=a(x+[3+\sqrt{2}]) (x+[3-\sqrt{2}])[/tex] for some constant a
Given the y-intercept is at (0, -5)
[tex]\sf \implies a(0+3+\sqrt{2}) (0+3-\sqrt{2})=-5[/tex]
[tex]\sf \implies a(3+\sqrt{2}) (3-\sqrt{2})=-5[/tex]
[tex]\sf \implies a(9-2)=-5[/tex]
[tex]\sf \implies 7a=-5[/tex]
[tex]\sf \implies a=-\dfrac57[/tex]
Substituting found value of a into the equation and simplifying:
[tex]\sf y=-\dfrac57(x+[3+\sqrt{2}]) (x+[3-\sqrt{2}])[/tex]
[tex]\sf \implies y=-\dfrac57(x^2+6x+7)[/tex]
[tex]\sf \implies y=-\dfrac57x^2-\dfrac{30}{7}x-5[/tex]
does 20, 40, 30 form a right triangle
Answer: No
Step-by-step explanation: In order for a triangle to be right, the first number and second number has to be smaller than the middle number.
20+30= 50
50>40
therefore 20,40,30 can not be a right triangle
Call the 3 sides a,b,c respectively. (a=20; b=30; c=40)
To form a right triangle with 3 lengths, they must satisfied the equation : [tex]a^{2} +b^{2} =c^{2}[/tex] (aka pythagorean theorem)
Replace numbers : [tex]20^{2} +30^{2} =40^{2}\\ 400 + 900 = 1600 (false)[/tex]
-> These lengths do not form a right triangle.
what is the height of the prism?
Answer:
option 1
Step-by-step explanation:
[tex]x - 3 + \frac{7 x- 9}{ {x}^{2} - 2 } [/tex]
your required answer
Find the balance in the account after the given period
$3000 principal earning 5% compounded annually, 8 years
i really need help im confused
Answer:
$1200
Step-by-step explanation:
5% of $3000 = $150
multiply 8 by $150 = $1200
If the area of a parallelogram is 5 ⅖ ft. height of the parallelogram is 2 ⅖ ft, what is the base of the parallelogram
Answer:
3 2/5
Step-by-step explanation:
.
What is the partial fraction decomposition of StartFraction 6 x + 17 Over (x + 1) squared EndFraction?
Answer:
6/(x + 1) + 11/(x + 1)^2.
Step-by-step explanation:
6x + 17 / (x +1)^2 = A / (x + 1) + B /(x + 1)^2
Multiply through by (x + 1)^2:
6x + 17 = A(x + 1) + B
Let x = -1, then:
-6 + 17 = 0 + b
So B = 11.
Let x = 1:
6 + 17 = A(1+1) + 11
23 = 2A + 11
A = (23-11)/ 2
A = 6.
a construction company is building a house based on the picture. The scale from picture to real house is 1 inch= 8 feet the height of the building in the picture is 2.5 inches what is the height of the real building the proportion i would use to solve this is ____ the height of the real building should be ______ feet. To explain to the construction workers how they would calculate the height of the final building. i would tell them ____
Answer:
The Height of the building would be 20 feet.
Step-by-step explanation:
1.) 1/8 = 2.5/X
2.) Answer: 20 Feet
3.) Cross Multiply
- 1 inch is to 8 feet as 2.5 inches is to 20 feet.
The diagram shown is two intersecting lines. The measure of 5 is 47°.
a. Using the vertical angles theorem, m∠7 = 47°.
b. Based on the definition of linear pair, the equation that can be used to solve for x is: 2x - 5 + 47 = 180.
c. x = 69
What is a Linear Pair?A linear pair is two angles whose sum equals 180°.
Given the image, where:
m∠5 = 47°
a. ∠5 and ∠7 are vertical angles. Since verticl angles are congurent, therefore:
m∠7 = m∠5 = 47°
m∠7 = 47°
b. m∠6 = (2x - 5)°
m∠6 + m∠5 = 180° (linear pair)
Substitute
2x - 5 + 47 = 180 (equation that can be used to solve x)
c. 2x - 5 + 47 = 180
2x + 42 = 180
2x = 180 - 42
2x = 138
x = 138/2
x = 69
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Suppose $a(x) = 3x - 7$ and $b(x) = 2 - x^3$. What is the value of $a(b(3)) - b(a(3))$?
Answer:
-76
Step-by-step explanation:
b(3)=2-3^3 = -25.
So a(b(3))=a(-25)=3(-25)-7=-82.
a(3)=3(3)-7=2.
So b(a(3))=2-2^3 = -6.
Therefore, the value of the desired expression is -82-(-6)=-76
The value of the required function [tex]a(b(3)) - b(a(3))[/tex] is (-88).
What is a function?
"A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math. f = {(a,b)| for all a ∈ A, b ∈ B}
A relation is said to be a function if every element of set A has one and only one image in set B.
A function is a relation from a non-empty set B such that the domain of a function is A and no two distinct ordered pairs in f have the same first element."
Given two functions are:
[tex]a(x) = 3x - 7\\b(x) = 2 - x^{3}[/tex]
When the value of 'x' is 3, then the values of the given two functions are:
[tex]a(3) \\= 3x - 7\\= 3(3)-7\\= 9-7\\= 2[/tex]
[tex]b(3)\\= 2 - x^{3}\\= 2-(3)^{3}\\= 2-27\\= -25[/tex]
Now the value of the required function is:
[tex]a(b(3)) - b(a(3))\\= a(-25)-b(2)\\= [3(-25)-7]-[2-2^{3}]\\= (-75-7)-(2-8)\\= -82-6\\= -88[/tex]
Therefore, the value of the required function is (-88).
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An angle measures 72.6° less than the measure of its complementary angle. What is the measure of each angle?
Answer:
Step-by-step explanation:
Which equation can be used to find A, the area of the parallelogram shown?
Answer A
Calculate it correctly you will get it
Answer:
c
Step-by-step explanation:
the area of a parallelogram is given by base ×height
in this case 10×5
Using the Linear equation 4x-3y=12, express each of the following.
y in terms of x. y=
Using the Linear equation 4x-3y=12, express each of the following.
x in terms of y. x=
Using the given linear function, it is found that the expressions are given by:
[tex]y = \frac{4x}{3} - 4[/tex].[tex]x = \frac{3y}{4} + 3[/tex].What is the given linear function?It is:
4x - 3y = 12.
To find y in terms of x, we isolate y, hence the expression is given by:
[tex]3y = 4x - 12[/tex]
[tex]y = \frac{4x}{3} - 4[/tex]
To find x in terms of y, we isolate x, hence the expression is given by:
[tex]4x = 12 + 3y[/tex]
[tex]x = \frac{3y}{4} + 3[/tex]
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I NEED HELP PLEASE ILL GIVE BRAINLIEST
WHICH GRAPH SHOWS Y = -6
Answer:B
Step-by-step explanation:
Answer: B
Step-by-step explanation:
The line on B is at the Y coordinate -6.
Horizontal is the X
Vertical is the Y
if y=5x-3, find the value of y when x=-2
Answer:
y = -13
Step-by-step explanation:
y = 5(-2) - 3
y= -10 -3
y = -13
Step-by-step explanation:
or, y = 5x - 3
or, y = 5 (-2) - 3
or, y = -10 - 3
y = -13
Diedra has $20 to spend. Can she buy shorts that cost $18.50?
Answer:
yes she can
Step-by-step explanation:
yes she can because $20 is great than $18.50
Ratio of boys to girls
Answer:
→Boys=6
→Girls=14
Step-by-step explanation:
[tex]Solution,\\\\Ratio\:of\:boys\:to\:girls=3:7\\\\Total\:students=20\\\\Let,\\\\\hookrightarrow Boys=3x\\\\\hookrightarrow Girls=7x\\\\Now\:we\: have,\\\\\hookrightarrow 3x+7x=20\\\\\hookrightarrow 10x=20\\\\\hookrightarrow x=20/10=2\\\\Again,\\\\\hookrightarrow Boys=3x=3\times2=6\\\\\hookrightarrow Girls=7x=7\times2=14[/tex]
A triangle has two sides of length 1 and 8. What is the smallest possible whole-number length for the third side?
Answer:
1/8 is the smallest possible whole number length for the third side
Kevin is 4 times as old as Daniel and Kevin is
also 6 years older than Daniel
Step-by-step explanation:
let kevein be x and daniel be y
x=4y (equation i)
x=6+y(equationii)
putting the value of x in equationii
4y=6+y
3x=6
x=2
In rectangle GRAM below GA =4×+17 and MR= 7x-4 find the value of x and the lenghts of GA MR
Answer: x=7, GA=MR=14
Step-by-step explanation:
Solve this for me pls
Answer:don’t delete my comment I need more points lol
Step-by-step explanation:
Find the scale of the 2 known sides:
40/8 = 5
the larger shape is 5 times the size.
Multiply the known sides by 5:
X = 5 *5 = 25
x = 25
When two lines intersect, are all the angles formed equal?
Answer: No
Step-by-step explanation:
If we don't know if the lines are parallel, we cannot conclude the angles are equal.
When two lines are parallel lines are intersected by a transversal, the corresponding angles formed are always equal in measure, and when the lines are not perpendicular the measure of the angle is not equal.
What are intersecting lines?The intersecting lines (two or more) always meet at a single point. The intersecting lines can cross each other at any angle.
When two lines intersect each other, the two opposite pairs of angles formed are called vertically opposite angles.
If two parallel lines are intersected by a transversal, the corresponding angles formed are always equal in measure.
If the corresponding angles formed at the two intersections are congruent, the two lines will then be considered parallel.
The pair of corresponding angles always lies on the same side of a transversal.
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Goal: create a budget meal for a day
role: you are an assistant cook in karinderya.
audience: teacher, friend, neighbours and loved one.
situation: the store manager give you task to prepare a budget meal for the day,
consisting 1 rice, 1 viand, 1 fruit and 1 drink.
available food: rice (fried and plain), viand (chicken meat, pork meat
and vegetables), dessert fruit (banana and apple) and juice (pineapple juice
and mango juice)
product: the expected output must be the following:
1. customer financial capability in ordering food
2. create at least three combination of your budget meal and put a necessary
amount.
using the combination formula
My budget meal for a day will be targeted towards people who wants (weight loss) and such I will prepare a food menu of plain rice, vegetables, apple fruit and a cup of mango juice.
The customer financial capability in ordering food is very simple as it is targeted towards weight loss and as such, the rice is plain along with vegetables and as such, it will be affordable.
The three combination of my budget meal are:
Plain rice and vegetable = $3.Plain rice and an apple fruit = $ 2.5.Plain rice and a cup of mango Juice= $ 2.What food budget?A food budget is known to be the purpose a person has so as to be able to spend on food groceries.
Note that food budget is one that often includes any items a person need to buy more, such as meat, fruit and vegetables, etc.
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Is 6km bigger then 54,000mm?
Answer:
Yes
Step-by-step explanation:
To answer this question, we will need to know how many millimeters are in a kilometer.
1 km = 1,000,000 mm
Therefore, 6km is WAY bigger than 54,000 mm
Which expression is equivalent to 125 x 15,??
y
O 5x®y3z
0 5x²y5z
O 25x²y3z
O 25x²y5z
Answer:
25²×3is the equivalent answer
HELP ME PLEASE
PRETTY PLEASEEEEEEEEEEE
Answer:
4/5
Step-by-step explanation:
Here is how to solve:
We start with a term called Rise over Run. We rise up 4. We then will run to the right 5. We have a slope of 4/5x. If the line is going up, then it will be a positive slope. If the line is going down., then it will be a negative slope. So, the line is going up, so it would be a positive 4/5x
Answer:
Positive slope or (2,3)_(-3,-2)
Step-by-step explanation:
I don't find your question very clear, but I have two possible answers for you.
Positive slope, the type/name of the slope.
(2,3)_(-3,-2), the coordinates.
I hope this answers your question ^^
Find the 14th term of the following geometric sequence 1,2,4,8,…
Answer:
The 14th term is 8,192
Step-by-step explanation:
Well we can see that it is multiplying every next term by 2.
2nd term : 1*2 = 2
3rd term : 2*2 = 4
4th term : 4*2 = 8
So, we can simply carry out this process.
5th term : 8*2 = 16
6th term : 16*2 = 32
7th term : 32*2 = 64
8th term : 64*2 = 128
9th term : 128*2 = 256
10th term : 256*2 = 512
11th term : 512*2 = 1024
12th term : 1024*2 = 2048
13th term : 2048*2 = 4096
14th term : 4096*2 = 8192
The 14th term is 8,192
Answer:
8192
Step-by-step explanation:
The rate is x2. Multiplying to the 14th term gets to 8192.
hope this helps!
Wes mixed different juices to make fruit punch. He filled one-half of the punch bowl with orange juice. Then he filled half of the remaining space with grape juice. Finally, he filled the rest of the punch bowl with 300 mL of cherry juice.
How many liters of fruit punch did Wes make?
Answer:
1.2 L
Step-by-step explanation:
3/4 of the bowl was full wes then filled the bowl with 300 ml so 300+300+600=1,200 = 1.2L
Angle α is drawn on the unit circle in standard position. The terminal side of angle α intersects the unit circle at point (-0.292, 0.956). What is the approximate decimal value of tan(α)?
The approximate decimal value of tan(α) is -3.274, α intersects the unit circle at point (-0.292, 0.956)
What is a unit circle?
A circle is the locus of a point such that its distance from a fixed point (center) is always constant.
A unit circle is a circle with a unit radius.
Given that:
The terminal side of angle α intersects the unit circle at point (-0.292, 0.956).
Hence:
tan(α) = (0.956 / -0.292) = -3.274
The approximate decimal value of tan(α) is -3.274, α intersects the unit circle at point (-0.292, 0.956)
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PLEASE HELP! DUE TODAY! TY!
In the figure, line segment AB is tangent to the circle at point A. Find the length of line segment AB.
Work:
AB =
Answer: 12 inches
Step-by-step explanation:
how do I do this??????
you take 99 divided by 22 = 4.5
I don't understand what exactly your teachers meaning so I would also suggest asking but the answer compered to everything I've learned in math would be 4.5.
have a good day/night!! :)
Please help! will give brainlest! locks in 30 min!
Answer:
[tex]\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\frac{4 \pi }{3} = \pi + \frac{\pi }{3}[/tex]
tan ([tex]\frac{4\pi }{3}[/tex]) = [tex]-\frac{\sqrt{3} }{2}[/tex] ÷ [tex](- \frac{1}{2} )[/tex]
= [tex]\sqrt{3}[/tex]
hope this helps and is right!! p.s. i really need brainliest :)